ABSTRACT Title of Dissertation: EPITAXIAL GROWTH AND CHARACTERIZATION OF 28Si AND ALUMINUM DELTA LAYERS FOR HYBRID QUANTUM COMPUTING Ke Tang Doctor of Philosophy, 2021 Dissertation directed by: Professor Raymond J. Phaneuf Department of Material Science and Engineering Dr. Joshua M. Pomeroy National Institute of Standards and Technology Novel isotopically enriched and aluminum (Al) delta-doped silicon crystals with exceptional material properties are proposed and developed, in an effort to bridge superconducting quantum information with silicon-based quantum devices for a new generation of solid-state quantum computing. Quantum computing platforms based on semiconducting and superconducting qubits are two powerful candidates. For semiconductor spin qubits, long coherence times can be achieved when using isotopically enriched 28Si as a host material. However, qubit coupling in semiconductor qubits is difficult to achieve due to the nanometer scale of the devices. For superconductor qubit devices, millimeter scale with long spatial coherence length makes them relatively easy to couple multiple qubits, but losses at the material interface are limiting the device performance. Our ultimate objective is to create a hybrid system where both Si spin qubits and superconductor qubits are coupled in a nuclear spin-free and interface-free material. To achieve this, a superconducting semiconductor with monocrystalline structure is proposed. One possible candidate is through Al delta-doped 28Si, as highly Al doped Si is expected to have a 10? higher critical temperature (Tc) than highly boron (B) doped Si (Tc ? 0.6 K). The focus of this thesis is to attack two materials limitations for realizing a monocrystalline, super- semiconducting hybrid architecture: 1) substantially reducing 29Si that limits coherence of semiconducting spin qubits and 2) exploring supersaturated, Al-doped silicon as a system for localized superconductivity within silicon with a potential Tc > 1K. In the first part of this thesis, we demonstrate the advancements in isotopically enriched 28Si in terms of chemical purity, enrichment, and electrical properties. In this work, a new, compact UHV version of the hyperthermal Penning ion source was designed and built. An improvement in the chemical purity from 98.47 % to 99.97 %, while maintaining a 28Si enrichment of > 99.999987 % (0.832 ppm 29Si) has been achieved. We broaden the material variety of 28Si at different levels in the quantum information community by demonstrating the ability to grow isotopically enriched 28Si epitaxial films with precisely controlled (? 90 % accuracy) enrichment levels, ranging from natural abundance to < 1 ppm 29Si. In addition, to better assess the quality of our 28Si material, we have successfully fabricated and measured 28Si MOSFET devices, and compared to those from natural abundance Si on the same substrate. The charge carrier mobility on isotopically enriched 28Si is found to be approximately a factor of 3 lower compared to the natural abundance Si, a result of the short-range scattering (impurity scattering). In the second part of this thesis, we report on the material growth and characterization of super-saturated Al delta layers in Si and explore the possibility for superconductivity. To reach a critical density needed for superconducting transition, the first step is to study the saturation density of this dopant and a way to confine it in 3D. Using a combination of different characterization tools, the maximum 2D atom density of one atomic layer of Al on Si(100) surface before cluster formation is found to be 3.4 ? 1014 cm-2. We also studied the effects of different material growth methods on electrical conduction and the possibility of reaching higher 3D density of Al in this Si-Al-Si heterostructure. We found that Al delta doping in Si behaves differently compared to other dopants: the incorporation anneal does not change the dopant activation efficiency. Standard molecular beam epitaxy (MBE) and locking layer (LL) growth on Al layer is not successful and Al dopant activation is found to be < 50 %, most likely due to the tendency of Al atoms to move toward the surface and the cluster states been developed from the thermal anneals. The electrical conduction of this delta layer at low temperature is also studied and modeled using a temperature dependent two-carrier type model, which is the first reported conducting Al delta layer in Si. We believe that reaching the superconducting transition using an Al delta layer as a dopant in Si is possible, but this requires further studies both experimentally and theoretically to minimize the Al segregation in order to achieve a high enough 3D dopant density. EPITAXIAL GROWTH AND CHARACTERIZATION OF 28Si AND ALUMINUM DELTA LAYERS FOR HYBRID QUANTUM COMPUTING by Ke Tang Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park, in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2021 Advisory Committee: Professor Raymond J. Phaneuf, Chair/Advisor Dr. Joshua M. Pomeroy, Co-Advisor Professor John Cumings Professor Lourdes G. Salamanca-Riba Professor Martin Peckerar ? Copyright by Ke Tang 2021 ii Foreword Chapter 3 is partially reproduced from Review of Scientific Instruments 90, 083308 (2019); https://doi.org/10.1063/1.5097937, with the permission of AIP publishing. (I am the first author of this paper). Chapter 4 is partially reproduced from Journal of physics communications, 4(3), 035006 (2020); https://doi.org/10.1088/2399-6528/ab7b33, under a Creative Commons Attribution (CC BY) license. (I am the first author of this paper). Chapter 5 is partially reproduced from AIP Advances 9, 125153 (2019); https://doi.org/10.1063/1.5128098, under a Creative Commons Attribution (CC BY) license. 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You can find further details on how to use this service here: CCC Republication Service This applies to any journals listed under IOP Publishing or The Electrochemical Society in the Publishing partners tab v Acknowledgements I would first like to express my sincere gratitude to Dr. Josh Pomeroy, my co- advisor at NIST, for supporting and guiding me through the years that I worked with him. I am grateful for his patience and concern. Josh?s way of critical thinking and problem-solving will always serve me well when moving forward. I also want to thank Professor Ray Phaneuf, my advisor at UMD, for his practical advices and kindness that helped me achieving the academic milestones in my Ph.D. study. I want to thank Dr. Kevin Dwyer, Josh?s previous student, for providing warm welcome and detailed guidance after I joined this group. Kevin was probably another ?professor? to me in my point of view, where he taught me how to manipulate all those complicated experimental apparatus in our lab. I want to thank our former group members, Dr. Aruna Ramanayaka and Dr. Hyun Soo Kim for fruitful collaborations and helpful discussions. This project cannot go anywhere further without their help. I also want to thank our group members and the PIs at NIST including Yanxue Hong, Zac Barcikowski, Ryan Stein, Dr. David Simons, Dr. Roy Murray, Dr. Binhui Hu, Dr. Michael Stewart, Dr. Neil Zimmerman and Dr. Garnett Bryant for helpful consultations and supports. I appreciate Dr. Karen A. DeRocher and Dr. Frederick Meisenkothen at NIST for the atom probe tomography (APT) measurements in Chapter 6. Thank you and great respect to other collaborators at NIST, including Terry Moore, Dr. Xiqiao Wang and Dr. Pradeep Namboodiri. I want to thank most to my family members who consistently supported me throughout my life. I want to thank my mom and dad for everything they have done vi for me. My dog Zena for the emotional support and especially my dear wife Sophia for the endless love and accompany throughout the years of this long journey. The work presented here would be impossible without them. Finally, I want to thank all the committee members: Professor John Cumings, Professor Lourdes G. Salamanca-Riba and Professor Martin Peckerar and their precious times for reviewing this thesis. vii Table of Contents Foreword ...................................................................................................................... iii Acknowledgements ...................................................................................................... vi Table of Contents ....................................................................................................... viii List of Figures ............................................................................................................... x Chapter 1: Introduction ................................................................................................. 1 1.1 Semiconductor and Superconductor Quantum Information ............................... 4 1.2 Superconducting Semiconductors ....................................................................... 9 1.3 Objectives and Project Goals ............................................................................ 11 1.4 Outline............................................................................................................... 14 Chapter 2: Experimental Apparatus and Methods ...................................................... 17 2.1 UHV Chamber Configuration ........................................................................... 17 2.2 Sample Preparation ........................................................................................... 20 2.2.1 Ex situ Preparation ..................................................................................... 20 2.2.2 In situ Preparation ...................................................................................... 21 2.3 UHV Deposition Systems ................................................................................. 25 2.3.1 Hyperthermal Ion Beamline ....................................................................... 25 2.3.2 Electron Beam Evaporation of Natural Si ................................................. 34 2.3.3 Thermal Evaporation of Al ........................................................................ 37 2.4 Scanning Tunneling Microscope (STM) .......................................................... 39 2.4 Hall Devices and Measurements ....................................................................... 41 Chapter 3: Ultra-high Vacuum Ion Source for 28Si Deposition .................................. 45 3.1 Introduction ....................................................................................................... 46 3.2 Experimental Setup ........................................................................................... 49 3.3 Ion Source Discharge Properties ....................................................................... 53 3.4 Vacuum and Chemical Purity Improvements ................................................... 56 3.5 Epitaxial Quality of 28Si Thin Film ................................................................... 64 3.6 Further Improvements ....................................................................................... 68 3.6.1 Lens Upgrade and Ion Beam Sweeper ....................................................... 68 3.6.2 UHV Gas Line with Purifier ...................................................................... 70 3.7 Conclusion ........................................................................................................ 71 Chapter 4: Targeted Enrichment of 28Si thin films ..................................................... 73 4.1 Introduction ....................................................................................................... 73 4.2 Experimental Methods ...................................................................................... 75 4.3 Targeted Enrichment Results ............................................................................ 80 4.3.1 First-Generation of Targeted Enrichment .................................................. 80 4.3.2 Methods of Improvements ......................................................................... 86 4.3.3 Second-Generation of Targeted Enrichment ............................................. 89 4.4 Conclusion ........................................................................................................ 93 Chapter 5: Potential Qualifying Metrics for ?Quantum Grade? Silicon - 28Si MOSFET ..................................................................................................................................... 95 5.1 Introduction ....................................................................................................... 96 5.2 28Si MOSFET Devices ...................................................................................... 99 viii 5.3 Magnetotransport Measurements .................................................................... 101 5.4 Conclusion ...................................................................................................... 111 Chapter 6: Al Delta-doping on Si(100): Solving the Puzzle of Max 2D Density ..... 114 6.1 Introduction ..................................................................................................... 115 6.2 Measuring 2D Protrusion Density of Al on Si(100) using STM .................... 121 6.3 Measuring 2D Atom Density of Al using SIMS ............................................. 127 6.4 Measuring 2D Atom Density of Al using Atom Probe Tomography (APT) .. 138 6.5 Conclusions ..................................................................................................... 143 Chapter 7: Al Delta-doping on Si(100): Material Growth and Characterization ...... 145 7.1 Introduction ..................................................................................................... 145 7.2 Effects of Different Growth Methods ............................................................. 150 7.2.1 Effects of the Incorporation Anneal ......................................................... 151 7.2.2 Solid Phase Epitaxy (SPE) or Molecular Beam Epitaxy (MBE) ............. 156 7.2.3 Effects of the Locking Layers .................................................................. 161 7.2.4 Effects of Al Doses on Dopant Activation .............................................. 163 7.2.5 Conclusions and Future Expectations ...................................................... 167 7.3 Temperature Dependent Carrier Densities and Mobilities ............................. 171 Chapter 8: Summary of Results and Future Experiments ......................................... 178 8.1 Summary of Results ........................................................................................ 178 8.2 Future Experiments ......................................................................................... 182 Appendix A: Al Delta Layers Catalog ...................................................................... 186 Bibliography ............................................................................................................. 188 ix List of Figures Figure 1.1: A schematic diagram of a Bloch sphere representing the qubit states. ...... 3 Figure 2.1: Top-down schematic of the experimental apparatus. ............................... 19 Figure 2.2: RGA spectrum of the deposition chamber baseline. ................................ 20 Figure 2.3: Sample stage on the manipulator and the wiring diagram. ...................... 23 Figure 2.4: STM images of a Si (100) substrate after 1200 ?C flash anneal. ............. 23 Figure 2.5: Hyperthermal ion beamline schematics. .................................................. 27 Figure 2.6: Ion beam mass spectra of working gas SiH4. ........................................... 31 Figure 2.7: Beam energy roll off curve for 28Si+. ....................................................... 33 Figure 2.8: 2D mapping of the ion beam spot with Ar. .............................................. 34 Figure 2 9: The schematics of the Si e-gun. ................................................................ 36 Figure 2.10: E-gun Si deposition rate vs power, measured by QCM. ........................ 37 Figure 2.11: A schematic of the thermal evaporation source of Al. ........................... 38 Figure 2.12: A schematic drawing of a STM. ............................................................. 40 Figure 2.13: Microscope image of Hall bar and Vander Pauw devices. ..................... 42 Figure 2.14: Schematic of Hall effect measurement. .................................................. 44 Figure 3.1: Oxide growth with 28Si thin film deposited by the prior ion source. ....... 48 Figure 3.2: Simplified, cross sectional schematic diagram of the UHV ion source. .. 52 Figure 3.3: 28Si ion current (black) and discharge current (blue) characteristics. ...... 55 Figure 3.4: Comparison of the two mass spectra and the enrichment SIMS. ............. 57 Figure 3.5: Comparison of the RGA and chemical SIMS. ......................................... 59 Figure 3.6: Chemical purities (C, N and O) of the 28Si thin film vs ion source base pressure. ...................................................................................................................... 62 Figure 3.7: STM surface topography of two 28Si films using both ion sources.......... 66 Figure 3.8: A schematic of the upgraded ion beam lens system and new sweeper. ... 69 Figure 4.1: A schematic illustration of the origin of 28Si and 29Si. ............................. 75 Figure 4.2: Demonstration of the targeted enrichment. .............................................. 78 Figure 4.3: A SIMS depth profile of a first-generation targeted enrichment sample. 83 Figure 4.4: A correlation plot showing the measured 29Si isotope fractions as a function of targeted 29Si isotope fractions for the first-generation samples. .............. 85 Figure 4.5: Ion source anodes and cathodes after hours of beam runs. ...................... 88 Figure 4.6: A SIMS depth profile of a second-generation targeted enrichment sample. ..................................................................................................................................... 90 Figure 4.7: A correlation plot showing the measured 29Si isotope fractions as a function of targeted 29Si isotope fractions. ................................................................. 92 Figure 5.1: 28Si MOSFET device and measurements. .............................................. 100 Figure 5.2: Magnetotranport data of the 28Si MOSFET. .......................................... 102 Figure 5.3: The magnetoresistance Rxx and the Hall resistance Rxy vs B field. ........ 105 Figure 5.4: The change in conductivity (??xx) vs external magnetic field (B) for devices fabricated on 28Si (?) and natSi (?) measured at 3 K. ................................... 107 x Figure 5.5: Quantum and transport lifetime extracted from the magnetotransport. . 110 Figure 6.1: Al adatoms on Si(100) surface. .............................................................. 116 Figure 6.2: STM images of Al deposited on Si(100) surface with low coverage. .... 119 Figure 6.3: Counting Al 2D density using STM and ImageJ. .................................. 123 Figure 6.4: Al 2D density counting with larger area of vacancies and fewer clusters. ................................................................................................................................... 125 Figure 6.5: SIMS depth profiles with different ion energies and sputter angles. ..... 128 Figure 6.6: SIMS depth profile of an Al delta-doped sample with 100% Al dosing at 1 keV. ........................................................................................................................... 131 Figure 6.7: 1st iteration of SIMS to STM number density ratio. ............................... 133 Figure 6.8: 2nd iteration of SIMS to STM number density ratio. .............................. 135 Figure 6.9: APT of the Al delta layer without thermal treatment. ............................ 141 Figure 7.1: STM images of the surface after each growth step of the first-generation Al delta layer. ............................................................................................................ 146 Figure 7.2: Electrical properties of our previously reported Al delta layer devices. 148 Figure 7.3: STM images of the surface with different incorporation annealing times. ................................................................................................................................... 152 Figure 7.4: Electrical measurements of the Al delta layer samples with and without 550 ?C 1 min incorporation anneal. .......................................................................... 154 Figure 7.5: STM images of the deposited Si capping layer on different starting surfaces. .................................................................................................................... 157 Figure 7.6: Comparison between MBE and SPE grown Al delta layer samples. ..... 159 Figure 7.7: STM images of the deposited Si surfaces with LL. ............................... 162 Figure 7.8: Effects of different Al doses on surface topography and dopant activation. ................................................................................................................................... 166 Figure 7.9:Summary of the variations in growth methods for Al delta layer synthesis. ................................................................................................................................... 168 Figure 7.10: Temperature dependent sheet density and mobility. ............................ 173 Figure 7.11: Two-carrier model fit to the temperature dependent sheet density and mobility. .................................................................................................................... 176 xi 1 Chapter 1: Introduction 2 3 4 Progress in the semiconductor industry has been greatly advanced and expanded 5 in the past decades largely in an attempt to follow Moore?s law. Originated from 6 Gordon Moore in 1965, this predicted that the number of transistors in an integrated 7 circuit (IC) should double every two years. Progressing from the first metal-oxide- 8 semiconductor field-effect transistors (MOSFET), which have critical dimensions that 9 are micron in size, IC?s now have billions of transistors. Recently, the mass 10 production of devices at the 3 nm node using fin field-effect transistor (FinFET) and 11 extreme ultraviolet lithography (EUVL) has been made commercially available [1]. 12 The race continues as IBM announced their new 2 nm process using nanosheet or 13 gate-all-around transistors recently. Although the ?2 nm? described here is not the 14 actual dimension of the transistors, the shrinking in size will eventually lead to a 15 fundamental limit where quantum effects dominate the device performance [2]. Even 16 with these great advancements, classical computers that use classical bits 0 and 1 are 17 still limited when solving certain types of problems. 18 The quantum computer, in analogy to its classical counterpart, is made up of 19 quantum bits or ?qubits?. A qubit is a two-level system (e.g. an electron spin that has 20 spin up and spin down or a photon that has vertical and horizontal polarization, etc.) 21 that exhibits unique quantum properties including superposition and entanglement. 22 Superposition is the ability of a quantum system to be in multiple states 23 simultaneously, at least until it is measured. It allows a qubit to not only be in the 24 states labeled |0? or |1?, but also in the state : 1 25 |?? = cos(??2) |0? + ???sin (?/2)|1? (1.1) 26 , where ? and ? are real phase angles defined on the Bloch sphere, as shown in Fig. 27 1.1. On the Bloch sphere, the basis states |0? and |1? are the north and south poles, 28 respectively and the superposition states are on the equator. An arbitrary qubit state 29 can be expressed as a point on the surface. The entanglement of the qubits describes 1 30 the correlation between qubit states. A two-qubit state (|01? + |10?) can be used to ?2 31 express entanglement, where one qubit depends on the other. By combining 32 superposition and entanglement with quantum algorithms, an exponential increase in 33 the computing power can be achieved when solving certain types of problems, such 34 as prime factorization [3], numerical optimization [4], machine learning [5], complex 35 simulations [6], data searching [7], etc. 36 Quantum algorithms are based on quantum computing models. One of the most 37 commonly used is the quantum circuit model [8]. In this model, it has been proved 38 that arbitrary single-qubit rotations with two-qubit controlled NOT gates are universal 39 and can provide a set of gates to implement any quantum algorithms [9]. Besides, one 40 qubit state can be controlled by another using a two-qubit controlled NOT (CNOT) 41 gate, where a ? rotation is applied around the x-axis if the control is in |1? [10]. The 42 core of building a quantum computer is to have a qubit with high-fidelity single and 43 two-qubit gates. The control fidelity (a measure of how ?close? the two quantum 44 states are) depends mainly on the manipulation time and the coherence time. The 45 manipulation time refers to the time required for a single manipulation, characterized 46 by a rotation angle of ? or 2?. The coherence time (T2) is also called the dephasing 2 47 48 Figure 1.1: A schematic diagram of a Bloch sphere representing the qubit states. 49 The north pole and south pole represent the basis states |0? and |1?, respectively. Any 50 point on this sphere represents a linear combination of the basis states. A ?/2 pulse 51 rotation changes the qubit from the |0? to a superposition state. (Modified from [10], 52 an Open Access article distributed under the terms of the Creative Commons 53 Attribution License.) 54 55 time, defined as the time that a qubit can keep its quantum coherence properties. In 56 coherent measurements, T2 can be obtained by measuring the decay time of Larmor 57 precession and Ramsey fringes [11]. Those decay times are usually denoted by T *2 as 58 they are smaller than T2 due to experimental or environmental imperfections. 59 Dynamical decoupling pulses [12] can be used to convert T *2 to T2. 60 61 3 62 1.1 Semiconductor and Superconductor Quantum 63 Information 64 65 There are many possible candidate approaches toward building a quantum 66 computer, such as ion traps [13, 14], superconducting circuits [15, 16], spins or 67 quantum dots in semiconductors [17, 18], nitrogen vacancy centers [19, 20], nuclear 68 magnetic resonance techniques [11], etc. Among those, semiconductor quantum 69 information is a powerful candidate due to its compatibility to the modern 70 semiconductor industry. In 1998, Loss and DiVincenzo first proposed to use 71 semiconductor quantum dots as qubits and demonstrated single spin manipulations 72 [21]. For a gate defined quantum dot device, the electrodes can be biased to form 73 potential well to trap electrons, and the electron spins can be manipulated via an 74 external magnetic field. Such quantum dots can also be formed in other material 75 systems, such as GaAs [22], Si MOS and silicon-on-insulator (SOI) [23], nanowires 76 [24], graphene [25], self-assembled crystals [26], etc. As an alternative to Si MOS 77 quantum dots that utilize electron spins, Bruce Kane proposed to use the nuclear spin 78 of a single 31P donor in silicon as a qubit [27]. STM lithography with atomic scale 79 precision and ion implantation are the two common ways to fabricate this kind of 80 qubit devices. For the STM lithography approach, a single phosphorus (P) donor and 81 a donor molecule are placed on the Si surface using STM lithography to selectively 82 lift off hydrogen from a H-passivated surface [28]. A single-electron transistor (SET) 83 for charge sensing is formed beneath it. The qubit is again surrounded by metallic 84 gates and an aluminum microwave antenna generates an oscillating magnetic field 85 over the device. The quantum information stored in each 31P nuclear spin is read out 4 86 by measuring the tunneling current between the target qubit and the adjacent neutral 87 donor. For the ion implantation approach, donor ions are implanted in a small region 88 in the silicon and the spins of both the electron bound to the donor and the donor 89 nucleus can be used as qubits [29]. 90 In silicon spin qubits, one of the greatest advantages is the potential for extremely 91 long coherence times. Silicon is a promising candidate due to its intrinsic material 92 properties and the existence of techniques for fabrication of devices at increasingly 93 smaller length scales. It has been widely accepted in this community that silicon can 94 be an excellent host material for quantum devices that utilize charges and/or spins. 95 Silicon can provide a nearly ideal environment for spins which results in a very long 96 coherence time, due to its weak spin-orbit coupling and the existence of a nuclear 97 spin-free isotope, 28Si. In Si spin qubits, the major source of decoherence comes from 98 the random strain field and the inhomogeneous magnetic field noise (or the 99 Overhauser field) generated by nuclear and impurity spins. Natural abundance Si is 100 composed of three isotopes: 28Si (92.2 %), 29Si (4.7 %) and 30Si (3.1 %). The 29Si 101 isotope has a non-zero nuclear spin (I = 1/2) that causes random fluctuations and 102 inhomogeneities in the background magnetic field, while 28Si and 30Si have no net 103 nuclear spin. By eliminating the presence of 29Si isotopes, both nuclear and electron 104 spins in isotopically enriched 28Si interact much less with their environment, resulting 105 in a great enhancement in coherence time T 2 [30, 31]. Theoretical studies have 106 predicted that the increase in coherence time is proportional to the reduction in 29Si 107 isotope concentration [32, 33]. Bulk electron spin resonance (ESR) and NMR 5 108 experiments of 31P spins in 28Si have been carried out by numerous research groups, 109 where coherence times exceeding seconds have been achieved [30, 31, 34, 35]. 110 Despite the advantages, there are also challenges associated with silicon-based 111 quantum information. The semiconductor qubits have been expected to have good 112 scalability and coupling considering the success in semiconductor industry, however, 113 the largest number of qubits that can be controlled in the same device to date is still 114 less than ten [36]. With isotopically purified 28Si, the complicated valley degeneracy 115 and resulting necessary elaborate control of the small electronic wave function still 116 remain as challenges [10, 23]. There are six degenerate minima of the conduction 117 band in Si and these subbands form valleys. For donors in Si, the valley degeneracy is 118 not a concern since the dopant atom (such as 31P) has a strong confinement potential 119 that can lift the valley states degeneracy easily. However, for Si quantum dots, there 120 are four in-plane valleys and two out-of-plane valleys and the two lower valleys 121 greatly affect the qubit control and manipulation [23]. As a consequence, the valley 122 state degeneracy can cause a significant decrease in spin lifetime [37], renormalize 123 the g-factor [38], deteriorate spin initialization and may limit the dephasing time [39]. 124 On the material standpoint, the supply of the isotopically enriched 28Si within this 125 community is very limited. Perhaps the most highly enriched single crystal bulk 28Si 126 is from the International Avogadro Project [40], which was produced using centrifuge 127 enriched gaseous silane and a long process chain resulting in zone refined, single 128 crystal silicon with a residual 29Si isotope fraction of about 10-5 mol/mol [41]. The end 129 goal in that case was to produce a macroscopic artifact (?1 kg) of enriched silicon for 130 metrological purposes. Quantum information applications do not require macroscopic 6 131 quantities of 28Si for each device, so an alternative, less expensive strategy has been 132 to grow epitaxial 28Si layers on natural silicon substrates using isotopically enriched 133 silane gas, e.g., chemical vapor deposition (CVD) grown 28Si epilayers on 300 mm2 134 substrates that is enriched to 99.992 % [42] . Remnants from other sources [43] of 28Si 135 also exist, providing access for research efforts, typically with enrichments ? 99.9 % 136 28Si, including the float-zone grown samples from Keio University[44], CVD grown 137 thin films at Princeton University [45], solid-source molecular beam epitaxy (MBE) 138 grown thin films at Technical University of Munich (TUM) [46], ion beam method 139 from Penning source based ion implanter [47], etc. 140 As an alternative, superconductor-based qubit is another promising candidate for 141 quantum information due to its macroscopic nature. Unlike semiconductor qubits 142 where coupling is challenging (mainly due to the nanometer scale), a degree of 143 scalability has already been demonstrated for superconductor qubits: a 53 144 superconducting qubit computer was demonstrated by Google in 2019 and a 65-qubit 145 computer was announced by IBM in 2020. In 1999, Nakamura et al. developed the 146 first qubit for superconducting quantum computing [48]: a Josephson junction (JJ) 147 based Cooper-pair Box (CPB) in the charge regime. Since then, superconducting 148 qubit has been developed rapidly. A high fidelity two-qubit gate using 5 qubits [49] 149 was demonstrated in 2014 and this provided an important step towards surface code 150 schemes [50, 51]. Depending on different degrees of freedom, superconducting qubits 151 can be divided into different categories: charge qubits [48, 52], phase qubits [53], flux 152 qubits [54, 55], transmission line shunted plasmon oscillation or ?transmon? qubits 7 153 [56], etc. An important step is to embed the qubits in a superconductor micro- 154 resonator to introduce circuit quantum electrodynamics (cQED) [16, 57-59]. 155 Compared to other quantum computation systems, superconductor qubits have the 156 following advantages. The first is the high design capability that is associated with 157 different types of qubits (charge, phase, flux, etc.). Secondly, different parameters 158 such as energy level and coupling strength can be adjusted by changing the 159 capacitance, energy, and inductance of the JJ. In addition, superconductor qubit has 160 good scalability and is easy to couple using capacitance or inductance due to its 161 circuit nature. 162 One limitation for this type of qubit is the relatively short coherence time. 163 Originally, the coherence time for charge qubit was only a few nanoseconds. In 2007, 164 a transmon CPB has been demonstrated with a longer coherence time [56]. By 165 embedding a transmon device in a 3D cavity, the coherence time has been further 166 extended to 100 ?s [60], but this is still orders of magnitude lower than that 167 achievable with semiconductor spin qubits that is in the range of seconds to even 168 minutes [30, 34]. This limit in the coherence time for the heterogeneous devices used 169 in superconducting qubits usually comes from the losses in or at the material 170 interfaces, such as the oxides on the superconductor, insulator and interlayer 171 dielectrics [61]. 172 Both semiconductor and superconductor qubits have their own strengths and 173 weaknesses, largely based on the nature of the material platforms that have been used. 174 Recently, an approach [61] trying to combine the superconducting and 175 semiconducting materials into a single crystalline lattice with no interface has been 8 176 proposed, where the strength of both types might be achieved simultaneously. This 177 proposed hybrid quantum device would consist of superconducting wires and 178 Josephson junctions in a single crystalline isotopically enriched 28Si to reduce the 179 coherence loss at the dielectric interface. Qubits with enhanced coherence time and 180 cQED coupling might be expected. In order to fabricate this new hybrid quantum 181 device, a two-dimensionally (2D) confined superconducting semiconductor material 182 with single crystalline properties would be beneficial. 183 184 1.2 Superconducting Semiconductors 185 186 187 A semiconductor with superconducting properties was first reported in a heavily 188 boron doped diamond grown by microwave plasma CVD with high temperature and 189 pressure. The highest reported critical temperature of this kind of superconductor is 190 11.4 K [62]. Superconducting semiconductors have also been demonstrated in other 191 semiconductor material systems, such as GeTe, SrTiO3, In2O3, PbTe [63-66], etc. For 192 a semiconductor, the band gap is usually larger than the superconducting energy gap, 193 so that an intrinsic semiconductor is not superconducting [67]. In order to reach 194 superconductivity, doping of impurity atoms in the semiconductor above the metal- 195 insulator-transition (MIT) is required. This is because impurity atoms that substitute 196 into the semiconductor lattice create energy states (donor or acceptor states) located 197 within the band gap. For a degenerately donor-doped semiconductor that has high 198 enough concentration, the electrons remain in the conduction band even at a 199 temperature of 0 K. Those electrons contribute to the electrical conduction and works 200 as unpaired electrons in the normal state of a superconductor [67]. However, such a 9 201 high density of dopants usually corresponds to a concentration higher than the 202 equilibrium solid solubility limit. And this non-equilibrium doping causes 203 inhomogeneous material properties such as dopant segregation, cluster formation and 204 polycrystalline materials [68-70]. 205 Non-equilibrium doping techniques have been used to produce doping density 206 above the solid solubility limit. These includes chemical vapor deposition, gas 207 immersion laser doping, high fluence ion implantation with high temperature 208 annealing [68, 71-74], etc. For example, single-crystalline Al and Ga in Ge made by 209 ion implantation and rear-side flash lamp annealing showed superconductivity at 0.15 210 K and 0.45 K, respectively, with a doping density of 6 at. % [74]. Heavily doped 211 boron (B) in silicon above the solubility limit (1.2 at. %) using gas immersion laser 212 doping has also been demonstrated [71]. A superconducting transition at 0.35 K has 213 been observed, with a doping density of 6.5 at. % (or 3.2 ? 1021 cm-3) [71]. The value 214 of Tc is expected to increase as the dopant concentration increases based on a phonon- 215 mediated BCS type mechanism [75]. Since this early work, exploring other dopants 216 with potentially higher Tc has become of great interest, especially for STM 217 lithography based nanodevices. Aluminum (Al) as a dopant in Si is one of the 218 possible candidates. A highly doped Al in Si structure is predicted to have a Tc ten 219 times higher than the case for B under the same doping concentration [75]. However, 220 superconducting Al in Si has not been demonstrated yet, mostly due to the extremely 221 low solid solubility limit of Al in Si (0.04 ? 0.06 at. %) and the tendency of 222 segregation at high doping density [76]. 10 223 Delta doping with low temperature molecular beam epitaxy (MBE) is an 224 alternative method that can be used to fabricate 2D dopant layers with high enough 225 atom density and low thermal budget. With this growth method, sharp dopant profiles 226 with atomically abrupt junctions might be made in Si. Those delta-doped layers have 227 a sharp spike in their dopant profiles that resembles a delta function in the growth 228 direction. Several groups have reported the growth of various delta-doped layers in 229 Si, such as B, P and Sb [77-80]. A dopant density higher than the solubility limit has 230 been demonstrated in Sb delta-doped layers [81, 82] and a density as high as 1 ? 1022 231 cm-3 has been reached in MBE-grown B delta layers [83]. Delta-doped 2D systems 232 might also be a precursor for many low-dimensional devices, such as nanowires, 233 SETs, etc. 234 235 1.3 Objectives and Project Goals 236 237 238 Given the advantages and limitations of the superconducting-based and 239 semiconducting-based quantum computation systems, the strength of the two might 240 be combined. It may be possible to merge the two approaches and make a single- 241 crystal superconducting device out of a semiconductor. In this case, qubits with 242 extremely long coherence times, good coupling and scalability might be realized. 243 28Si with sufficiently high refinement nearly eliminates unwanted nuclear spins 244 and provides an excellent environment to host spin qubits. On the other hand, Al delta 245 layers in Si is a new material system that has the potential to have a much higher Tc 246 compared to that for B doping. By combining the two, a nanometer scale spin qubit 247 can be coupled together with a millimeter scale superconducting qubit. Our ultimate 11 248 objective is to create a hybrid system where both Si spin qubits and superconductor 249 qubits are coupled in a nuclear spin-free and interface-free material. The focus of this 250 thesis is to attack two materials limitations for realizing a monocrystalline, super- 251 semiconducting hybrid architecture: 1) substantially reducing 29Si that limits 252 coherence of semiconducting spin qubits and 2) exploring supersaturated, Al-doped 253 silicon as a system for localized superconductivity within silicon with a potential Tc > 254 1K. 255 There are challenges associated with each of the material systems that we want to 256 pursue. In this work, we will break down those challenges in smaller parts. For 257 isotopically enriched 28Si, one of the difficulties is the material supply. As we briefly 258 described in the previous section, the 28Si materials within this community are of very 259 limited quantity or are not being replenished. A material source that can provide high 260 isotopic enrichment and chemical purity simultaneously, while keeping the growth 261 process simple and flexible is needed. Another difficulty for enriched silicon is the 262 determination of metrics for quantum information, in terms of enrichment, 263 crystallinity, and purity. Unlike classical specifications like electronic-grade and 264 metallurgical-grade Si (EGS and MSG), a quantum metric for ?how good is good 265 enough? is still unclear. Achieving superconductivity with Al delta layers in silicon 266 is quite an ambitious goal. Hole-based dopant systems have drawn a lot of attentions 267 recently, as a longer coherence time due to the suppression of hyperfine interaction 268 between the hole and nuclear spins can be achieved [84, 85]. But they are generally 269 not as well studied as electron-based systems. Al delta layer has only been 270 successfully fabricated recently by our group [86]. However, the material properties 12 271 of the Al delta-doped layers in silicon are largely unknown, such as Al dopant 272 configuration at various growth temperatures, dopant incorporation and activation in 273 silicon lattice, low temperature electrical conduction, etc. 274 To overcome the challenges listed above and provide insights on this field for 275 further studies, we have developed the follow specific goals for those two material 276 systems: 277 Isotopically enriched 28Si: 278 1. Produce 28Si material with high enrichment (< 1 ppm 29Si) and chemical purity (< 279 1016 cm-3) simultaneously. 280 2. Demonstrate precise control (< 50 % deviation) of the 28Si enrichment levels in a 281 wide range to support the correlation study of 29Si concentrations and coherence 282 times. 283 3. Fabricate a 28Si MOSFET as part of an effort to underpin the material standards 284 needed for quantum grade silicon and establish a standard approach for the inter- 285 comparison of these materials. 286 Al delta layers: 287 1. Study the 2D configuration of Al on Si(100) and the maximum atom density for 288 one atomic layer. 289 2. Explore possible improvements in material growth methods for dopant activation 290 and reaching the critical 3D density (2 at.%) for superconductivity. 291 3. Study the low temperature electrical conduction mechanism of the Al delta layer in 292 Si. 293 13 294 1.4 Outline 295 296 297 ? Chapter 2: The experimental apparatus and methods used to grow and 298 characterize the 28Si thin film, Al delta layer and natural MBE Si are 299 introduced. This includes the description of the hyperthermal energy ion beam 300 system, the ultra-high vacuum (UHV) preparation and deposition chamber and 301 the in-situ characterization STM chamber. The basic principles for ion beam 302 deposition, STM scanning and the Hall measurements used for device 303 characterization are also presented. 304 ? Chapter 3: Design and characterization of a new UHV ion source to produce 305 28Si with improved chemical purity while maintaining the same level of 306 isotopic enrichment. The vacuum has been improved by a factor of ? 100, 307 result in an improve in chemical purity from 98.47 % to 99.97%, measured by 308 SIMS. The enrichment capability is preserved, with a 28Si isotope fraction of 309 99.99987 %. 310 ? Chapter 4: Targeted enrichment: the ability to grow isotopically enriched 28Si 311 epitaxial films with precisely controlled enrichment levels over a wide range. 312 A model is developed to predict and control the 29Si concentration and the 313 targeted enrichment is achieved by periodically switching the mass analyzer 314 magnetic field to the appropriate ion species (28Si+ and 29Si+). An accuracy of 315 ? 90 % is achieved between the targeted enrichment value and the deposited 316 enrichment value. 14 317 ? Chapter 5: 28Si MOSFET is fabricated and characterized compared to 318 commercial silicon. A maximum mobility of ? (1740 ? 2) cm2/V.s and an 319 electron density of (2.7 ? 1012 ? 3 ? 108) cm?2 and ? (6040 ? 3) cm2/V.s at an 320 electron density of (1.2 ? 1012 ? 5 ? 108) cm?2 at T = 1.9 K for devices 321 fabricated on 28Si and natSi have been measured, respectively, a result of the 322 short-range scattering (impurity scattering). 323 ? Chapter 6: For Al delta layers in Si, the 2D configuration and the maximum 324 2D density of Al as a dopant on Si(100) surface is studied using STM, SIMS 325 and APT. The result is compared to the theoretical studies from the literature. 326 The maximum density of one atomic layer of Al that can be deposited on 327 Si(100) is found to be most likely 3.4 ? 1014 cm-2, in accord with the literature 328 prediction. The 3D density of the Al delta layer peak is also found to be 6.2 ? 329 1020 cm-3 (1.2 at. %). 330 ? Chapter 7: A systematic study of the growth methods for Al delta layers in Si 331 and the materials characterization using STM and low temperature 332 magnetotransport measurements are presented. Possible ways to improve 3D 333 dopant confinement and dopant activation are explored. The conduction 334 mechanism of this delta layer at low temperature is also measured using Hall 335 devices and a two-carrier type conduction model is used to explain the 336 observed behavior: carriers from the delta layer dominated at low T and 337 thermally excited carriers dominated at higher T. 15 338 ? Chapter 8: A summary of the technical and scientific results is presented. 339 Future research directions and possible experiments enabled by this work are 340 discussed. 341 342 343 344 345 346 16 347 Chapter 2: Experimental Apparatus and Methods 348 349 In this chapter, the experimental apparatus and methods for 28Si and Al delta layer 350 materials synthesis will be introduced. Most of the experiments involving the 351 preparation, fabrication and characterization of the materials are conducted in the 352 ultra-high vacuum (UHV) chambers. First, I will introduce the UHV vacuum 353 condition and chamber configuration, which consists of a 28Si ion source deposition 354 chamber, a UHV deposition and analysis chamber, and a scanning tunneling 355 microscopy (STM) chamber. Then I will talk about the sample preparation for both ex 356 situ and in situ cleaning of Si (100) substrates. Followed by an introduction on the 357 UHV deposition of the hyperthermal ion beam system, the electron beam evaporated 358 natural Si system and the thermal evaporated elemental Al deposition system. Finally, 359 the STM used for materials characterization will also be introduced. 360 361 2.1 UHV Chamber Configuration 362 363 364 To achieve high cleanliness for material growth and to suppress various 365 contaminations from the background, all the chambers are designed and built to be 366 UHV compatible. The schematic of the experimental apparatus is shown in Fig. 2.1. 367 The hyperthermal ion beam chamber is located at the left with green dashed lines. Ion 368 source, electromagnetic lenses and apertures are in this chamber. The deposition and 369 analysis chamber is in the middle with blue lines. Sample manipulation and heating 370 stage, natural Si and elemental Al deposition sources, reflection high energy electron 17 371 diffraction (RHEED) and Auger spectrometer are in this chamber. A portion of the 372 magnetic transfer rod is shown on the top, which was used to transfer sample from the 373 deposition chamber to the STM chamber. The deposition chamber is also connected 374 to a separate load lock system on the right, where sample loading and unloading take 375 place. The bottom is the STM chamber surrounded by orange lines. The four vacuum 376 chambers (including the load lock) are all maintained at UHV condition and separated 377 by gate valves. 378 All chambers are kept at UHV conditions. The deposition chamber has two 379 turbopumps (Pfeiffer and Edward Vacuum, with pumping speed of 685 L/s and 300 380 L/s, respectively), an ion pump and a titanium sublimation pump with a liquid 381 nitrogen cryoshroud. To reach an acceptably low base pressure, a bake out of the 382 chamber is necessary. The procedure includes wrapping the chamber with Al foils 383 and heating up the chamber with heat tapes to above 150 ?C for a few days for better 384 thermal conductivity and stability. During the process, water and other impurity gases 385 are slowly desorbed from the chamber interiors and are pumped out. The typical 386 pressure after bake out is about 5 ? 10-11 Torr (6.67 ? 10-9 Pa). We use a residual gas 387 analyzer (RGA) to monitor the partial pressure of the vacuum components in our 388 chamber. As shown in Fig. 2.2, the partial pressures of the main contributors, such as 389 H2, H2O, O2, CO2 and N2 are shown. 18 390 391 392 Figure 2.1: Top-down schematic of the experimental apparatus. 393 This includes the ion beam chamber (green), deposition and analysis chamber (blue), 394 STM chamber (orange) and the load lock used for sample loading into the deposition 395 chamber. All four sections of the chambers are separated by UHV compatible gate 396 valves. (Modified from Ref. [87] with permission) 397 398 A 5-axis sample manipulator is located in the middle of deposition chamber to 399 position samples, surrounded by the 28Si ion beamline, RHEED, RGA, e-beam 400 evaporator (natural Si) and quartz crystal microbalance (QCM). This allows quick 401 access for multiple processes, such as substrate preparation, material growth and in 402 situ characterizations. 403 19 404 405 Figure 2.2: RGA spectrum of the deposition chamber baseline. 406 The pressure is at pressure 6 ? 10-11 Torr. The partial pressure peaks of the typical 407 components: H2, H2O, O2, CO2 and N2 can be seen. 408 409 2.2 Sample Preparation 410 411 2.2.1 Ex situ Preparation 412 413 414 To prepare a clean substrate for further deposition and fabrication with low 415 contamination and high crystallinity, we divide our sample preparation into two steps: 416 ex situ and in situ. Ex situ preparation is introduced to the sample before entering the 417 vacuum chamber. In this work, most of the samples used are intrinsic float-zone 418 refined Si(100) wafers with resistivity > 10 k?.cm. The wafer is first spin coated with 20 419 S1813 photo-resist to protect the surface from scratches and diced into pieces (chips) 420 with dimensions 4 mm ? 10 mm. Then the chips are taken into the cleanroom and 421 cleaned with complementary-metal-oxide semiconductor (CMOS) procedures. This is 422 to remove the organic and metal contaminations from the surface. The cleaning recipe 423 is as followed: 424 1. Remove photo-resist in PG remover 80 ?C, 20 mins 425 2. Isopropanol (IPA) 1 min, RT; rinse with DI water 426 3. Downstream asher or RIE photo-resist Descum 60 s 427 4. 50:1 H2O:HF dip, 10s; DI rinse 428 5. SC-1 clean 10:1:1 H2O:NH4OH:H2O2 at 80 ?C, 12 mins; DI rinse 429 6. Piranha clean 3:1 H2SO4:H2O 12 mins; DI rinse 430 7. 50:1 H2O:HF dip, 10s; DI rinse 431 8. SC-2 clean 5:1:1 H2O:HCl:H2O2 at 80 ?C, 12 mins; DI rinse 432 9. Blow dry with N2 433 The sample is then loaded into the load lock chamber within 1 hour to reduce surface 434 contamination. Note that during the transfer, the sample will have a thin chemical 435 oxide layer with a few nm grown naturally on the surface. This will act as a 436 protecting layer and will be thermally removed during in situ preparation. 437 438 2.2.2 In situ Preparation 439 440 441 Once the samples are loaded into the vacuum chamber, two methods of heating 442 are performed for in situ cleaning of the substrate. One method is called ?RH?, which 443 consists of a back heater utilizing the radiative heating from a tungsten wire, typically 21 444 with current and voltage < 10A and 15V, respectively. Another method is called 445 ?DH?, or Joule heating, which uses resistive heating by passing current through the 446 sample. Fig. 2.3 shows a glowing Si substrate at 1000 ?C, the sample stage and the 447 wiring diagram of the RH and DH. RH is located at the back of the sample and a 448 finger is connecting from DH+ through the sample to DH-. Usually for intrinsic 449 silicon samples, since the resistance is too high at room temperature, RH is needed to 450 pre-heat the sample to about 300 ?C to reduce the resistance and thus allow 451 conduction through DH. The loaded sample will first be heated with both RH and DH 452 to a temperature of about 600 ?C. This is process is called ?degas?, which slowly 453 removes water molecules sticking to the sample surface. After degassing, the sample 454 will be flash annealed using DH from 600 ?C to 1200 ?C in a few seconds. This 455 process will be repeated for 5-6 times, each with a duration of 10 s at 1200 ?C. This is 456 to remove the thin native oxide layer of SiO2 grown on the surface by a sublimation 457 process at high temperature, without the formation of SiC and step bunching at the 458 surface [88, 89]. Each heating cycle is kept short so as to prevent outgassing of the 459 manipulator parts. After flash anneal process, the substrate will be cooled down 460 rapidly to 600 ?C and then ramped down to RT, with a rate of 1 ?C/s. The sample 461 substrate is then either examined using RHEED or transferred to the STM chamber 462 for surface characterization. Typically, a flat, clean surface of Si (100) with (2 ? 1) 463 reconstructed dimer rows and adjacent Si terraces perpendicular to each other 22 464 465 Figure 2.3: Sample stage on the manipulator and the wiring diagram. 466 The glowing Si (100) substrate is heated to 1000 ?C by running current through the 467 sample using DH. Typical current and voltage for flash anneal is ? 10 A and 5 V, 468 respectively. (Modified from Ref. [87] with permission) 469 470 471 472 Figure 2.4: STM images of a Si (100) substrate after 1200 ?C flash anneal. 473 (a) 2 ? 1 reconstructed dimer rows are clearly observed. (b) A larger scale image: Si 474 dimer rows and terraces perpendicular to each other can be seen. Images are acquired 475 with a tip bias of -2 V and a current setpoint of 110 pA. Some dark spots are also 476 visible in this image, those are the vacancy defects or missing Si atoms on the 477 surface. 478 23 479 480 can be seen, as shown in Fig. 2.3. Some dark spots are also visible in Fig. 2.4, which 481 are most likely vacancy defects or missing Si atoms on the surface. 482 Since we need to rapidly change and accurately control the temperature of our 483 sample for both sample preparation, deposition and post-anneal processes, an accurate 484 way for temperature measurement is very important. In this work, we use a Process 485 Sensor pyrometer with temperature range 300 ?C to 1300 ?C and spectral range of 486 1.45 to 1.8 ?m to measure temperatures. The temperature reading of the pyrometer 487 depends on the emissivity e and it changes rapidly according to the temperature. For 488 example, e changes from < 0.1 to > 0.7 when T changes from 100 ?C to above 1000 489 ?C, respectively [90, 91]. Although the emissivity values are well studied, and 490 reported in the literature, deviations due to difference in experimental equipment can 491 be introduced to the ?true? emissivity values, such as the aging and covering of the 492 deposition materials on the view window. People use both Au-Si and Al-Si eutectic 493 samples to calibrate the emissivity. A eutectic is a homogenous mixture of two 494 materials that has a lower melting point than any of the constituents. The eutectic 495 temperature for Al-Si is about 577 ?C [92] and for Au-Si is about 363 ?C [93]. The 496 Au-Si eutectic is produced by an Au wire on the edge of Si substrate and the Al-Si 497 eutectic is produced by depositing 500 nm of Al onto the center of a Si substrate. As 498 we increase the current from DH across the sample, the substrate temperature 499 increases until a phase transition is visible at the eutectic point. After stabilizing at the 500 eutectic point, the pyrometer emissivity is adjusted so that it matches the eutectic 501 temperatures of the alloy. 3 calibrated emissivity has been obtained with different 24 502 temperature range: e ? 0.25 with T < 475 ?C; e ? 0.42 with T < 625 ?C and e ? 0.68 503 with T > 800 ?C, which is very close to the values reported in the literature [94]. 504 505 2.3 UHV Deposition Systems 506 507 2.3.1 Hyperthermal Ion Beamline 508 509 510 This section relies heavily on the previous works done within our group, mainly 511 contributed from my NIST supervisor Dr. Josh Pomeroy and his previous group 512 member Dr. Kevin Dwyer. During my PhD, I was responsible for the modifications 513 and upgrades of the beamline, such as the new UHV ion source, ion beam sweeper, 514 new gas system, etc. Those changes will be introduced in section 3. Here I will 515 present the important features of this ion beamline in terms of basic functioning and 516 characterization. 517 518 2.3.1.1 Experimental Setup 519 520 521 The hyperthermal ion beamline system consists of four main parts: the gas manifold, 522 the ion source, the transport system and the magnetic sector mass analyzer. In the 523 initial setup, the ion source is a traditional Penning-type ion source, also known as 524 Penning Ionization Gauge (PIG), built by a partnership of Physicon Corporation and 525 Dr. Barbara Cooper. The transport system (including electromagnetic lenses) and 526 magnetic sector mass analyzer are a result of creative partnership between Cornell 527 University and Dr. Pomeroy?s group. The basic principle of this type of gas discharge 528 was firstly demonstrated by Phillips [95]. Later on, Baumann and Bethge have 25 529 extensively studied and optimized the PIG ion source, which included the dependence 530 of ion current on gas flow, magnetic field and anode/cathode voltages [96-99]. The 531 schematic of the ion beamline system is shown in Fig. 2.5. The insert shows the 532 design of this gas mode Penning ion source with gas inlet, source magnet, anode, 533 cathode and extraction cusp. During operation, a plasma is generated between the 534 cathode and anode of the PIG ion source with a radially confined magnetic field. The 535 anode is typically at 50 V and the cathode varies from -1 kV to -3.5 kV. The plasma 536 ionizes and breaks down the working gas molecules (mostly SiH4 in this work) to 537 mostly singly charged ions [87]. Those ions are then extracted by a high voltage 538 extraction cusp, accelerated by a transport voltage of about -4 kV and focused by an 539 Einzel lens onto the focal point of the mass analyzer. This transport voltage is applied 540 to the whole ion beam chamber with other voltage components floating on top of it. 541 The purpose of this high voltage transport is to suppress the effect from space charge 542 (continuum of electrical charges distributed over a three-dimensional region) [100] 543 repulsion of the positively charged ions. 26 544 545 Figure 2.5: Hyperthermal ion beamline schematics. 546 The details of the gas mode Penning ion source including the gas inlet, source 547 magnet, anode, cathode and extraction cusp are shown in the inset. A potential 548 landscape is shown from anode (A) all the way to the end of deceleration lenses (K) 549 in the bottom figure. Ions from the ion source are first accelerated to the transport 550 voltage (-4 keV) and then decelerated back to ? 40 eV before hitting the target sample 551 at ground potential in the deposition chamber. (Taken from Ref. [101] with 552 permission of the Journal) 553 554 After being focused and accelerated, positively charged ions are transported into a 555 magnetic sector mass analyzer (bending magnet). Due to the Lorentz force, ions of 556 the same kinetic energy but with different mass-to-charge ratio will have different 557 trajectories at the exit location where an aperture is tuned at a particular value of m/Z 27 558 (where Z is the ionic charge in units of the proton charge e). In the case of 28Si, the 559 mass-to-charge ratio is tuned to be 28 amu/e and all other ions like 29Si+ and 30Si+ will 560 be blocked by the aperture. The mass resolution of the current aperture is changing as 561 a function of mass in units of amu, and the value of m/?m at 28 amu is ? 74 [101]. At 562 the bottom of Fig. 2.5, the potential changes of the ions in the ion beam as they pass 563 through each component (with label A to K) is shown. After passing through the 564 aperture, the ions will pass through a series of deceleration lenses (labeled F to K) 565 that refocus and decelerate them to a desired energy before reaching the final stage in 566 the deposition chamber. 567 The operation procedures of the hyperthermal ion beam deposition of 28Si are 568 described below: 569 1. Inject working gas (SiH4 in this work) from the gas line into the ion source using a 570 high precision leak valve. 571 2. Turn on and set the voltages for anode and cathode. For SiH4 operation, a typical 572 anode voltage is ? 50 V and cathode voltage is in the range of ? -1.5 kV to -3.2 kV. 573 3. Set the voltage VT for transport to be -4 kV. 574 4. Turn on voltages VE and VF for extraction cusp and focus, those are floating on top 575 of the transport. 576 5. Turn on the ion source magnet to ignite a plasma in the ion source. 577 6. Set the magnetic sector mass analyzer to the target ion mass (28 amu). 578 7. Turn on the deceleration lenses A2, B1-B4 and X. Collect and monitor the ion 579 current at the deposition position using an aperture. 28 580 8. Starting from the anode voltage, fine tuning the voltages along the beamline all the 581 way to the final lens to maximize the ion current detected at the deposition location. 582 9. Prepare sample to target temperature and open gate valve to start deposition. 583 584 2.3.1.2 Ion Beam Characterization 585 586 587 Here we introduce the methods to characterize the ion beam for isotopically 588 enriched 28Si deposition. The first important aspect is the ion beam mass spectrum 589 collected from the magnetic sector mass analyzer. The ion current is measured using a 590 home-made aperture located at the deposition position with a picoammeter (with a 591 typical background noise of 10 pA) while sweeping the magnetic field of the mass 592 analyzer, which corresponds to sweeping the mass/charge ratio, m/Z of the ions. 593 Measuring and analyzing the mass spectrum of the ion beam is a critical step for both 594 assessing the mass separation of the ion species, which limits the enrichment level of 595 28Si, and detecting the contamination levels in the ion source, such as gas molecules 596 contributed from background C, O and N. The mass spectra for SiH4 gas and other 597 background gas species are shown in Fig. 2.6. Panel (a) shows an example of the 598 mass spectrum using SiH4 gas during 28Si deposition. The y-axis is the ion current in 599 log scale collected at the sample location, the x-axis is the magnetic current of the 600 mass analyzer, which also corresponds to the mass of the ions. Ion current peaks are 601 marked according to the ion species, such as the 28Si+ and various Si hydride ions due 602 to incomplete cracking of the SiH4 molecules. For example, the ions at 28 amu are 603 from 28Si+, the ions at 29 amu consists of both 29Si+ and 28SiH+, and the ions at 30 604 amu are from a combination of 30Si+, 29SiH+ and 28SiH +2 , etc. Those ion species are 29 605 distinguishable with a higher mass separation, for example, during the SIMS 606 measurement of the isotope fractions [102]. The typical ion current obtained for 28Si+ 607 is a few hundred nA, which is about 10% of the total current of SiH4. To obtain the 608 mass separation ability of the system, a phenomenological Gaussian fit of the 609 following form is used to fit the spectrum: ? ??? 2 610 ? = ?0 + exp ( 1 ( ?? ) ) (2.1) ??2? 2 ? 611 where I is the ion current measured, I0 is the current offset from the background 612 noise, B is the area of the Gaussian, m is the mass, mc is the center of the mass peak 613 and ? is the standard deviation of the fit. The factors that affect the mass resolution 614 include the width of the aperture, energy spread of the ion beam, angular distribution 615 due to lensing effects, etc... The fluctuation of the current from the detector is < 100 616 pA. As shown in panel (a), the Gaussian peak fits well with the collected data with 617 symmetrical shape, indicating that the beam is experiencing very small perturbation 618 from scattering effects, which usually can be seen with the presence of a non- 619 symmetrical shoulder peak that is ? 10 % of the primary peak height. From the 620 fitting, the separation between 28 amu and 29 amu peak centers is about 11 ?, which 621 corresponds to a lower bound on the 29Si concentration of about 10-26 isotope fraction 622 in the 28Si film, assuming negligible gas scattering and side wall scattering [103]. In 623 some occasions, there might be a small shoulder peak observed in addition to the 624 main peaks. This is likely due to non-ideal beam tuning, resulting from the ion 625 scattering off the mass analyzer aperture. 626 Ion beam mass spectra of the possible background contaminations that are 627 presented in the ion beam along with the SiH4 gas are also shown. Panel (b) shows a 30 628 629 630 631 Figure 2.6: Ion beam mass spectra of working gas SiH4. 632 Panel (a) shows the ion current collected at the sample deposition location using a 4.9 633 mm2 aperture. 28Si ions and Si hydride ions can be seen from 28 amu to 33 amu. 634 Gaussian fits using equation (2.1) are presented as red solid lines, showing a good fit. 635 Panel (b) and (c) are taken using the new UHV ion source. They show the related 636 background gas contaminations and doubly charged Si hydride ions ranging from 12 637 amu to 50 amu. Possible contaminants include: CO2, N, O and H2O. Ar is present in 638 the ion beam since we are using Ar gas as a dilution gas and some residual gas may 639 be remained in the gasline. (Panel (a) is modified from Ref. [87] with permission) 31 640 spectrum in the range of 11 amu to 20 amu. Possible candidates for those peaks are: 641 12C+ (12 amu), 14N+ (14 amu), 16O+ (16 amu) and H O+ 2 (18 amu). The presence of 12C, 642 14N and 16O can be a source of chemical impurities in the 28Si film since they can pass 643 through the mass-selective aperture in the form of CO+ and N +2 (28 amu). 644 Contributions from the doubly charged silane molecules and Si ions are also possible, 645 such as 28Si2+ (14 amu),28SiH2+ (14.5 amu), 28SiH 2+2 (15 amu), etc. Panel (c) shows 646 the possible contributions from higher mass peaks, such as 40Ar+ (40 amu) and CO +2 647 (44 amu). 648 Another important aspect of the ion beam characterization is the energy. The 649 energy distribution of the ion beams can be measured by a ?roll off? curve (Fig. 2.7) 650 by reverse biasing the aperture in front of the current collector. As the aperture 651 voltage is increased, the current initially decreases as a power law, approximately 652 linearly, corresponding to an increasing collection of secondary electrons produced 653 by ions colliding on the metal surfaces. As the bias voltage exceeds the energy of the 654 slower ions, those ions are repelled and result in a further, sharper decrease in current 655 until only secondary electrons are being collected, producing a negative current at 656 high bias voltages [101]. The total current as a function of bias voltage can be 657 modelled as: ??? 658 ?(?) = ? - ? erf ( ? ?0 ? ) ? ??? (2.2) ?2?? 659 where I0 is the zero bias current, the second term is the integrated Gaussian of the 660 total ion beam current with Eb the mean ion energy, the third term is a 661 phenomenological power law accounting for the increase in secondary electron 662 current [104]. An example of the energy distribution curve is shown in Fig. 2.7. 32 663 664 Figure 2.7: Beam energy roll off curve for 28Si+. 665 As the bias voltage increases, the ion current first decreases linearly as the positively 666 charged are repelled. At the bias voltage, the ion current decreases more rapidly until 667 a negative current is reached. The anode voltage is set at 57V, the extracted mean ion 668 energy is about 30 eV. 669 670 The spatial distribution of the beam spot of our 28Si deposition is measured by 671 using the same aperture for collecting the ion current while scanning in two 672 dimensions. The aperture hole is about 3mm in diameter and it is attached to a 673 collector plate behind it. As a result, ion current passing through the aperture can be 674 collected and used to estimate the flux of the ion beam. Fig.2.8 is an example of the 675 collected 2D map of the ion current using Ar gas [87]. The typical maximum current 676 at the center is about 550 nA, where the adjacent contour line represents a 10 % drop 677 in the measured ion current respect to the center. The spatial distribution is 4 mm in 33 678 z-direction and 8 mm in y-direction. However, the size of the actual ion beam with 679 relatively large thickness (since the current density at the edges are too small) is 680 smaller, usually ? 4? mm2. A beam spot with similar size is used for 28Si deposition. 681 682 Figure 2.8: 2D mapping of the ion beam spot with Ar. 683 The detector aperture is moving in y and z direction during the scan. The center 684 maximum current is about 550 nA, with 10% drop to the adjacent contour lines. The 685 real beam spot size with relatively large thickness is estimated to be about 4? mm2. 686 (Taken from Ref. [87] with permission) 687 688 2.3.2 Electron Beam Evaporation of Natural Si 689 690 691 The natural Si deposition source is located at the bottom of the UHV deposition 692 chamber. It is an electron beam evaporator from Thermionics Lab, Inc. The schematic 693 of the design of this electron gun is shown in Fig. 2.9. Panel (a) is the CAD drawing 694 of the electron gun from Thermionics, where the source material is put in the middle 34 695 of a copper pocket. One advantage of this design compared to the previously used Si 696 source is that the electrons from the filament are generated at the side of the pocket 697 and re-focused onto the source material by a magnetic field. This prevents the source 698 material and evaporated flux to be exposed from the filament, both reducing the 699 source of contamination to the deposited samples and increasing the lifetime of the 700 filament. Cooling water lines are used to prevent the overheating of the electron gun, 701 with a typical water flow of 1.0 GPM at a source power < 3000W. Panel (b) shows 702 the assembly of the system on the deposition chamber, where the e-gun is at the 703 bottom of the housing. A liquid nitrogen cryoshroud is located on top of the e-gun 704 with a hole aligned to the source center. A float zone (FZ) refined, intrinsic silicon 705 source with volume of 1 cm3 is used in this work, the chemical purity of this Si is 706 99.999%. 707 A QCM is mounted on top of the deposition chamber with a linear translator so 708 that it can be moved to the same deposition location as the substrate. The deposition 709 rate varies depending on the power that we put into the e-gun. Fig. 2.10 shows the 710 deposition rate measured at the deposition location as a function of source power, 711 which is approximately 30 cm away from the Si source. Note that this rate is 712 measured with newly loaded source material, a gradual decrease in deposition rate is 713 expected as the Si source is consumed after hours of deposition. The typical pressure 714 during deposition is about 1 ? 10-9 Torr (1.35 ? 10-7 Pa). 35 715 716 Figure 2 9: The schematics of the Si e-gun. 717 (a) the electron beam evaporation source, with copper pocket for source material. The 718 filament is located at the side of this e-gun so that the evaporated flux will not be in 719 contact with the filament. This will increase both the lifetime of the filament and the 720 chemical purity of the deposited film. (b) a side view assembly of the electron gun 721 with cryoshroud. The e-gun system is located at the bottom of the deposition chamber 722 (see Fig. 2.1), where the manipulator can rotate the sample to allow normal incidence 723 of the evaporated flux. (Panel a is taken from Thermionics). 724 725 36 726 727 Figure 2.10: E-gun Si deposition rate vs power, measured by QCM. 728 The deposition rate is controlled by the power of the Si source. Note that this rate is 729 measured with newly loaded source material, a gradual decrease in deposition rate is 730 expected as the Si is consumed after hours of deposition. 731 732 2.3.3 Thermal Evaporation of Al 733 734 735 The Al delta layers are deposited using a thermal evaporation furnace similar to a 736 Knudson cell in UHV deposition chamber. It is a commercial Radak furnace from 737 Luxel. The Al source is located at the end of the deposition chamber near the STM, 738 which has a shutter controlled by a pneumatic valve. Ultra-high purity Al pellets 739 (99.999%) are used as source materials and are loaded in a pyrolytic boron nitride 740 (PBN) liner. The liner is then mounted inside an alumina crucible, with a 741 thermocouple at the bottom, as shown in Fig. 2.11. Since the liner and the crucible are 742 made of two different materials, the difference in thermal expansion coefficient may 37 743 cause the cracking of the crucible during cool down where Al will contract more 744 strongly than the PBN liner, putting it in a mixture of tensile and shear stress. To 745 prevent this from happening, we have to be extra cautious during the cool down 746 process, usually with less than 0.5 ?C/s around the melting point. We normally keep 747 the Al furnace at a temperature (? 770 ?C) above the melting point of the Al (660 ?C) 748 while maintaining a low rate of evaporation to ensure longer lifetime. 749 750 Figure 2.11: A schematic of the thermal evaporation source of Al. 751 The furnace is located at the bottom of the deposition chamber (as shown in Fig. 2.1) 752 near the STM. A shutter is installed with a pneumatic valve control. A transfer arm 753 (mag rod) is used to move samples to target location for Al deposition and to STM 754 chamber for characterization. (Modified from Ref. [76] with permission) 755 756 757 38 758 2.4 Scanning Tunneling Microscope (STM) 759 760 761 The samples grown from the ion beamline and deposition chamber can be 762 transferred to the STM chamber for in situ characterization. This prevents 763 contamination to the surface during transport out of vacuum and provide flexibility 764 for surface inspection during the deposition and annealing steps. STM is a non- 765 destructive tool for imaging surfaces at the atomic level. It can be used to distinguish 766 features smaller than 0.1 nm with a 0.01 nm depth resolution [105]. The STM is 767 based on quantum tunneling and piezoelectric effect, where the first allows us to 768 image the surface and the second allows us to control the tip position with angstrom- 769 level precision. As shown in Fig. 2.12, a typical setup includes a sharp metallic tip 770 that is brought within several angstroms to the sample surface using a piezoelectric 771 tube with electrodes. This 3D piezoelectric tube rasters the tip position in the lateral x 772 and y directions and the axial z direction is controlled by a feedback loop which 773 compares the tunneling current with the set value. When voltage is applied between 774 the tip and the sample, electrons can tunnel through and the current can be calculated 775 using the time-dependent perturbation theory. The tunneling current IT is 776 exponentially dependent to the distance between the tip and the sample d. It can be 777 expressed as [106]: ? 778 I? ? ? ??(? ? ???)??(?)(??(? ? ???) ? ??(?)) |?(? ? ?? 2 ? , ?)| ?? (2.3) ?? 779 where ?t and ?s are the density of state of the tip and sample, respectively, f (E) is the 780 Fermi-Dirac distribution for the electrons and |?|2 is the tunneling matrix element, 39 781 which is a function of the bias voltage VT, electron mass and wavefunctions of the 782 tunneling electron before and after tunneling. 783 784 Figure 2.12: A schematic drawing of a STM. 785 When the tip is brought within a few nm to the surface with a bias voltage applied 786 between the two, electrons can tunnel from the apex of the tip to the sample, or vice 787 versa. A constant current mode is used in this work. The tunneling current is 788 maintained at the setpoint by a 3D piezoelectric feedback loop, which provides the 789 topography of the sample surface. (Taken from Ref. [107]) 790 791 In this work, STM is frequently used to determine the surface quality of the 792 sample between each processing steps. For example, after substrate flashing, 793 isotopically enriched 28Si and natural abundance Si deposition, Al delta layer 794 deposition and thermal annealing. It is also used to estimate the 2D areal density of Al 795 being deposited on the substrate, as will be discussed in Chapter 6. For a Si substrate, 796 the typical scanning parameters are -2 V, 100 pA with a pixel resolution of 300 ? 300. 40 797 For deposited Si epitaxial thin films and Al delta layers, positive tip bias of +2 V, 100 798 pA are used. From time to time, the tip becomes ?dirty?, meaning that contaminant 799 molecules accumulate on the tip end, resulting in a degradation in image quality. 800 When this happens, the tip either needs to be replaced or re-conditioned using a tip 801 preparation tool. The tip preparation tool is located at the bottom of the deposition 802 and analysis chamber near the load lock (see Fig. 2.1). A thoriated tungsten filament 803 is used to emit electrons (emission current < 3 mA). The tip is moved to a short 804 distance (1 mm or less) right opposite the filament and is biased up to 1 kV. In this 805 high electric field, the emitted electrons are accelerated and bombard the apex of the 806 tip. This will clean the deposits from the tip and extend the lifetime of that tip for 807 STM imaging. 808 809 2.4 Hall Devices and Measurements 810 811 Hall bar devices have been made on the Al delta layer samples in order to 812 characterize the electrical properties (carrier type, density and mobility) of this 813 heterostructure at low temperature. Fig. 2.13 shows a microscope image of a Hall bar 814 and a Van der Pauw devices after fabrication. The device was fabricated on top of a 815 Si-Al-Si heterostructure with ? 50nm Si capping layer. This mesa-etched Hall bar 816 device was patterned using photolithography and RIE etching. The dimension of one 817 Hall bar is 50 ?m ? 1000 ?m. The bright yellow pads are the Al contact pads for wire 818 bonds and electrical conduction. 819 41 820 821 Figure 2.13: Microscope image of Hall bar and Vander Pauw devices. 822 Mesa-etched Hall bar devices after fabrication. The bright yellow pads are the Al 823 contact pads for electrical conduction. The rectangular device is the Van der Pauw 824 and the bottom device is the Hall bar. 825 826 The Hall effect measurement was originated from Edwin H. Hall, where a voltage 827 difference is produced across an electrical conductor with a transverse current and 828 perpendicular magnetic field (to the current) [108]. From the Hall measurement, the 829 carrier type, carrier density and mobility of the dopant can be obtained. The basic 830 principle of Hall measurement is based on the Lorentz force, which is a combination 831 of both electric and magnetic forces. A total force of -q(E + v ? B) will be 832 experienced by a charge when moving along the electric field direction perpendicular 833 to an applied magnetic field. A schematic of the Hall measurement setup is shown in 42 834 Fig. 2.14, assume a constant current is applied from top to the bottom of the Hall bar 835 in the presence of a perpendicular magnetic field. Due to the Lorentz force, electrons 836 will drift away from the current direction toward the left, resulting in an excess 837 negative charge on this side of the device. This will result in a potential difference 838 between the two sides of the device, called Hall voltage VH (or Vxy as marked in 839 Fig.2.14). The magnitude of this voltage is equal to IB/qnd, where q is the elementary 840 charge, n is the bulk density and d is the thickness of the sample. It can be converted 841 to a 2D sheet density ns = nd. The relationship between the Hall voltage and the 842 carrier density and mobility is described as: 843 ?? = ????|??| (2.4) 844 ? = |??|?????? = 1??????? (2.5) 845 ,where Rsq is the sheet resistance. 846 847 848 43 849 850 Figure 2.14: Schematic of Hall effect measurement. 851 Hall effect caused by the Lorentz force applied on moving charges. A voltage 852 difference is produced across an electrical conductor/semiconductor with a transverse 853 current and perpendicular magnetic field (to the current). 854 44 855 Chapter 3: Ultra-high Vacuum Ion Source for 28Si 856 Deposition 857 858 In this chapter, an ultra-high vacuum (UHV) compatible Penning ion source is 859 presented as an upgrade to our prior ion source. The main goal of this new design is 860 to improve chemical purity of our 28Si thin films while preserving the same 861 enrichment capability (< 1 ppm 29Si). Enriched 28Si is a critical material for quantum 862 information due to the absence of nuclear spins. In some cases, the material must be 863 grown by low temperature molecular beam epitaxy (MBE), followed by scanning 864 tunneling microscopy (STM) hydrogen lithography to produce qubit devices. 865 Traditional high-purity physical vapor methods typically deliver a very small fraction 866 of source material onto the target substrate, making the cost for use with highly 867 enriched source materials very high. Thus, directed beam sources provide an efficient 868 alternative. This UHV Penning source uses all metal or ceramic parts and a 869 removable electromagnet to allow bake-out. The source gas is commercial (natural 870 isotope abundance) silane gas (SiH4), an inexpensive source material. High 871 enrichment levels up to 99.99987 % (corresponding to 8.32 ? 10-7 mol/mol 29Si) and 872 a high chemical purity of 99.965 % are obtained without post-processing. I will 873 discuss the design concept and the capabilities of this new UHV ion source, including 874 its discharge properties with SiH4, the ion mass spectrum, STM surface topography of 875 a deposited film, and the chemical purity improvements measured by secondary ion 876 mass spectroscopy (SIMS). Further upgrades including the ion beam sweeper and 877 UHV gas line system with purifier will also be presented. 45 878 879 3.1 Introduction 880 881 882 Isotopically enriched silicon-based qubits that utilize electron and/or nuclear spins 883 in quantum dots and/or donors are competitive candidates for quantum computation 884 (or memory) due to very long coherence times [109], [29] and high gate fidelities 885 [110],[111]. Compared to natural abundance silicon, the coherence times increase orders 886 of magnitude when using isotopically enriched 28Si as host material. Natural silicon 887 contains ? 4.7 % 29Si (nuclear I = ?), which causes random fluctuations and 888 inhomogeneities in the background magnetic field and dramatically reduces the qubit 889 coherence time. By reducing the 29Si nuclear spin density to < 0.005 %, 31P nuclear 890 spin coherence times (T ) approaching an hour [30]2n and electron spin coherence times 891 (T2e) exceeding a second [31] have been reported in 28Si. However, as was introduced 892 in Chapter 1, the supply of isotopically enriched 28Si is scarce and limited. The 893 isotopically enriched 28Si materials within this community are either not extremely 894 enriched (? 99.9 % 28Si), are of very limited quantity, or are not being replenished. 895 We have previously reported on our ability to make very highly enriched 28Si, 896 where we used a Penning ion source to ionize natural abundance SiH4 gas, mass 897 filtered the ions, decelerated them to hyperthermal energies, and thus deposited 898 isotopically enriched 28Si in situ [103],[101],[112]. Using this method, enrichment of 28Si > 899 99.99983 % (< 10-6 mol/mol 29Si) was achieved. This is the highest 28Si enrichment 900 known to be reported so far. However, the chemical purity of the silicon films using 901 this ion source was relatively poor (98.47 %). SIMS was used to determine the 902 dominant chemical impurities of carbon (C), oxygen (O) and nitrogen (N). Our prior 46 903 system analysis assumed only background impurities in the growth chamber could be 904 incorporated, however, mass 28 amu impurities mixed into the silane source gas in 905 the inferior vacuum region of the ion source were also transported ballistically (not 906 just diffusively) along with the silicon ion beam, due to their similar molecular mass. 907 For example, N +, CO+ and other mass 28 amu ionized compounds such as C H +2 2 4 and 908 CNH + 2 can pass through our mass selector to the sample since our mass resolution 909 does not discriminate at that level (< 0.03 amu). 910 Therefore, here we target the vacuum condition of the ion source chamber for 911 improving the chemical purity of our films. Our prior Penning source was not ultra- 912 high vacuum (UHV) compatible. It used rubber O-rings for vacuum seal and plastics 913 for high voltage isolation with a base pressure of ? 2.7 ? 10-6 Pa (? 2 ? 10-8 Torr). 914 Consequently, the 28Si films grown using that ion source had C concentrations in the 915 range of 1020 cm-3, and O and N concentrations in the range of 1019 cm-3, respectively. 916 This impurity level is a problem for device fabrication (e.g., high quality oxide 917 growth) and can potentially act as a source of decoherence for qubits in silicon [113, 918 114]. Fig. 3.1 (a) shows an ellipsometry measurement on a 4mm ? 10mm sample after 919 thermal oxide growth on 28Si thin film using the prior ion source. The 28Si beam spot 920 (mountain shape) is marked with red arrow. The color scale on the right represents 921 the thickness of the oxide. As we can see, oxide growth on top of 28Si is limited, with 922 an average oxide thickness of < 20nm, compared to > 80nm on the area without 28Si. 923 Fig. 3.1 (b) is a summary plot of the oxide thickness vs oxidation time on a natural Si 924 substrate and deposited 28Si. The oxide grows smoothly on natural Si vs time but is 925 largely limited on 28Si sample. Further analysis has been done with SEM and 47 926 927 Figure 3.1: Oxide growth with 28Si thin film deposited by the prior ion source. 928 Panel (a) shows an ellipsometry measurement of the oxide thickness on a 4 mm ? 10 929 mm sample with 28Si deposited. The middle area marked with red arrow is the 28Si 930 spot. Oxide growth is largely limited at that area. Panel (b) is a summary of the oxide 931 thickness vs oxidation time for two samples: natural Si substrate and 28Si thin film. 932 Oxide was grown successfully on the natural Si but not 28Si. (Taken from Dr. A. N. 933 Ramanayaka with permission) 934 935 energy-dispersive X-ray spectroscopy (EDS), but none of them showed evidence of a 936 surface impurity layer that is present before going into furnace. Nonetheless, it is 48 937 most likely that the chemical impurity concentration presents in the 28Si is too high, 938 and that suppresses the oxidation process. Therefore, a new UHV ion source is 939 needed to eliminate residual gases in the ion source and the chemical impurities in the 940 28Si film. 941 As described above, the system with the newly designed UHV ion source must 942 produce highly enriched 28Si (< 10-6 mol/mol 29Si) and improved chemical purity (< 943 1018 cm-3 impurities) at the same time. The specific goals are: 1) to reduce ionization 944 source base pressure to < 3 ? 10-8 Pa (? 2 ? 10-10 Torr) to increase the film chemical 945 purity; 2) to identify the source?s optimum operating conditions for epitaxial thin film 946 deposition; and 3) to enrich epitaxial 28Si thin films to < 10-6 mol/mol 29Si. In this 947 chapter, we present the details of our new ion source able to achieve these goals, 948 present the data and discuss these performance metrics. 949 950 3.2 Experimental Setup 951 952 953 The design of the UHV ion source is described below in Fig. 3.2. In addition to 954 achieving ultra-high vacuum, this UHV ion source must also be compatible with the 955 existing ion transport, mass filter and deposition system. The details of the associated 956 system are introduced in Chapter 2 and can be found elsewhere [87, 101], however, a 957 brief description is presented here to assist understanding. To recap, the enriched 958 silicon system consists of five subsystems: the gas line, the ionization source, ion 959 transport, the deposition chamber and a scanning tunneling microscope (STM) 960 chamber. The ion source is a Penning-type ion source [115], which has a cylindrical 961 anode and cathodes at each end that creates an axial confining potential well. The 49 962 ion?s radial confinement is provided by an axial magnetic field from an 963 electromagnet, which also helps focus ions for extraction. During the discharge, a 964 plasma is formed by accelerating electrons from the cathodes that ionize the gas 965 molecules. SiH4 is used in this case, although Ar and Ne have also been used for 966 diagnostics. Ions are extracted using an extraction cusp adjacent to one end of the 967 source and transmitted into a system of electrostatic lenses. Since we are using 968 hyperthermal energy ions (< 50 eV kinetic energy) that are susceptible to Coulomb 969 repulsion (space charge) effects [100], the transport system is typically operated at -4 970 kV (i.e., ions are accelerated to > 4 keV while transiting the lenses and mass filter) 971 and decelerated before deposition. As a result, high voltage isolation between the ion 972 source and the rest of the systems (transport and gas inlet) is required. In the prior ion 973 source, a plastic transition plate between the ion source and transport chamber was 974 used as electric isolation and was one of the major causes of poor vacuum. In the new 975 design, we use an 8? CF reducer nipple with ceramic neck to mate the ion source to 976 the transport system and use ceramic standoffs for the gas inlet, as shown in Fig. 3.2. 977 Apart from the compatibility with the existing system, several other factors 978 constrain the design of this UHV ion source. First, all components need to be UHV (< 979 1.33 ? 10-7 Pa or 10-9 Torr) compatible and bakeable (> 150 ?C), including the gas 980 injection. Therefore, all tubes from the SiH4 gas bottle to the ion source feedthrough 981 use vacuum coupling radiation (VCR) fittings to prevent air (C, O, N rich) from 982 leaking into the gas line. Second, all plastics components such as 983 polytetrafluoroethylene (PTFE) and nylon are replaced with ceramics. Plastics can 984 contribute fluorine and chlorine compounds, as well as lighter gases, and present 50 985 problems when the ion source becomes hot during baking. Third, the prior ion 986 source?s electromagnet was buried inside the housing without efficient cooling. 987 Heating of the electromagnet caused outgassing and source instability, the wire 988 insulation commonly failed, and baking was not possible. In the new design, the 989 magnet is a separate component outside the vacuum system, water-cooled and 990 removable for baking. The central field at 50 A, 12.5 V is 0.11 T. Furthermore, to 991 ease replacement of the anode and cathodes, the core of the ion source can be easily 992 taken in and out without disturbing the magnet or other elements. Finally, the new ion 993 source is designed to be compact and easy to maintain, using mostly simple or 994 commercial parts. 995 A schematic of the UHV Penning ion source is shown in Fig. 3.2 and discussed in 996 detail below. Our design goal was to keep the ion source dimensions as compact as 997 possible and fully supported by the 70 mm CF base flange, while also having > 5 kV 998 electrical isolation between the anode and the cathodes. The ion source is shown in 999 Fig. 3.2 with dimensions and geometry correct according to the scale bar. The ion 1000 source?s plasma region has three main consumable components shown as dark red: 1001 the anode, cathode and anti-cathode inserts. The distance between the cathodes and 1002 the anode is based on Ref. [96], where the performance of the gas discharge has been 1003 optimized. The anode, cathode and anti-cathode supports are 304 stainless steel (SS). 1004 The cathode inserts are constantly eroded by ions during plasma discharge and this 1005 design allows the anode and cathode inserts to be replaced easily, minimizing the 1006 maintenance steps and time. The lifetime of the cathodes depends on material type, 1007 gas source and energy of the impact, but typical insert lifetimes are about 20 - 30 h. 51 1008 1009 1010 Figure 3.2: Simplified, cross sectional schematic diagram of the UHV ion source. 1011 Sliced along the axis ? most parts are cylindrically symmetric. Insulating parts are 1012 shown in off-white. Consumable parts are in dark red. The vacuum housing is 1013 unhatched with the stainless-steel components shown in gray. The electromagnet 1014 solenoid is shown shaded brown and cross-hatched above and below the ion source 1015 insert. Source gas enters from the right, and ions are extracted to the left, where a 1016 system of electrostatic optics transports them downstream (not shown). 1017 1018 For the purpose of hyperthermal (5 eV to 100 eV) 28Si epitaxial thin film growth, 1019 the plasma potential and the final energy of the ions are approximately set by the 1020 anode voltage [101], which is typically at around 40 - 50 V. The hyperthermal energy 1021 range allows atoms to land relatively softly onto the substrate during deposition, 1022 improving the 28Si island density and crystalline quality without introducing large 1023 number of point defects [101]. 52 1024 The high voltage feedthroughs and the gas inlet are also shown on the base flange 1025 at right. The anode and cathode supports are connected by small copper wires that 1026 pass through thin insulating tubes to the feedthroughs and are fixed with vented 1027 screws (to prevent virtual leaks). Ceramic rings and top hat washers are inserted to 1028 provide electrical isolation between cathodes and anode, which typically have a 3 kV 1029 potential difference, and to maintain good geometric alignment. The main body 1030 (vacuum wall) is designed to be at the cathode potential (copper standoffs) or at a 1031 different potential, e.g., earth ground (ceramic standoffs?shown). For example, 1032 using ceramic standoffs allows the ion source body to be grounded so that a mass 1033 flow controller can be installed to provide precise control of the gas flow. Under 1034 some circumstances, the plasma power can substantially heat the central components 1035 leading to high voltage breakdown, which can be better mitigated with the copper 1036 standoffs that conduct heat away efficiently. 1037 1038 3.3 Ion Source Discharge Properties 1039 1040 1041 The discharge properties of this UHV ion source using SiH4 gas are studied to 1042 determine the optimum operation conditions. The arc (plasma) current and the total 1043 ion beam current extracted from the ion source are affected by the ion density and the 1044 electron temperature of the discharge, and those quantities are influenced by the arc 1045 voltage, flow rate and source magnetic field [96]. In Fig. 3.3, the total 28Si+ ion current 1046 and arc current are shown as functions of these three parameters. The measurements 1047 were done by first maximizing the ion current while changing source magnetic field 1048 and flow rate at -2.7 kV arc voltage. These values of magnetic field and flow rate are 53 1049 then marked as optimum values Hopt and Fopt in Fig. 3.3. Then, each of the three 1050 parameters is uniaxially varied while the other two are kept constant at their optimum 1051 values. 1052 The ion and arc current dependence on arc voltage is shown in Fig. 3.3 (a). The 1053 discharge begins at around -1.7 kV and the ion current increases monotonically with 1054 the arc voltage up to a first maximum at -2.7 kV, and then shows weak structure 1055 suggestive of higher order plasma modes at -3.4 kV and -3.8 kV. The arc current 1056 shows a similar trend but reaches a maximum at -2.4 kV and has weaker mode 1057 structure. In Fig. 3.3 (b), the ion current versus source magnetic field is shown while 1058 keeping the arc voltage at -2.7 kV and the gas flow at -0.02 sccm. The plasma ignites 1059 at about 0.06 T and the total ion current increases rapidly reaching a maximum at 1060 0.067 T. Here the mode structure is more pronounced with two other ion current 1061 maxima appearing at 0.077 T and 0.086 T. The arc current again shows a similar 1062 trend to the ion current, where three somewhat weaker, corresponding maxima are 1063 observed. The variation of the ion current vs. the flow rate while keeping the arc 1064 voltage at -2.7 kV and the magnetic field at 0.077 T (the ion current at 0.067 T is 1065 slighter higher, but less stable during the beam operation) is shown in Fig. 3.3 (c). 1066 Unlike in arc voltage and source magnetic field, the ion current vs. flow rate shows a 1067 large peak at 0.02 sccm and a softer, broader peak at 0.11 sccm. The arc currents 1068 increase monotonically after ignition over the entire range studied. The optimum 1069 operating condition for 28Si deposition using SiH4 gas is therefore at -2.7 kV arc 1070 voltage, 0.077 T source magnetic field and 0.02 sccm (1.87 ? 10-4 Pa or 1.4 ? 10-6 1071 Torr) flow rate. 54 1072 1073 1074 1075 1076 Figure 3.3: 28Si ion current (black) and discharge current (blue) characteristics. 55 1077 (a) as a function of arc voltage; (b) as a function of source magnetic field, and (c) as a 1078 function of SiH4 flow rate. The measurement uncertainties are ? 1 nA for ion current 1079 and ? 0.2 mA for arc current, respectively. Optimum conditions at: -2.7 kV arc 1080 voltage, 0.077 T source magnetic field and 0.02 sccm (1.87 ? 10-4 Pa or 1.4 ? 10-6 1081 Torr) flow rate. 1082 1083 These values closely match those of the previous ion source on which this source was 1084 based [96]. 1085 1086 3.4 Vacuum and Chemical Purity Improvements 1087 1088 1089 Having discussed the plasma performance of the ion source, we now move on to 1090 evaluating the improvements in gas cleanliness and efficacy for silicon enrichment 1091 that motivate this effort. To enrich the silicon effectively, once the ion source is 1092 coupled to the beamline [101], the transmitted silicon ions must have trajectories well 1093 separated from each other when sweeping the magnetic field of the ion mass 1094 separator in the beamline. This allows one mass to be selected by the separator 1095 aperture while rejecting other masses. The mass spectra of the silicon ion beam taken 1096 with the prior and UHV ions sources are compared and shown in Fig. 3.4 (a). The ion 1097 mass spectrum is collected using a second, custom aperture plate on the sample stage 1098 to monitor the ion current while scanning the magnetic field of the mass analyzer. Six 1099 singly charged SiH4 related peaks are shown. The first peak at mass 28 amu 1100 corresponds to 28Si+ ions, while the rest of the peaks result from a combination of 1101 isotopes and hydrides due to the incomplete cracking of SiH4 gas molecules. In an ion 1102 beam deposition, there are a lot of factors that can affect the enrichment of the 1103 deposited film, such as the substrate temperature, background silane partial pressures, 56 1104 1105 1106 Figure 3.4: Comparison of the two mass spectra and the enrichment SIMS. 1107 (a) The ion beam mass spectra of the prior (red dashed) and new (solid black) UHV 1108 ion source are shown for comparison. The ion current after passing through the mass 1109 selecting magnet shows six peaks, which consist mostly of 28Si+ ions at 28 amu and 1110 other isotopes combined with hydrides at higher masses. The peak shapes and isotope 1111 separation between 28 amu and 29 amu indicate similar enrichment capability. (b) A 1112 SIMS depth profile of 28Si thin film shows the isotope fractions of 28Si, 29Si and 30Si 1113 using the UHV ion source, confirming excellent enrichment with an average of 1114 99.99987(3) %. 1115 57 1116 etc. Among them, one of the most important factors is the mass separation between 1117 mass 28 amu and 29 amu peaks (See ref. [103] for detailed analysis of mass 1118 selectivity). An overlap of the two peaks means that part of 29Si+ also passes through 1119 the aperture and will be introduced into the deposited film. The UHV ion source?s 1120 similar peak shape and separation compared to the prior source indicate good mass 1121 selectivity (> 5 ? from center to center) for enrichment, and similar current suggests a 1122 similar growth efficiency with this ion source. Note that there is some degradation in 1123 separation at higher mass peaks (> 30 u), but for 28Si thin film, the primary peaks to 1124 be considered are 28 amu and 29 amu. Typically, we use a deposition rate of 1 1125 nm/min and the ion source is stable throughout the deposition (usually 6 h to 8 h). 1126 Higher growth rate might be achieved by using different plasma modes (e.g. higher 1127 flow rate), but generally results in shorter cathode lifetime and larger surface 1128 roughness of the deposited film (see Ref. [87] for details in higher pressure plasma 1129 mode). 1130 The enrichment of a typical 28Si film is shown in Fig. 3.4 (b). SIMS was used to 1131 profile the isotopic fraction of 28Si, 29Si and 30Si of the deposited 28Si film grown 1132 using this UHV ion source. The SIMS measurement was taken near the center part of 1133 the enriched silicon film, which is usually the thickest. The residual isotope fraction 1134 of 29Si is shown as squares with an average value of 8.32(80) ? 10-7 mol/mol in the 1135 film and 30Si is shown as triangles with an average value of 4.91(65) ? 10-7 mol/mol. 1136 The 28Si total enrichment for this sample is 99.99987(3) %. The enrichment level can 1137 vary some from run to run, but comparing several samples deposited using the prior 58 1138 1139 1140 Figure 3.5: Comparison of the RGA and chemical SIMS. 1141 (a) Residual gas analysis (RGA) demonstrating the comparison in background gas 1142 density between the two ion sources. The red curve in (a) is the prior ion source with 1143 base pressure 2.7 ? 10-6 Pa (2 ? 10-8 Torr) and the black curve is the UHV ion source 1144 with base pressure 2.7 ? 10-8 Pa (2 ? 10-10 Torr). Major peaks are labeled with the 1145 dominant gases. (b) A SIMS depth profile of the residual chemical impurities in a 28Si 1146 thin film deposited using the UHV ion source. The estimated chemical purity of this 1147 sample is 99.965(2) %. 1148 59 1149 ion source with samples from this ion source, we conclude that the 28Si enrichment is 1150 maintained (<1 ppm 29Si) with this UHV ion source. 1151 Since the growth chamber pressure is typically maintained at 6.7 ? 10-9 Pa (5 ? 1152 10-11 Torr), the background gas composition in the ion source was estimated to be the 1153 leading contributor to film contamination in the prior source and the primary 1154 motivation for building a UHV ion source. The baseline pressure as measured with an 1155 1156 TABLE I. Partial pressure peaks of the key gas contaminants relevant to silicon thin 1157 film purity as measured by residual gas analysis (RGA). The estimated uncertainty is 1158 in the range of 10 % to 20 %. Pressure in prior ion Pressure in UHV ion Impurity Mass (u) source (Pa) source (Pa) H -72O 18 > 1.4 ? 10 6.1 ? 10 -10 N -82 28 7.3 ? 10 1.1 ? 10 -9 O2 32 6.3 ? 10-8 2.8 ? 10 -11 CO2 44 6.5 ? 10-8 3.5 ? 10 -10 1159 1160 ion gauge (uncertainty of 10 % to 20 %) has been improved by a factor of a hundred 1161 in this UHV ion source compared to the prior ion source, now reaching 2.7 ? 10-8 Pa 1162 (2 ? 10-10 Torr). The partial pressures of various gas components as measured by a 1163 residual gas analysis (RGA) in the prior and UHV ion sources are shown in Fig. 3.5 1164 (a) and Table I. These show the qualitative improvement in vacuum conditions and 1165 chemical compositions and confirm that the impurities contributed from the ion 1166 source vacuum have been reduced by a factor of 100. 1167 A SIMS depth profile showing the chemical impurity concentrations for C, N, O, 1168 F and Cl in a 28Si thin film deposited using this UHV ion source is shown in Fig. 3.5 1169 (b). The average concentration level for carbon is 9.5(8) ? 1018 cm-3; nitrogen is 60 1170 5.5(5) ? 1018 cm-3 and oxygen is 2.1(2) ? 1018 cm-3 between 30 nm and 235 nm. As a 1171 comparison, the total chemical purity of the 28Si film has been improved from ? 98.5 1172 % (first chemical SIMS using the prior ion source) to 99.965(2) %. From previous 1173 SIMS measurement (not shown), we found that the 12C concentration in the film is 1174 roughly 400 times higher than 13C. This means that the 12C is also enriched (> 98.9 1175 %) in the ion beam process and the 13C concentration is approximately 3 ? 1016 cm-3. 1176 Similarly, the 15N concentration is < 2 ? 1016 cm-3. Therefore, at this contamination 1177 level, the largest factor for the nuclear spin bath is still expected to be 29Si (? 0.83 1178 ppm), plus some contributions from 13C (< 0.6 ppm) and 15N (< 0.4 ppm) as well. 1179 Further improvement in chemical purity is needed to reduce the effects from 13C and 1180 15N. 61 1181 1182 Figure 3.6: Chemical purities (C, N and O) of the 28Si thin film vs ion source base 1183 pressure. 1184 The higher-pressure data are from the prior ion source. Panel (a) shows the total 1185 chemical impurity increases exponentially vs base pressure. The improvements in 1186 purity seem to become negligible at pressure < 10-9 Torr. Panel (b) shows the 1187 impurity concentrations of the main contributors: C, N and O. N showed the largest 1188 improvement (260?) with ion source vacuum while C (5?) and O (10?) showed less 1189 improvements. 62 1190 The correlation between the chemical purities vs ion source base pressure is 1191 studied in Fig. 3.6. Panel (a) shows a summary of the total chemical purity in our 28Si 1192 film vs the source base pressure. The data is taken from both the prior and the new 1193 UHV ion source. An exponential decay in total impurity level is observed in terms of 1194 base pressure. Panel (b) shows the impurity concentrations of the main contributors: 1195 C, N and O. Despite the substantial improvement in total chemical purity (43 ?) 1196 compared to the prior ion source, we found the improvement was not fully correlated 1197 to the vacuum improvement (100 ?). This indicates that at this concentration level, 1198 the vacuum condition of the ion source is not the only limiting factor that affects the 1199 chemical purity of the 28Si film. For example, N showed the largest improvement (? 1200 260 times) with the base pressure, varying from 7 ? 1020 cm-3 to 2.7 ? 1018 cm-3. C 1201 and O showed smaller improvements, varying from 4.5 ? 1019 cm-3 to 9.5 ? 1018 cm-3 1202 (? 5 times) and 2 ? 1019 cm-3 to 2.1 ? 1018 cm-3 (? 10 times), respectively. It is likely 1203 that for N, the ion source base pressure is the dominating factor as it showed the 1204 strongest correlation. Note that in Fig. 3.6 (b), the chemical impurities of C, N and O 1205 increased a little at the lowest base pressure. We believe that this is due to the 1206 degradation and contamination presented in the silane gas system over time, again 1207 indicating that the ion source base pressure is not the only dominating factor for 1208 chemical purity. 1209 We also found that the impurity concentrations are not correlated to the growth 1210 rate and background partial pressures, where the background impurities should be 1211 much less than 1018 cm-3, indicating the origin of the impurities is from the ion source 1212 chamber instead of the growth chamber. Therefore, the cleanliness of the silane gas 63 1213 system, impurity ions sputtering from the cathodes and anode materials and chemical 1214 compounds formed in the ion source plasma may also be contributing factors. Further 1215 study is needed to fully explore the origin of the contaminations in the film and to 1216 seek additional purity improvements. Possible solutions may include post-annealing 1217 at 950 ?C in UHV (preliminary work shows that the N concentration can be reduced 1218 to low 1017 cm-3 after annealing), installation of silane gas purifier to purify the gas 1219 line, etc. 1220 1221 3.5 Epitaxial Quality of 28Si Thin Film 1222 1223 1224 Molecular beam epitaxy (MBE) growth of Si has been extensively studied and 1225 characterized in the past decades [116]. In 1990, Eaglesham and his coworkers 1226 reported the existence of a critical thickness hepi for epitaxy at a given temperature 1227 [117], where the epitaxial film breaks down and becomes amorphous. The critical 1228 thickness increases exponentially as the deposition temperature increases (also 1229 dependent on deposition rate). For example, for a deposition rate of 0.4 nm/min, the 1230 critical thickness is 25 nm at 200 ?C on Si (100) surface and increases to 120 nm at 1231 300 ?C. In general, hepi is limited to a deposition rate of a few nm/min at low 1232 temperatures. When T > 500 ?C, solid phase epitaxy (SPE) dominates because the 1233 recrystallization process becomes faster than the deposition rate, resulting in a very 1234 large value of hepi [87]. Further studies have pointed out that for low temperature 1235 MBE of Si, a highly defective region is formed in the epitaxial film before the 1236 development of amorphous phase [118-122]. Most of the defects observed are 1237 stacking faults and microtwins [119]. Several hypotheses have been raised to explain 64 1238 the transition from epitaxy to amorphous. One possible explanation is the 1239 incorporation of H during deposition, where H could segregate and accumulate onto 1240 the surface and disturb the surface bonding of the lattice [123]. Another possibility is 1241 the accumulation of defects during growth process until epitaxial breakdown of the 1242 film [124]. However, very large defect density (1014 cm-2) is required to support this 1243 assumption. Eaglesham also raised the hypothesis that the roughening of the growth 1244 surface itself can cause breakdown of the epitaxial layer at low temperature [125]. 1245 In this work, we use ion beam deposition to grow epitaxial 28Si. Ion beam 1246 deposition has been demonstrated to have similar results to MBE in terms of hepi and 1247 defect density. However, it has also been shown that the use of hyperthermal energy 1248 ions helps to extend hepi to be thicker values at given temperature and deposition rate 1249 [119, 126-130]. Low energies in the range of 10 ? 50 eV also provide other benefits 1250 to the deposited surface. For example, energy can be transferred to the film through 1251 neutralization of the ions (approximately the ionization potential of 8.15 eV) and this 1252 energy can enhance the mobility of the nearby atoms [131]. In addition, hyperthermal 1253 energy ions help to suppress the formation of 3D islands and step pinning from 1254 impurities [127, 128] and they can also create vacancies that facilitate adatom 65 1255 1256 Figure 3.7: STM surface topography of two 28Si films using both ion sources. 1257 (a) through (c) are from the new UHV ion source. The images are taken using a bias 1258 voltage of +2 V and tunneling current of 100 pA. Panel (a) is a 50 nm ? 50 nm scan 1259 of the 28Si surface with 2 ? 1 reconstructed Si dimer rows, steps and terraces, 1260 indicating the epitaxial alignment of the 28Si atoms with the Si (100) substrate. Panel 1261 (b) and (c) shows a larger area scan of the sample, where relatively smooth, epitaxial 1262 3D islands are observed. This film is deposited at 450 ?C with a thickness of 191 nm 1263 measured by SIMS depth profiling. Panel (d) shows another sample deposited using 1264 prior ion source. The film is deposited at 400 ?C with a thickness of 120 nm also 1265 measured by SIMS. Similar structures and surface roughness are seen in this image, 1266 indicating a similar epitaxial quality of the deposited film. (The STM images shown 1267 in this figure is taken by Dr. Hyun-soo Kim). 1268 66 1269 incorporation [132]. As a result, the energy of the deposited 28Si we use is usually in 1270 the range of 30 - 50 eV. The growth temperature is chosen to be ? 450 ?C to ensure a 1271 high enough hepi but the lowest contribution of 29Si from the background SiH4 gas 1272 since higher T results in thermally activated incorporation of the silane molecules 1273 [133]. 1274 STM was used to characterize the surface topography of the deposited 28Si thin 1275 films. Fig. 3.7 shows the 3D island growth of the epitaxial surface of the deposited 1276 28Si films using both prior and our improved UHV ion sources. Images were taken 1277 with a tip bias of +2 V and tunneling current of about 100 pA. Panel (a) through (c) 1278 are from the same sample deposited at 450 ?C with thickness of about 191 nm using 1279 the UHV ion source. The film thickness was determined by the SIMS depth profiling. 1280 Panel (a) is a small area scan of the sample showing multiple islands with clear 2 ? 1 1281 reconstructed Si dimer rows, steps and terraces, indicating the epitaxial alignment of 1282 the 28Si atoms with the Si (100) substrate. The relatively smooth epitaxial surface has 1283 a root mean squared (RMS) roughness value of 0.32 nm in the 50 nm ? 50 nm image 1284 range. Very few defects are observed in this image. Panel (b) and (c) are the larger 1285 scale images, where multiple 3D islands are visible. As a comparison, panel (d) 1286 shows a 28Si film deposited under similar condition by the prior ion source where the 1287 sample is deposited at 400 ?C with a thickness of 120 nm. Similar structures and 1288 surface roughness are observed, indicating similar quality of the deposited film. In 1289 general, the deposited 28Si thin films are epitaxial with relatively good surface 1290 qualities. It also means that the crystal quality of the deposited film is relatively 1291 insensitive to its chemical purity, at least at this level. 67 1292 1293 3.6 Further Improvements 1294 1295 3.6.1 Lens Upgrade and Ion Beam Sweeper 1296 1297 1298 To further improve the cleanliness and deposition capabilities of this ion source, 1299 we have upgraded the deceleration lens system and designed a new ion beam 1300 sweeper. In the previous set up of the transport and deceleration lens system, plastics 1301 including Teflon were used for high voltage isolations. Those polymers contribute to 1302 outgassing and may act as sources of contamination to the vacuum chamber, 1303 especially when closer to the higher temperature regions. To avoid this, all plastics 1304 and Teflon parts were removed and the new design for mechanical support and high 1305 voltage isolation is demonstrated in Fig. 3.8. Plastic rods and screws were used to 1306 connect and separate each lens elements from A2 to B2 and X. They are now replaced 1307 by a mounting tray made of high purity stainless-steel with metal screws and ceramic 1308 washers. Ceramic saddles are also used between the mounting tray and the lens 1309 elements for high voltage isolation. Two insulating rods with cylindrical stainless- 1310 steel frames are used to support the weight of the lens while providing alignment for 1311 the lens elements. 1312 68 1313 1314 Figure 3.8: A schematic of the upgraded ion beam lens system and new sweeper. 1315 All plastics and Teflon parts are removed from the lens system. Alumina insulating 1316 rods, ceramic washers and mounting saddles are used to provide high voltage 1317 isolation and mechanical support of the lens elements. The sweeper is located at the 1318 end of the deceleration lens X right before the deposition sample stage. The sweeper 1319 is made of copper and is connected to lens X by an adapter. Sweeper fins are fixed on 1320 the adapter using metal screws and ceramic washers for isolation. Electrical 1321 feedthroughs are connected to the fin with kapton coated copper wires. To deflect the 1322 ion beam (? 40 eV energy) for 2 mm in one direction, a voltage of ? 10 V is used on 1323 the sweeper fin. 1324 1325 An ion beam sweeper was designed and installed at the end of the deceleration 1326 lenses. The reason for the ion beam sweeper is to smooth out the topography of the 1327 28Si film. As mentioned in Chapter 2, the deposited 28Si film is a few mm in size and 1328 has a mountain shape with the thickest area in the middle of the beam spot. This can 1329 cause problems for further device fabrication due to the uneven thickness of the film. 1330 By using parallel plate electrodes, the ion beam can be deflected and controlled in 1331 two dimensions using a function generator. The schematic of this sweeper is also 1332 shown in Fig. 3.8. An adapter is mounted at the end of the deceleration lens element 1333 X. Four sweeper fins are attached but electrically isolated from the adapter by metal 1334 screws and ceramic washers. Electrical feedthroughs are connected to those fins with 69 1335 kapton coated copper wires. To produce a relatively smooth film on our 4 mm ? 10 1336 mm sample, we would need to sweep the ion beam periodically with a spatial range 1337 of ? 2 mm in the horizontal direction while keeping the other direction constant. The 1338 final beam spot will be in the dimension of about 3 mm ? 6 mm (this is largely 1339 because 3 - 4 mm in the horizontal direction of the sample is covered by the clamps 1340 of the sample holder). To deflect an ion beam with energy ? 40 eV, a voltage 1341 difference of ? 10 V and ? 8 V is needed between the left/right and top/bottom 1342 electrodes, respectively. Only preliminary tests have been done using this sweeper; 1343 further experiments are needed to better tune the sweeper with the deceleration lenses 1344 and SIMS would be used to measure the thickness of the deposited film at various 1345 locations on the sample. 1346 1347 3.6.2 UHV Gas Line with Purifier 1348 1349 1350 Another possible improvement for chemical purity is the upgrade of the silane gas 1351 line system. In the past, VCR tubings and UHV leak valves were used for gas 1352 manipulation. However, silane gas is highly reactive and can slowly react with the 1353 interior of the metal tubing overtime. To address this problem, a UHV gas line with a 1354 silane purifier was designed and a routine replacement of the metal parts was needed. 1355 The silane purifier is a micro gas purification and filtration system purchased from 1356 Matheson. It is made of some porous materials that can absorb H2O, CO2 and O2 1357 molecules to < 0.1 parts per billion (ppb) and CO to < 1 ppb. It can also adsorb other 1358 contaminants such as NOx, SOx and H2S from the gas line. Future effort is needed to 1359 install and deposit 28Si using this purifier. SIMS will be performed to measure the 70 1360 improvements in chemical purity and a reasonable guess for the improved level of C, 1361 N and O will be in the ? 1017 ? 1018 cm-3 level. 1362 1363 1364 3.7 Conclusion 1365 1366 1367 In this chapter, an upgraded version of the UHV hyperthermal ion beam system 1368 has been introduced. We demonstrated the design, experimental implementation and 1369 performance of this UHV ion source system. The discharge properties based on arc 1370 voltage, source magnetic field and flow rate have been studied and optimized for 28Si. 1371 The performance of the UHV ion source for enriched silicon deposition is 1372 demonstrated through the ion mass spectrum and SIMS measurements of an enriched 1373 film. As a result, the vacuum has been improved from 2.7 ? 10-6 Pa (? 2 ? 10-8 Torr) 1374 to 2.7 ? 10-8 Pa (? 2 ? 10-10 Torr), with a factor of 100?. A total purity of 99.965 % is 1375 obtained, with a factor of 43? improvement. We found that for N concentration, it is 1376 largely correlated to the ion source base vacuum; while for C and O, less 1377 improvements were seen. This means that below the 1019 cm-3 concentration region, 1378 ion source vacuum might not be the only dominating factor that affects the chemical 1379 purity of the 28Si film. Other factors such as cleanliness of the gas line, background 1380 contamination, ion sputtering might be limiting. In addition, we showed that the 1381 isotopically enriched 28Si thin film deposited is epitaxial with good surface quality 1382 and crystallinity using STM. The deposited film also has high enrichment level of 1383 99.99987(3) %, indicating that the ability for highest enrichment among all methods 1384 reported is maintained. With possible future improvements, such as the ion beam 71 1385 sweeper and UHV gas line with purifier, we believe we can further improve the 1386 chemical purity of the film to have C, O and N contents < 1017 ? 1018 cm-3. This will 1387 be an important step forward to produce high quality 28Si that is suitable for quantum 1388 information studies. 1389 1390 This chapter is reproduced from Ref. [134] with permissions from all the co- 1391 authors. 1392 72 1393 Chapter 4: Targeted Enrichment of 28Si thin films 1394 1395 In this chapter, we report on the growth of isotopically enriched 28Si epitaxial 1396 films with precisely controlled enrichment levels, ranging from natural abundance 1397 ratio of 92.2 % all the way to 99.99987 % (0.832 ? 10-6 mol/mol or 0.832 ppm 29Si). 1398 Isotopically enriched 28Si is regarded as a nearly ideal host material for 1399 semiconducting quantum computing due to the lack of 29Si nuclear spins. However, 1400 the detailed mechanisms for quantum decoherence and the exact level of enrichment 1401 needed for quantum computing remain uncertain. In the previous chapters, we 1402 introduced the use of hyperthermal energy ion beam for 28Si deposition with certain 1403 mass-to-charge ratio (28 amu/e). Here we switch the mass selective magnetic field 1404 periodically to control the 29Si concentration. We develop a model to predict the 1405 residual 29Si isotope fraction based on the deposition parameters and measure the 1406 deposited film using secondary ion mass spectrometry (SIMS). The first generation of 1407 the targeted enrichment film had a value which agreed with the predicted value within 1408 a factor of 2. With the improvements in current measurement and ion source stability, 1409 the second generation of targeted enrichment showed improved, excellent agreement 1410 with the prediction, deviating on average by only 10 %. 1411 1412 4.1 Introduction 1413 1414 1415 As interest grows in using isotopically enriched 28Si to achieve longer coherence 1416 times in quantum information processing, better understanding of the mechanisms 73 1417 behind decoherence in electron spin becomes important. In 1958, Gordon and Bowers 1418 first measured the coherence time T2 of electrons bound to lithium and phosphorus 1419 donors in isotopically enriched Si with T2 = 0.5 ms [135], [136] , which was much longer 1420 than the coherence time in natural Si. This demonstrated that, in those donor electron 1421 spin systems, residual 29Si contributes significantly to the electron spin decoherence. 1422 Recently, theoretical studies using cluster expansion techniques [137], [32], [33] by Witzel 1423 et al. predicted that every order of magnitude increase in isotopic enrichment results 1424 in approximately the same order of magnitude increase in the coherence time, until 1425 limited by non-Si spins. Excellent agreement between the theory and experiment has 1426 been shown with bulk ESR measurements, with one measurement done at 0.0005 % 1427 29Si [138] and others from 0.08 % to 99.2 % 29Si [32]. However, emerging single 31P 1428 spin measurements in 28Si have indicated performance better than predicted [35], [139], 1429 motivating additional studies. The discrepancy found between the experiments and 1430 theory indicates that the phase space of coherence versus enrichment, especially in 1431 the limit of few spins and high isotopic enrichment regimes, remain largely unknown. 1432 As a result, a specific need exists for enriched 28Si to have different, targeted 1433 values of enrichment to study the dependence of quantum coherence time on residual 1434 29Si concentration. Although various research groups have been able to make 1435 isotopically enriched 28Si [140], [141], [44], [45], [102] (explained in detail in Ref. [43]), the 1436 ability to predict and control the residual 29Si isotope fraction within 28Si precisely 1437 has not yet been demonstrated. The discreteness and the limited number of the 1438 enrichment levels available within this community make a detailed determination of 1439 the optimal enrichment difficult to accomplish. 74 1440 In this chapter, we present a method that allows us to produce 28Si with precisely 1441 controlled isotopic enrichments. We develop a model that allows us to choose and 1442 predict the level of enrichment for our 28Si. We deposit 28Si thin films with 29Si 1443 concentrations ranging from our baseline (< 1 ? 10-6 mol/mol) to natural abundance 1444 (4.7 %) and measure the isotope fractions of the residual 29Si and 30Si using 1445 secondary ion mass spectroscopy (SIMS). The measured enrichments are then 1446 compared to the model prediction and show excellent agreement, deviating on 1447 average by only 10 %. 1448 1449 Figure 4.1: A schematic illustration of the origin of 28Si and 29Si. 1450 The solid green and red lines represent 28Si+ and 29Si+ ion beam respectively. During 1451 28Si deposition, mass selective magnetic field is tuned such that only 28Si+ ions can 1452 pass through and 29Si+ ions are blocked by the aperture. Apart from the Si ions, SiH4 1453 gas molecules can also pass through the aperture and adhere to the substrate. The 1454 background silane gas contribution to the film is approximately 10-6 mol/mol. 1455 1456 4.2 Experimental Methods 1457 1458 1459 To achieve a targeted enrichment, sources of 29Si that can enter the film are 1460 studied, as shown in Fig. 4.1. Even with the magnetic field tuned at a certain mass-to- 75 1461 charge ratio, for example 28 amu/e, 29Si+ ions might still pass through the mass 1462 selective aperture if the mass resolution (determined by the width of the ion beam 1463 exiting the ion source, the aperture width and the spread in ion energy) is poor. Here 1464 we use a mass spectrum to characterize the Si ions. It is generated by monitoring the 1465 ion current at the deposition location while scanning the mass analyzer magnetic 1466 field. A mass spectrum is shown in Fig. 4.2 (a) for targeted enrichment, where peaks 1467 for 28Si+ ions (mass 28 amu), 29Si+ ions (mass 29 amu) and the corresponding ionized 1468 hydrides (mass 29 amu to 32 amu) due to incomplete cracking, can be seen. It is very 1469 similar to the previously shown mass spectra (Fig. 3.4), the values in height of the 28 1470 amu and 29 amu peaks are extracted to estimate the deposition parameters. The mass 1471 separation is obtained by fitting the mass peaks with Gaussians. The center of the 1472 mass 28 amu peak is about 7.4 ? (standard deviation) away from the center of 29 amu 1473 peak, indicating a lower bound of 29Si isotope fraction of 10-13 at the 28 amu mass 1474 position. Another source of 29Si comes from the residual background SiH4 molecules 1475 as they can diffuse through the aperture hole and adhere to the sample substrate. In 1476 addition, mass 29 amu ions might lose energy and fall into the 28 amu trajectory in 1477 the mass analyzer. However, this effect would be asymmetric, and since there is no 1478 observed scattering tail effect, we assume that all the current at mass 28 amu peak is 1479 from 28Si+. Therefore, the main active contributors of 29Si considered in this chapter 1480 are from ion beam itself and the diffused background silane gas from the ion source 1481 to the deposition chamber. 1482 76 1483 1484 1485 77 1486 Figure 4.2: Demonstration of the targeted enrichment. 1487 (a) An ion beam mass spectrum used for checking mass resolution and calculating the 1488 deposition parameters described in equation 1 and 2. Gaussian fits for both mass 28 1489 amu and mass 29 amu are shown in red, with a mass separation of 7.4 ?. (b) The 1490 block diagram of the targeted enrichment control. A DAQ function generator is used 1491 to trigger a periodic asymmetric square wave to control the output of the mass 1492 analyzer. (c) An example of an ion current for targeted enrichment, plotted as the 1493 current collected at the sample stage versus time. The corresponding mass positions at 1494 28 amu and 29 amu peaks are also shown on the right. The duty cycle is selected such 1495 that the dwelling time at mass 28 amu is 75 % and the dwelling time at mass 29 amu 1496 is 25 %. 1497 1498 The experimental concept for targeted enrichment is described in detail here. In 1499 previous work, we produced isotopically pure 28Si that has a 29Si isotope fraction < 1 1500 ? 10-6 mol/mol by tuning the mass selective magnetic field to be centered on the mass 1501 28 amu peak only. However, if we tune the magnetic field to the value at mass 29 1502 amu peak for a certain fraction of the cycle, we can mix 29Si into our 28Si film. By 1503 controlling the dwelling times ?t28 (time spent on the mass 28 amu peak) and ?t29 1504 (time spent on the mass 29 amu peak), we can control the amount of 29Si+ deposited 1505 onto the sample. This periodic switching is achieved by using a pulse generator (DAQ 1506 with LABVIEW) to trigger an asymmetric square wave to control the output of the 1507 mass analyzer. The block diagram for the control is shown in Fig. 4.2 (b). The output 1508 of the mass analyzer, which contains both the magnet current and the switching 1509 periods, determines the mass positions and the dwelling times of the ion beam. Fig. 1510 4.2 (a) and (c) demonstrate an example of the control parameters. The peak of the 1511 square wave (green) corresponds to the mass 28 amu peak (28Si+ only), at a magnet 1512 current of 50.6 A, with an ion current of 620 nA and ?t28 of 6 s. The valley of the 1513 square wave (red) corresponds to the mass 29 amu peak (29Si+ and 28SiH+, where the 1514 ratio of 29Si at this mass peak is approximately equal to the natural abundance ratio), 78 1515 at a magnet current of 51.6 A, with an ion current of 124 nA and ?t29 of 2 s. These 1516 parameters would correspond to a 29Si isotope fraction of 3000 ppm (3 ? 10-3 1517 mol/mol), with roughly 1 monolayer of Si deposited per cycle. 1518 In this way, by tuning the dwelling times ?t28 and ?t29, we are able to produce any 1519 desired enrichment level, ranging from natural abundance (4.7 % 29Si) to our baseline 1520 (< 1 ? 10-6 mol/mol 29Si).The dwelling time ?t28 at mass 28 amu, and ?t29 at 29 amu 1521 can be any combination as long as it is within the response time of the analyzer power 1522 supply and the magnet, which is about 2 ms and 50 ms in the range of our interests, 1523 respectively. However, to ensure the epitaxial quality and homogeneity of the 1524 deposited 28Si material, ?t28 + ?t29 should be a short cycle, generally corresponding to 1525 less than a monolayer of material growth. 1526 During deposition, the ion beam is tuned to its optimum fluence condition, where a 1527 SiH4 flow rate of 0.02 sccm (corresponds to a chamber pressure of 1.87 ? 10-4 Pa or 1528 1.4 ? 10-6 Torr) and a growth rate of about 1.0 to 1.5 nm/min [134] is used, as 1529 discussed in Chapter 3. Higher growth rate is also achievable using high pressure 1530 plasma mode of the ion source, but generally results in a higher surface roughness of 1531 the deposited film. The substrate temperature is chosen to be 450 ?C, which produces 1532 the lowest baseline 29Si isotope concentration and highest epitaxial film quality [133] 1533 for this experimental setup. 1534 A model (assuming transport limited kinetics) is developed to calculate the 1535 isotope fractions of the deposited 28Si layer, including the contributions from the 1536 background silane gas: ?? ?? ??+2929 29 29 ???(??29??29+??? = 28 ??28) 1537 (4.1) (??29??29+??28??28)?(1+ 28? +29? ? + 30 ? ??) 79 1538 ? = (??29 ? ?29 + ?? 28 29 30 28 ? ?28) ? (1 + ?? + ?? + ??) (4.2) 1539 1540 where f 29 is the isotope fraction of 29Si, L is the number of monolayers per cycle, D28 1541 is the deposition rate of 28Si at mass 28 amu peak current, D29 is the deposition rate at 1542 29 amu peak current, A is the atomic percentage of 29Si at 29 amu peak, which 1543 consists both 29Si+ and 28SiH+ ions. 28,29,30Cz are the flux ratios from the background 1544 silane diffusion, which can be calculated using the equation derived from Ref. [23]: ??????? 1545 ??? = , (4.3) ????+?? 1546 where Fg is the silane gas flux and Fi is the 28Si ion flux, s is the effective 1547 incorporation fraction and ax is the natural abundance ratio of the corresponding 1548 silicon isotopes in SiH4. In this experimental setup, since we are using a low SiH4 1549 pressure mode for 28Si deposition, the background gas contribution is typically < 1 1550 ppm (10-6 mol/mol) 29Si, which has negligible impact on most of the enrichment 1551 levels but is still included in the calculation. 1552 1553 4.3 Targeted Enrichment Results 1554 1555 4.3.1 First-Generation of Targeted Enrichment 1556 1557 1558 In each deposition, typically two or three layers of 28Si with different enrichments 1559 are grown on one substrate based on the model described above, each with a layer 1560 thickness of about 100 nm. The experimental sequence is to choose a target value 1561 first, then estimate the value after deposition based on the actual experimental 1562 parameters and finally compare to the measured value using SIMS. It is worth 80 1563 noticing that the ion beam growth condition might change a little during deposition 1564 due to ion source instability. Therefore, the estimated values calculated after 1565 deposition may deviate from the targeted values before deposition, but generally the 1566 deviation is small (5.7 % on average for the 2nd generation). The comparison between 1567 the estimated values and the measured values are shown in Table III and V. 1568 The isotope fractions of 28Si, 29Si and 30Si as a function of layer thickness in the 1569 film and the substrate are measured using SIMS. Isotopic measurements of silicon 1570 were made in a CAMECA IMS-1270E7 large geometry secondary ion mass 1571 spectrometer. The samples were bombarded with a primary ion beam of O +2 ions at 1572 an impact energy of 8 keV and a current of 1 nA (for most of the samples). The beam 1573 was focused to a probe size of a few micrometers in diameter and it was raster- 1574 scanned over a 50 ?m x 50 ?m area. Positive secondary ions were accepted for 1575 detection from the central 20 ?m x 20 ?m portion of the rastered area as defined by a 1576 field aperture in a focal plane of the mass spectrometer. The entrance and exit slits of 1577 the spectrometer were selected to produce a mass resolving power of about 6000 1578 (M/?? at ?? ? of peak maximum). This resolving power is necessary to separate 1579 cleanly the 29Si peak from the 28SiH peak that is produced during the SIMS process. 1580 Under these conditions we estimate that less than 10-5 of the 28SiH signal contributes 1581 to the 29Si measurement. Depth profiles of the silicon isotopes 28Si, 29Si and 30Si 1582 through a deposited film were acquired by monitoring 28Si for 1 s, 29Si for 10 s, 28SiH 1583 for 1 s and 30Si for 10 s in each data cycle and collecting a sufficient number of data 1584 cycles until the profile penetrated into the silicon substrate. The sputter rate as 1585 determined by measuring the final crater depths with a stylus profilometer was 81 1586 approximately 0.16 nm/s under these conditions. The depths of only a few craters 1587 were measured, and the determined sputter rate was used to determine the depth 1588 scales for all profiles. In a few profiles the ion current was reduced to 0.5 nA to 1589 acquire a higher data density and the sputter rate was taken as half of the value for 1 1590 nA. In those cases, the entrance slit was widened slightly to regain the same signal 1591 levels as with a 1 nA beam. Isotope ratios of 29Si/28Si and 30Si /28Si were calculated 1592 on a cycle-by-cycle basis. Average isotopic ratios for a film or a layer of a multilayer 1593 film were calculated by averaging the cycle-by-cycle ratio measurements in the 1594 portion of a profile where the ratios were at a relatively constant value. These values 1595 were then corrected for instrumental mass fractionation based on the differences 1596 between the measured ratios from a natural silicon wafer and the accepted natural 1597 values. Uncertainties were determined from the standard deviation of the mean of the 1598 measurements and were usually similar to Poisson estimations based on the total 1599 number of detected counts of the minor isotopes. In some cases, the minor isotope 1600 signals were not constant, and the standard deviations were larger than the Poisson 1601 estimates. 1602 82 1603 1604 Figure 4.3: A SIMS depth profile of a first-generation targeted enrichment sample. 1605 The inset shows a schematic diagram of the targeted enrichment sample layer 1606 structures. Usually a few layers with different 29Si isotope fractions are deposited on a 1607 float-zone silicon substrate and then capped with pure 28Si layer. The 29Si and 30Si 1608 isotope fractions are shown in blue dots and red squares, respectively. Natural 1609 abundance ratios of 29Si and 30Si are shown in dashed lines. 1610 1611 Fig. 4.3 shows an example of the SIMS depth profile of the first-generation 1612 targeted enrichment samples, where three different enrichment levels can be 1613 distinguished. The SIMS measurements were taken near the center of the 28Si deposit, 1614 which is usually the thickest, to match the parameters used in the model. The average 1615 isotope fraction of 29Si in the surface layer (baseline) is measured to be (2.05 ? 0.46) 1616 ? 10-6 mol/mol, from the range of 20 nm to 170 nm depth. From 0 nm to 20 nm, the 1617 higher values of 29Si and 30Si are due to the artifacts from the surface tail effect. This 1618 surface tail is formed because the sample has been exposed to air and contamination 83 1619 during the transport from UHV chamber to the SIMS measurement. Those impurity 1620 atoms from surface contamination were pushed into the material by the primary ion 1621 beam of SIMS [142]. Two subsequent layers are also shown from 170 nm to 270 nm 1622 and 270 nm to 340nm, with an average 29Si isotope fraction of (332 ? 5) ? 10-6 1623 mol/mol and (885 ? 38) ? 10-6 mol/mol, respectively. The estimated values are 215 ? 1624 10-6 mol/mol and 460 ? 10-6 mol/mol. The deviation is approximately within a factor 1625 of 2. Note that some fluctuations can be seen in layer 1, this is not due to the 1626 measurement error of SIMS since there is enough number of counts for measuring 1627 29Si (this is in contrast with < 1 ppm region where the fluctuation is largely due to 1628 insufficient atom counts). The reason for this fluctuation might be due to the 1629 instability of the ion source during deposition and it will be discussed in detail in the 1630 next section. 1631 Four samples with different layers of enrichment are measured. The comparison 1632 between the targeted and measured 29Si isotope fractions is shown in detail in Table. 1633 III and a correlation plot of the estimated versus the measured 29Si isotope fraction is 1634 shown in Fig. 4.4. The range is shown from the baseline values (around 1 ppm of 1635 29Si) up to 10000 ppm. The data points generally follow the line of the linear fit, but 1636 the deviation between the estimated and measured values is still quite high, with an 1637 average of 57.77%. Improvements are needed to achieve a better control of the 1638 deposited samples. 84 1639 1640 Figure 4.4: A correlation plot showing the measured 29Si isotope fractions as a 1641 function of targeted 29Si isotope fractions for the first-generation samples. 1642 The average total deviation from the estimated values is 57.8%. 1643 1644 1645 1646 Table III. A comparison between the estimated and measured 29Si isotope fractions of 1647 the first-generation samples. The deviations shown here are between the estimated 1648 and the measured values. The total deviation on average is (57.8 ? 11.1) %. 1649 Targeted Estimated Measured Deviation (10-6 from deposition by SIMS mol/mol) (10-6 mol/mol) (10-6 mol/mol) 100 80 21 73.8% 200 215 332 54.4% 400 460 855 85.9% 800 760 1361 79.1% 3000 2988 1858 37.8% 6000 5500 6361 15.7% 1650 85 1651 4.3.2 Methods of Improvements 1652 1653 1654 From the SIMS depth profile, we observed fluctuations in some of the deposited 1655 layers of 28Si. We believe the main reason for this deviation is the instability of the 1656 ion source during deposition process. For example, the estimated values of 1657 enrichment depend largely on the deposition rate of the peak current D28 and D29. Any 1658 changes in the ion current will result in a deviation from the estimated value. During 1659 deposition in the first-generation samples, we observed both gradual and abrupt 1660 changes in the total ion current ratio between mass 28 amu and 29 amu peaks. A 1661 gradual decrease of the ion current is likely due to the erosion of cathodes from the 1662 ion sputtering and precipitation of solids on the anodes inside the UHV Penning ion 1663 source. The cathode and anode material used was copper (Cu), which has a sputter 1664 yield of 5.41 atoms/ion using 28Si+ with energy of 3 keV. This number is calculated 1665 using the simulation software ?The Stopping and Range of Ions in Matter? (SRIM). 1666 Fig. 4.5 shows the pictures of the eroded anodes and cathodes. As the erosion 1667 happens, the shape of the anode and cathode changes during beam run. This will 1668 affect the geometry of the plasma formed and the efficiency of ions been extracted 1669 into the transport system, as observed as a gradual decrease in the ion current during 1670 deposition. As the service time gets longer, Si will be deposited and forms flakes at 1671 the surface of the Cu anodes and cathodes, as shown in the black materials in Fig. 4.5. 1672 Those flakes will alter the potential inside the ion source and will cause either an arc 1673 during beam run or even a short between the cathode and anode. Usually when a short 1674 happens, maintenance has to be done by breaking the vacuum and reassembling the 1675 ion source to replace anode and cathodes. 86 1676 To improve the stability and lifetime of the ion source, different cathode materials 1677 are investigated. As compared to Cu, titanium (Ti), tungsten (W), iron (Fe), stainless- 1678 steel (SS) and molybdenum (Mo) all have smaller sputter yields when bombarded by 1679 Si ions. However, other properties also need to be considered when depositing 28Si 1680 thin films, such as the price of the material, ease of machining, chemical purity, 1681 alloying, etc. Table IV. shows a summary of the SRIM simulation result with three 1682 candidate materials. Ti is chosen to be the new anode and cathode material because it 1683 has the lowest sputter yield and highest purity (99.999%), with relatively low cost. 1684 High purity Ti rods with 3 cm in diameter and 5 cm in length are purchased from 1685 American Elements and are machined into cylindrical anodes and cathodes. 1686 1687 Table IV. Summary of the SRIM results on different anode and cathode materials. 1688 The ion energy of the Si+ used in the simulation is 3 keV, with 10000 ions in total. 1689 Material type Atomic mass Density Sputter yield (u) (g/cm3) (atoms/ion) Cu 63.54 8.92 5.41 W 183.8 19.35 2.09 Ti 47.9 4.52 1.42 1690 1691 Fig.4.5 shows a comparison between the anodes and cathodes using Cu and Ti after 1692 hours of service. Panel (a) and (b) are the Cu cathodes and anti-cathodes used in the 1693 ion source after 26 hours of service. Due to ion bombardment, the center of the 1694 cathode rings was eroded. Si flakes (shown as dark deposit on Cu) adhered on the 1695 cathode surfaces were also observed after long hours of service. The average lifetime 1696 of a Cu anode/cathode before maintenance is ? 21 hours. Either a low ion current or a 87 1697 short between anode and cathode was experienced, indicating the need for 1698 maintenance. 1699 1700 Figure 4.5: Ion source anodes and cathodes after hours of beam runs. 1701 (a) and (b) are the copper cathodes after 26 hours of service. Erosion from the ion 1702 bombardment at the center of the cathode rings can be seen, with some silicon flakes 1703 adhered on the surface. (c) and (d) are the titanium anode and cathodes, respectively, 1704 after 37 hours of service. Less erosion is observed on titanium, with less Si flakes 1705 adhered on the surface. Titanium anodes and cathodes in general have a longer (2?) 1706 lifetime and better stability. 1707 1708 Panel (c) and (d) showed the anode and cathodes made of high purity Ti, respectively, 1709 after 37 hours of service. Less erosion and less Si flakes were observed. The average 1710 lifetime using Ti is ? 38 hours, roughly 2? longer than using Cu. This also means 88 1711 better stability in terms of ion current. A smoother ion current with less fluctuation 1712 and slower decrease rate is obtained with Ti anodes and cathodes. 1713 Another factor that affects the accuracy of the prediction for targeted enrichment 1714 is the ion current measurement. In the first-generation samples, the ion current was 1715 measured using a large aperture of 4.9 mm2. This introduces uncertainty because the 1716 SIMS crater is measuring at the center of the beam spot (<< 1 mm2) while using a 1717 larger aperture is estimating the average over a larger area. And as we introduced in 1718 Chapter 2, the contour map of the ion beam shape shows a higher ion density closer 1719 to the center compared to the edges. To solve this problem, a smaller aperture with 1720 0.785 mm2 is used to estimate the ion current in the second-generation samples. This 1721 allows better estimation because the area of the ion current density used to calculate 1722 the enrichment is closer to the area measured by SIMS. In addition, the ion current is 1723 measured both at the beginning and at the end of the deposition to account for any 1724 changes in the ion current (28 amu and 29 amu) peak shapes due to long deposition 1725 times. 1726 1727 4.3.3 Second-Generation of Targeted Enrichment 1728 1729 1730 With the improvements in both ion source stability after replacing the cathode 1731 materials and ion current measurement, better accuracy between target and measured 1732 enrichment values has been achieved in the second-generation targeted enrichment 1733 samples. Fig. 4.6 is an example of the SIMS depth profile of a second-generation 1734 targeted enrichment sample. The average isotope fraction of 29Si in the surface layer 1735 (baseline) is measured to be (0.83 ? 0.09) ? 10-6 mol/mol, from the range of 30 nm to 89 1736 170 nm depth. Two subsequent layers are also shown from 170 nm to 310 nm and 1737 310 nm to 417 nm, with an average 29Si isotope fraction of (1599 ? 7) ? 10-6 mol/mol 1738 and (3583 ? 20) ? 10-6 mol/mol, respectively. The targeted values are 1600 ? 10-6 1739 mol/mol, with a deviation (compared to the measured value) of 0.06 % and 3500 ? 1740 10-6 mol/mol, with a deviation of 2.4 %. 1741 1742 1743 Figure 4.6: A SIMS depth profile of a second-generation targeted enrichment sample. 1744 The inset shows a schematic diagram of the targeted enrichment sample layer 1745 structures. Two layers with different 29Si isotope fractions are deposited on a float- 1746 zone silicon substrate and then capped with pure 28Si layer. The 29Si and 30Si isotope 1747 fractions are shown in blue dots and red squares, respectively. Natural abundance 1748 ratios of 29Si and 30Si are shown in dashed lines. Better stability is seen in each layer 1749 with a flatter 29Si concentration profile. 1750 1751 1752 1753 90 1754 Table V. A comparison between the target, estimated and measured 29Si isotope 1755 fractions. The deviation shown here are between the target and the measured values. 1756 The total deviation on average is (10.4 ? 5.0) %. 1757 Target Estimated Measured Deviation (10-6 mol/mol) from deposition by SIMS (10-6 mol/mol) (10-6 mol/mol) 1 0.7 0.83 17.0% 10 9.9 10.5 5.0% 30 34.1 30 0.0% 40 40.7 20.5 48.8% 60 62.1 81 35.0% 75 77 74 1.3% 90 88.1 87 3.3% 300 316 300 0.0% 800 797 784 2.0% 1600 1630 1599 0.1% 3500 3530 3583 2.4% 1758 1759 As a comparison, the estimated values from the model after deposition are calculated 1760 to be (1630 ? 15) ? 10-6 mol/mol, with a deviation of 1.9 % and (3530 ? 30) ? 10-6 1761 mol/mol, with a deviation of 1.5 %. 1762 The comparison between the target and measured 29Si isotope fractions is shown 1763 in detail in Table. V and a correlation plot of the targeted versus the measured 29Si 1764 isotope fraction is shown in Fig. 4.7. In total, 11 targeted enrichment levels have been 1765 plotted on a log scale, ranging from 0.83 ? 10-6 mol/mol to 3583 ? 10-6 mol/mol of 1766 29Si. Both a linear fit and a confidence band in log-log scale are included to show the 1767 accuracy of the prediction. As shown in the figure, all data points are within 95 % 1768 confidence band. The average deviation between the targeted and measured 1769 enrichments across the entire range of measurements is found to be 10 %. The one 1770 data point measured at 20 ? 10-6 mol/mol has the largest deviation from the targeted 1771 value and the largest relative uncertainty. This deviation was caused by the ion 91 1772 1773 Figure 4.7: A correlation plot showing the measured 29Si isotope fractions as a 1774 function of targeted 29Si isotope fractions. 1775 A linear fit and 95 % confidence band are included to assist comparison. An average 1776 deviation of 10 % has been obtained over a wide range, from 0.83 ? 10-6 mol/mol to 1777 3.58 ? 10-3 mol/mol of 29Si. 1778 1779 source, where the ion beam condition was unstable during this deposition compared 1780 to others. To further improve the stability of the ion source, cleaning of the ion source 1781 using argon plasma between each run may be helpful. This will remove excess silicon 1782 flakes that slowly aggregated on the interior of the ion source, which causes 1783 fluctuation in the plasma region. Another source of uncertainty may come from the 1784 location of the 28Si spot. Since our 28Si deposit is in the shape of a hill instead of flat 1785 surface, the measured location might still be different from where it has been 1786 estimated, even with a smaller aperture. For example, if the measured spot is closer to 1787 the edge, the ion current density will be smaller compared to the center of the beam 1788 spot. This usually results in a higher 29Si concentration, partially from the background 92 1789 silane gas (since the background pressure is constant) and partially from the slight 1790 changes in the 28 amu and 29 amu peak shapes. The installation of an ion beam 1791 sweeper to smooth out the deposited film may help. Furthermore, the SIMS 1792 measurement uncertainty also acts as a factor, mainly limited by counting statistics, 1793 especially at lower 29Si concentrations, where the number of counts is dramatically 1794 lower compared to higher 29Si concentrations. 1795 1796 4.4 Conclusion 1797 1798 1799 In this chapter, we have reported on a method that allows us to achieve targeted 1800 enrichment of the 28Si epitaxial thin films. We have developed a model to predict and 1801 control the residual isotope fraction of the 29Si in the film precisely and compare its 1802 results to the values measured using SIMS. The first-generation of targeted 1803 enrichment showed a relatively good accuracy, within a factor of 2 compared to the 1804 targeted values. With the improvements in ion source stability and ion current 1805 measurement, we have achieved an excellent agreement between the targeted and the 1806 measured values over a wide range of enrichments in the second-generation samples, 1807 with small deviation of only 10 % on average. This deviation can be improved by 1808 further increasing the stability of our ion source and possibly by using an ion beam 1809 sweeper. We believe this is an important step forward to enrich the material supply of 1810 28Si at different levels within this community and to explore the qualifying metric for 1811 ?quantum grade? silicon in terms of enrichments. 1812 This chapter is reproduced from Ref. [143] with permissions from all the co- 1813 authors. 93 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 94 1834 Chapter 5: Potential Qualifying Metrics for 1835 ?Quantum Grade? Silicon - 28Si MOSFET 1836 1837 Across solid state quantum information, material deficiencies limit performance 1838 through enhanced relaxation, charge defect motion, or isotopic spin noise. While 1839 classical measurements of device performance provide cursory guidance, specific 1840 qualifying metrics and measurements applicable to quantum devices are needed. For 1841 quantum applications, new material metrics, e.g., enrichment, are needed, while 1842 existing classical metrics such as mobility might be relaxed compared to conventional 1843 electronics. In this chapter, we examine locally grown silicon that is superior in 1844 enrichment, but inferior in chemical purity compared to commercial-silicon, as part of 1845 an effort to underpin the material standards needed for quantum grade silicon and 1846 establish a standard approach for the inter-comparison of these materials. We use a 1847 custom, mass-selected ion beam deposition technique, which has produced isotopic 1848 enrichment levels up to 99.999 98 % 28Si, to isotopically enrich 28Si, but with 1849 chemical purity of only > 99.97% due to the molecular beam epitaxy techniques used. 1850 From this epitaxial silicon, we fabricate top-gated Hall bar devices simultaneously on 1851 28Si and on the adjacent natural abundance Si substrate for inter-comparison. Using 1852 standard-methods, we measure maximum mobilities of ? (1740 ? 2) cm2/V.s at an 1853 electron density of (2.7 ? 1012 ? 3 ? 108) cm?2 and ? (6040 ? 3) cm2/V.s 1854 at an electron density of (1.2 ? 1012 ? 5 ? 108) cm?2 at T = 1.9 K for devices 1855 fabricated on 28Si and natSi, respectively. For magnetic fields B > 2 T, both devices 1856 demonstrate well developed Shubnikov-de Haas oscillations in the longitudinal 95 1857 magnetoresistance. This provides the transport characteristics of isotopically enriched 1858 28Si and will serve as a benchmark for the classical transport of 28Si at its current state 1859 and low temperature, epitaxially grown Si for quantum devices more generally. 1860 1861 5.1 Introduction 1862 1863 1864 Conventional electronics have been industrialized for decades; consequently, 1865 precise metrics based on macroscopic properties, such as chemical purity, charge 1866 carrier mobility, and defect density, are established for qualifying a material, e.g., 1867 silicon, for conventional electronics. While silicon has long been the workhorse of 1868 conventional electronics, it is also becoming a promising host for spin based quantum 1869 information processing devices [21, 136]. 1870 Even though silicon has improved tremendously over the decades to meet demands 1871 of today?s state-of-the-art transistors, this excellent material is still not sufficient to 1872 support quantum information. For example, in spin-based quantum information 29 1873 systems, the presence of the Si isotope in natural abundance silicon reduces 1874 coherence times due to its nonzero nuclear spin of I = 1/2. Nuclei with nonzero spin in 1875 the host lattice act as a source of decoherence for spin based qubits [135], as they 1876 interact with the electron spin through hyperfine interactions [144, 145]. However, by 1877 placing a spin qubit in an isotopically enriched 99.995% 28Si environment [40], the 1878 development of silicon based quantum devices has gained considerable momentum, 1879 with reports of exceptionally long quantum coherence times [30, 34]. 96 1880 The need for some level of enrichment provides an example of how 1881 ?semiconductor grade? silicon quality may be necessary but is not sufficient to meet 1882 the needs of quantum information processing (QIP). Furthermore, the metrics for 1883 conventional silicon may not always be relevant for QIP, e.g., the ease of carrier 1884 motion as quantified by mobility may not be directly relevant to quantum device 1885 performance where confinement and coherence in the absence of motion are critical. 1886 Additionally, as we establish properties and their numerical thresholds that are 1887 sufficient for QIP, relatively simple qualifying metrics that act as general proxies for 1888 properties more challenging to measure are invaluable. However, it may be noted that 1889 mobility in and of itself is not important, but it could be a good proxy for estimating 1890 spin-qubit relaxation or coherence [146]. 1891 As part of a larger program to identify and quantify ?quantum grade? silicon, we 1892 are identifying (1) properties beyond those considered for semiconductor grade 1893 silicon critical to QIP; (2) the relevance and priority of properties currently 1894 considered critical for semiconductors; and (3) standard methods that may be used for 1895 QIP properties or provide a general indicator for challenging properties, e.g., 1896 coherence time, as three main goals that are paramount for the development of 1897 metrics for ?quantum grade? silicon. This work is part of a broader effort to find ways 1898 besides making and measuring qubits to provide diagnostics that will indicate the 1899 likely performance of qubits early in a fabrication stream. 1900 This chapter presents devices, methods, and results for a comparative study of 1901 magnetotransport properties between (1) high isotopic enrichment, low chemical 1902 purity and (2) high chemical purity, natural abundance (low isotopic enrichment) 97 1903 silicon. This characterization sets the stage for determining whether coherence 1904 properties in quantum dot devices correlate with the trends in simpler, traditional 1905 measurements since the benefit of enrichment on coherence may outpace the liability 1906 of some additional contaminants. In a detailed theoretical study, Witzel et al. [147] 1907 illustrated that the coherence of a spin qubit can, in principle, be increased by an 1908 order of magnitude for every order of magnitude increase in the isotopic enrichment 1909 of 28Si in the qubit?s Si environment. A comprehensive experimental investigation of 1910 this prediction, however, is hindered due to the discreteness of the available isotopic 1911 enrichment levels. Among the four different enrichment levels that have been 1912 reported [40, 148-150] only 99.98% 28Si and 99.995% 28Si have been utilized for 1913 quantum electronic device fabrication [29, 30, 139]. Moreover, contemporary 1914 methods for producing isotopically enriched 28Si materials are based on chemical 1915 vapor deposition (CVD) techniques and are not compatible with qubit architectures 1916 requiring low temperature processing, e.g., STM fabricated single dopant atom qubits 1917 [151]. In contrast, the method used for producing 28Si reported here is compatible 1918 with all the contemporary qubit architectures and represents molecular beam epitaxy 1919 (MBE) grown Si more generally. While the coherence of a spin qubit is predicted to 1920 improve at higher isotopic enrichment levels [147], how other material properties will 1921 limit the expected enhancement of qubit coherence is unclear. To the best of our 1922 knowledge, no study yet has attempted to correlate macroscopic electrical 1923 characteristics with the performance of quantum devices. Yet, such a study will be an 1924 essential component for defining metrics for ?quantum grade? silicon within the three 1925 main goals identified earlier. 98 1926 5.2 281927 Si MOSFET Devices 1928 1929 1930 The 28Si materials are produced using the ion beam deposition method introduced in 1931 Chapter 2 and 3. Gated Hall bar devices are fabricated on isotopically enriched 28Si 1932 epilayers in order to electrically characterize the material. Typically, the isotopically 1933 purified 28Si spot is ? 4 mm2 ? 8 mm2 in area and covers only a small fraction of the 1934 starting float-zone grown, natural abundance, intrinsic Si substrate with dimensions of 1935 4 mm ? 10 mm; see Fig. 5.1 (a). Due to the reduced coverage of the 28Si spot, devices 1936 on isotopically enriched and natural abundance Si can be fabricated on the same Si 1937 chip at the same time. This eliminates the effect of certain imperfections on the 1938 fabrication process (e.g., oxide growth) when comparing the electrical properties of 1939 the devices. A schematic cross section of a device fabricated on a 28Si spot is shown 1940 in Fig. 5.1 (b). The structure of the devices fabricated on natSi, i.e., outside the 28Si 1941 spot, is identical (went through sample vacuum, thermal and fabrication processes) 1942 except without the 28Si layer. An optical micrograph of the gated multiterminal Hall 1943 bar device is shown in Fig. 5.1 (c). 1944 The isotope fraction of the 28Si epilayers is measured by SIMS. In Fig. 5.1 (d), the 1945 SIMS-derived isotopic ratio of 29Si/28Si is shown as a function of depth at several 1946 locations near the fabricated Hall bar device. For the device reported here, the level of 1947 isotopic enrichment measured at locations 1, 2, and 3 corresponds to ? 99.976 %, ? 1948 99.980 %, and ? 99.993 % 28Si, respectively. This confirms that the Hall bar device is 1949 located on top of the deposited 28Si spot as we expected. Figure 5.1 (d) also reveals 99 1950 1951 Figure 5.1: 28Si MOSFET device and measurements. 1952 (a) A schematic illustrating the device layout of a given sample. Reduced coverage of 1953 the 28Si spot allows us to fabricate devices on 28Si and natSi simultaneously. (b) 1954 Schematic representation of the gated Hall bar device fabricated on 28Si is shown. (c) 1955 An optical micrograph of a gated multiterminal Hall bar device fabricated on 28Si is 1956 shown. (d) The isotopic ratios of 29Si/28Si at positions 1 (?), 2 (?), and 3 (?) in (c) 1957 are shown. The shift in the rising edge at different positions corresponds to the 1958 thickness variation in the deposited 28Si film. Measured 29Si isotopic ratios at 1959 locations 1, 2, and 3 are (149 ? 18) ? 10?6 mol/mol, (128 ? 14) ? 10?6 mol/mol, and 1960 (45 ? 2) ? 10?6 mol/mol, respectively. 1961 1962 the thickness nonuniformity of the deposited 28Si epilayer, i.e., the thickness of 1963 the 28Si epilayer at location 3 is greater than those of locations 1 and 2. Moreover, 1964 separate SIMS measurements on these isotopically enriched 28Si epilayers reveal that 100 1965 the films contain adventitious chemical impurities, namely, C, N, and O, with 1966 approximate atomic concentrations of 2 ? 1019 cm?3, 3 ? 1017 cm?3, and 3 ? 1967 1018 cm?3. However, the atomic concentrations of these chemical impurities on the 1968 handle wafer were below the SIMS detection limit (? 1016 cm?3). We believe that 1969 these chemical impurities were being introduced by the ion beam. 1970 1971 5.3 Magnetotransport Measurements 1972 1973 1974 The low field magnetotransport data of 28Si and natSi on the same sample are 1975 shown in Fig. 5.2. Panel (a) shows the drain current (top and bot end of the Hall bar 1976 as shown in Fig. 5.1(c)) vs gate voltage at T = 4K. The drain current is proportional to 1977 inversion charge and the velocity that the charge travels from source to drain and the 1978 gate voltage controls the amount of inversion charge that carriers the current. Three 1979 curves with different symbols (square, circle and triangle) show the corresponding 1980 source drain voltage and a threshold voltage (VG needed to turn on the device) is 1981 obtained at around 2 V. Panel (b) shows the extracted charge carrier mobility as a 1982 function of carrier density for both natSi (red square) and 28Si (blue circle) at T = 1.9 1983 K. We find that maximum mobilities at T = 1.9 K for 28Si and natSi are: ?28Si?=?(1740 ? 1984 2)?cm2/V.s at an electron density n of (2.7 ? 1012 ? 3 ? 108) cm?2 and ?natSi = (6040 ? 1985 3) cm2/V.s at an electron density of (1.2 ? 1012 ? 5 ? 108) cm?2. Charge carrier 1986 mobilities for these devices are within the typical range of mobilities for Si-MOS 1987 (Metal Oxide Semiconductor) devices fabricated using non-MBE (e.g., CVD) growth 1988 techniques [23, 152], the maximum mobility for a Si-MOS device to date being > 4 ? 1989 104 cm2/V.s [153]. In contrast, mobilities reported for Si-MOS devices fabricated on 101 1990 MBE grown Si range from 900 cm2/V.s to 1250 cm2/V.s [116, 154], likely due to the 1991 excess chemical impurities presented in the MBE film. 1992 1993 1994 1995 Figure 5.2: Magnetotranport data of the 28Si MOSFET. 1996 (a) the drain current vs gate voltage at T = 4 K. Three curves with different symbols 1997 shows the corresponding source drain voltage. (b) Charge carrier mobility as a 1998 function of carrier density for both natSi (red square) and 28Si (blue circle) at T = 1.9 1999 K. 2000 102 2001 2002 2003 Table VI. Macroscopic materials and electrical properties of natural abundance natSi, 2004 and isotopically enriched 28Si. 2005 2006 2007 2008 In order to estimate the percolation electron density np which refers to the critical 2009 density for conduction, we extrapolate the electron density as a function of gate 2010 voltage (as determined from Hall measurements) back to the threshold voltage (as 2011 determined from the channel current Isd vs Vg), i.e., np = ne(Vth). Using this method, 2012 we find percolation densities of (2.3 ? 2) ? 1011 cm?2 for natSi and (4.2 ? 2) ? 2013 1011 cm?2 for 28Si. Since the percolation density is a measure of the disordering of a 2014 system, the two times larger density in 28Si supports the fact that there are more 2015 impurity scatterings in the film than in natSi. A summary of these macroscopic 2016 materials and electrical properties for the on-chip natSi and 28Si is provided in Table 2017 VI. 2018 The magnetoresistance (Rxx) and the Hall resistance (Rxy) at 1.9 K for isotopically 2019 enriched 28Si and natural abundance Si are shown in Fig. 5.3 (a) and Fig. 5.3 (b), 2020 respectively. Both devices show well developed SdH oscillations in Rxx with 2021 accompanying plateaus in Rxy. SdH oscillations are oscillations of the resistivity 103 2022 parallel to the current flow in the edge states of a 2D electron gas when an external 2023 magnetic field is applied. They are related to the quantum-Hall effect and have a 2024 periodicity of 1/B. When a magnetic field is applied to the 2D electron gas, the 2025 electrons in the bulk perform circular motions. In the border region, the electrons 2026 circular motion is suppressed due to the scattering events occurred at the interface. 2027 These scattering events give those electrons a higher energy and the magnetic field 2028 causes the quantization of the energy band (Landau-level). With a higher magnetic 2029 field, the energy gap between the Landau-levels becomes larger. As the field 2030 increases, the highest Landau-level gets nearer to the Fermi energy and there will be 2031 states available for scattering in the bulk region. This is the cause of the peaks in the 2032 SdH oscillations. The slight asymmetry in Rxx in Fig. 5.3 (a) could be due to several 2033 reasons, e.g., magnetic impurities in the grown 28Si film or inhomogeneity of the 2034 magnetic field which might be a cause of the non-planar 2D electron gas [155, 156]. 2035 The Hall resistance shows nonidealities particularly in the natSi device [Fig. 5.3 (b)] 2036 where Rxy is nonmonotonic. These nonidealities could be due to scattering between 2037 discrete degenerate states at the tails due to level broadening [157, 158]. However, a 2038 detailed discussion of the asymmetry of Rxx and the flatness of the Hall plateaus is 2039 outside the scope of this article. We also see a lifting of the four-fold degeneracy 2040 at B > 5 T for natSi, which is likely due to the spin degree of freedom, but, at this time, 2041 we are unable to determine whether this is due to the spin or valley degree of 2042 freedom, due to the limitations in the experimental setup. 104 2043 2044 2045 Figure 5.3: The magnetoresistance Rxx and the Hall resistance Rxy vs B field. 2046 The resistances measured for the devices fabricated on (a) isotopically enriched 28Si 2047 epi-layer and (b) natural Si substrate are shown. For both devices, the corresponding 2048 filling factors (?) are shown at the minima of Shubnikov-de Hass oscillations. In 2049 contrast to the device on the isotopically enriched 28Si epi-layer, the device on natSi 2050 demonstrates spin-splitting for B > 3 T. Both devices are fabricated on the same Si 2051 chip; see main text for more information. The relative uncertainty associated 2052 with Rxx and Rxy is typically less than 0.1% and is mostly due to the uncertainty of the 2053 measured current. 2054 2055 Near zero magnetic field, both devices demonstrate a peak in the sample 2056 resistance; see Fig. 5.3. This increase in resistance near zero magnetic field is known 105 2057 as weak localization (WL). Weak localization is a quantum mechanical phenomenon 2058 that can be observed in two-dimensional (2D) electron systems at low temperatures 2059 where the phase coherence length (l?) is greater than the mean free path (l) [159, 2060 160]. Relative to the zero-field resistance, the weak-localization is larger for the 2061 device fabricated on isotopically enriched 28Si. 2062 To further investigate the WL behavior of these devices, we plot the change in 2063 conductivity ??xx as a function of magnetic field B applied perpendicular to the 2D 2064 electron system (see Fig. 5.4). The change in conductivity due to WL ??xx = ?xx(B) 2065 ? ?xx(B = 0), where ?xx = ?xx/(?2xx+?2xy). For nonzero B, the change in conductivity due 2066 to WL in a 2D electron system can be modeled by the Hikami-Larkin-Nagaoka 2067 (HLN) equation [161]: ?2 1 ? 1 ? ? ????(B) = ? ( 2 ) [? ( + 2 ) ? ? ( + 2 ) ? ?? ( )] (5.1) 2? ? 2 4???? 2 2?? ? 2?? 2068 where ? is the digamma function, l is the mean free path, l? is the phase coherence 2069 length that determines the magnitude of the effect, and ? is a constant close to unity, 2070 which comes from the scattering symmetry of the system [162]. In Fig. 5.4, the solid 2071 lines are the fits to experimental data (symbols) using the HLN equation. For these 2072 fits, we use the calculated values of l using the relation l = ?2??. Here, D is the 2073 diffusion coefficient defined as D = v2F?/2, where the Fermi 2074 velocity vF = ?kF/m* and ? is the elastic scattering time, also known as the transport 2075 lifetime, defined as ? = ?m*/e. The effective mass m* is defined as m*/m0 = 0.19, 2076 where m0 is the rest mass of an electron [163, 164]. The Fermi wavevector kF can be 2077 calculated for a 2D electron system in Si as k 1/2F = (4?n2D/gsgv) , where n2D, gs 2078 and gv are the charge carrier density, spin degeneracy and valley degeneracy, 106 2079 respectively. We leave ? and l? as the free fitting parameters, constraining the value 2080 of ? to be close to unity. From the fit-extracted values of l?, we calculate 1/??, where 2081 inelastic scattering time ? 2? = l ?/D. The fit derived values of 1/?? as a function of T are 2082 plotted in the inset of Fig. 5.4 for devices fabricated on isotopically enriched 28Si and 2083 natural abundance Si, respectively. The solid lines in the inset of Fig. 5.4 are the 2084 least-squares-fit to the data using the equation: 1 = ? + ?? + ??2 (5.2) ?? 2085 2086 2087 Figure 5.4: The change in conductivity (??xx) vs external magnetic field (B) for 2088 devices fabricated on 28Si (?) and natSi (?) measured at 3 K. 2089 Solid lines are the least-squares-fits to the HLN equation [Eq. (1)]. Estimated 2090 uncertainty for ??xx is < 0.3 %. Inset: The inelastic scattering rates (1/??) for 28Si 2091 and natSi vs the measurement temperature are shown. Here, the solid lines are the 2092 least-squares-fit to a quadratic equation; see main text for details. Error bars in the 2093 inset represent the fit uncertainty associated with the values extracted for 1/?? at each 2094 temperature. 2095 107 2096 The linear in the T term captures the scattering from impurities, and the quadratic 2097 in the T term is related to the electron-electron scattering [165]. Table VII. shows the 2098 parameters extracted from the least-squares-fit to the data, the fit uncertainties for 2099 both devices, and the adjusted R-square. For the natural abundance Si, the best fit is 2100 achieved when the linear term is set to zero, i.e., b = 0. Consequently, for natural 2101 abundance Si, the dominant scattering mechanism appears to be the electron-electron 2102 (long-range) scattering. In contrast, for isotopically enriched 28Si, the best fit is 2103 2104 Table VII. Parameters extracted from the least-squares-fits of Eq. (2) to the data in the 2105 inset of Fig. 5.4. 2106 2107 achieved with a significant linear in the T term. This large linear term implies that 2108 impurity (short-range) scattering is a significant contribution in 28Si. The temperature 2109 independent parameter a is similar (within the uncertainties) for both the devices 2110 indicating that the processes (e.g., interface roughness) contributing to a are likely the 2111 same. 2112 Line shape analysis of the SdH oscillations as a function of temperature is also 2113 used to investigate the underlying scattering mechanisms in 2D electron systems. The 2114 amplitude of the SdH oscillations can be written as ASdH = X(T)R0 exp(??/?c?q) [166, 2115 167], where R0 is the zero field resistance, X(T) = (2?2kBT/??c)/sinh(2?2kBT/??c) is 2116 the temperature damping factor, and ?c = eB/m* is the cyclotron frequency. 108 2117 Here, kB is Boltzmann?s constant and ?q is the single particle (quantum) lifetime [166- 2118 168]. To extract the amplitude of SdH oscillations, we first subtract a slow varying 2119 background (external disturbance, background dopant conductivity, measurement 2120 conditions, etc.) from Rxx [169] to isolate the oscillatory part of Rxx. The Rxx after 2121 background subtraction (?Rxx) is plotted against 1/B in Fig. 5.5 (a). Then, we extract 2122 the amplitude ASdH as schematically defined in Fig. 5.5 (a) at each minimum of 2123 ?Rxx and calculate ln(ASdH/X(T)). Fig. 5.5 (b) is a plot of ln(ASdH/X(T)) vs 1/B, also 2124 known as the ?Dingle plot? [166, 167] for the device fabricated on 28Si measured 2125 at T = 3 K. The approximately linear dependence of ln(ASdH/X(T)) on 1/B [see Fig. 5.5 2126 (b)] indicates a magnetic field independent quantum lifetime, ?q. In Fig. 5.5 (c), we 2127 plot the quantum lifetimes, ?q, for devices fabricated on 28Si and natSi extracted from a 2128 linear least-squares-fit to Dingle plots at each temperature. The calculated values of 2129 the transport lifetimes, where ? = ?m*/e, using the magnetotransport measurement at 2130 low magnetic fields for both devices, are also plotted in Fig. 5.5 (c). 2131 For the device fabricated on 28Si, the ratio of ?/?q ? 1, and for the device on natSi, 2132 the ratio of ?/?q ? 1.4. The transport lifetime ? is primarily affected by the large angle 2133 scattering events that cause a large momentum change, whereas ?q is affected by all 2134 the scattering events [170]. It can either be dominated by the background impurities, 2135 where the scattering ratio ?/?q is less than or equal to 10, or dominated by short-range 2136 isotropic scattering [170], where the ratio ? 1 when the scattering is, e.g., surface 2137 roughness scattering [171]. However, the thickness of the gate oxide for the devices 2138 reported here is ? 60 nm, which is too thick for a surface scattering effect. We 2139 therefore neglect the scattering due to remote interface roughness (i.e., the interface 109 2140 2141 2142 Figure 5.5: Quantum and transport lifetime extracted from the magnetotransport. 2143 (a) The background subtracted (see text) Rxx, i.e., ?Rxx, vs the inverse of the external 2144 magnetic field (1/B) for the 28Si device is shown. (b) A ?Dingle plot? of ln(ASdH/X(T)) 2145 vs 1/B. Error bars represent the uncertainty associated with extracting ASdH from the 2146 ?Rxx vs 1/B plot. (c) The single particle lifetimes, ?q, extracted from the Dingle plots 2147 and transport lifetimes, ?, at different temperatures for devices on 28Si and natSi. Error 2148 bars represent the uncertainty associated with calculating the values of ?q (?) using the 2149 Dingle plots (charge carrier mobilities) at each temperature. 2150 110 2151 between the gate oxide and the gate metal) as a dominant scattering mechanism for 2152 these devices [172]. Therefore, the ratio ?/?q implies that the charge carrier mobility is 2153 limited by the background impurity scattering. 2154 The analysis of the weak-localization, SdH oscillations, and low-field 2155 magnetotransport data indicates the shortest scattering length scale to be the elastic 2156 (transport) scattering length l calculated as ? 33 nm and ? 71 nm for 28Si and natSi, 2157 respectively. Capacitance voltage (CV) measurements of MOS capacitors fabricated 2158 on natural abundance silicon (data not shown) with gate oxides grown using similar 2159 conditions to the devices reported here reveal a fixed charge density of approximately 2160 3 ? 1010 cm?2 corresponding to the nearest neighbor distance of ? 58 nm. This nearest 2161 neighbor distance is in close agreement with the transport scattering length l. 2162 2163 5.4 Conclusion 2164 2165 2166 In conclusion, we have reported on the first low temperature electrical 2167 measurements of MBE grown isotopically enriched 28Si. For this report, we 2168 fabricated and characterized the low temperature magnetotransport of gated Hall bar 2169 devices fabricated on highly enriched 28Si. In comparison to control devices 2170 fabricated on float-zone grown, intrinsic, natural abundance Si on the same substrate, 2171 the charge carrier mobility on isotopically enriched 28Si is approximately a factor of 3 2172 lower. Nevertheless, the magnetotransport measurements of devices fabricated on 2173 isotopically enriched 28Si demonstrate strong manifestations of quantum effects. 2174 Based on the analysis of temperature dependence of the weak localization and SdH 2175 oscillations, we believe that the dominant scattering mechanism is short-range 111 2176 scattering (impurity scattering). We believe that adventitious chemical impurities 2177 detected in the 28Si epilayers act as the impurity scatters in the devices fabricated 2178 on 28Si. However, higher levels of adventitious chemical impurities detected in 2179 the 28Si epilayers are too high to be considered as isolated scattering centers since the 2180 nearest neighbor distance is considerably shorter than the scattering lengths extracted 2181 from the transport data. Furthermore, for these impurity levels, the dipolar 2182 interactions between randomly distributed electron spins associated with impurities 2183 and the central spin of a potential qubit are considered to be the dominant 2184 decoherence mechanism at high enrichment [147]. For the worst-case analysis, if all 2185 the N and O chemical impurities are considered as randomly distributed single 2186 electron spins, the influence of these dipolar interactions on the central spin could 2187 result in qubit coherence times poorer than high purity natural abundance Si. 2188 However, we are confident that the recent and planned improvements, as well as 2189 techniques for depleting impurities near the surfaces, will allow us to move forward 2190 and study the tension between chemical impurities and enrichment on quantum 2191 coherence. 2192 Next, we plan to fabricate quantum dot devices on control (natural abundance) 2193 and isotopically enriched 28Si to more rigorously assess the impact of purity and 2194 enrichment, e.g., charge offset drift, as the chemical purity of these MBE grown 28Si 2195 films is improved. Therefore, macroscopic transport and material characteristics of 2196 the devices reported here will serve as a benchmark for finding the correlations 2197 between macroscopic properties and the performance of future nanoscale devices, 112 2198 e.g., quantum dots, and lead to identifying qualifying metrics for ?quantum grade? 2199 silicon. 2200 This chapter is reproduced from Ref. [173] with permissions from all the co- 2201 authors. The authors acknowledge stimulating discussions with Michael Stewart, Neil 2202 Zimmerman, Roy Murray, Ryan Stein, Binhui Hu, and Peihao Huang. For the 2203 contribution of this work, I was responsible for the material preparation and growth of 2204 the 28Si thin films, SIMS data analysis and part of other analysis processes. The 2205 devices were fabricated, measured, and analyzed mostly by Dr. Aruna Ramanayaka 2206 and Dr. Joe Hagmann. 2207 2208 2209 113 2210 Chapter 6: Al Delta-doping on Si(100): Solving the 2211 Puzzle of Max 2D Density 2212 2213 The previous chapters discussed isotopically enriched 28Si, one of the two core 2214 materials that we are interested in when pursuing hybrid quantum computing. In the 2215 following chapters, we will be focusing on the second core material: Al delta layers. 2216 Unlike other delta-doped material systems that have been extensively studied, such as 2217 boron (B) and phosphorus (P) [77, 83, 174, 175], Al delta-doping in Si is a new 2218 material system where its material properties are largely unknown. To pursue a 2219 superconducting Al delta-doped Si, understanding the maximum number of atoms in 2220 the smallest possible distance (one atomic layer) is critical for maximizing the 3D 2221 density of this dopant. In this chapter, we will first introduce the previously studied 2222 results of Al atomic layer growth on Si(100). Then we will demonstrate our approach 2223 to study the absolute number density of one atomic layer of Al on Si(100) before 2224 cluster formation, using different techniques such as STM, SIMS and APT. The 2D 2225 density will be extracted and compared and the uncertainties associated with each of 2226 those techniques will be discussed. 2227 2228 2229 2230 2231 2232 2233 2234 114 2235 6.1 Introduction 2236 2237 2238 Si(100) surfaces have been studied extensively in the past decades because of 2239 their importance in semiconductor technology. The surface is reconstructed with 2240 basic 2 ? 1 dimer rows from the surface atoms. At low temperature (< 350 ?C for Al), 2241 the structure and growth of the metal layers depends strongly on this reconstructed 2242 surface [176]. Previous studies [177-180] using low energy electron diffraction 2243 (LEED) have demonstrated the formation of well-ordered structures of Al on Si(100) 2244 surface that is also coverage dependent. Several phases of Al have been found on the 2245 Si surface. Those studies indicated that the most common phases of Al as the 2246 coverage increases up to a full coverage or one atomic layer (or equivalently, 0.5 ML 2247 as commonly used in the literature) are: 2 ? 1, 2 ? 3 and 2 ? 2. Note that for Si(100), 2248 1 monolayer (ML) corresponds to a surface density of 6.8 ? 1014 cm-2. Therefore, it is 2249 suggested that Al are adatoms that form dimers on top of the Si(100) surface without 2250 disruption of the Si dimers. An orthogonal-dimer model has been proposed by Ide et 2251 al. [177] where the Al dimers are located between and oriented orthogonally to the Si 2252 dimers. Initially as Al atoms reach the Si(100) substrate, they adsorb onto the surface 2253 and form chains perpendicular to the Si dimer rows. As the coverage increases (from 2254 0 to 1 atomic layer), Al dimer rows run perpendicularly to the Si dimer rows and an 2255 intermediate phase of 2 ? 3 is formed when those dimer rows are 2a or 3a apart (a = 2256 3.84 ?). At full coverage (one atomic layer) of Al, a closely packed 2 ? 2 structure is 2257 formed by saturating all the dangling bonds on the Si surface [181]. 2258 2259 115 2260 2261 Figure 6.1: Al adatoms on Si(100) surface. 2262 (a) ? (e) possible structures of Al dimers on Si(100) surface using ab initio 2263 calculation. The bond length of the Al-Al, Al-Si and Si-Si are given in small numbers 2264 in ?. (e) and (f) show the STM images of the Al adsorbed Si(100) surface, taken at 2265 dual-bias condition. Al atoms are observed as two bean-shaped protrusions in 2266 negative bias and single bright protrusions in positive bias. (Panel a ? d are modified 2267 from [182]; panel e and f are modified from [181] with permissions) 2268 116 2269 The proposed structures were firstly studied by Nogami et al. using STM [183], 2270 which provided direct observations of the Al dimer chains and the transitions into 2 ? 2271 3 and 2 ? 2 phases. However, in contrast to the orthogonal-dimer model, Nogami et 2272 al. described a parallel-dimer model, where the Al dimers are parallel to the Si 2273 dimers. Follow on studies [176, 182, 184] based on total energy calculations revealed 2274 that the parallel-dimer model is more energetically favorable. Fig. 6.1 (a) to (d) show 2275 the schematic drawing of possible structures of an Al ad-dimer on the Si(100) surface. 2276 The black circles represent the Al atoms and the gray circles represent the Si atoms 2277 from the substrate. The total energies of the structures are given on the top with 2278 respect to the minimum, where the Al-dimer is parallel to the Si substrate dimers, as 2279 shown in structure (a) [182]. This model is further supported by other experimental 2280 techniques, such as a tensor LEED study [185] and an ion-scattering spectroscopy 2281 study [186]. However, the absence of atomically resolved STM makes it difficult to 2282 distinguish between those two models. Since then, higher resolution STM have been 2283 demonstrated and the details of the atomic structure have been studied with dual tip 2284 biases (filled state and empty state) [181, 187]. Ref. [181] described the STM 2285 topography of the Al structures on Si surface, as shown in Fig. 6.1 (e) and (f). In a 2286 positive sample (or equivalently, negative tip) bias condition (panel f), electrons 2287 tunnel from the tip into the empty state of the sample surface, double maxima of each 2288 Si dimer that reflect the symmetric properties of the antibonding state ?* [188] and Al 2289 dimers as bright oblong protrusions between the Si dimers can be seen (marked in 2290 blue circle). In a negative sample (or equivalently positive tip) bias condition (panel 2291 e), electrons tunnel out of the filled state of the sample surface to the tip, each 117 2292 protrusion observed in the positive bias is replaced with two bean-shaped protrusions 2293 located on the Si dimers (marked in blue circle) [181]. The reasons for the changes in 2294 the Al features were also described. For positive sample bias, the bright protrusions 2295 represent the local density of states (LOD) that consist mostly of the dangling bond 2296 states of Al dimers. The protrusion between the Si dimers are the Al-Al dimer bonds. 2297 For negative sample bias, the two bean-shaped protrusions represent the local density 2298 of occupied states around Al dimers, showing the location of the Al-Si backbond 2299 states [181]. 2300 The growth mechanism of the Al atoms on Si(100) surface with coverage above 2301 one full atomic layer (0.5 ML) is more complicated compared to the coverage below. 2302 Different results have been shown with somewhat contradictory conclusions. For 2303 example, one study showed that the 2 ? 2 structure persists at a coverage higher than 2304 one atomic layer [179] while the other showed that the 2 ? 2 surface is not simply 2305 covered by the clusters, but is disrupted due to embedment of the clusters (brighter 2306 objects shown in Fig. 6.3a) [181]. Despite the differences in the detailed surface 2307 structure, it is generally true that as the coverage exceeds one atomic layer, all the Si 2308 dangling bonds are saturated, and some clusters start to form on top of the Al 2 ? 2 2309 structures. In this work, we are focusing on the 2D delta layer growth, mostly with a 2310 coverage of ? one atomic layer. 2311 2312 2313 118 2314 2315 Figure 6.2: STM images of Al deposited on Si(100) surface with low coverage. 2316 The images are taken simultaneously under dual-bias. Si dimer rows can be seen 2317 clearly, with Si terraces perpendicular to each other. (a) Filled state image (+2 V, 100 2318 pA): an Al dimer chain is marked with blue circle, 5 bright protrusions are observed. 2319 (b) Empty state image (-2 V, 100 pA): the same area of the Al chain is marked. 5 dim 2320 protrusions are observed. The bean-shaped protrusions described in the literatures are 2321 not seen. (This image is taken from Dr. Hyun-soo Kim with permission) 2322 2323 Since our objective is to obtain a superconducting Al delta layer in Si, 2324 understanding the maximum 2D density of Al that we can put on Si(100) in order to 2325 reach the critical 3D density of the dopant is important. The strategy here is to: 1) 2326 reach a saturation density of Al dopant and 2) confine the dopant as good as possible 2327 by depositing a Si overgrowth layer on top of the delta layer. However, there are a 2328 few discrepancies between our observation and the previous studies. For instance, the 2329 literature studies seem to suggest that there are roughly 2 Al atoms on top of 4 Si, 2330 indicating a maximum 2D Al density of 3.4 ? 1014 cm-2, our STM did not reveal the 2331 same structure. Fig. 6.2 shows a set of STM images with Al deposited on Si(100) at 2332 very low coverage. The two images are taken simultaneously under dual-bias tip 2333 condition with a dimension of 20 nm ? 20 nm. The Si substrate was prepared in UHV 119 2334 with high temperature flashing, described earlier in Chapter 2. Si dimer rows can be 2335 seen clearly, with terraces perpendicular to each other. Panel (a) shows the filled state 2336 image (+2 V tip voltage, 100 pA). An Al dimer chain is marked with blue circle, 2337 where 5 bright protrusions are observed. This structure seen is similar to what was 2338 reported in the previous literature results. Panel (b) shows the empty state image (-2 2339 V tip voltage, 100 pA). The same area of the Al chain is marked as a comparison, 2340 where 5 dimmed protrusions are observed. The two bean-shaped protrusions 2341 described from the literatures are not seen. Instead, we are seeing single circular 2342 protrusions under both bias conditions. The reason that we saw a different feature 2343 could be due to potential different structures of Al on Si or from the tip effect. Since 2344 STM is a convolution of the LDOS of both the tip and the sample, atoms can be 2345 picked up by the tip and that might cause difference in resolution between the two 2346 bias conditions [189]. In addition, the Al protrusions seem to be located on top of the 2347 Si dimer rows instead of between the Si dimer rows, different compared to the 2348 configuration shown in Fig. 6.1. More interestingly, the first electrical measurement 2349 of this delta layer type showed that the carrier densities of the Al samples with similar 2350 doses are measured to be ? 1.4 ? 1014 cm-2 to 1.7 ? 1014 cm-2, very close to the density 2351 of single protrusions measured in STM. The discrepancies mentioned above either 2352 indicate that there is a different Al surface configuration on Si(100) or the dopant 2353 activation of our delta layer is limited. 2354 Given the differences between our STM, electrical measurements and the STM 2355 shown in previous studies, the question really simplifies to whether there are two Al 2356 atoms/protrusion or there is only one Al atom/protrusion. In the next section, we are 120 2357 going to study the maximum 2D number density of Al (for one atomic layer) that can 2358 be deposited on the Si(100) surface. Different technical approaches are demonstrated, 2359 which include STM, SIMS and APT. Since each sample has a small variation in 2360 dosing, the 2D density extracted from those techniques will be compared to the STM 2361 number density obtained at positive tip bias (filled states) for better consistency. 2362 2363 6.2 Measuring 2D Protrusion Density of Al on Si(100) using 2364 STM 2365 2366 Here, we investigate the Al surface saturation density using STM, with one 2367 atomic layer of Al on Si(100) surface before second layer formation. The details of 2368 the material growth processes for Al delta layer are introduced in Chapter 7, a brief 2369 summary is given here. We started with a high temperature flashing of the Si 2370 substrate in UHV condition as described in Chapter 2. The sample was ramped down 2371 from 800 ?C to 300 ?C and slowly cooled down to RT. After 15 mins waiting time, 2372 the sample was moved to the STM chamber for initial characterization. At this point, 2373 the sample would be at RT and it was then transferred to the Al source (Radak) for 2374 deposition. 2375 To estimate the 2D density of the Al atoms on Si under full coverage, we use a 2376 filled state image and count the number of bright protrusions in that area. An 2377 example of the counting procedure is shown in Fig. 6.3. Panel (a) shows a surface 2378 close to one atomic layer (full coverage) of Al deposited on Si(100) at room 2379 temperature (RT). The deposition rate is close to 1/3 ML per min. 2 ? 2 structures of 2380 Al are shown as the bright circular protrusions. Note that apart from the Al 121 2381 protrusions, there are two more important features in this image: vacancies (dark) and 2382 Al-Al clusters (larger white areas). When counting the total number of Al protrusions 2383 accurately, contributions from the vacancies and clusters must be taken into account. 2384 ImageJ with Image-based Tool for Counting Nuclei (ITCN) plugin was used to 2385 set the threshold and count the total number of Al features in the image. ITCN is a 2386 plugin developed by Thomas Kuo and Jiyun Byun at UC Santa Barbara [190]. The 2387 algorithm assumes blob-like nuclei with roughly convex local intensity distributions 2388 where the iso-level contour is approximately ellipsoidal and the nuclei are fitted by an 2389 inverted Laplacian of Gaussian filter [190, 191]. In the case of our images, ITCN 2390 works pretty well for features that are close together and yields better results when 2391 identifying Al features compared to the build-in functions of thresholding and 2392 watershed processing. 2393 The standard procedure of the protrusion counting is described here. The image 2394 from panel (a) was converted to 8-bit greyscale before using ITCN. The protrusion 2395 detection was performed with the following parameters: width of protrusions is 2396 selected between 7 - 10 pixels and minimum distance between 3.5 - 5 pixels, 2397 depending on the quality of the final detection. This agrees with the pixel size based 2398 on the area density taken from 4 Si atoms (assuming one Al protrusion takes the same 2399 area of 4 Si atoms). For all samples analyzed here, a constant image scale of 50 nm ? 2400 50 nm (566 ? 566 pixels) was used for consistency. An example of the image after 2401 detection is shown in Fig. 6.3 (b), where each of the red dot represents one Al 2402 protrusion. A total number of 3153 protrusions was detected in panel (b). Note that 2403 this number includes the counting from the larger clusters that appeared as brighter 122 2404 2405 Figure 6.3: Counting Al 2D density using STM and ImageJ. 2406 (a) is a filled state image of the surface of Al deposited on Si(100) at RT, close to full 2407 coverage. (b) shows the auto-counting of the Al protrusions using ImageJ. There are 2408 3153 protrusions in this image. Note that the total number of protrusions excluded the 2409 contribution from the vacancies but included the clusters. 123 2410 white areas. Each cluster feature was counted as either one or two protrusions 2411 depending on the size. However, this is still an underestimate of the number of Al 2412 atoms been deposited on the Si surface since there are clearly more than one or two 2413 Al atoms in each of the clusters. 2414 To address this problem, an estimation for the number of Al atoms in these 2415 clusters is needed. By using the fill down function of the ImageJ, we can mark the 2416 cluster areas with larger height values and calculate the percentage of these areas 2417 compared to the total area of the image. For example, in Fig. 6.3 (a), 1.51 % of the 2418 total area corresponds to the larger cluster features. This is 37.75 nm2 in the 50 nm ? 2419 50 nm image scale. Here we assume that the Al-Al clusters have a bulk Al crystal 2420 structure (FCC). The lattice constant of Al is 0.405 nm, the bulk density is 2.7 g/cm3 2421 and the molar mass is 26.98 g/mol. In 2D following the (100) direction, the density of 2422 Al atoms in these clusters is therefore 1.22 ? 1015 cm-2. For a 1.51 % cluster area, 2423 which is equivalent to an area of 37.75 nm2, it corresponds to 460 Al atoms. This is 2424 the estimated number of Al atoms from clusters, which should be added to the total 2425 number of protrusions as shown in Fig. 6.3 (b). Now, since we are not sure if each Al 2426 protrusion shown in the STM represents one or two Al atoms, we will use 460 Al 2427 atoms as the first try and compare that to SIMS extracted density (in next section). 2428 The total number of protrusions including the clusters is therefore 3153 + 460 = 3613 2429 in this 50 nm ? 50 nm region. This corresponds to a 2D protrusion number density of 2430 1.45 ? 1014 cm-2. If the final ratio of SIMS/STM is closer to 1, which represents there 2431 are 1 Al atom per STM protrusion, then 460 Al atoms coming from the clusters is 2432 valid. The 2D density of Al atoms should be 1.45 ? 1014 cm-2. However, if the 124 2433 2434 Figure 6.4: Al 2D density counting with larger area of vacancies and fewer clusters. 2435 (a) is a filled state image of the surface of Al deposited on Si(100) at RT, close to full 2436 coverage. (b) shows the auto-counting of the Al protrusions using ImageJ. There are 2437 3415 protrusions in this image. More vacancies are shown in this sample, this 2438 counting method is able to exclude the vacancies accurately. 2439 2440 125 2441 2442 SIMS/STM ratio is closer to 2, which represents 2 Al atoms per protrusion, then we 2443 need to re-calibrate by adding only 230 (half of 460) Al protrusions from the clusters 2444 to the total density. And the corrected number of protrusions will be 3153 + 230 = 2445 3383. This corresponds to a 2D protrusion number density of 1.35 ? 1014 cm-2. That 2446 means, the 2D density of Al atoms will be 2.66 ? 1014 cm-2. Another Al sample that 2447 has a higher areal density of vacancies but fewer clusters was scanned and counted 2448 using the same method, as shown in Fig. 6.4. The area percentage of vacancies in this 2449 image is ? 6.63 %. Using this ITCN method, the vacancy areas were accurately 2450 avoided and not included in the final number of protrusions. The image in Fig. 6.4 has 2451 a total number of protrusions of 3415, which corresponds to a 2D protrusion density 2452 of 1.46 ? 1014 cm-2 and 1.41 ? 1014 cm-2, respectively. A total of 10 samples have 2453 been analyzed, a summary of the STM counted protrusion density and the 2454 corresponding uncertainties is shown in Table. VIII. 2455 The uncertainty of this method falls in two parts. First is the miss counted Al 2456 protrusions that the software did not pick up due to the relatively weaker contrast and 2457 the miss counted vacancies. However, the estimated number of miss counts due to 2458 these two uncertainties in Fig. 6.3 is small, with a value of < 10 (< 0.3 %), which is 2459 negligible. The second type of uncertainty is from the STM scale bar. We can 2460 calibrate the scale bar by comparing it to the known Si dimer row width, which is 2461 measured to be 0.76 nm from the literature. Although this calibration depends largely 2462 on the image quality during substrate scanning (before Al deposition), the average 2463 uncertainty is estimated to be ? 7 % (5 % in each direction, corresponds to ? 7 % in 2464 two-dimension). 126 2465 2466 Table VIII. A summary of the STM protrusion density count. The cluster area 2467 percentage, STM protrusion density including the contribution from surface clusters 2468 under two different assumptions are shown. The estimated uncertainty is 2469 approximately 7 %. 2470 Cluster area Protrusion density Protrusion density percentage assuming 1 protrusion assuming 1 protrusion = = 1 atom (cm-2) 2 atoms (cm-2) 14 2.59 % 1.51 ? 1014 1.35 ? 10 14 1.60 % 1.38 ? 1014 1.28 ? 10 14 1.51 % 1.45 ? 1014 1.35 ? 10 14 0.79 % 1.45 ? 1014 1.40 ? 10 0.88 % 1.47 ? 1014 1.42 ? 10 14 0.17 % 1.52 ? 1014 1.50 ? 10 14 0.82 % 1.37 ? 1014 1.32 ? 1014 0.38 % 1.37 ? 1014 1.33 ? 1014 0.89 % 1.45 ? 1014 1.40 ? 1014 0.80 % 1.46 ? 1014 1.41 ? 1014 2471 2472 6.3 Measuring 2D Atom Density of Al using SIMS 2473 2474 One method of measuring the 2D density of Al delta layer in Si is using SIMS. 2475 SIMS is a powerful tool that can be used to access the profile of the delta-doped 2476 layers accurately. The 3D peak density can be extracted, with relatively good 2477 sensitivity down to < 5 nm/decade and the 2D density can be calculated by integrating 2478 the area of the delta layer peak. Although extensive studies have been done with 2479 boron (B) and phosphorus (P) delta layers using SIMS [83, 192], none has been done 2480 with Al delta layers. To obtain the optimum measurement conditions (that could 2481 result in a sharpest delta layer peak) for Al delta layers, the SIMS parameters in terms 2482 of the ion beam energy and sputter beam angle are studied. This is because the choice 127 2483 of primary ion beam energy will affect the depth resolution, secondary ion yield and 2484 the sputter rate of the measurement. For example, depth resolution degrades as the ion 2485 energy increases and 2486 2487 Figure 6.5: SIMS depth profiles with different ion energies and sputter angles. 2488 A range of primary ion energies are studied from 500 eV to 5000 eV and 2489 bombardment angles are chosen from 0 ? to 90 ? relative to the surface normal. The 2490 optimum condition in terms of peak height and FWHM is 1keV with 60 ? angle, 2491 shown in solid black line. A peak density of 6.58 ? 1020 cm-3 and a FWHM of 3.26 2492 nm is obtained. There is more Al tailing toward the surface (3.5 nm/decades) than 2493 toward the substrate (2.3 nm/decades). The precision of this measurement 2494 (repeatability and reproducibility) is dependent on the impurity matrix combination 2495 and the analysis tool. 2496 2497 sputtering yield increase (then saturates) as the ion energy increases. To extract the 2498 highest peak density and sharpest delta layer width, a range of primary ion energies 2499 are studied from 500 eV to 5000 eV and bombardment angles are chosen from 0 ? to 128 2500 90 ? relative to the surface normal. The sample measured was a delta layer sample 2501 with one atomic layer of Al sandwiched between the Si substrate and an electron- 2502 beam evaporated Si capping layer deposited at RT. Unlike other delta layer samples 2503 with different thermal anneals, no thermal treatment has been done on this sample 2504 after substrate flashing, this is to minimize the Al movement. A summary of the depth 2505 profiles of this Al delta layer is shown in Fig. 6.5 (a) using O2 bombardment. The y- 2506 axis is the Al concentration and x-axis is the depth from the surface. The insert shows 2507 the extracted delta layer peak density and full width half maximum (FWHM) for each 2508 parameter set, using the Origin built in integration function. This integration tool 2509 performs numerical integration on the data plot using the trapezoidal rule, where the 2510 area under the curve is evaluated by dividing the total area into small trapezoids. As a 2511 result, 1 keV ion energy with 60 ? sputter angle (black solid line) gives the highest 3D 2512 density and lowest FWHM. The Al delta layer is located at 60 nm from the surface, 2513 with a peak 3D density of 6.58 ? 1020 cm-3 and a FWHM of 3.26 nm. Note that the 2514 FWHM extracted here is larger than the real delta layer thickness, as it is a mixing of 2515 both delta layer roughness and instrumental effects. The integrated 2D density is 2.64 2516 ? 1014 cm-2. The STM counting of this sample has a protrusion density of 1.46 ? 1014 2517 cm-2. This results in a SIMS/STM ratio of 1.81, indicating that there is ? 2 Al atoms 2518 in each protrusion seen in the STM. Since the atom number is discretized (either an 2519 integer of 1 or 2), the extracted ratio of 1.81 means that the probability of having 2 2520 atoms/protrusion is much higher compared to the probability of having only 1 2521 atom/protrusion. A more detailed comparison is described later. The data point 2522 density of this measurement is 5 nm-1. One thing to note is that the SIMS profile 129 2523 shows more Al tailing toward the surface (3.5 nm/decades) than toward the substrate 2524 (2.3 nm/decades). This indicates that although there is no thermal anneal, the Al still 2525 migrated a little toward the surface since we generally expect more SIMS depth 2526 resolution artifact on the substrate side than the surface side. The reason for this is 2527 due to the forward recoil of the sputtered ions (or recoil mixing) which is a forward 2528 momentum component of the sputtering and will push some atoms deeper into the 2529 sample. Or it is possible that Al-Al clusters are formed at the interface and is causing 2530 a broadening in the peak toward the Si capping layer. 2531 With the optimum SIMS, i.e. condition that generates the sharpest peak, now we 2532 look at our Al delta layer devices. An example of the SIMS depth profile of an Al 2533 delta layer device at full coverage (one atomic layer) is presented in Fig. 6.6. The 2534 insert in (c) is a schematic of the sample structure. Mesa-etched Hall bar devices are 2535 fabricated on top of the sample, as shown in (d). Panel (a) is the SIMS data from the 2536 device without background subtraction, where the Al delta layer peak (located at 60 2537 nm from the surface) can be seen. As shown in the figure, there appears to be a high 2538 concentration region closer to the surface (0 ? 40 nm). For the moment, we are going 2539 to assume that the tail is not dominated by the segregation of the Al delta layer 2540 (although there must be some contribution) and that is coming predominantly from 2541 the surface contamination during the transport out of the UHV environment (from 2542 vacuum chamber to EAG) and from the Al metal contact of the Hall bar device that is 2543 fabricated on top of the delta layer sample (Al metal dust on the sample surface). To 2544 obtain a better estimation of the delta layer peak, the surface tail is fitted to an 130 2545 2546 Figure 6.6: SIMS depth profile of an Al delta-doped sample with 100% Al dosing at 1 2547 keV. 2548 The SIMS measurement is performed on this sample after mesa-etched Hall bar 2549 device fabrication. (a) shows the raw data, where a delta layer peak is located at about 2550 60 nm from the surface. A high concentration surface tail is observed, from the 2551 surface to ? 40 nm down. This is mostly from the surface contamination during 2552 transport and the Al metal contact on the surface during device fabrication. (b) an 2553 exponential decay fit to the surface tail. The background noise level is also included. 2554 (c) The delta layer peak after subtracting the surface tail effect and background noise 2555 (subtracting a constant average). A peak density of 2.10 ? 1020 cm-3 and a FWHM of 2556 10.1 nm is extracted. The integrated 2D density is 2.62 ? 1014 cm-2. (d) Optical 2557 microscope image of an Al delta layer Hall bar device, the SIMS crater is focused on 2558 one of the Van der paw (VDP) device, marked in red. 2559 2560 exponential decay function and subtracted from the raw data, as shown in panel (b). 2561 The Al delta layer peak without surface tail is shown in panel (c). A 3D peak density 2562 of 2.10 ? 1020 cm-3 is extracted, with a FWHM of 10.1 nm. The integrated 2D density 2563 of this delta layer peak is 2.62 ? 1014 cm-2. The uncertainty in the 2D density before 131 2564 and after the surface tail subtraction for this sample is 20.2 %, which is the largest 2565 among all samples we characterized by SIMS. However, this sample is a special case, 2566 where the same analysis has been done on multiple samples, and the uncertainty for 9 2567 other samples only range from 0.04 % to 2.5 %. 2568 It is observed that the delta layer peak is broadened compared to the sample 2569 shown in Fig. 6.5, and it is not symmetric, with left side of the peak shape flatter than 2570 the right side. By comparing to the profile from the sample without any thermal 2571 treatment, it seems likely that there is some thermal redistribution of the Al atoms and 2572 more Al atoms have been migrated toward the surface of the Si capping layer than 2573 into the Si substrate. This is not surprising because multiple thermal processes have 2574 been done to this sample, including the incorporation anneal at 550 ?C for 1 min and 2575 the final solid phase epitaxial (SPE) anneal at 550 ?C for 10 mins. Al can diffuse 2576 along the grain boundaries much faster than through the gains. As a result, under the 2577 same SIMS measurement conditions, the peak density of the thermally annealed 2578 sample (2.10 ? 1020 cm-3) is approximately 1/3 of that for the sample without thermal 2579 anneal (6.58 ? 1020 cm-3). Another reason for peak broadening is due to the SIMS 2580 measurement, where forward recoil of the sputtered ions is inevitable, especially for 2581 delta layer samples with FWHM < 10 nm. Note that the direction of this effect is 2582 towards the substrate side, which is opposite to the segregation process (toward the 2583 surface). Both effects will reduce the 3D peak density and increase the FWHM of the 2584 delta layer peak. Furthermore, since most of the area on this sample was etched away 2585 during device fabrication, the remaining areas of the Hall bar devices are usually too 132 2586 small compared to the diameter of the primary beam, results in a reduction in 2587 detection sensitivity. 2588 2589 Figure 6.7: 1st iteration of SIMS to STM number density ratio. 2590 10 Samples with slightly different Al doses are measured using SIMS. Error bars for 2591 both SIMS measurements and STM counts are shown. The average SIMS/STM 2592 density ratio is 1.69 ? 0.96, closest to an integer of 2. This indicates that it is most 2593 likely to have 2 atoms per protrusion at positive tip bias. 2594 2595 One important note here is that there is a discrepancy between the 2D density 2596 number extracted here and the actual Al dosing on the sample. This is because we are 2597 assuming no Al segregated onto the surface. However, this is not always the case, 2598 especially for the samples that went through multiple thermal treatments. Some Al 2599 migration to the surface has been observed, as will be introduced in Chapter 7. 2600 Therefore, the SIMS extracted density is an underestimated value of the actual Al 133 2601 atoms that have been deposited on the surface and is expected to be smaller than the 2602 actual maximum 2D density of one atomic layer of Al on Si(100). 2603 A set of 10 samples has been measured using SIMS, and the 2D densities are 2604 extracted using the method described above. Since the estimated Al doses may vary 2605 slightly from sample to sample and from STM tip to STM tip, the number density is 2606 compared by taking the ratio between the two techniques. For example, a SIMS/STM 2607 ratio of 2 means that there are two Al atoms (most likely dimers due to energy 2608 calculation) in each of the circular protrusion observed in the positive bias STM 2609 image. In another word, there are 2 Al atoms sitting on top of 4 Si atoms and the max 2610 surface density of this dopant is therefore 50 % of the Si(100) surface density. As 2611 introduced in the last section, since we are not sure about the exact number of atoms 2612 in one protrusion yet (there should be either one or two atoms/protrusion), we are 2613 going to treat the contribution calculated from surface clusters in an one to one ratio 2614 first and add that to the total protrusion count (see Table. VIII middle column). Fig. 2615 6.7 shows a summary plot of the SIMS/STM number density ratio versus STM 2616 density under this assumption and we this is the 1st iteration of SIMS/STM ratio. On 2617 average, a density ratio of 1.69 ? 0.96 is obtained. This means that for each bright 2618 protrusion shown at positive tip bias condition (filled state), there are roughly 1.7 Al 2619 atoms. Since the atom number is always an integer, the probability of having 2 Al 2620 atoms in each protrusion is much bigger than 1, indicating the max 2D density of Al 2621 on Si(100) is 3.4 ? 1014 cm-2. 134 2622 2623 2624 Figure 6.8: 2nd iteration of SIMS to STM number density ratio. 2625 The contribution of clusters on protrusion density is corrected by assuming 1 2626 protrusion = 2 Al atoms. The average SIMS/STM density ratio is 1.77 ? 0.88, closest 2627 to an integer of 2. This verifies that there are 2 atoms per protrusion at positive tip 2628 bias. 2629 2630 From Fig. 6.7, we know that it is more likely to have 2 Al atoms per protrusions, 2631 therefore we need to correct the assumption made in the 1st iteration that each of the 2632 estimated cluster atoms on the surface contributes to 1 protrusion. Instead, the number 2633 of protrusions from the clusters should be divided by two. For example, a 1 % cluster 2634 area contributes to 305 Al atoms (calculated in the last section), which is equivalent 2635 to 153 protrusions. As seen in the third column of Table. VIII, the corrected STM 2636 density is smaller than in the 1st iteration, this will give a slightly higher ratio of 135 2637 SIMS/STM. A corrected version of the SIMS/STM ratio plot is shown in Fig. 6.8, this 2638 is the 2nd iteration. On average, a density ratio of 1.77 ? 0.88 is obtained. This verifies 2639 that for each bright protrusion shown at positive tip bias condition (filled state), there 2640 are 2 Al atoms. This again indicates that the max 2D density of Al on Si(100) is 3.4 ? 2641 1014 cm-2. 2642 The error bars are estimated for both SIMS measurements and for STM density 2643 counts. For SIMS, two uncertainties are taken into account: tool calibration and 2644 surface tail. As will be introduced in the next paragraph, the tool calibration error 2645 from EAG (a commercial lab that did SIMS measurements for our Al samples) is in 2646 the range of 10 ? 15 %, an average value of 12.5 % is used in the analysis. The 2647 uncertainties for the surface tail subtraction is summarized in Table IX. The total 2648 uncertainty is a quadrature sum of the two. 2649 2650 2651 Table IX. A summary of the SIMS density count and uncertainties. The SIMS density 2652 value shown here is after surface tail subtraction. The total uncertainty is the 2653 quadrature sum of the tool calibration and surface tail. 2654 SIMS density Uncertainty in surface tail Total (cm-2) uncertainty 2.62 ? 1014 20.2 % 23.8% 2.55 ? 1014 0.4 % 12.5% 2.00 ? 1014 2.5 % 12.7% 2.52 ? 1014 0.4 % 12.5% 2.43 ? 1014 2.9 % 12.8% 2.24 ? 1014 1.3 % 12.6% 2.47 ? 1014 0.3 % 12.5% 2.34 ? 1014 0.5 % 12.5% 2.56 ? 1014 0.4 % 12.5% 2.64 ? 1014 0.0 % 12.5% 2655 136 2656 The reasons for a non-integer number of the density ratio can be complicated. One 2657 of the possibilities is that there are some systematic errors present in the SIMS 2658 measurements that lower the total number of counts. An ultimate weak link for SIMS 2659 is the calibration of the measurements. The calibration relies primarily on NIST 2660 Standard Reference Materials - As, B and P in the case of our measurements done by 2661 EAG. Outside this small subset of elements, the calibration is relying on ion 2662 implanter dosimetry. Al as a dopant is not well studied and as a result, the calibration 2663 error for Al is much more significant compared to other dopants (the standard error 2664 for B is 3.5 %, P is 1.65 % and As is 0.4 %). This is because instead of using a known 2665 reference material, the integrated signal under the measured implant distribution is set 2666 equal to the dose of the implanter. However, the ion implanters have relatively large 2667 uncertainties. In general, the uncertainty in sensitivity calibration using Al as a dopant 2668 can be as large as 30 %. By comparing several ion-implanted standards of Al in Si 2669 and average the results, a ?consensus? sensitivity with lower uncertainty can be 2670 obtained, but still in the range of 10 ? 15 %. Another possible reason is the subsurface 2671 Al atoms that are not seen during the STM scan. It is also likely that some Al atoms 2672 migrated towards the surface due to the thermal treatments and were subtracted from 2673 the surface tail during analysis, as we described before. 2674 In conclusion, the obtained SIMS/STM ratio of 1.77 ? 0.88 indicates that it is 2675 most likely to have 2 Al atoms adsorbed on top of 4 Si atoms in the form of 2 ? 2 2676 dimer structures, in accord with the literature predictions that were described in 2677 section 6.1. The most likely maximum 2D density of Al on Si(100) at one atomic 2678 layer coverage is therefore 3.4 ? 1014 cm-2, neglecting the presence of dimer 137 2679 vacancies on the Si(100) surface. In the next section, we will further explore this 2680 density using another powerful technique: the atom probe tomography. 2681 2682 6.4 Measuring 2D Atom Density of Al using Atom Probe 2683 Tomography (APT) 2684 2685 2686 The APT data presented in this section is acquired in collaboration with Dr. Karen 2687 A. DeRocher and Dr. F. Meisenkothen. 2688 APT is a powerful microscopy technique that can be used to identify and quantify 2689 individual chemical species in a fast and accurate way. The high spatial resolution 2690 and three-dimensional characterization capabilities make it a good complement to 2691 other microscopy techniques such as SIMS and tunneling electron microscopy 2692 (TEM). The mechanism for APT is briefly described here. The APT uses a time-of- 2693 flight mass spectrometer with a point projection microscope that is capable of atomic 2694 scale imaging [193]. When combined with the position sensing, a full three- 2695 dimensional reconstruction of the sample species can be obtained. The sample is 2696 usually prepared in advance with focused ion beam (FIB) into needle-shaped tips that 2697 are nanometer in size. By applying a high voltage between the specimen and the local 2698 electrode, a high electric field of ~1010 V/m is applied to the apex of the specimen tip, 2699 usually at cryogenic temperatures. The atoms will be evaporated from the apex as 2700 ions and accelerated toward the imaging camera. When laser or high voltage pulses 2701 are used during evaporation, atoms are evaporated from the surface by field effect and 2702 project onto a Position Sensitive Detector (PSD). The flight time of each ion can be 2703 measured, and the corresponding mass-to-charge ratio can be calculated. The position 138 2704 at which the ions hit the detector is used to determine the original position on the 2705 specimen apex and the sequence of evaporation events is used to provide depth 2706 information [194]. The combination of those collected data allows 3D imaging of the 2707 element distribution with atomic resolution. 2708 In our case, an Al delta layer sample that has no thermal treatment was studied, 2709 this is the same sample used in Fig. 6.5. Prior to the FIB milling, a thin capping layer 2710 of cobalt (Co) with a thickness of 75 nm was deposited. In the FIB, a protective Pt 2711 film was deposited on a 30 ?m ? 2 ?m region of the sample surface to protect it from 2712 Ga beam damage. The sample was then tilted to 22 degrees relative to the ion beam 2713 and an angled cut was made on one side of the protective Pt. The sample was rotated 2714 180 degrees in azimuth so the same kind of cut could be made on the opposite side. 2715 By repeating this cutting step until these angled cuts have met below the sample and 2716 what is left is a bridge with a triangular cross section. The sample is then un-tilted so 2717 that it is now perpendicular to the electron beam, and one side of the sample is cut 2718 free from the bulk. A tungsten needle inside the FIB chamber was then welded with 2719 Pt to the side that was already cut free. The other side of the sample was then cut free 2720 from the bulk and the entire 30 ?m ? 2 ?m sample was lifted out of the bulk on the W 2721 needle and transferred over to a microtip array. The free end of the sample was 2722 positioned on top of the first Si post of the microtip array, welded on with Pt, and cut 2723 from the remainder of the sample. Each tip was then sharpened using the Ga ion beam 2724 and annular mill patterns with progressively smaller outer and inner diameters until 2725 the tip radius was around 50 nm. Finally, a low kV ion bombardment step was 139 2726 performed to remove Ga ions implanted during tip sharpening, and the entire microtip 2727 array was moved into the atom probe [195]. 2728 The APT was measured at a 30 K specimen temperature with a pulse frequency of 2729 333 to 500 kHz and laser energy of 15 pJ. Fig. 6.9 (a) shows the collected atom probe 2730 data of the delta layer using tip 1 (R37_03481). The cone represents the apex of the 2731 tip and the distribution of the chemical species (Si, Al, Co and SixOy) are shown in 2732 four different colors. The atom probe reconstruction of the Al delta layer is 2733 constrained using the SIMS depth profile, where the delta layer is located at ? 60 nm 2734 from the surface. The left cone shows the distribution of the Al delta layer in Si and 2735 the right cone shows the distribution of the Co. It seems some Co has penetrated into 2736 the Si layer. Fig. 6.9 (b) is the reconstructed concentration profiles of each chemical 2737 species as a function of depth. In addition to the Co (red) and O (green), an Al delta 2738 layer peak is observed (blue). Each concentration profile is obtained by choosing a 2739 cylindrical region at the middle area of Fig. 6.9 (a) and counting the number of atoms 2740 of each element in 1 nm slices (in z-direction) of the cylinder. 2741 140 2742 2743 2744 2745 Figure 6.9: APT of the Al delta layer without thermal treatment. 2746 (a) The cone represents the apex of the tip and the distribution of the chemical species 2747 (Si, Al, Co and SixOy) are shown. Co is penetrated into the capping layer and some Si 2748 has been oxidized during the evaporation. (b) the concentration profile of each 2749 species. A 3D density of 6.34 ? 1020 cm-3 and a 2D density of 3.46 ? 1014 cm-2 is 2750 obtained for Al. 2751 141 2752 From Fig. 6.9 (b), the peak density of this Al delta layer is 6.34 ? 1020 cm-3 with a 2753 FWHM of 5.24 nm. The integrated 2D density is calculated to be (3.46 ? 0.69) ? 1014 2754 cm-2. The STM density count for this sample after Al deposition is 1.46 ? 1014 cm-2, 2755 which gives an APT/STM density ratio of 2.37 ? 0.50. Since we are counting the Al 2756 protrusions in STM assuming a 2D layer, there might be Al atoms in the lower (Al 2757 atoms going in the substrate) or higher (Al atoms further up in the clusters) plane that 2758 are not taken into account. That means the ratio extracted here might be an over- 2759 estimation. However, since we do not have a good way to evaluate the quantitative 2760 contribution of this effect, it would not be included in the uncertainty calculation. The 2761 uncertainty of this measurement is approximately 20 %, mainly comes from the 2762 reconstruction of the Al delta layer thickness from the atom probe. The extracted 2763 value means that each of the protrusion that we see in the STM filled state image 2764 represents 2.37 Al atoms. Of course, the atom number of each protrusion is an 2765 integer, indicating that most likely there are 2 Al atoms in each protrusion or the max 2766 2D density of Al on Si(100) is 3.4 ? 1014 cm-2, in accord with the density measured 2767 by SIMS. Similarly, the APT extracted 2D density is also a non-integer number that is 2768 close but not exactly equal to 2. This difference might be due to the reconstruction of 2769 the Al profile in APT. The reconstruction of the concentration profile was done by 2770 selecting an analysis region along the long axis of the tip with a cylinder that is ? 20 2771 nm in diameter. In fact, Fig. 6.9 (a) showed an Al delta layer that is uneven in 2772 thickness, where the middle blue area is thicker compared to the edges of the tip. This 2773 uneven thickness of the delta layer is either an artifact or a consequence of solid 2774 migration caused by laser heating of this specimen. It could also be the strain effect 142 2775 from the excess Co diffused into the Si. Since the data was collected by an analysis 2776 region located closer to the middle of the tip, an overestimate of the 2D density is 2777 possible. 2778 2779 6.5 Conclusions 2780 2781 2782 In this chapter, we have reviewed the previous results on growing atomic layers of Al 2783 on Si(100) surface and studied the max 2D number density of Al dopant that can be 2784 grown on this surface, using various techniques. STM was used to determine the 2785 dosing of our Al atomic layer until full coverage or one atomic layer. Number 2786 densities were counted under positive tip condition. SIMS and APT were used to 2787 measure the total number of Al dopant atoms remained in the delta layer sample. The 2788 extracted 2D densities are then compared to the STM protrusion densities to minimize 2789 the variation in Al doses. As a result, an average SIMS/STM density ratio of 1.77 ? 2790 0.88 and APT/STM ratio of 2.37 ? 0.50 is obtained, respectively. The mean ratio 2791 from the two measurements is therefore 2.07 ? 1.11. This indicates that for each 2792 protrusion observed in the filled state STM image, there are 2 Al atoms. This 2793 extracted density ratio confirmed the literature results that Al dimers are formed on 2794 Si(100) surface at low temperature. The maximum 2D density of Al that can be 2795 reached on Si(100) surface for one atomic layer is therefore 3.4 ? 1014 cm-2, half of 2796 the Si(100) surface density. We believe this fills the gap for the missing information 2797 that is needed to confirm the Al atomic layer structure on Si(100) and provides help 2798 on reaching the critical density needed for superconducting transition using Al as a 143 2799 dopant. In the next chapter, we will compare this 2D density value to our 2800 magnetotransport measurements using Hall bar devices and explore the relation 2801 between Al doses, dopant activation and delta layer conduction. 2802 2803 2804 2805 2806 2807 2808 2809 2810 2811 2812 2813 2814 2815 2816 2817 2818 2819 144 2820 Chapter 7: Al Delta-doping on Si(100): Material 2821 Growth and Characterization 2822 2823 7.1 Introduction 2824 2825 As stated in Chapter 1, the main goal of this project is to develop a 2826 superconducting Al delta layer in 28Si. From the last chapter, we verified that the 2827 maximum achievable 2D density of Al on Si is 3.4 ? 1014 cm-2 and the highest 3D 2828 density of our delta layer film is ? 6 ? 1020 cm-3 (1.2 at. %), which is still lower than 2829 the predicted critical density needed for superconducting transition (> 2 at. %). In 2830 order to reach this high enough 3D density, the 3D confinement of this dopant 2831 material needs to be improved. In this chapter, we will perform studies on three major 2832 process steps during material synthesis and explore the possibility of 2833 superconductivity using this Al delta-doped layer in Si. 2834 In our previous work [86], we have successfully demonstrated the ability to grow 2835 a Si-Al-Si heterostructure that is electrically conducting at low temperature. Here?s a 2836 summary of the previous results. The growth method for this first-generation Al delta 2837 layer is summarized in Fig. 7.1. As a starting point, intrinsic, float-zone Si(100) 2838 substrate was flash annealed at high temperature under UHV condition in the 2839 deposition chamber, as described in Chapter 2, under sample preparation. After 2840 flashing, the sample was ramped down from 800 ?C to 300 ?C then slowly cooled 2841 down to RT. The sample is then transferred to the STM chamber after 15 mins 145 2842 2843 2844 Figure 7.1: STM images of the surface after each growth step of the first-generation 2845 Al delta layer. 2846 The schematics for each of the growth steps are included. (a) STM image showing the 2847 prepared surface of Si(100) after high temperature flashing in UHV. (b) After full 2848 coverage (100% dose) of Al deposited on top of Si substrate. Some vacancies and 2849 brighter Al clusters can be seen. The estimated Al protrusion density is (1.5 ? 0.2) ? 2850 1014 cm-2. (c) surface after incorporation anneal at 550 ?C for 1 min. Some ejected Si 2851 island (as brighter streaks) can be seen. (d) After 60 nm of Si overgrowth at room 2852 temperature and 550 ?C anneal for 10 min for re-crystallization. (Those images are 2853 modified from Ref. [76] with permission) 2854 2855 interval and scanned. Fig. 7.1 (a) shows a typical surface after sample preparation, 2856 where 2 ? 1 reconstructed dimer rows and Si terraces perpendicular to each other can 2857 be seen. The defect density is very small (< 5 %). After scanning, the sample is 2858 transferred back to the Al deposition source (Radak) in deposition chamber and Al is 2859 deposited without substrate heating. Although there is no sample heating, there might 2860 be some radiation heat from the Radak source that is placed below the sample, but we 2861 don?t have an accurate measurement of the temperature at this moment. A constant 146 2862 deposition rate of Al (1/3 ML/min) is used on most samples to reduce deviation from 2863 this radiation heat. 2864 Fig. 7.1 (b) shows the surface after close to full coverage of Al onto the Si(100) 2865 surface. We refer to this as one atomic layer of Al or 100 % dose since it covers the 2866 whole Si substrate. The estimated Al protrusion density from STM is approximately 2867 (1.5 ? 0.2) ? 1014 cm-2, under positive tip bias condition. This corresponds to a 2D 2868 dosing density of ? 3.0 ? 1014 cm-2. After that, the sample will be heated up to 550 ?C 2869 for 1 min. This is known as an incorporation anneal, which allows the Al atoms to 2870 substitute into the Si lattice site and eject Si atoms that form islands at the surface 2871 [196, 197]. Fig. 7.1 (c) shows those elongated Si islands and dark lines that represent 2872 incorporated Al, with the Si terraces still visible. The final step is the Si overgrowth, 2873 where a 60 nm Si capping layer is grown on top of the Al delta layer. The silicon is 2874 grown at room temperature using an electron-beam evaporation source. The Si 2875 capping layer is then annealed at 550 ?C for 10 mins, which served as re- 2876 crystallization and dopant activation steps. As a result, a reconstructed Si surface with 2877 similar quality to the starting substrate is formed, as shown in Fig. 7.1 (d). 2878 The sample is then transported out of the UHV chamber and used for device 2879 fabrication. Mesa-etched Hall bar devices are fabricated on top of it. The details of 2880 the device fabrication process and the principle of Hall measurement are described in 2881 Chapter 2. Fig. 7.2 (a) is a schematic of the mesa-etched Hall bar device. The light 2882 blue areas are the metal contact pads. A DC current ISD is applied from the top to the 2883 bottom electrode and the magnetoresistance Rxx is measured along the current 2884 direction with Vxx. The Hall voltage Vxy is measured between the two electrodes 147 2885 2886 Figure 7.2: Electrical properties of our previously reported Al delta layer devices. 2887 (a) A schematic of the Hall bar device and measurement circuit. (b) The sheet 2888 resistance per square (R ) as a function of temperature. (c) Hall resistance (Rxy) vs 2889 external magnetic field B at 2 K. From the slope, a 2D carrier density of 1.39 ? 1014 2890 cm-2 and a mobility of 20 cm2/V.s are extracted. (d) Magnetoresistance Rxx as a 2891 function of B field. Anti-weak localization behavior has been observed. (This is taken 2892 from Ref. [86] with permission) 2893 2894 perpendicularly. An external magnetic field is applied out of the plane, normal to the 2895 Hall bar. Fig. 7.2 (b) shows the resistance per square (R ) as a function of 2896 temperature, where R is defined as the sheet resistance divided by the number of 2897 squares between the two electrodes measured (Vxx). The data points plotted in red (T 148 2898 > 3 K) were measured in a closed cycle refrigerator, while the data points plotted in 2899 purple (< 1K) were measured in a dilution refrigerator with base temperature down to 2900 10 mK. As shown in (b), R increases rapidly when T decreases to around 30 K, then 2901 slowly levels off at lower temperature. This is mostly due to the freeze out of the 2902 substrate carriers and delta layer is dominating the conduction at T < 30 K. No 2903 superconductivity is observed in this sample. Fig. 7.2 (c) shows the Hall resistance 2904 Rxy as a function of external field B. The positive slope of this curve indicates that the 2905 majority charge carriers are holes. From the slope, a 2D carrier density of 1.39 ? 1014 2906 cm-2 and a mobility of 20 cm2/V.s is extracted. The mobility value of this Al delta 2907 layer is comparable to other hole-doped systems at similar density, like B [198]. Note 2908 that the mobility values for the delta layer samples are usually lower compared to the 2909 Si MOSFET. In a delta layer system, the mobilities are typically in the range of 10 ? 2910 200 cm2/V.s [199]. However, in Si-MOS devices, peak mobilities in the range of 2911 thousands [200-202] or even > 104 cm2/V.s [153] are measured. The main reason is 2912 because the confinement potentials are defined differently in two systems. The delta 2913 layer is confined by the delta function potential well while the Si-MOS is defined by 2914 the sinusoidal function of the Si Bloch states. Furthermore, at low temperature range, 2915 since the delta layer carriers are confined to a dopant plane by strong confining 2916 electric fields, the mobility is limited by the charged Coulomb scattering from the 2917 ionized dopants. For Si-MOS devices, the surface roughness scattering is usually the 2918 dominating factor [203]. Fig. 7.2 (d) is the magnetoresistance vs magnetic field, 2919 where at low B field, it demonstrates parabolic behavior of the 2D conducting 149 2920 channel [204]. At higher B field, Rxx deviates from parabolic to linear and this linear 2921 behavior can be due to the polycrystallinity or topological effects [205-207]. 2922 Let us now compare the measured 2D carrier density to the 2D dosing density of 2923 Al on Si(100). From the last chapter using different techniques, we know that the max 2924 2D density for a full coverage of Al delta layer on Si(100) is most likely to be 3.4 ? 2925 1014 cm-2. However, this value is 2.4 times larger compared to the carrier density 2926 measured by Hall, which indicates that the dopant activation of this Al delta layer is 2927 only 41 %. Or equivalently, only 41 % of the dopants were contributing to the 2928 electrical conduction. This is quite an interesting phenomenon because in other delta 2929 layer systems such as B and P, a dopant activation efficiency close to 100 % is 2930 achievable [80, 83]. Possible reasons for a limited dopant activation could be due to 2931 electrically inactive cluster formation, excess dopants forming dopant-pair defects, 2932 some Al carriers fall below metal-insulator-transition (MIT) due to dopant diffusion 2933 or segregation, or even opposite polarity charge carriers from contamination during 2934 growth. Although there is no direct evidence connecting the 2D density to the 2935 superconducting transition observed in silicon, it is generally believed that increasing 2936 the active 2D carrier density would be beneficial [192] and a better 2D conduction of 2937 the delta layer would facilitate other device applications. 2938 2939 7.2 Effects of Different Growth Methods 2940 2941 2942 To pursue superconductivity and understand the material properties of this new Al 2943 delta layer system, we will be focusing on the following parts: 1) study the correlation 150 2944 between each growth methods to carrier density and dopant activation and 2) explore 2945 the possibilities to improve 3D confinement of this dopant. In the following sections, 2946 we will modify and explore our material growth methods in 4 different ways to study 2947 the effect of each growth steps. This includes: 1) incorporation anneal; 2) solid phase 2948 epitaxy (SPE) or molecular beam epitaxy (MBE) for Si capping layer; 3) locking 2949 layer (LL) and 4) different Al doses. For each growth method, STM will be used to 2950 characterize the surface properties and magnetotransport measurements will be 2951 performed using Hall bar devices to characterize the electrical properties of this 2952 material. 2953 2954 7.2.1 Effects of the Incorporation Anneal 2955 2956 2957 In other dopant systems, such as B, Sb and P delta-doped Si, incorporation anneal 2958 is a critical step for dopant activation [208-210]. The annealing process provides 2959 enough energy for the dopant species to substitute into the silicon lattice sites and 2960 become electrically conductive. In this section, we will explore the effects of 2961 incorporation anneal on surface topography and dopant activation in our Al delta 2962 layer samples. 2963 The first two steps for delta layer growth are the same as introduced in the 2964 beginning of this chapter: prepare the substrate by UHV flash anneal and deposit 2965 thermally evaporated Al onto the Si(100) surface. For 100 % dose (full coverage or 2966 one atomic layer), three different heat treatments were studied: no anneal, as well as 1 2967 minute and 10 minutes incorporation anneal times at 550 ?C. The no anneal and 10 2968 minutes anneal treatments were repeated for 200 % Al dose. Fig. 7.3 shows the STM 151 2969 2970 2971 Figure 7.3: STM images of the surface with different incorporation annealing times. 2972 The images are taken at the same tip bias conditions: +2 V, 110 pA demanded. (a) No 2973 anneal with 100 % of Al dose (one atomic layer) on Si (100) substrate. Circular bright 2974 protrusions of Al (dimer) can be seen. (b) After 1 minute anneal with 100 % of Al 2975 dose. Dark lines (possibly incorporated Al) and brighter elongated streaks are 2976 observed. Those streaks are most likely the ejected Si from the lattice that formed 2977 islands on the surface. (c) After 10 minutes anneal with 100 % of Al dose. Similar 2978 features and structural sizes are observed compared to (b). This indicates that 1 2979 minute anneal is having the same effect compared to 10 minutes anneal. (d) After 10 2980 minutes anneal with 200 % Al dose. The structure is very different compared to (b) 2981 and (c). Closely packed, periodic arrays with two widths are seen. Further arrays are 2982 deposited in parallel on top of the gap between two underneath arrays. 2983 2984 images of the surface after different incorporation anneal times with the two doses 2985 described above. Fig. 7.3 (a) is a Si(100) surface after 100 % Al dose with no (0 min) 152 2986 incorporation anneal, scanned using a +2 V tip bias and 110 pA demanded current. 2987 This is similar to Fig. 7.1 (b) where Al 2 ? 2 structures are covering the Si terraces. 2988 Fig. 7.3 (b) and (c) are the surfaces with the same dose (100 %) after incorporation 2989 anneal for 1 minute and 10 minutes, respectively. Elongated streaks of silicon islands 2990 formed from ejected Si atoms and dark lines of incorporated Al can be seen in both 2991 figures. The feature sizes are also very similar. Considering the difference in contrast 2992 and tip conditions, we can say that Al with 10 mins anneal displays comparable 2993 surface topography compared to 1 minute anneal. And any further anneal at the same 2994 temperature does not change the surface structures. However, if the Al dose is 2995 increased to 200 %, the surface structure changes dramatically after annealing, as 2996 shown in Fig. 7.3 (d). Panel (d) shows the incorporated Al surface after 10 minutes 2997 anneal, using the same tip bias and current setpoint. Unlike (b) and (c), closely 2998 packed, periodic arrays are seen in (d). This is quite surprising because based on the 2999 Al-Si phase diagram, Al solubility limit in Si is very low. We would expect Al to 3000 form clusters on top of Si surface instead of these well-organized arrays following the 3001 underlying Si dimer row and terrace structures. There appears to be two array types, 3002 one with single circular protrusions and one with double protrusions binding together. 3003 The measured width of these arrays under STM are ? 1.0 nm (marked with green 3004 lines) and 2.0 nm (marked with blue lines), respectively. Some arrays with brighter 3005 color (marked with white arrow) are also seen, with growing direction parallel to the 3006 underneath arrays. Those arrays seem to follow the direction of the Si terraces. 3007 Next, let us compare the effects on the electrical properties from different Al 3008 incorporation anneal processes. Fig. 7.4 shows the magnetotransport measurements of 153 3009 3010 Figure 7.4: Electrical measurements of the Al delta layer samples with and without 3011 550 ?C 1 min incorporation anneal. 3012 The measurements were taken at 4 K. Same substrate and device fabrication steps 3013 were used. (a) shows the Hall measurement with incorporation anneal. A carrier 3014 density ? 1.50 ? 1014 cm-2 and a mobility of 10 cm2/V.s is extracted. (b) shows the 3015 Hall measurement without incorporation anneal, with a carrier density ? 1.41 ? 1014 3016 cm-2 and a mobility of 16.5 cm2/V.s. Repeat samples and measurements have been 3017 done, all showed similar results, indicating that incorporation anneal (at least as a 3018 separate step) is not necessary for dopant activation. 3019 154 3020 two samples, one with 1 min incorporation anneal and one without. Other processing 3021 conditions such as the substrate type, dosing (100%), annealing time and temperature 3022 and Si overgrowth (SPE) are kept being the same. Both samples were measured in a 3023 closed cycle refrigerator with base temperature of about 4.5 K. Fig. 7.4 (a) shows the 3024 Hall measurement with 550 ?C incorporation anneal. A carrier density ? 1.50 ? 1014 3025 cm-2 and a mobility of 10 cm2/V.s is extracted. Fig. 7.4 (b) shows the Hall 3026 measurement without 550 ?C incorporation anneal, with a carrier density ? 1.41 ? 3027 1014 cm-2 and a mobility of 16.5 cm2/V.s. Multiple samples with the same growth 3028 methods were measured, all showed similar carrier density, i.e. approximately 1.4 ? 3029 1014 cm-2 to 1.5 ? 1014 cm-2. Considering possible slight differences in sample 3030 substrate, Al dosing and wire bonds, we can conclude that there is essentially no 3031 difference in carrier density with and without incorporation anneal. However, the R sq 3032 values of the two samples are different, resulting in different mobility values. This 3033 might indicate that there are other differences in the processing steps or with/without 3034 this incorporation step is having different effects on scattering of the carriers. In 3035 general, the incorporation anneal, as a separate step, does not seem to change Al 3036 dopant activation efficiency. It is likely that other growth processes, such as the final 3037 SPE anneal, served as the dopant activation of this Al delta layer. Since our focus is 3038 to reach a high enough 3D density, with or without this incorporation step can go in 3039 both directions. This is because although thermal budget is reduced when ignoring the 3040 incorporation, an incorporation step might be able to lock down the dopants into Si 3041 lattice positions and prevents further diffusion or segregation. 3042 155 3043 7.2.2 Solid Phase Epitaxy (SPE) or Molecular Beam Epitaxy (MBE) 3044 3045 3046 In the previous section, we have found that with a SPE grown Si capping layer, an 3047 incorporation anneal does not affect the carrier density of the Al sample and the 3048 incorporation step seems be included in the final SPE overgrowth. In this section, we 3049 will discuss and compare the two methods of Si overgrowth: SPE and MBE as an 3050 effort to improve the 3D confinement of the Al delta layer by suppressing the 3051 segregation process and reduce the thermal budget. 3052 SPE is an important processing step in the semiconductor community [211]. It is a 3053 crystallization process that allows atoms to rearrange their bonding configurations 3054 and transfer from a metastable amorphous phase to a crystalline phase [212]. When 3055 an amorphous material is heated, atoms in amorphous phase will reorder at the 3056 crystalline-amorphous (c-a) interface, using the starting substrate as a template. It can 3057 aid the dopant activation above the solid solubility limit and recover from damage 3058 after processes such as ion implantation, with a relatively low thermal budget. 3059 MBE is another important process for growing thin films with epitaxial quality. In 3060 this process, beams of atoms in UHV are incident on a heated substrate (for most of 3061 the case) and the arriving atoms form a crystalline layer in registry with the substrate 3062 [213]. The beams are usually produced by evaporation or sublimation using an ultra- 3063 pure crucible. Since our goal is to maximize the carrier density while minimizing the 3064 dopant movement, MBE growth of the capping layer is expected to have several 3065 advantages over SPE growth. One of the advantages of MBE is the very low thermal 3066 budget, where epitaxial Si can be grown at temperatures from 300 ? 350 ?C with a 3067 deposition rate of ? 0.4 nm/min [78]. Another expected advantage of MBE over SPE 156 3068 is that the diffusion mechanism is greatly suppressed in crystalline Si than in 3069 amorphous Si, where the diffusion is mediated by the dangling-bonds [214]. The 3070 reduction in defect density with MBE growth also decreases the chance of defect- 3071 enhanced diffusion processes [77, 215]. As a result, B delta layers with extremely 3072 high 3D density has been achieved using low-temperature MBE, with n = 1 ? 1022s 3073 cm-3 or 20 at. % [83, 216], even higher than the delta-doped layer using gas 3074 immersion laser doping (ns = 2.8 ? 1021 cm-3) [71]. 3075 3076 3077 Figure 7.5: STM images of the deposited Si capping layer on different starting 3078 surfaces. 3079 (a) a test sample using the e-gun Si source deposited at 350 ?C. 4 nm of Si has been 3080 deposited on Si substrate with a deposition rate of 0.2 nm/min. 3D epitaxial island 3081 growth with Si dimer rows and terraces can be seen. (b) 20 nm of Si using the same 3082 Si source, deposited on top of a Al delta layer at 325 ?C, with a rate of 0.12 nm/min. 3083 Polycrystalline Si instead of monocrystalline has been observed. 3084 3085 The SPE overgrowth on our Al delta layer sample has been introduced in section 3086 7.1: a polycrystalline Si layer is grown at room temperature, followed by a 550 ?C 3087 anneal for 10 mins. The Si surface after annealing usually has similar epitaxial quality 3088 (in terms of defect density and terrace size) compared to the starting substrate. For 157 3089 MBE overgrowth, the same e-gun Si source was used. The substrate was heated up to 3090 350 ?C. A test sample with 4 nm of Si overgrowth layer was deposited on a Si 3091 substrate and is shown in Fig. 7.5 (a). The deposition rate was 0.2 nm/min. 3D islands 3092 with clear Si dimer rows were seen, indicating the epitaxial quality of the grown layer 3093 using our Si source. However, when trying to grow MBE Si over an Al delta layer 3094 with the same parameters, the deposited surfaces were always polycrystalline. For 3095 example, in Fig. 7.5 (b), a 20 nm thick Si capping layer was grown on top of a Al 3096 layer at 325 ?C with a rate of 0.12 nm/min, well below the threshold of epitaxial 3097 thickness and growth rate (< 0.4 ? 0.6 nm/min) at this temperature [82, 119, 217]. 3098 One possible reason for a polycrystalline Si overgrowth may be due to the fact that 3099 epitaxial growth requires a starting surface (as a template) that is monocrystalline. 3100 The Al-Si structure formed after incorporation anneal is likely in a meta-stable state 3101 with cluster-like structure instead of crystalline structures, deviating from the required 3102 crystalline template. Interdiffusion between the heteroepitaxial Al-Si interface might 3103 be another possible explanation, where interdiffusion has been reported for Al and Si 3104 at the temperature range of 400 ? 500 ?C despite the small solubility of Si into Al (0.4 3105 % at 400 ?C) and the non-existing solubility of Al into Si below the eutectic 3106 temperature of 577 ?C [218]. 3107 Additional efforts have been carried out to pursue MBE growth: for example, 3108 grow the Si capping layer at 350 ?C with an additional thermal anneal at 550 ?C for 3109 10 mins at the end to help for recrystallization. Fig. 7.6 (a) shows the deposited 3110 surface after final annealing. Although Si dimer rows and terraces can be seen, 3111 indicating the epitaxial quality of the deposited Si layer, high density of Al chains and 158 3112 clusters are also present on the surface. Fig. 7.6 (c) is a SIMS depth profile of the 3113 same sample, where two Al peaks can be observed. One is the original delta layer 3114 peak, buried at a depth of 30 nm from the surface. A higher density peak is 3115 3116 3117 3118 Figure 7.6: Comparison between MBE and SPE grown Al delta layer samples. 3119 (a) shows the STM images after Si overgrowth at 350 ?C and thermal anneal at 550 3120 ?C for 10 mins. The Si layer is epitaxial with visible Si dimer rows and terraces, but 3121 excess Al chains and clusters are also observed on the surface. (b) shows a SIMS 3122 depth profile of the same sample. A high-density surface peak along with the delta 3123 layer peak is observed, most likely due to the combination of surface segregation and 3124 Al contamination from the Hall device. (c) shows the STM image after SPE 3125 overgrowth with 550 ?C anneal. (d) shows a SIMS depth profile of the SPE grown 3126 sample, only surface tail but no surface peak observed. 3127 159 3128 observed at < 5 nm, closer to the Si surface. Since this is the sample with Hall bar 3129 devices on top, the peak at the surface might be a combination of both the surface 3130 contamination from the metal contact and the migrated Al observed from the STM 3131 images. Fig. 7.6 (c) and (d) are measured from a SPE overgrown sample, as a 3132 comparison to the MBE overgrowth. This sample has the exact same processing steps 3133 compared to the MBE case (also has surface tail). Panel (c) shows an epitaxial surface 3134 of Si after SPE overgrowth and (d) shows the SIMS profile of this SPE grown 3135 sample. The Al delta layer can be observed at ? 50 nm with a surface tail, but no 3136 surface peak of Al is seen. This indicates that during MBE overgrowth with 550 ?C 3137 final anneal, some Al migrated to the surface, results in a worse dopant confinement 3138 compared to the SPE overgrowth method. 3139 From the results described above, we can conclude that for Al delta layers at full 3140 coverage, SPE growth method is preferred over MBE method. This is due to: 1) the 3141 MBE growth method results in polycrystalline Si overgrowth instead of epitaxial 3142 overgrowth, probably due to the lack of crystalline template to start with; 2) evidence 3143 showed that there are more Al atoms migrated to the surface (Fig. 7.6 a, c) compared 3144 to the SPE growth method, indicating a worse dopant confinement. We believe this is 3145 largely due to the formation of an Al-Si meta-stable state whose coexistence has a 3146 lower free energy compared to the Si crystalline phase alone. And this broken 3147 symmetry allows the Al to segregate up to the surface during MBE growth process, 3148 probably through the defects and interstitial sites that are created during the epitaxial 3149 growth. 3150 160 3151 7.2.3 Effects of the Locking Layers 3152 3153 3154 In B and P delta-doped systems, a locking layer (LL), a thin (monolayers thick) 3155 room temperature grown silicon layer, is helpful for suppressing dopant segregation 3156 and diffusion into the Si capping layer, resulting in a higher 3D dopant confinement 3157 and electrical activation [79, 192, 219, 220]. A locking layer might be helpful for 3158 achieving better dopant confinement. In this section, we will explore the effects of a 3159 locking layer on the Al delta layer samples. 3160 Fig. 7.7 (a) shows a STM image after 1.6 nm of LL growth on Al delta layer at 3161 full coverage. The LL was deposited at room temperature, with a deposition rate of 3162 0.138 nm/min. The deposited LL surface looks very similar to the ones reported in the 3163 P delta layer system [79, 220], where grains of polycrystalline Si can be observed. 3164 The LL was then annealed at 550 ?C for 1 min to recrystallize the surface. However, 3165 unlike what was reported in P delta layer system [220], where the locking layer 3166 recrystallized and formed epitaxial Si dimers and terraces, the LL on Al delta layer 3167 surface showed clear evidence of Al migration (bright Al chains and circular 3168 protrusions that look like Al clusters) on top of the reconstructed Si dimers and 3169 terraces, as shown in Fig. 7.7 (b). Note that the samples shown in Fig. 7.7 (a) and (b) 3170 had the same processing steps. This might be an indication of the Al segregation 3171 towards the growth front of the Si. 3172 LL combined with Si overgrowth with elevated temperature was also 3173 investigated. Fig. 7.7 (c) shows the surface of a Si capping layer grown at 325 ?C on 3174 top of the LL after the process of Fig. 7.7 (a). Evidence for polycrystalline Si is 3175 observed, which is not surprising since the starting surface was not monocrystalline. 161 3176 The topography of the surface of this poly-Si after thermal annealing at 550 ?C for 10 3177 mins is also shown in Fig. 7.7 (d). The resulting surface topography is very similar to 3178 what was presented in Fig. 7.6, where excess Al were seen on top of the epitaxial Si 3179 surface. 3180 3181 Figure 7.7: STM images of the deposited Si surfaces with LL. 3182 (a) 1.6 nm of LL grown at RT with a rate of 0.138 nm/min. Polycrystalline surface is 3183 seen with a similar quality compared to other LL growth methods. (b) LL after 550 3184 ?C 1 min to recrystallize the surface. Epitaxial Si is observed, but with high density of 3185 Al chains and clusters on the top. (c) Si overgrowth on top of the LL at 325 ?C, 3186 however, poly-Si is seen instead of epitaxial Si. (d) The overgrown Si followed by a 3187 final 550 ?C 10 mins anneal. Reconstructed Si is observed, but with excess Al on the 3188 surface. 3189 162 3190 In summary, there are three outcomes: 1) Epitaxial Si overgrowth layer was not 3191 grown successfully using MBE method due to a lack of epitaxial starting surface. In 3192 B and P systems, the LL was usually annealed and recrystallized for a good starting 3193 surface for capping layer. However, Fig.7.7 (b) showed that an epitaxial LL surface 3194 after annealing is not possible due to Al migration. 2) directly grow Si at elevated 3195 temperature on RT LL, but it showed poly-Si (Fig.7.7 c). 3) grow a RT LL with MBE 3196 Si then anneal at 550C, but excess Al were shown on the surface (Fig.7.7 d). As a 3197 result, the LL method on Al delta layer was not successful. Chains and clusters of 3198 excess Al are observed on the surface of this LL after thermal annealing (which is a 3199 typically step to recrystallize the LL). However, without this thermal annealing step, 3200 the surface of the MBE overgrown Si becomes polycrystalline, due to the absence of 3201 an epitaxial surface to start with. A final SPE anneal after MBE overgrowth also 3202 experiences Al segregation toward the surface. Further efforts (e.g. higher Si 3203 deposition rate and lower annealing T) are needed to develop a better LL growth on 3204 Al samples. 3205 3206 7.2.4 Effects of Al Doses on Dopant Activation 3207 3208 3209 In Chapter 6, we studied the atom density of Al on Si(100) surface using various 3210 techniques. The results showed that the 2D density at full coverage is most likely 3.4 3211 ? 1014 cm-2. However, when compared to our Hall measurements, the extracted 3212 carrier densities of Al samples are approximately 1.5 ? 1014 cm-2, which corresponds 163 3213 to a dopant activation of only ? 44 %. In this section, we will explore and discuss the 3214 factors that might affect dopant activation of the Al delta layer. 3215 The first obvious factor is the incorporation anneal. However, as we have 3216 discussed in the previous section, the incorporation anneal does not change the carrier 3217 density of our delta layer sample (but changes the mobility. The second factor that 3218 might improve the dopant activation is the use of a locking layer (LL) as it suppresses 3219 dopant segregation and preserved the 3D confinement. However, in Al case, the LL 3220 process that we tried does not prevent the dopant from segregating onto the Si 3221 surface. A better approach is yet to be developed. 3222 In this section, we will study the correlation between different Al doses (amount 3223 of Al that we put down) and dopant activation. 8 Al delta layer samples with 3 3224 different doses were prepared and fabricated into Hall bar devices: 50 % dose (half 3225 atomic layer), 100 % dose (one atomic layer) and 200 % dose (two atomic layer). The 3226 100 % dose was determined by topographical imaging of the result in STM after Al 3227 deposition, while the other two doses were calibrated based on the deposition rate 3228 used for 100 % dose. All samples were deposited using the SPE method, while some 3229 of them employed an incorporation anneal step and some of them did not. The STM 3230 images of the surface after Al deposition at 50 % and 200 % doses are shown in Fig. 3231 7.8 (a) and (b), respectively. For the 50 % dose, both the Al chains and the underlying 3232 Si dimer rows can be seen. For the 200 % dose, the Si surface is completely covered 3233 with 2 ? 2 Al dimer structures before forming clusters. After that, some clusters are 3234 formed on top of the adsorbed Al atoms. These Al adatoms tend to wet the Si 164 3235 substrate first before forming larger Al-Al clusters. Thee clusters appear as larger 3236 bright islands in the image. 3237 Transport measurements have been done in a closed cycle refrigerator at 3238 temperatures from 4 ? 10 K. A summary plot of the Al carrier density measured at 3239 low temperature vs Al dosing is shown in Fig. 7.8 (c). Samples with incorporation 3240 anneal are marked as blue triangles and samples without incorporation anneal are 3241 marked in black circles. As seen in Fig. 7.8, the carrier density increases non-linearly 3242 against dosing. The carrier density increases rapidly from 50 % dose to 100 % dose, 3243 then slowly saturates at 200 % dose. A logarithmic function (red solid line) has been 3244 used to fit this data. The dopant activation efficiency as a function of Al doses is 3245 plotted in Fig. 7.8 (d). As the carrier density was doubled from 100 % to 200 % dose, 3246 the carrier density was only increased by 30 %, resulting in a decrease in activation 3247 efficiency from ? 48 % to 26 %. The maximum activation is at 100 % dose, ranging 3248 from 41 % to 48 %. 165 3249 3250 Figure 7.8: Effects of different Al doses on surface topography and dopant activation. 3251 (a) 50 % Al dose (half coverage of Al on Si surface). Al chains can be seen on top of 3252 the Si dimers and terraces. (b) 200 % Al dose. Si substrate is completely covered with 3253 Al 2 ? 2 dimer structures, with the formation of some Al clusters on top (shown as 3254 bright islands). (c) A summary plot of the carrier density vs Al dose. A non-linear 3255 increase in carrier density is observed, with a saturation at about 1.8 ? 1014 cm-2. (d) 3256 Dopant activation vs Al doses. The activation efficiency is having a maximum value 3257 of 48 % at 100 % dose. 3258 3259 We can conclude that under the current growth methods, there seems to be a cap 3260 in Al dopant activation efficiency at < 50 %. One possible reason for the cap in 3261 activation efficiency of this Al delta layer might be that a meta-stable state of Al-Si 166 3262 has been formed during the thermal annealing of this dopant. For example, as shown 3263 in Fig. 7.3 (d), Al tends to form closely packed periodic arrays that are most likely 3264 Al-Si clusters, containing multiple Al atoms and Si atoms. It is possible that only part 3265 of the Al atoms has been substituted into the Si lattice and contributed to electrical 3266 conduction, while part of the Al atoms was bonded in those cluster forms that is 3267 electrically inactive. Another reason might be due to the incomplete confinement of 3268 the delta layer in the z-direction. Diffusion along the grain boundary (which is 3269 expected to be faster than through the grain) or segregation of the dopants during 3270 thermal activation either at the incorporation anneal or the SPE anneal stage can be 3271 significant. For higher doses, such as 200 % dose, it is also possible that the excess Al 3272 atoms form Al-Al dopant pairs (since there are more Al dopants in the nearest- 3273 neighbor lattice sites) that can act as de-activation precipitates, like in the case of B 3274 and P delta layers [80, 192, 221]. 3275 3276 7.2.5 Conclusions and Future Expectations 3277 3278 In this chapter so far, we discussed the effects of different material growth 3279 methods on electrical conduction (carrier density and dopant activation) and explored 3280 the possibility of improving the dopant confinement in the Si-Al-Si heterostructure. A 3281 summary plot is shown in Fig. 7.9 for the variations in growth methods for Al delta 3282 layer samples studied in this work. We start with a clean Si substrate processed in 167 3283 3284 3285 Figure 7.9: Summary of the variations in growth methods for Al delta layer synthesis. 3286 Three different major processing steps were studied: Al doses, dopant activation and 3287 Si (capping layer) encapsulation. The Si-Al-Si heterostructures were turned into Hall 3288 bar devices and characterized at low temperature. 3289 3290 UHV condition. Three different major processing steps during delta layer growth 3291 were studied: Al doses, dopant activation and Si (capping layer) encapsulation. The 3292 delta layer samples were then turned into Hall bar devices and characterized in low 3293 temperature cryostat. The summary of the electrical measurements is shown in the 3294 last column. The conclusion is that: the incorporation anneal does not affect the 3295 carrier density of this delta layer (although it changes mobility); SPE overgrowth is 3296 preferred over MBE; the LL growth was not successful on this delta layer and did not 168 3297 seem to suppress Al segregation. Finally, the Al carrier density does not increase 3298 linearly with dosing, a cap in the dopant activation is found be ? 50 %. A detailed 3299 summary of the processing steps and characterization results of the Al delta layer 3300 samples is included in the Appendix, Table. A1. 3301 Based on the information that we have learned so far, we will discuss the factors 3302 that still need to be improved for achieving superconducting transition (SC) and the 3303 future expectations of this Al delta-doped material system. One of the most important 3304 factors that needs to be considered when pursuing superconductivity in this Si-Al-Si 3305 heterostructure is the critical 3D atom density. From the previous SIMS and APT 3306 data, the highest Al delta layer peak density that we have is 6.58 ? 1020 cm-3 and 6.34 3307 ? 1020 cm-3, respectively. These correspond to an atomic percentage of ? 1.3 at. %. 3308 Assume that the same condition for B:Si applies for Al:Si, where a standard electron- 3309 phonon mediated BCS mechanism is accounted for the observed SC [75]. The 3310 obtained value of ? 1.3 at. % is lower than the critical value needed (? 2 at. %) for 3311 superconducting transition [222]. However, we believe the numbers that are extracted 3312 from SIMS and APT may be at the lower bound of the actual density value, since 3313 peak broadening effects have been expected from both measurements. For example, 3314 the forward recoil of the sputtered ions in SIMS is usually limiting the depth 3315 resolution at this delta layer thickness and laser heating during APT measurement 3316 may cause the migration of the Al atoms in Si. Therefore, we think that reaching a 2 3317 at. % (this is assuming 100 % dopant activation) of the Al dopant concentration in Si 3318 using delta doping method is still possible. However, considering the fact that Al 3319 behaves quite differently in many ways compared to other dopant systems, the 169 3320 simplified theoretical prediction that Al will experience a standard phonon-mediated 3321 BCS-type mechanism based on B case for the occurrence of superconductivity [75] 3322 might not be correct. Further theoretical studies will be needed to provide more 3323 insights into this material system. 3324 From the experimental standpoint, the 3D atom density described above is from 3325 the Al sample without post-anneal, and a larger gap exists between the density of our 3326 Al delta layer devices and the critical density needed for SC. A typical 3D carrier 3327 density of our Al delta layer device that is conducting at low temperature is ? 1.1 ? 3328 1020 cm-3 or 0.2 at. % (half of 2.1 ? 1020 cm-3 based on 50 % activation). Some 3329 diffusion toward the Si substrate and segregation towards the Si capping layer surface 3330 were observed after thermal annealing steps, which degraded the dopant confinement. 3331 Unfortunately, unlike B and P delta layers in Si, the standard MBE growth and 3332 locking layer methods that can be used to suppress dopant segregation in other 3333 systems do not help in the Al case. In addition, the meta-stable cluster-like features 3334 observed in Fig. 7.3 that might be the origin of a limited dopant activation efficiency 3335 of ? 50 % makes it even more challenging. This is because the 2 at. % critical density 3336 is assuming that all dopants are fully activated, a 50 % dopant activation means only 3337 half of the dopants are contributing to electrical conduction and the other half remains 3338 inactive. 3339 Despite the difficulties described above (the gap between a critical density of 2 at. 3340 % and 0.2 at. % conducting Al carriers), we think that there are still opportunities to 3341 make this new material system superconduct. Al segregation seems to be the biggest 3342 limiting factor for reaching high enough 3D dopant density. A method will need to be 170 3343 developed in the future to suppress this segregation during the growth process better. 3344 With this limit to the material structure, it is very hard to achieve the critical density 3345 needed for SC, especially for a single delta layer. However, it is possible to deposit 3346 superlattices of multiple Al delta layers, which might still exhibit 2D conduction 3347 properties after thermal processes but would result in a much higher 3D density and 3348 2D carrier density. A more detailed study on thicker spacer layers or locking layers 3349 between those Al delta layers may also be beneficial. 3350 3351 7.3 Temperature Dependent Carrier Densities and 3352 Mobilities 3353 3354 3355 The Al delta layer is a new system where the conduction at low T has not been 3356 studied before. In this section, the electrical transport properties of the 2D Al delta 3357 doped layers at low temperature are investigated. The temperature dependence of the 3358 Hall 2D carrier density and mobility of the Al delta layer samples with 100 % Al dose 3359 and SPE growth methods have been studied, over a temperature range of 4 K to 80 K. 3360 Transport through Al delta layer samples, with variable temperature, has been 3361 measured using Hall devices. Instead of using a fixed magnetic field and rotate the 3362 sample direction 180o as in the standard Van der Pauw measurement, we are 3363 sweeping the magnetic field ranging from ? 0.2 T to + 0.2 T while keeping the sample 3364 position unchanged. Unlike other delta doped layers in silicon that display a metallic 3365 conduction and characterized by constant values of carrier density and mobility, a 3366 two-regime conduction behavior is observed in Al delta layer samples. As shown in 3367 Fig. 7.10 (a), in the temperature range of 4 K < T < 20 K, a metallic conduction with 171 3368 a nearly constant carrier density (? 10 % variation) of 1.5 ? 1014 cm-2 is obtained. As 3369 T > 20 K, a sharp transition occurs and the carrier density decreases to a minimum 3370 value of 4.4 ? 1014 cm-2, then levels off. The mobility vs T is shown in (b), where the 3371 mobility increases from 14.3 cm2/V.s at 4 K to a maximum value of 1917.5 cm2/V.s 3372 and then gradually decreases when T > 50K. Similar behavior has been observed for 3373 multiple Al samples, both with and without incorporation anneal. 3374 To interpret this temperature dependence carrier density and mobility, we use a 3375 delta layer conduction model that considers carriers with different densities and 3376 mobilities, inspired by similar studies of B delta-doped structures in diamond [223, 3377 224]. This model describes a two-level system where one level can be thermally 3378 promoted to the other. For example, holes can be thermally activated from the delta- 3379 doped layer into bulk states [225] or from the ground state subband of the delta 3380 function potential well into higher energy subbands in the valence band with higher 3381 mobilities [226]. 3382 A multi-carrier conduction mechanism is assumed, and the Hall mobility of a 3383 multi-carrier model is described by [227]: ? ? 3384 ?? = ? ? 2 ???? ?? ????? (7.1) ?=1 ?=1 3385 For the simplest case of two-carrier conduction, the Hall mobility becomes: 3386 ?? = (? 2 2 ?1?1 + ??2?2)?(??1?1 + ??2?2 ) (7.2) 3387 172 3388 3389 Figure 7.10: Temperature dependent sheet density and mobility. 3390 The sample is measured in a closed cycle refrigerator with an external magnetic field 3391 of ? 0.2 T. Sharp transitions have been observed in both carrier density and mobility. 3392 The carrier density decreases from ? 1.5 ? 1014 cm-2 to ? 1.0 ? 1013 cm-2 and mobility 3393 increases to a max value of 1917.5 cm2/V.s and then gradually decreases. 3394 3395 , where ps1 and ps2 are the carrier densities, ?1 and ?2 are the mobilities for each 3396 carrier type (or subband), respectively. The apparent carrier density can be expressed 3397 as [227]: 173 3403 ? 2 2?,??? = (??1?1 + ??2?2 )?(??1?1 + ??2?2) (7.3) 3398 We take the holes in the lowest energy state to have a carrier density of ps1 (here 3399 assuming a constant ps1 at base T) and mobility of ?1. At a higher temperature, when 3400 the holes are thermally excited into either a bulk state or higher energy subbands, the 3401 carrier density and mobility are expressed as ps2 and ?2. ps2 can be then calculated 3402 from the Fermi-Dirac probability distribution [223]: 3404 ? ~ ?3/2?2 exp[(?? ? ??)????] (7.4) 3405 In a doped semiconductor system, the T3/2 dependence usually corresponds to an 3406 impurity scattering mechanism. However, previously reported studies showed that 3407 predicting the mobility in heavily doped systems are non-trivial [223, 228]. The most 3408 frequently used mobility expression is an empirical function with a T2/3 dependence: 3409 ? (?) = ? (?/300)2/31 1,0 (7.5) 3410 , where ?1,0 is the single channel mobility extracted at base temperature. 3411 For the second carrier type which has a high mobility and low density at higher 3412 temperature, we assume it is dominated by the acoustic and optical phonon-type 3413 scatterings (proportional to T-3/2). The total density of the two carriers is conserved 3414 and the mobility of the second carrier type is expressed by an empirical function with 3415 a T-3/2 dependence: 3416 ?2(?) = ?2,0(?/300) ?3/2 (7.6) 3417 The two equations described in (7.2) and (7.3) are used to fit the experimental 3418 Hall data. The constraint is that the total carrier density is conserved, and ps2 = 0 at T 3419 = 0. The activation energy, ? 2,0 and a constant in ps2 are the free fitting parameters. 3420 The fitted curves are shown in Fig. 7.11. In general, the fitted curves are in good 174 3421 agreement with the experimental data. The transitions observed in both carrier density 3422 and mobility are reproduced successfully. At low temperature, the delta layer is at 3423 ground state with a triangular potential well. The conduction mechanism is dominated 3424 by metallic conduction from carrier type 1 and carrier type 2 freezes out. Note that the 3425 carrier density does show a weak temperature dependence at this temperature range 3426 (T < 20 K); this suggests that the transport is also occurring by a mechanism such as 3427 hopping [229], either from the impurity band or the disorder induced band tail state 3428 [230]. As the temperature increases, the additional type of carrier that has very high 3429 mobility gets into this a triangular potential well. The apparent carrier density begins 3430 to drop because some carriers have been thermally re-distributed to the other carrier 3431 type 2, while the total number of carriers remain constant. Our results indicate that 3432 this second type of carrier has a much smaller population compared to carrier type 1. 3433 According to equation (7.2), since the Hall mobility that we measured depends on the 3434 quadratic sum of the two carriers, even a small population (< 1 %, for example) of the 3435 type 2 carrier with a high mobility will dominate the total Hall mobility, resulting in a 3436 mobility value much higher than the type 1 carrier at the base temperature regime. 3437 For this type 2 carrier, an activation energy of -38 meV is extracted, meaning that the 3438 Fermi level lies 38 meV below the top of the valence band maximum. At T > 40 K, 3439 the apparent carrier density gradually levels off, with a small increase at higher 3440 temperature. We believe this weak temperature dependence is either coming from the 3441 substrate, since we are using intrinsic Si substrate with resistivity > 10 k?, or the 3442 conduction from the bulk Si capping layer. 175 3443 3444 Figure 7.11: Two-carrier model fit to the temperature dependent sheet density and 3445 mobility. 3446 The fitted curves are shown in red solid lines. The theoretical model is in good 3447 agreement with the experimental data. The transitions observed in both carrier density 3448 and mobility are reproduced successfully. 3449 3450 In conclusion, the temperature dependent Hall carrier density and mobility of this 3451 Al delta layer in Si can be explained by the two-carrier type model, based on 176 3452 activation of the localized donor states in the delta layer region to higher energy states 3453 in the bulk of the Si. Most of the carriers are remained in the metallic conduction 3454 region where ionized impurity scattering is dominating, results in a low mobility 3455 value. At higher temperatures, a small portion of the carriers are thermally activated 3456 to higher energy subbands, resulting in a much higher Hall mobility because the Hall 3457 mobility is a quadratic sum of the two carrier types. 3458 3459 3460 3461 3462 3463 3464 3465 3466 3467 3468 3469 3470 3471 3472 3473 3474 3475 3476 3477 3478 3479 3480 3481 177 3482 Chapter 8: Summary of Results and Future 3483 Experiments 3484 8.1 Summary of Results 3485 3486 3487 In this thesis, two materials: isotopically enriched 28Si (chapter 3 to 5) and Al 3488 delta-doped layers (chapter 6 and 7) were synthesized and studied as an effort to 3489 develop new approach toward superconducting semiconductor qubits. 3490 High quality 28Si material within the quantum computing community is scarce 3491 and limited. In chapter 3, a new UHV version of the hyperthermal Penning ion source 3492 was designed and built to improve the chemical purity of our 28Si thin film. The 3493 discharge properties based on arc voltage, source magnetic field and flow rate have 3494 been studied and optimized for 28Si. The base pressure has been reduced by a factor 3495 of ? 100 and the total chemical purity of the deposited 28Si film has been improved 3496 from 98.47 % to 99.97 %. The isotopic enrichment capability of this new ion source 3497 is also investigated. No degradation in enrichment has been found, and a typical 3498 isotope fraction of 28Si using this UHV ion source is 99.999987 % (8.32 ? 10-7 3499 mol/mol 29Si). Further improvements in chemical purity is still needed. Future efforts 3500 including implementation of the ion beam sweeper and UHV gas line with purifier. 3501 Improvements in chemical purity of the film with C, O and N contents < 1017 ? 1018 3502 cm-3 might be possible. The results described here serve as an important step forward 3503 to produce high quality 28Si material that is suitable for quantum information studies. 178 3504 In chapter 4, the material variety of 28Si at different levels in the quantum 3505 information community is broadened by demonstrating the ability to grow 3506 isotopically enriched 28Si epitaxial films with precisely controlled (? 90 % accuracy) 3507 enrichment levels, ranging from natural abundance to < 1 ppm 29Si.. This targeted 3508 enrichment of 28Si is achieved by periodically switching the mass analyzer magnetic 3509 field to modulate the isotope being deposited. Precise control of the 29Si 3510 concentration, with an average accuracy of ? 90 % between the targeted and 3511 measured value is achieved. This method also enables measurement studies such as 3512 the coherence time T2 vs 29Si concentration over a wide range. 3513 In chapter 5, to better assess the quality of our 28Si material, we have successfully 3514 fabricated and characterized 28Si MOSFET devices, and compared to those from 3515 natural abundance Si on the same substrate. The charge carrier mobility on 3516 isotopically enriched 28Si is found to be approximately a factor of 3 lower. 3517 Nevertheless, the magnetotransport measurements of devices fabricated on 3518 isotopically enriched 28 Si has demonstrated strong manifestations of quantum effects. 3519 Based on the analysis of temperature dependence of the weak localization and SdH 3520 oscillations, we believe that the dominant scattering mechanism is short-range 3521 scattering (impurity scattering). The macroscopic transport and material 3522 characteristics of the devices reported here will serve as a benchmark for finding 3523 correlations between macroscopic properties and the performance of future nanoscale 3524 devices. will lead to identifying qualifying metrics for ?quantum grade? silicon. 3525 The impact of this work so far is that we have made substantial improvements on 3526 the chemical purity while keeping the 29Si isotope fraction far less than other 28Si 179 3527 sources. We have broadened the material supply of 28Si with different enrichment 3528 levels to allow further studies and provided insights on setting qualifying metrics for 3529 ?quantum grade? silicon. The demonstration of this cheap, flexible source of high 3530 quality 28Si is a crucial step forward to make 28Si as an ideal host material for both 3531 semiconductor spin qubits and the proposed hybrid semi-superconductor qubit 3532 structure. 3533 Al delta-doping in Si is a brand-new material system with a lot of opportunities. 3534 In Chapter 6, we performed studies on Al delta doped layers on Si for reaching 3535 localized superconductivity. To pursue a superconducting Al delta-doped Si, a way to 3536 reach the critical 3D density is needed. The first step is to understand the maximum 3537 number of atoms in the smallest possible distance (one atomic layer) so that a 3538 maximized the 3D density can be realized. We used a combination of different 3539 characterization tools: STM, SIMS and APT. For one atomic layer of Al dopant on 3540 Si(100) surface, the extracted average density ratio between SIMS/STM and 3541 APT/STM is 1.77 and 2.37, respectively. This indicates that for each protrusion 3542 observed in the filled state STM image, there are 2.07 ? 1.11 Al atoms. This extracted 3543 density ratio confirmed the literature results that Al dimers are formed on Si(100) 3544 surface at low temperature. The maximum 2D atom density of Al that can be reached 3545 on Si(100) surface for one atomic layer is therefore 3.4 ? 1014 cm-2, half of the 3546 Si(100) surface atom density. We believe this fills the gap for the missing information 3547 that is needed to determine the Al atomic layer structure on Si(100) and provides help 3548 in reaching the critical density needed for superconducting transition using Al as a 3549 dopant. The 3D density of an Al delta-doped layer is also extracted from SIMS and 180 3550 APT: 6.58 ? 1020 cm-3 and 6.34 ? 1020 cm-3, which is approximately 1.2 at. %, still 3551 lower than the critical density needed for superconducting (2 at. %). 3552 In Chapter 7, we studied the effects of different material growth methods on 3553 electrical conduction (carrier density and dopant activation) and explored the 3554 possibility of improving the dopant confinement in the Si-Al-Si heterostructure. We 3555 found a number of aspects of Al delta doping in Si which are different compared to 3556 other dopants: the incorporation anneal does not affect the carrier density of this delta 3557 layer (although it changes mobility); standard MBE and LL growth methods were not 3558 successful on this delta layer and do not seem to suppress Al segregation. Finally, the 3559 Al dopant activation is capped at < 50 %, most likely due to the meta-stable state 3560 developed during thermal anneals. The conduction mechanism of this delta layer at 3561 low temperature is also studied and explained using a temperature dependent two- 3562 carrier type model. The possibility of reaching superconducting transition using Al 3563 delta layer as a dopant in Si is also discussed. We believe this is possible but will 3564 require further studies both experimentally and theoretically on suppressing the Al 3565 segregation for a high enough 3D dopant density. A summary table showing the 3566 processing steps and characterization results is included in Appendix A. 3567 A summary of the accomplishments of this work is included in Table. X. So far, 3568 we have discussed the advancements in 28Si material and provided initial studies on 3569 this new super-saturated Al delta layer in Si. The exploration of the phase space of 3570 this delta layer growth and the low temperature electrical measurements provided 3571 valuable insights on further pursuing superconductivity using this dopant. The results 3572 of this work serve as a pioneer and building block to fabricate new, nuclear spin-free 181 3573 and interface-free monocrystalline material system that is beneficial for combining 3574 the strengths of superconducting and semiconducting QIP. 3575 3576 Table X. A summary of the accomplishments of this work. 3577 System Major Accomplishment Note 28Si material Best isotopic enrichment Best reported enrichment 99.99987 % elsewhere: 99.9985 % [231] (with 29Si < 1 ppm) 28Si material Targeted enrichment with 90 % 1st demonstrated accuracy over 104 ppm range UHV ion source Improved vacuum of Penning 1st Penning type ion source type ion source to 2 ? 10-10 Torr with UHV capability (by 100 ?) Al delta layer Demonstrated high density 1st conducting Al delta layer conducting Al delta layer in Si structure Al delta layer Measured and modelled T- 1st measured T-dependent dependent carrier density and conduction of Al delta layer mobility at low T in Si 3578 3579 8.2 Future Experiments 3580 3581 3582 With the improvements in chemical purity of our 28Si and ability to produce 3583 targeted enrichment of the deposited films, a natural next step is to measure the 3584 coherence time T2 of the spins within this material and study the correlation between 3585 29Si concentration and T2. This would provide direct experimental evidences for the 3586 theoretical studies done by Witzel et al. and match the phase space of T2 vs 29Si 3587 concentration, especially in the < 800 ppm region. Since the 28Si material produced in 3588 this work is a flexible, lab scale production with relatively small quantity (nanometer 182 3589 scale). The traditional ESR measurement which is an ensemble measurement that 3590 require large number of spins, thus large volume of 28Si is not suitable. Fortunately, 3591 smaller ESR probe can be fabricated onto the 28Si thin film with 31P implantation that 3592 have enough sensitivity down to a few tens of spins [232]. A Josephson parametric 3593 microwave amplifier combined with high-quality-factor superconducting 3594 microresonators at millikelvin temperature [233] can also be used as a high sensitivity 3595 tool to measure T2 of our 28Si. 3596 Another approach for studying the spin properties of the 28Si is through the 3597 magnetotransport measurements with the presence of microwave excitation. This 3598 proposed idea is based on the electrically detected magnetic resonance (EDMR) 3599 method and the work from [234], where a strong microwave-induced resonance in the 3600 resistance results in the resistive detection of spin resonance [234]. It can be used to 3601 provide measurements of the g-factor, spin relaxation time and valley splitting in 3602 graphene. The gated Hall bar devices fabricated on 28Si samples will be mounted at 3603 the end of a microwave waveguide and cooled down to low temperature in an applied 3604 magnetic field. The longitudinal resistance Rxx will then be measured as a function of 3605 applied magnetic field under microwave irradiation over the frequency range 10 ? 50 3606 GHz and power range of 0.1 ? 10 mW. With the microwave excitation, we expect to 3607 see microwave-induced resonance in Rxx. By plotting the ?Rxx (the difference in Rxx 3608 value with and without microwave) as a function of magnetic field strength (B), we 3609 can extract both the low B-field resonance and the high B-field resonance, which 3610 correspond to intra-valley spin resonance and inter-valley spin resonance, 3611 respectively. From the linewidth of these resonances, we can calculate the relaxation 183 3612 times [234]. Although the resonance linewidth might be affected by various of 3613 factors, including background donor concentration, defects, local nuclear spin 3614 contributions from 29Si, etc., we can potentially improve it by reducing the dimension 3615 of the MOSFET devices. As the size of the devices approach nanometer scale, we 3616 will be able to reduce the components that contribute to the inhomogeneities that 3617 serve to broaden the linewidth and be able to extract the dominating factor that limits 3618 the quantum coherence. We can then extend the measurements to devices with 3619 different enrichment levels of 28Si while keeping the other parameters optimized and 3620 the relationship between the coherence time and the 29Si concentration will be 3621 studied. Furthermore, if we change the microwave frequency f, we expect to see the 3622 shift of the resonances to higher B with increasing f and we can calculate the electron 3623 g-factor from the f vs B plot. Valley splitting can also be detected using this method. 3624 In the measurement with graphene [234], a fourfold degeneracy is lifted in the 3625 absence of magnetic field and produced a pair of spin degenerate levels separated by 3626 E/h = f0, where E is the energy between two valleys and f0 is the corresponding 3627 frequency. Zeeman splitting then lifts the spin degeneracy of the two valleys and 3628 microwave excitation induced spin-flip transitions can be seen [234]. 3629 For the Al delta doped layers in Si, we have measured the Al delta layer peak 3630 density and studied the effects of different growth methods. To achieve a 3631 superconducting transition in this Al delta doped Si, several possible future steps can 3632 be made. The first is to better tune the recipe for the locking layer (LL) and the 3633 epitaxial MBE growth of the Si capping layer on top of the Al delta layer. We have 3634 tried several standard growth methods for growing LL and MBE Si, none of them 184 3635 succeeded in the limited time frame of this project. However, there might be other 3636 possible ways to combine LL with MBE Si overgrowth, e.g., using a lower annealing 3637 temperature and a lower deposition rate. I still believe that a suppression in Al 3638 segregation can be made possible. Another possible way to achieve superconducting 3639 transition is by increasing the 3D density and dopant activation. This can be done by 3640 introducing a superlattice structure of the Al delta layers with spacer layers. It has 3641 been demonstrated in P that superlattices of delta layers can increase the active carrier 3642 density from 1.9 ? 1014 cm-2 to 4.5 ? 1014 cm-2 and remained 2D conduction [192]. 3643 Another possibility might be to reduce the thermal budget of the growth process to 3644 suppress segregation process. This might be possible by fine-tuning the deposition 3645 and annealing temperatures and further explore the phase space of the delta layer 3646 growth methods. 3647 3648 3649 3650 3651 3652 3653 3654 3655 3656 3657 3658 3659 185 3660 Appendix A: Al Delta Layers Catalog 3661 3662 The details of the Al delta layer sample processing steps introduced in Chapter 7 are 3663 shown in Table. A1. This table is a summary of the synthesis processes (including 3664 doses, anneals, overgrowth), electrical characterization at low temperature, STM 3665 counts and SIMS density measurements. 3666 3667 3668 3669 3670 3671 3672 3673 3674 3675 3676 3677 3678 3679 3680 3681 3682 3683 186 3684 Table A1: Processing steps and characterizations results of Al delta layer samples 3685 studied in Chapter 7. 3686 3687 3688 187 3689 Bibliography 3690 3691 1. Zhang, S. Review of Modern Field Effect Transistor Technologies for Scaling. 3692 in Journal of Physics: Conference Series. 2020. IOP Publishing. 3693 2. Shalf, J.M. and R. Leland, Computing beyond moore's law. Computer, 2015. 3694 48(12): p. 14-23. 3695 3. Shor, P.W., Polynomial-time algorithms for prime factorization and discrete 3696 logarithms on a quantum computer. SIAM review, 1999. 41(2): p. 303-332. 3697 4. Wiebe, N., D. Braun, and S. Lloyd, Quantum algorithm for data fitting. 3698 Physical review letters, 2012. 109(5): p. 050505. 3699 5. Biamonte, J., P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, 3700 Quantum machine learning. Nature, 2017. 549(7671): p. 195-202. 3701 6. Moll, N., P. Barkoutsos, L.S. Bishop, J.M. Chow, A. Cross, D.J. Egger, S. 3702 Filipp, A. Fuhrer, J.M. Gambetta, and M. Ganzhorn, Quantum optimization 3703 using variational algorithms on near-term quantum devices. Quantum Science 3704 and Technology, 2018. 3(3): p. 030503. 3705 7. Grover, L.K. A fast quantum mechanical algorithm for database search. in 3706 Proceedings of the twenty-eighth annual ACM symposium on Theory of 3707 computing. 1996. 3708 8. Yao, A.C.-C. Quantum circuit complexity. in Proceedings of 1993 IEEE 34th 3709 Annual Foundations of Computer Science. 1993. IEEE. 3710 9. Nielsen, M.A. and I. Chuang, Quantum computation and quantum 3711 information. 2002, American Association of Physics Teachers. 3712 10. Zhang, X., H.-O. Li, G. Cao, M. Xiao, G.-C. Guo, and G.-P. Guo, 3713 Semiconductor quantum computation. National Science Review, 2019. 6(1): 3714 p. 32-54. 3715 11. Vandersypen, L.M. and I.L. Chuang, NMR techniques for quantum control 3716 and computation. Reviews of modern physics, 2005. 76(4): p. 1037. 3717 12. Medford, J., C. Barthel, C. Marcus, M. Hanson, and A. Gossard, Scaling of 3718 dynamical decoupling for spin qubits. Physical review letters, 2012. 108(8): p. 3719 086802. 3720 13. H?ffner, H., C.F. Roos, and R. Blatt, Quantum computing with trapped ions. 3721 Physics reports, 2008. 469(4): p. 155-203. 3722 14. Monroe, C. and J. Kim, Scaling the ion trap quantum processor. Science, 3723 2013. 339(6124): p. 1164-1169. 3724 15. Devoret, M.H. and R.J. Schoelkopf, Superconducting circuits for quantum 3725 information: an outlook. Science, 2013. 339(6124): p. 1169-1174. 3726 16. Wendin, G., Quantum information processing with superconducting circuits: 3727 a review. Reports on Progress in Physics, 2017. 80(10): p. 106001. 3728 17. Awschalom, D.D., L.C. Bassett, A.S. Dzurak, E.L. Hu, and J.R. Petta, 3729 Quantum spintronics: engineering and manipulating atom-like spins in 3730 semiconductors. Science, 2013. 339(6124): p. 1174-1179. 3731 18. Zhang, X., H.-O. Li, K. Wang, G. Cao, M. Xiao, and G.-P. Guo, Qubits based 3732 on semiconductor quantum dots. Chinese Physics B, 2018. 27(2): p. 020305. 3733 19. Childress, L. and R. Hanson, Diamond NV centers for quantum computing 3734 and quantum networks. MRS bulletin, 2013. 38(2): p. 134-138. 188 3735 20. Weber, J., W. Koehl, J. Varley, A. Janotti, B. Buckley, C. Van de Walle, and 3736 D.D. Awschalom, Quantum computing with defects. Proceedings of the 3737 National Academy of Sciences, 2010. 107(19): p. 8513-8518. 3738 21. Loss, D. and D.P. DiVincenzo, Quantum computation with quantum dots. 3739 Physical Review A, 1998. 57(1): p. 120. 3740 22. Hanson, R., L.P. Kouwenhoven, J.R. Petta, S. Tarucha, and L.M. 3741 Vandersypen, Spins in few-electron quantum dots. Reviews of modern 3742 physics, 2007. 79(4): p. 1217. 3743 23. Zwanenburg, F.A., A.S. Dzurak, A. Morello, M.Y. Simmons, L.C. 3744 Hollenberg, G. Klimeck, S. Rogge, S.N. Coppersmith, and M.A. Eriksson, 3745 Silicon quantum electronics. Reviews of modern physics, 2013. 85(3): p. 961. 3746 24. Nadj-Perge, S., S. Frolov, E. Bakkers, and L.P. Kouwenhoven, Spin?orbit 3747 qubit in a semiconductor nanowire. Nature, 2010. 468(7327): p. 1084-1087. 3748 25. Wei, D., H.-O. Li, G. Cao, G. Luo, Z.-X. Zheng, T. Tu, M. Xiao, G.-C. Guo, 3749 H.-W. Jiang, and G.-P. Guo, Tuning inter-dot tunnel coupling of an etched 3750 graphene double quantum dot by adjacent metal gates. Scientific reports, 3751 2013. 3(1): p. 1-6. 3752 26. Klein, D.L., P.L. McEuen, J.E.B. Katari, R. Roth, and A.P. Alivisatos, An 3753 approach to electrical studies of single nanocrystals. Applied Physics Letters, 3754 1996. 68(18): p. 2574-2576. 3755 27. Kane, B.E., A silicon-based nuclear spin quantum computer. nature, 1998. 3756 393(6681): p. 133-137. 3757 28. Hile, S.J., L. Fricke, M.G. House, E. Peretz, C.Y. Chen, Y. Wang, M. 3758 Broome, S.K. Gorman, J.G. Keizer, and R. Rahman, Addressable electron 3759 spin resonance using donors and donor molecules in silicon. Science 3760 advances, 2018. 4(7): p. eaaq1459. 3761 29. Muhonen, J.T., J.P. Dehollain, A. Laucht, F.E. Hudson, R. Kalra, T. 3762 Sekiguchi, K.M. Itoh, D.N. Jamieson, J.C. McCallum, A.S. Dzurak, et al., 3763 Storing quantum information for 30 seconds in a nanoelectronic device. 3764 Nature Nanotechnology, 2014. 9(12): p. 986 DOI: 10.1038/Nnano.2014.211. 3765 30. Saeedi, K., S. Simmons, J.Z. Salvail, P. Dluhy, H. Riemann, N.V. Abrosimov, 3766 P. Becker, H.J. Pohl, J.J.L. Morton, and M.L.W. Thewalt, Room-Temperature 3767 Quantum Bit Storage Exceeding 39 Minutes Using Ionized Donors in Silicon- 3768 28. Science, 2013. 342(6160): p. 830-833 DOI: 10.1126/science.1239584. 3769 31. Tyryshkin, A.M., S. Tojo, J.J.L. Morton, H. Riemann, N.V. Abrosimov, P. 3770 Becker, H.J. Pohl, T. Schenkel, M.L.W. Thewalt, K.M. Itoh, et al., Electron 3771 spin coherence exceeding seconds in high-purity silicon. Nature Materials, 3772 2012. 11(2): p. 143 DOI: 10.1038/Nmat3182. 3773 32. Abe, E., A.M. Tyryshkin, S. Tojo, J.J.L. Morton, W.M. Witzel, A. Fujimoto, 3774 J.W. Ager, E.E. Haller, J. Isoya, S.A. Lyon, et al., Electron spin coherence of 3775 phosphorus donors in silicon: Effect of environmental nuclei. Physical Review 3776 B, 2010. 82(12) DOI: ARTN 121201 3777 10.1103/PhysRevB.82.121201. 3778 33. Witzel, W.M., M.S. Carroll, L. Cywinski, and S. Das Sarma, Quantum 3779 decoherence of the central spin in a sparse system of dipolar coupled spins. 3780 Physical Review B, 2012. 86(3) DOI: ARTN 035452 189 3781 10.1103/PhysRevB.86.035452. 3782 34. Steger, M., K. Saeedi, M.L.W. Thewalt, J.J.L. Morton, H. Riemann, N.V. 3783 Abrosimov, P. Becker, and H.J. Pohl, Quantum Information Storage for over 3784 180 s Using Donor Spins in a Si-28 "Semiconductor Vacuum". Science, 2012. 3785 336(6086): p. 1280-1283 DOI: 10.1126/science.1217635. 3786 35. Muhonen, J.T., J.P. Dehollain, A. Laucht, F.E. Hudson, R. Kalra, T. 3787 Sekiguchi, K.M. Itoh, D.N. Jamieson, J.C. McCallum, A.S. Dzurak, et al., 3788 Storing quantum information for 30 seconds in a nanoelectronic device. 3789 Nature Nanotechnology, 2014. 9(12): p. 986-991 DOI: 3790 10.1038/Nnano.2014.211. 3791 36. Ito, T., T. Otsuka, T. Nakajima, M.R. Delbecq, S. Amaha, J. Yoneda, K. 3792 Takeda, A. Noiri, G. Allison, and A. Ludwig, Four single-spin Rabi 3793 oscillations in a quadruple quantum dot. Applied Physics Letters, 2018. 3794 113(9): p. 093102. 3795 37. Yang, C., A. Rossi, R. Ruskov, N. Lai, F. Mohiyaddin, S. Lee, C. Tahan, G. 3796 Klimeck, A. Morello, and A. Dzurak, Spin-valley lifetimes in a silicon 3797 quantum dot with tunable valley splitting. Nature communications, 2013. 4(1): 3798 p. 1-8. 3799 38. Ruskov, R., M. Veldhorst, A.S. Dzurak, and C. Tahan, Electron g-factor of 3800 valley states in realistic silicon quantum dots. Physical Review B, 2018. 3801 98(24): p. 245424. 3802 39. Kawakami, E., P. Scarlino, D.R. Ward, F. Braakman, D. Savage, M. Lagally, 3803 M. Friesen, S.N. Coppersmith, M.A. Eriksson, and L. Vandersypen, Electrical 3804 control of a long-lived spin qubit in a Si/SiGe quantum dot. Nature 3805 nanotechnology, 2014. 9(9): p. 666-670. 3806 40. Becker, P., H.J. Pohl, H. Riemann, and N. Abrosimov, Enrichment of silicon 3807 for a better kilogram. Physica Status Solidi a-Applications and Materials 3808 Science, 2010. 207(1): p. 49-66 DOI: 10.1002/pssa.200925148. 3809 41. Abrosimov, N.V., D.G. Aref'ev, P. Becker, H. Bettin, A.D. Bulanov, M.F. 3810 Churbanov, S.V. Filimonov, V.A. Gavva, O.N. Godisov, A.V. Gusev, et al., A 3811 new generation of 99.999% enriched (2)8(S)i single crystals for the 3812 determination of Avogadro's constant. Metrologia, 2017. 54(4): p. 599-609 3813 DOI: 10.1088/1681-7575/aa7a62. 3814 42. Mazzocchi, V., P.G. Sennikov, A.D. Bulanov, M.F. Churbanov, B. Bertrand, 3815 L. Hutin, J.P. Barnes, M.N. Drozdov, J.M. Hartmann, and M. Sanquer, 3816 99.992% 28Si CVD-grown epilayer on 300?mm substrates for large scale 3817 integration of silicon spin qubits. Journal of Crystal Growth, 2019. 509: p. 1-7 3818 DOI: 10.1016/j.jcrysgro.2018.12.010. 3819 43. Itoh, K.M. and H. Watanabe, Isotope engineering of silicon and diamond for 3820 quantum computing and sensing applications. Mrs Communications, 2014. 3821 4(4): p. 143-157 DOI: 10.1557/mrc.2014.32. 3822 44. Takyu, K., K.M. Itoh, K. Oka, N. Saito, and V.I. Ozhogin, Growth and 3823 characterization of the isotopically enriched Si-28 bulk single crystal. 3824 Japanese Journal of Applied Physics, 1999. 38(12b): p. L1493 DOI: Doi 3825 10.1143/Jjap.38.L1493. 190 3826 45. Li, J.Y., C.T. Huang, L.P. Rokhinson, and J.C. Sturm, Extremely high electron 3827 mobility in isotopically-enriched Si-28 two-dimensional electron gases grown 3828 by chemical vapor deposition. Applied Physics Letters, 2013. 103(16): p. 3829 162105 DOI: Artn 162105 3830 10.1063/1.4824729. 3831 46. Sailer, J., V. Lang, G. Abstreiter, G. Tsuchiya, K.M. Itoh, J.W. Ager, E.E. 3832 Haller, D. Kupidura, D. Harbusch, S. Ludwig, et al., A Schottky top-gated 3833 two-dimensional electron system in a nuclear spin free Si/SiGe 3834 heterostructure. Physica Status Solidi-Rapid Research Letters, 2009. 3(2-3): 3835 p. 61-63 DOI: 10.1002/pssr.200802275. 3836 47. Fiedler, H., P. Gupta, J. Kennedy, and A. Markwitz, 28Si+ ion beams from 3837 Penning ion source based implanter systems for near-surface isotopic 3838 purification of silicon. Review of Scientific Instruments, 2018. 89(12): p. 3839 123305 DOI: Artn 123305 3840 10.1063/1.5048949. 3841 48. Nakamura, Y., Y.A. Pashkin, and J.S. Tsai, Coherent control of macroscopic 3842 quantum states in a single-Cooper-pair box. nature, 1999. 398(6730): p. 786- 3843 788. 3844 49. Barends, R., J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeffrey, T.C. White, 3845 J. Mutus, A.G. Fowler, and B. Campbell, Superconducting quantum circuits 3846 at the surface code threshold for fault tolerance. Nature, 2014. 508(7497): p. 3847 500-503. 3848 50. Fowler, A.G., M. Mariantoni, J.M. Martinis, and A.N. Cleland, Surface codes: 3849 Towards practical large-scale quantum computation. Physical Review A, 3850 2012. 86(3): p. 032324. 3851 51. Huang, H.-L., D. Wu, D. Fan, and X. Zhu, Superconducting quantum 3852 computing: a review. Science China Information Sciences, 2020. 63(8): p. 1- 3853 32. 3854 52. Bouchiat, V., D. Vion, P. Joyez, D. Esteve, and M. Devoret, Quantum 3855 coherence with a single Cooper pair. Physica Scripta, 1998. 1998(T76): p. 3856 165. 3857 53. Martinis, J.M., Superconducting phase qubits. Quantum Information 3858 Processing, 2009. 8(2): p. 81-103. 3859 54. Mooij, J., T. Orlando, L. Levitov, L. Tian, C.H. Van der Wal, and S. Lloyd, 3860 Josephson persistent-current qubit. Science, 1999. 285(5430): p. 1036-1039. 3861 55. Friedman, J.R., V. Patel, W. Chen, S. Tolpygo, and J.E. Lukens, Quantum 3862 superposition of distinct macroscopic states. nature, 2000. 406(6791): p. 43- 3863 46. 3864 56. Koch, J., M.Y. Terri, J. Gambetta, A.A. Houck, D.I. Schuster, J. Majer, A. 3865 Blais, M.H. Devoret, S.M. Girvin, and R.J. Schoelkopf, Charge-insensitive 3866 qubit design derived from the Cooper pair box. Physical Review A, 2007. 3867 76(4): p. 042319. 3868 57. Yang, C.-P., S.-I. Chu, and S. Han, Possible realization of entanglement, 3869 logical gates, and quantum-information transfer with superconducting- 3870 quantum-interference-device qubits in cavity QED. Physical Review A, 2003. 3871 67(4): p. 042311. 191 3872 58. You, J. and F. Nori, Quantum information processing with superconducting 3873 qubits in a microwave field. Physical Review B, 2003. 68(6): p. 064509. 3874 59. Blais, A., R.-S. Huang, A. Wallraff, S.M. Girvin, and R.J. Schoelkopf, Cavity 3875 quantum electrodynamics for superconducting electrical circuits: An 3876 architecture for quantum computation. Physical Review A, 2004. 69(6): p. 3877 062320. 3878 60. Paik, H., D. Schuster, L.S. Bishop, G. Kirchmair, G. Catelani, A. Sears, B. 3879 Johnson, M. Reagor, L. Frunzio, and L. Glazman, Observation of high 3880 coherence in Josephson junction qubits measured in a three-dimensional 3881 circuit QED architecture. Physical Review Letters, 2011. 107(24): p. 240501. 3882 61. Shim, Y.-P. and C. Tahan, Bottom-up superconducting and Josephson 3883 junction devices inside a group-IV semiconductor. Nature communications, 3884 2014. 5(1): p. 1-8. 3885 62. Takano, Y., T. Takenouchi, S. Ishii, S. Ueda, T. Okutsu, I. Sakaguchi, H. 3886 Umezawa, H. Kawarada, and M. Tachiki, Superconducting properties of 3887 homoepitaxial CVD diamond. Diamond and related materials, 2007. 16(4-7): 3888 p. 911-914. 3889 63. Lasbley, A., R. Granger, and S. Rolland, High temperature superconducting 3890 behaviour in PbTe Pb system. Solid State Communications, 1973. 13(8): p. 3891 1045-1048. 3892 64. Zhang, Y., R. Zhao, and W. Yang, Surface superstructures of the Pb/Ge (001) 3893 system. Surface Science Letters, 1993. 293(1-2): p. L821-L825. 3894 65. Schooley, J., W. Hosler, E. Ambler, J. Becker, M.L. Cohen, and C. Koonce, 3895 Dependence of the superconducting transition temperature on carrier 3896 concentration in semiconducting srti o 3. Physical Review Letters, 1965. 3897 14(9): p. 305. 3898 66. Makise, K., N. Kokubo, S. Takada, T. Yamaguti, S. Ogura, K. Yamada, B. 3899 Shinozaki, K. Yano, K. Inoue, and H. Nakamura, Superconductivity in 3900 transparent zinc-doped In2O3 films having low carrier density. Science and 3901 technology of advanced materials, 2009. 9(4): p. 044208. 3902 67. Koonce, C. and M.L. Cohen, Theory of superconducting semiconductors and 3903 semimetals. Physical Review, 1969. 177(2): p. 707. 3904 68. Fiedler, J., V. Heera, R. H?bner, M. Voelskow, S. Germer, B. Schmidt, and 3905 W. Skorupa, High-fluence Ga-implanted silicon?The effect of annealing and 3906 cover layers. Journal of Applied Physics, 2014. 116(2): p. 024502. 3907 69. Seeger, A. and K. Chik, Diffusion Mechanisms and Point Defects in Silicon 3908 and Germanium. Phys. Status Solidi, 29: 455-542 (Oct. 1, 1968). 1968. 3909 70. Fiedler, J., V. Heera, R. Skrotzki, T. Herrmannsd?rfer, M. Voelskow, A. 3910 M?cklich, S. Oswald, B. Schmidt, W. Skorupa, and G. Gobsch, 3911 Superconducting films fabricated by high-fluence Ga implantation in Si. 3912 Physical Review B, 2011. 83(21): p. 214504. 3913 71. Bustarret, E., C. Marcenat, P. Achatz, J. Ka?mar?ik, F. L?vy, A. Huxley, L. 3914 Ort?ga, E. Bourgeois, X. Blase, and D. D?barre, Superconductivity in doped 3915 cubic silicon. Nature, 2006. 444(7118): p. 465-468. 3916 72. Ekimov, E., V. Sidorov, E. Bauer, N. Mel'Nik, N. Curro, J. Thompson, and S. 3917 Stishov, Superconductivity in diamond. nature, 2004. 428(6982): p. 542-545. 192 3918 73. Takano, Y., Superconductivity in CVD diamond films. Journal of Physics: 3919 Condensed Matter, 2009. 21(25): p. 253201. 3920 74. Prucnal, S., V. Heera, R. H?bner, M. Wang, G.P. Mazur, M.J. Grzybowski, X. 3921 Qin, Y. Yuan, M. Voelskow, and W. Skorupa, Superconductivity in single- 3922 crystalline aluminum-and gallium-hyperdoped germanium. Physical Review 3923 Materials, 2019. 3(5): p. 054802. 3924 75. Bourgeois, E. and X. Blase, Superconductivity in doped cubic silicon: An ab 3925 initio study. Applied physics letters, 2007. 90(14): p. 142511. 3926 76. Kim, H.S., Monocrystalline Supersaturated Aluminum Layers Buried in 3927 Epitaxial Silicon. 2019, University of Maryland, College Park. 3928 77. Gossmann, H.-J. and E. Schubert, Delta doping in silicon. Critical Reviews in 3929 Solid State and Material Sciences, 1993. 18(1): p. 1-67. 3930 78. Jewell, A.D., M.E. Hoenk, A.G. Carver, and S. Nikzad, Low-temperature 3931 homoepitaxial growth of two-dimensional antimony superlattices in silicon. 3932 Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, 3933 2018. 36(6): p. 061513. 3934 79. Wang, X., J.A. Hagmann, P. Namboodiri, J. Wyrick, K. Li, R.E. Murray, A. 3935 Myers, F. Misenkosen, M.D. Stewart, and C.A. Richter, Quantifying atom- 3936 scale dopant movement and electrical activation in Si: P monolayers. 3937 Nanoscale, 2018. 10(9): p. 4488-4499. 3938 80. McKibbin, S., C. Polley, G. Scappucci, J. Keizer, and M. Simmons, Low 3939 resistivity, super-saturation phosphorus-in-silicon monolayer doping. Applied 3940 Physics Letters, 2014. 104(12): p. 123502. 3941 81. Thomsen, E., O. Hansen, K. Harrekilde?Petersen, J.L. Hansen, S.Y. Shiryaev, 3942 and A. Nylandsted Larsen, Thermal stability of highly Sb?doped molecular 3943 beam epitaxy silicon grown at low temperatures: Structural and electrical 3944 characterization. Journal of Vacuum Science & Technology B: 3945 Microelectronics and Nanometer Structures Processing, Measurement, and 3946 Phenomena, 1994. 12(5): p. 3016-3022. 3947 82. Gossmann, H.J., E. Schubert, D. Eaglesham, and M. Cerullo, Low? 3948 temperature Si molecular beam epitaxy: Solution to the doping problem. 3949 Applied physics letters, 1990. 57(23): p. 2440-2442. 3950 83. Weir, B., L. Feldman, D. Monroe, H.J. Grossmann, R. Headrick, and T. Hart, 3951 Electrical characterization of an ultrahigh concentration boron delta?doping 3952 layer. Applied physics letters, 1994. 65(6): p. 737-739. 3953 84. Salfi, J., M. Tong, S. Rogge, and D. Culcer, Quantum computing with 3954 acceptor spins in silicon. Nanotechnology, 2016. 27(24): p. 244001. 3955 85. van der Heijden, J., T. Kobayashi, M.G. House, J. Salfi, S. Barraud, R. 3956 Lavi?ville, M.Y. Simmons, and S. Rogge, Readout and control of the spin- 3957 orbit states of two coupled acceptor atoms in a silicon transistor. Science 3958 advances, 2018. 4(12): p. eaat9199. 3959 86. Ramanayaka, A.N., H.-S. Kim, J.A. Hagmann, R.E. Murray, K. Tang, F. 3960 Meisenkothen, H. Zhang, L. Bendersky, A. Davydov, and N.M. Zimmerman, 3961 Towards superconductivity in p-type delta-doped Si/Al/Si heterostructures. 3962 AIP Advances, 2018. 8(7): p. 075329. 193 3963 87. Dwyer, K.J., In Situ Enrichment and Epitaxial Growth of 28 Si Films via Ion 3964 Beam Deposition. 2017, University of Maryland, College Park. 3965 88. Swartzentruber, B.S., Y.W. Mo, M. Webb, and M. Lagally, Scanning 3966 tunneling microscopy studies of structural disorder and steps on Si surfaces. 3967 Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, 3968 1989. 7(4): p. 2901-2905. 3969 89. Poppendieck, T.D., T.C. Ngoc, and M.B. Webb, An electron diffraction study 3970 of the structure of silicon (100). Surface Science, 1978. 75(2): p. 287-315. 3971 90. Nulman, J., S. Antonio, and W. Blonigan, Observation of Silicon-Wafer 3972 Emissivity in Rapid Thermal-Processing Chambers for Pyrometric 3973 Temperature Monitoring. Applied Physics Letters, 1990. 56(25): p. 2513- 3974 2515 DOI: Doi 10.1063/1.102874. 3975 91. Rudakov, V.I., V.V. Ovcharov, and V.P. Prigara, Influence of optical 3976 properties of the SOI structure on the wafer temperature during rapid thermal 3977 annealing. Russian Microelectronics, 2012. 41(1): p. 15-24 DOI: 3978 10.1134/s1063739712010106. 3979 92. Vander Voort, G.F. and J. Asensio-Lozano, The Al-Si Phase Diagram. 3980 Microscopy and Microanalysis, 2009. 15: p. 60-61 DOI: 3981 10.1017/S1431927609092642. 3982 93. Gerlach, G. and W. D?tzel, Introduction to microsystem technology : a guide 3983 for students. Wiley microsystem and nanotechnology series. 2008, Chichester, 3984 England ; Hoboken, NJ: J. Wiley & Sons. xxiii, 351 p. 3985 94. Sato, T., Spectral Emissivity of Silicon. Japanese Journal of Applied Physics, 3986 1967. 6(3): p. 339-& DOI: Doi 10.1143/Jjap.6.339. 3987 95. Phillips, C.E.S., "The action of magnetised electrodes upon electrical 3988 discharge phenomena in rarefied gases.". Proceedings of the Royal Society of 3989 London, 1901. 68(444): p. 147-149 DOI: DOI 10.1098/rspl.1901.0030. 3990 96. Baumann, H. and K. Bethge, Pig Ion-Source with End Extraction for Multiply 3991 Charged Ions. Nuclear Instruments & Methods, 1974. 122(3): p. 517-525 3992 DOI: Doi 10.1016/0029-554x(74)90521-7. 3993 97. Baumann, H. and K. Bethge, The Frankfurt Pig Ion-Source. Nuclear 3994 Instruments & Methods in Physics Research, 1981. 189(1): p. 107-110 DOI: 3995 Doi 10.1016/0029-554x(81)90131-2. 3996 98. Rohwer, P., H. Baumann, K. Bethge, and W. Schutze, Ion Energy Analysis of 3997 a Penning Ion-Source Using a High-Resolution Mass-Spectrometer. Nuclear 3998 Instruments & Methods in Physics Research, 1982. 204(1): p. 245-248 DOI: 3999 Doi 10.1016/0167-5087(82)90103-X. 4000 99. Rohwer, P., H. Baumann, W. Schutze, and K. Bethge, Studies of the Center 4001 Potential in a Penning Discharge. Nuclear Instruments & Methods in Physics 4002 Research, 1983. 211(2-3): p. 543-546 DOI: Doi 10.1016/0167- 4003 5087(83)90285-5. 4004 100. Pierce, J.R., Theory and design of electron beams. 2nd ed. The Bell Telephone 4005 Laboratories series. 1954, New York,: Van Nostrand. 4006 101. Pomeroy, J.M., A.J. Couture, M.V.R. Murty, E.N. Butler, and B.H. Cooper, 4007 Hyperthermal ion beam system optimized for studying the effects of kinetic 194 4008 energy on thin-film growth. Review of Scientific Instruments, 2002. 73(11): p. 4009 3846-3852 DOI: 10.1063/1.1512337. 4010 102. Dwyer, K.J., J.M. Pomeroy, D.S. Simons, K.L. Steffens, and J.W. Lau, 4011 Enriching Si-28 beyond 99.9998% for semiconductor quantum computing. 4012 Journal of Physics D-Applied Physics, 2014. 47(34): p. 345105 DOI: Artn 4013 345105 4014 10.1088/0022-3727/47/34/345105. 4015 103. Dwyer, K.J., J.M. Pomeroy, D.S. Simons, K.L. Steffens, and J.W. Lau, 4016 Enriching Si-28 beyond 99.9998% for semiconductor quantum computing. 4017 Journal of Physics D-Applied Physics, 2014. 47(34) DOI: Artn 345105 4018 10.1088/0022-3727/47/34/345105. 4019 104. Kanaya, K. and S. Ono, Secondary electron emission from solid surfaces by 4020 bombardment with charged particles. Japanese Journal of Applied Physics, 4021 1974. 13(6): p. 944. 4022 105. Bai, C., Scanning tunneling microscopy and its application. Vol. 32. 2000: 4023 Springer Science & Business Media. 4024 106. Chen, C.J., Introduction to scanning tunneling microscopy. Vol. 4. 1993: 4025 Oxford University Press on Demand. 4026 107. Wikipedia, Scanning Tunneling Microscope 4027 https://en.wikipedia.org/w/index.php?title=Scanning_tunneling_microscope& 4028 oldid=1010053950, 2021. 4029 108. Hall, E.H., On a new action of the magnet on electric currents. American 4030 Journal of Mathematics, 1879. 2(3): p. 287-292. 4031 109. Veldhorst, M., J.C.C. Hwang, C.H. Yang, A.W. Leenstra, B. de Ronde, J.P. 4032 Dehollain, J.T. Muhonen, F.E. Hudson, K.M. Itoh, A. Morello, et al., An 4033 addressable quantum dot qubit with fault-tolerant control-fidelity. Nature 4034 Nanotechnology, 2014. 9(12): p. 981 DOI: 10.1038/Nnano.2014.216. 4035 110. Yoneda, J., K. Takeda, T. Otsuka, T. Nakajima, M.R. Delbecq, G. Allison, T. 4036 Honda, T. Kodera, S. Oda, Y. Hoshi, et al., A quantum-dot spin qubit with 4037 coherence limited by charge noise and fidelity higher than 99.9%. Nature 4038 Nanotechnology, 2018. 13(2): p. 102-+ DOI: 10.1038/s41565-017-0014-x. 4039 111. Veldhorst, M., C.H. Yang, J.C.C. Hwang, W. Huang, J.P. Dehollain, J.T. 4040 Muhonen, S. Simmons, A. Laucht, F.E. Hudson, K.M. Itoh, et al., A two-qubit 4041 logic gate in silicon. Nature, 2015. 526(7573): p. 410 DOI: 4042 10.1038/nature15263. 4043 112. Dwyer, K.J., H.S. Kim, D.S. Simons, and J.M. Pomeroy, Temperature- 4044 dependent Si-29 incorporation during deposition of highly enriched Si-28 4045 films. Physical Review Materials, 2017. 1(6): p. 064603 DOI: ARTN 064603 4046 10.1103/PhysRevMaterials.1.064603. 4047 113. Tyryshkin, A.M., J.J.L. Morton, S.C. Benjamin, A. Ardavan, G.A.D. Briggs, 4048 J.W. Ager, and S.A. Lyon, Coherence of spin qubits in silicon. Journal of 4049 Physics-Condensed Matter, 2006. 18(21): p. S783 DOI: 10.1088/0953- 4050 8984/18/21/S06. 4051 114. Culcer, D. and N.M. Zimmerman, Dephasing of Si singlet-triplet qubits due to 4052 charge and spin defects. Applied Physics Letters, 2013. 102(23): p. 232108 4053 DOI: Artn 232108 195 4054 10.1063/1.4810911. 4055 115. Penning, F.M., A new manometer for low gas pressures especially between 4056 10(-3) and 10(-5) mm. Physica, 1937. 4: p. 71-5 DOI: Doi 10.1016/S0031- 4057 8914(37)80123-8. 4058 116. Ota, Y., Silicon molecular beam epitaxy. Thin Solid Films, 1983. 106(1-2): p. 4059 1-136. 4060 117. Eaglesham, D., H.-J. Gossmann, and M. Cerullo, Limiting thickness h epi for 4061 epitaxial growth and room-temperature Si growth on Si (100). Physical 4062 review letters, 1990. 65(10): p. 1227. 4063 118. Eaglesham, D., Semiconductor molecular?beam epitaxy at low temperatures. 4064 Journal of applied physics, 1995. 77(8): p. 3597-3617. 4065 119. Nerding, M., L. Oberbeck, T. Wagner, R. Bergmann, and H. Strunk, Single to 4066 polycrystalline transition in silicon growth by ion-assisted deposition at low 4067 temperatures. Journal of applied physics, 2003. 93(5): p. 2570-2574. 4068 120. Lee, N.E., G. Xue, and J. Greene, Epitaxial Si (001) grown at 80?750 C by 4069 ion?beam sputter deposition: Crystal growth, doping, and electronic 4070 properties. Journal of applied physics, 1996. 80(2): p. 769-780. 4071 121. Murty, M.R., H.A. Atwater, A. Kellock, and J. Baglin, Very low temperature 4072 (< 400? C) silicon molecular beam epitaxy: The role of low energy ion 4073 irradiation. Applied physics letters, 1993. 62(20): p. 2566-2568. 4074 122. Murty, M.R. and H.A. Atwater, Crystal-state?amorphous-state transition in 4075 low-temperature silicon homoepitaxy. Physical Review B, 1994. 49(12): p. 4076 8483. 4077 123. Thiesen, J., H.M. Branz, and R.S. Crandall, Explanation of the limiting 4078 thickness observed in low-temperature silicon epitaxy. Applied Physics 4079 Letters, 2000. 77(22): p. 3589-3591. 4080 124. Jorke, H., H.-J. Herzog, and H. Kibbel, Kinetics of ordered growth of Si on Si 4081 (100) at low temperatures. Physical Review B, 1989. 40(3): p. 2005. 4082 125. Eaglesham, D., H.-J. Gossmann, M. Cerullo, L. Pfeiffer, and K. West, Limited 4083 thickness epitaxy of semiconductors and Si MBE down to room temperature. 4084 Journal of crystal growth, 1991. 111(1-4): p. 833-837. 4085 126. Lee, N.E., G. Tomasch, and J. Greene, Low?temperature Si (001) epitaxy 4086 using low?energy (< E>? 18 eV) Si atoms. Applied physics letters, 1994. 4087 65(25): p. 3236-3238. 4088 127. Chason, E., P. Bedrossian, K. Horn, J. Tsao, and S. Picraux, Ion beam 4089 enhanced epitaxial growth of Ge (001). Applied physics letters, 1990. 57(17): 4090 p. 1793-1795. 4091 128. Choi, C.-H., R. Ai, and S. Barnett, Suppression of three-dimensional island 4092 nucleation during GaAs growth on Si (100). Physical review letters, 1991. 4093 67(20): p. 2826. 4094 129. Orrman-Rossiter, K.G., D. Mitchell, S. Donnelly, C. Rossouw, S. Glanvill, P. 4095 Miller, A.H. Al-Bayati, J. Van Den Berg, and D. Armour, Evidence for 4096 competing growth phases in ion-beam-deposited epitaxial silicon films. 4097 Philosophical Magazine Letters, 1990. 61(6): p. 311-318. 196 4098 130. Tsubouchi, N., A. Chayahara, Y. Mokuno, A. Kinomura, and Y. Horino, 4099 Epitaxial Growth of Pure 28Si Thin Films Using Isotopically Purified Ion 4100 Beams. Japanese Journal of Applied Physics, 2001. 40(12A): p. L1283. 4101 131. Rabalais, J., A. Al-Bayati, K. Boyd, D. Marton, J. Kulik, Z. Zhang, and W. 4102 Chu, Ion-energy effects in silicon ion-beam epitaxy. Physical Review B, 1996. 4103 53(16): p. 10781. 4104 132. Kitabatake, M., P. Fons, and J. Greene, Molecular dynamics and 4105 quasidynamics simulations of low-energy ion/surface interactions leading to 4106 decreased epitaxial temperatures and increased dopant incorporation 4107 probabilities during Si MBE. Journal of crystal growth, 1991. 111(1-4): p. 4108 870-875. 4109 133. Dwyer, K.J., H.S. Kim, D.S. Simons, and J.M. Pomeroy, Temperature- 4110 dependent Si-29 incorporation during deposition of highly enriched Si-28 4111 films. Physical Review Materials, 2017. 1(6) DOI: ARTN 064603 4112 10.1103/PhysRevMaterials.1.064603. 4113 134. Tang, K., H. Kim, A. Ramanayaka, D. Simons, and J. Pomeroy, A compact, 4114 ultra-high vacuum ion source for isotopically enriching and depositing 28Si 4115 thin films. Review of Scientific Instruments, 2019. 90(8): p. 083308. 4116 135. Gordon, J.P. and K.D. Bowers, Microwave Spin Echoes from Donor Electrons 4117 in Silicon. Physical Review Letters, 1958. 1(10): p. 368-370 DOI: DOI 4118 10.1103/PhysRevLett.1.368. 4119 136. Morton, J.J.L., D.R. McCamey, M.A. Eriksson, and S.A. Lyon, Embracing 4120 the quantum limit in silicon computing. Nature, 2011. 479(7373): p. 345-353 4121 DOI: 10.1038/nature10681. 4122 137. Witzel, W.M. and S. Das Sarma, Quantum theory for electron spin 4123 decoherence induced by nuclear spin dynamics in semiconductor quantum 4124 computer architectures: Spectral diffusion of localized electron spins in the 4125 nuclear solid-state environment. Physical Review B, 2006. 74(3) DOI: ARTN 4126 035322 4127 10.1103/PhysRevB.74.035322. 4128 138. Tyryshkin, A.M., S. Tojo, J.J.L. Morton, H. Riemann, N.V. Abrosimov, P. 4129 Becker, H.J. Pohl, T. Schenkel, M.L.W. Thewalt, K.M. Itoh, et al., Electron 4130 spin coherence exceeding seconds in high-purity silicon. Nature Materials, 4131 2012. 11(2): p. 143-147 DOI: 10.1038/Nmat3182. 4132 139. Tracy, L.A., D.R. Luhman, S.M. Carr, N.C. Bishop, G.A. Ten Eyck, T. 4133 Pluym, J.R. Wendt, M.P. Lilly, and M.S. Carroll, Single shot spin readout 4134 using a cryogenic high-electron-mobility transistor amplifier at sub-Kelvin 4135 temperatures. Applied Physics Letters, 2016. 108(6): p. 063101 DOI: Artn 4136 063101 4137 10.1063/1.4941421. 4138 140. Abrosimov, N.V., D.G. Aref'ev, P. Becker, H. Bettin, A.D. Bulanov, M.F. 4139 Churbanov, S.V. Filimonov, V.A. Gavva, O.N. Godisov, A.V. Gusev, et al., A 4140 new generation of 99.999% enriched 28Si single crystals for the determination 4141 of Avogadro's constant. Metrologia, 2017. 54(4): p. 599 DOI: 10.1088/1681- 4142 7575/aa7a62. 197 4143 141. Mazzocchi, V., P.G. Sennikov, A.D. Bulanov, M.F. Churbanov, B. Bertrand, 4144 L. Hutin, J.P. Barnes, M.N. Drozdov, J.M. Hartmann, and M. Sanquer, 4145 99.992% Si-28 CVD-grown epilayer on 300 mm substrates for large scale 4146 integration of silicon spin qubits. Journal of Crystal Growth, 2019. 509: p. 1-7 4147 DOI: 10.1016/j.jcrysgro.2018.12.010. 4148 142. Reshchikov, M., M. Vorobiov, O. Andrieiev, K. Ding, N. Izyumskaya, V. 4149 Avrutin, A. Usikov, H. Helava, and Y. Makarov, Determination of the 4150 concentration of impurities in GaN from photoluminescence and secondary- 4151 ion mass spectrometry. Scientific reports, 2020. 10(1): p. 1-7. 4152 143. Tang, K., H.S. Kim, A.N. Ramanayaka, D.S. Simons, and J.M. Pomeroy, 4153 Targeted enrichment of 28Si thin films for quantum computing. Journal of 4154 physics communications, 2020. 4(3): p. 035006. 4155 144. Petta, J.R., A.C. Johnson, J.M. Taylor, E.A. Laird, A. Yacoby, M.D. Lukin, 4156 C.M. Marcus, M.P. Hanson, and A.C. Gossard, Coherent manipulation of 4157 coupled electron spins in semiconductor quantum dots. Science, 2005. 4158 309(5744): p. 2180-2184. 4159 145. Reilly, D., J. Taylor, J. Petta, C. Marcus, M. Hanson, and A. Gossard, 4160 Suppressing spin qubit dephasing by nuclear state preparation. Science, 2008. 4161 321(5890): p. 817-821. 4162 146. de Leon, N.P., K.M. Itoh, D. Kim, K.K. Mehta, T.E. Northup, H. Paik, B. 4163 Palmer, N. Samarth, S. Sangtawesin, and D. Steuerman, Materials challenges 4164 and opportunities for quantum computing hardware. Science, 2021. 4165 372(6539). 4166 147. Witzel, W.M., M.S. Carroll, A. Morello, L. Cywinski, and S. Das Sarma, 4167 Electron Spin Decoherence in Isotope-Enriched Silicon. Physical Review 4168 Letters, 2010. 105(18): p. 187602 DOI: ARTN 187602 4169 10.1103/PhysRevLett.105.187602. 4170 148. Itoh, K.M., J. Kato, M. Uemura, A.K. Kaliteevskii, O.N. Godisov, G.G. 4171 Devyatych, A.D. Bulanov, A.V. Gusev, I.D. Kovalev, and P.G. Sennikov, 4172 High purity isotopically enriched 29Si and 30Si single crystals: isotope 4173 separation, purification, and growth. Japanese journal of applied physics, 4174 2003. 42(10R): p. 6248. 4175 149. Petit, L., J. Boter, H. Eenink, G. Droulers, M. Tagliaferri, R. Li, D. Franke, K. 4176 Singh, J. Clarke, and R. Schouten, Spin lifetime and charge noise in hot 4177 silicon quantum dot qubits. Physical review letters, 2018. 121(7): p. 076801. 4178 150. Mazzocchi, V., P. Sennikov, A. Bulanov, M. Churbanov, B. Bertrand, L. 4179 Hutin, J. Barnes, M. Drozdov, J. Hartmann, and M. Sanquer, 99.992% 28Si 4180 CVD-grown epilayer on 300 mm substrates for large scale integration of 4181 silicon spin qubits. Journal of Crystal Growth, 2019. 509: p. 1-7. 4182 151. Koch, M., J.G. Keizer, P. Pakkiam, D. Keith, M.G. House, E. Peretz, and 4183 M.Y. Simmons, Spin read-out in atomic qubits in an all-epitaxial three- 4184 dimensional transistor. Nature nanotechnology, 2019. 14(2): p. 137-140. 4185 152. Pillarisetty, R., N. Thomas, H. George, K. Singh, J. Roberts, L. Lampert, P. 4186 Amin, T. Watson, G. Zheng, and J. Torres. Qubit device integration using 4187 advanced semiconductor manufacturing process technology. in 2018 IEEE 4188 International Electron Devices Meeting (IEDM). 2018. IEEE. 198 4189 153. Kravchenko, S. and M. Sarachik, Metal?insulator transition in two- 4190 dimensional electron systems. Reports on Progress in Physics, 2003. 67(1): p. 4191 1. 4192 154. Swartz, R., G. Chin, A. Voshchenkov, P. Ko, B. Wooley, S. Finegan, and R. 4193 Bosworth, Digital NMOS test circuits fabricated in silicon MBE. IEEE 4194 electron device letters, 1984. 5(2): p. 29-31. 4195 155. Leadbeater, M., C. Foden, J. Burroughes, M. Pepper, T. Burke, L. Wang, M. 4196 Grimshaw, and D. Ritchie, Magnetotransport in a nonplanar two-dimensional 4197 electron gas. Physical Review B, 1995. 52(12): p. R8629. 4198 156. Vorob?ev, A., K.-J. Friedland, H. Kostial, R. Hey, U. Jahn, E. Wiebicke, J.S. 4199 Yukecheva, and V.Y. Prinz, Giant asymmetry of the longitudinal 4200 magnetoresistance in high-mobility two-dimensional electron gas on a 4201 cylindrical surface. Physical Review B, 2007. 75(20): p. 205309. 4202 157. Komiyama, S. and H. Hirai, Theory of contacts in a two-dimensional electron 4203 gas at high magnetic fields. Physical Review B, 1989. 40(11): p. 7767. 4204 158. Van Degrift, C., K. Yoshihiro, E. Palm, J. Wakabayashi, and S. Kawaji, Re- 4205 examination of quantum Hall plateaus. IEEE transactions on instrumentation 4206 and measurement, 1993. 42(2): p. 562-567. 4207 159. Lee, P.A. and T. Ramakrishnan, Disordered electronic systems. Reviews of 4208 Modern Physics, 1985. 57(2): p. 287. 4209 160. Hagmann, J.A., X. Wang, P. Namboodiri, J. Wyrick, R. Murray, M. Stewart 4210 Jr, R.M. Silver, and C.A. Richter, High resolution thickness measurements of 4211 ultrathin Si: P monolayers using weak localization. Applied Physics Letters, 4212 2018. 112(4): p. 043102. 4213 161. Hikami, S., A.I. Larkin, and Y. Nagaoka, Spin-orbit interaction and 4214 magnetoresistance in the two dimensional random system. Progress of 4215 Theoretical Physics, 1980. 63(2): p. 707-710. 4216 162. Hagmann, J.A., Magnetotransport investigation of bismuth chalcogenide 4217 topological insulators. 2013: University of Notre Dame. 4218 163. Ando, T., A.B. Fowler, and F. Stern, Electronic properties of two-dimensional 4219 systems. Reviews of Modern Physics, 1982. 54(2): p. 437. 4220 164. Sze, S.M., Y. Li, and K.K. Ng, Physics of semiconductor devices. 2021: John 4221 wiley & sons. 4222 165. Davies, R. and M. Pepper, Electron-electron scattering in silicon inversion 4223 layers. Journal of Physics C: Solid State Physics, 1983. 16(12): p. L353. 4224 166. Padmanabhan, M., T. Gokmen, N. Bishop, and M. Shayegan, Effective mass 4225 suppression in dilute, spin-polarized two-dimensional electron systems. 4226 Physical review letters, 2008. 101(2): p. 026402. 4227 167. Mi, X., T. Hazard, C. Payette, K. Wang, D. Zajac, J. Cady, and J.R. Petta, 4228 Magnetotransport studies of mobility limiting mechanisms in undoped Si/SiGe 4229 heterostructures. Physical Review B, 2015. 92(3): p. 035304. 4230 168. Mani, R., W. Johnson, V. Umansky, V. Narayanamurti, and K. Ploog, Phase 4231 study of oscillatory resistances in microwave-irradiated-and dark- 4232 GaAs/AlGaAs devices: Indications of an unfamiliar class of the integral 4233 quantum Hall effect. Physical Review B, 2009. 79(20): p. 205320. 199 4234 169. Coleridge, P., Inter-subband scattering in a 2D electron gas. Semiconductor 4235 science and technology, 1990. 5(9): p. 961. 4236 170. MacLeod, S., K. Chan, T. Martin, A. Hamilton, A. See, A. Micolich, M. 4237 Aagesen, and P. Lindelof, Role of background impurities in the single-particle 4238 relaxation lifetime of a two-dimensional electron gas. Physical Review B, 4239 2009. 80(3): p. 035310. 4240 171. Gold, A., Scattering time and single-particle relaxation time in a disordered 4241 two-dimensional electron gas. Physical Review B, 1988. 38(15): p. 10798. 4242 172. Li, J. and T.P. Ma, Scattering of silicon inversion layer electrons by 4243 metal/oxide interface roughness. Journal of applied physics, 1987. 62(10): p. 4244 4212-4215. 4245 173. Ramanayaka, A.N., K. Tang, J.A. Hagmann, H.-S. Kim, D.S. Simons, C.A. 4246 Richter, and J.M. Pomeroy, Use of quantum effects as potential qualifying 4247 metrics for ?quantum grade silicon?. AIP Advances, 2019. 9(12): p. 125153. 4248 174. Carter, D.J., O. Warschkow, N.A. Marks, and D.R. McKenzie, Electronic 4249 structure models of phosphorus ?-doped silicon. Physical Review B, 2009. 4250 79(3): p. 033204. 4251 175. Goh, K.E., L. Oberbeck, M. Simmons, and R. Clark, Electrical activation of 4252 phosphorus in silicon. 2003. 4253 176. Brocks, G., P. Kelly, and R. Car, Aluminum on Si (100): Growth and structure 4254 of the first layer. Journal of Vacuum Science & Technology B: 4255 Microelectronics and Nanometer Structures Processing, Measurement, and 4256 Phenomena, 1994. 12(4): p. 2705-2708. 4257 177. Ide, T., T. Nishimori, and T. Ichinokawa, Surface structures of Si (100)-Al 4258 phases. Surface Science, 1989. 209(3): p. 335-344. 4259 178. Murakami, K.-i., K. Nishikata, M. Yoshimura, and A. Kawazu, Structural 4260 studies of Al/Si (100) by LEED. Applied surface science, 1992. 60: p. 146- 4261 151. 4262 179. Yeom, H., T. Abukawa, M. Nakamura, S. Suzuki, S. Sato, K. Sakamoto, T. 4263 Sakamoto, and S. Kono, Initial stage growth of In and A1 on a single-domain 4264 Si (001) 2? 1 surface. Surface science, 1995. 341(3): p. 328-334. 4265 180. Lander, J. and J. Morrison, Surface reactions of silicon with aluminum and 4266 with indium. Surface Science, 1964. 2: p. 553-565. 4267 181. Zhu, C., S. Misawa, S. Tsukahara, A. Kawazu, and S. Pang, Adsorption and 4268 growth of Al on Si (100) in the initial stage. Applied Physics A: Materials 4269 Science & Processing, 1999. 68(2). 4270 182. Brocks, G., P. Kelly, and R. Car, Adsorption of Al on Si (100): A surface 4271 polymerization reaction. Physical review letters, 1993. 70(18): p. 2786. 4272 183. Nogami, J., A. Baski, and C. Quate, Aluminum on the Si (100) surface: 4273 Growth of the first monolayer. Physical Review B, 1991. 44(3): p. 1415. 4274 184. Northrup, J.E., M. Schabel, C. Karlsson, and R. Uhrberg, Structure of low- 4275 coverage phases of Al, Ga, and In on Si (100). Physical Review B, 1991. 4276 44(24): p. 13799. 4277 185. Sakama, H., K.-i. Murakami, K. Nishikata, and A. Kawazu, Structural 4278 determination of Si (100) 2? 2-Al by tensor LEED. Physical Review B, 1993. 4279 48(8): p. 5278. 200 4280 186. Steele, B., L. Li, J. Stevens, and I. Tsong, Structure of the Si (100)-(2? 2) In 4281 surface. Physical Review B, 1993. 47(15): p. 9925. 4282 187. Kucera, M., F. Rozboril, P. Sobotik, and I. Ostadal, Aluminium on the Si 4283 (100)-2? 1?Growth, Morphology, and Different Modifications of Aluminium 4284 Dimers Studied by STM. 4285 188. Appelbaum, J.A., G. Baraff, and D. Hamann, The si (100) surface. iii. surface 4286 reconstruction. Physical Review B, 1976. 14(2): p. 588. 4287 189. Tromp, R., E. Van Loenen, J. Demuth, and N. Lang, Tip electronic structure 4288 in scanning tunneling microscopy. Physical Review B, 1988. 37(15): p. 9042. 4289 190. Byun, J., M.R. Verardo, B. Sumengen, G.P. Lewis, B. Manjunath, and S.K. 4290 Fisher, Automated tool for the detection of cell nuclei in digital microscopic 4291 images: application to retinal images. Mol Vis, 2006. 12(105-07): p. 949-60. 4292 191. Drey, L.L., M.C. Graber, and J. Bieschke, Counting unstained, confluent cells 4293 by modified bright-field microscopy. Biotechniques, 2013. 55(1): p. 28-33. 4294 192. Keizer, J.G., S.R. McKibbin, and M.Y. Simmons, The impact of dopant 4295 segregation on the maximum carrier density in Si: P multilayers. ACS nano, 4296 2015. 9(7): p. 7080-7084. 4297 193. M?ller, E.W., J.A. Panitz, and S.B. McLane, The atom?probe field ion 4298 microscope. Review of Scientific Instruments, 1968. 39(1): p. 83-86. 4299 194. Cerezo, A., P.H. Clifton, M.J. Galtrey, C.J. Humphreys, T.F. Kelly, D.J. 4300 Larson, S. Lozano-Perez, E.A. Marquis, R.A. Oliver, and G. Sha, Atom probe 4301 tomography today. Materials Today, 2007. 10(12): p. 36-42. 4302 195. Barroo, C., A.J. Akey, and D.C. Bell, Atom probe tomography for catalysis 4303 applications: a review. Applied Sciences, 2019. 9(13): p. 2721. 4304 196. Schofield, S., N. Curson, M. Simmons, F. Rue?, T. Hallam, L. Oberbeck, and 4305 R. Clark, Atomically precise placement of single dopants in Si. Physical 4306 review letters, 2003. 91(13): p. 136104. 4307 197. Hallam, T., T. Reusch, L. Oberbeck, N. Curson, and M. Simmons, Scanning 4308 tunneling microscope based fabrication of nano-and atomic scale dopant 4309 devices in silicon: The crucial step of hydrogen removal. Journal of applied 4310 physics, 2007. 101(3): p. 034305. 4311 198. Gossmann, H.-J. and F. Unterwald, Dopant electrical activity and majority- 4312 carrier mobility in B-and Sb-?-doped Si thin films. Physical Review B, 1993. 4313 47(19): p. 12618. 4314 199. Murakami, M., Critical Reviews in Solid State and Materials. Science, 1998. 4315 23: p. 1. 4316 200. Tsui, D. and G. Kaminsky, Observation of Higher Sub-band in n-Type (100) 4317 Si Inversion Layers. Physical Review Letters, 1975. 35(21): p. 1468. 4318 201. Cham, K. and R. Wheeler, Temperature-dependent resistivities in silicon 4319 inversion layers at low temperatures. Physical Review Letters, 1980. 44(22): 4320 p. 1472. 4321 202. Zieve, R., D. Prober, and R. Wheeler, Low-temperature electron-phonon 4322 interaction in Si MOSFETs. Physical Review B, 1998. 57(4): p. 2443. 4323 203. Hwang, E. and S.D. Sarma, Electronic transport in two-dimensional Si: P ?- 4324 doped layers. Physical Review B, 2013. 87(12): p. 125411. 201 4325 204. Sommerfeld, A. and N.H. Frank, The Statistical theory of thermoelectric, 4326 galvano-and thermomagnetic phenomena in metals. Reviews of Modern 4327 Physics, 1931. 3(1): p. 1. 4328 205. Kapitza, P., The study of the specific resistance of bismuth crystals and its 4329 change in strong magnetic fields and some allied problems. Proceedings of 4330 the Royal Society of London. Series A, Containing Papers of a Mathematical 4331 and Physical Character, 1928. 119(782): p. 358-443. 4332 206. Novak, M., S. Sasaki, K. Segawa, and Y. Ando, Large linear 4333 magnetoresistance in the Dirac semimetal TlBiSSe. Physical Review B, 2015. 4334 91(4): p. 041203. 4335 207. Abrikosov, A., Quantum linear magnetoresistance; solution of an old 4336 mystery. Journal of Physics A: Mathematical and General, 2003. 36(35): p. 4337 9119. 4338 208. Goh, K., L. Oberbeck, and M. Simmons, Relevance of phosphorus 4339 incorporation and hydrogen removal for Si: P ??doped layers fabricated using 4340 phosphine. physica status solidi (a), 2005. 202(6): p. 1002-1005. 4341 209. Reusch, T., N. Curson, S. Schofield, T. Hallam, and M. Simmons, Phosphorus 4342 and hydrogen atoms on the (0 0 1) surface of silicon: A comparative scanning 4343 tunnelling microscopy study of surface species with a single dangling bond. 4344 Surface science, 2006. 600(2): p. 318-324. 4345 210. Warschkow, O., H.F. Wilson, N.A. Marks, S. Schofield, N. Curson, P. Smith, 4346 M. Radny, D. McKenzie, and M. Simmons, Phosphine adsorption and 4347 dissociation on the Si (001) surface: An ab initio survey of structures. 4348 Physical Review B, 2005. 72(12): p. 125328. 4349 211. Bottoms, B. The International Roadmap for Semiconductors 2007. in 2007 4350 8th International Conference on Electronic Packaging Technology. 2007. 4351 IEEE. 4352 212. Johnson, B.C., J.C. McCallum, and M.J. Aziz, Solid-phase epitaxy, in 4353 Handbook of Crystal Growth. 2015, Elsevier. p. 317-363. 4354 213. Arthur, J.R., Molecular beam epitaxy. Surface science, 2002. 500(1-3): p. 4355 189-217. 4356 214. Mirabella, S., D. De Salvador, E. Bruno, E. Napolitani, E.F. Pecora, S. 4357 Boninelli, and F. Priolo, Mechanism of boron diffusion in amorphous silicon. 4358 Physical review letters, 2008. 100(15): p. 155901. 4359 215. Krause, O., H. Ryssel, and P. Pichler, Determination of aluminum diffusion 4360 parameters in silicon. Journal of Applied Physics, 2002. 91(9): p. 5645-5649. 4361 216. Weir, B., D. Eaglesham, L. Feldman, H. Luftman, and R. Headrick, Electron 4362 microscopy of the ordered boron 2? 1 structure buried in crystalline silicon. 4363 Applied surface science, 1995. 84(4): p. 413-418. 4364 217. Nishida, S., T. Shiimoto, A. Yamada, S. Karasawa, M. Konagai, and K. 4365 Takahashi, Epitaxial growth of silicon by photochemical vapor deposition at a 4366 very low temperature of 200? C. Applied physics letters, 1986. 49(2): p. 79- 4367 81. 4368 218. Brillson, L., M. Slade, A. Katnani, M. Kelly, and G. Margaritondo, Reduction 4369 of silicon?aluminum interdiffusion by improved semiconductor surface 4370 ordering. Applied physics letters, 1984. 44(1): p. 110-112. 202 4371 219. Yamada, M., K. Sawano, M. Uematsu, and K.M. Itoh, Suppression of surface 4372 segregation of the phosphorous ?-doping layer by insertion of an ultra-thin 4373 silicon layer for ultra-shallow Ohmic contacts on n-type germanium. Applied 4374 Physics Letters, 2015. 107(13): p. 132101. 4375 220. Keizer, J.G., S. Koelling, P.M. Koenraad, and M.Y. Simmons, Suppressing 4376 segregation in highly phosphorus doped silicon monolayers. ACS nano, 2015. 4377 9(12): p. 12537-12541. 4378 221. Moon, C.-Y., W.-J. Lee, and K.-J. Chang, Formation of dopant-pair defects 4379 and doping efficiency in B-and P-doped silicon nanowires. Nano letters, 2008. 4380 8(10): p. 3086-3091. 4381 222. Marcenat, C., J. Ka?mar??k, R. Piquerel, P. Achatz, G. Prudon, C. Dubois, B. 4382 Gautier, J. Dupuy, E. Bustarret, and L. Ortega, Low-temperature transition to 4383 a superconducting phase in boron-doped silicon films grown on (001)- 4384 oriented silicon wafers. Physical Review B, 2010. 81(2): p. 020501. 4385 223. Balmer, R.S., I. Friel, S. Hepplestone, J. Isberg, M.J. Uren, M.L. Markham, 4386 N.L. Palmer, J. Pilkington, P. Huggett, and S. Majdi, Transport behavior of 4387 holes in boron delta-doped diamond structures. Journal of Applied Physics, 4388 2013. 113(3): p. 033702. 4389 224. Chicot, G., T. Tran Thi, A. Fiori, F. Jomard, E. Gheeraert, E. Bustarret, and J. 4390 Pernot, Hole transport in boron delta-doped diamond structures. Applied 4391 Physics Letters, 2012. 101(16): p. 162101. 4392 225. Sussmann, R.S., CVD diamond for electronic devices and sensors. Vol. 26. 4393 2009: John Wiley & Sons. 4394 226. Davies, J.H., The physics of low-dimensional semiconductors: an 4395 introduction. 1998: Cambridge university press. 4396 227. Schroder, D.K., Semiconductor material and device characterization. 2015: 4397 John Wiley & Sons. 4398 228. Aono, M., O. Maida, and T. Ito, Hall data analysis of heavily boron-doped 4399 CVD diamond films using a model considering an impurity band well 4400 separated from valence bands. Diamond and related materials, 2011. 20(10): 4401 p. 1357-1362. 4402 229. Borst, T. and O. Weis, Boron?Doped Homoepitaxial Diamond Layers: 4403 Fabrication, Characterization, and Electronic Applications. physica status 4404 solidi (a), 1996. 154(1): p. 423-444. 4405 230. Mott, N., Metal-insulator transitions. 2004: CRC Press. 4406 231. Bartl, G., P. Becker, B. Beckhoff, H. Bettin, E. Beyer, M. Borys, I. Busch, L. 4407 Cibik, G. D?Agostino, and E. Darlatt, A new 28Si single crystal: counting the 4408 atoms for the new kilogram definition. Metrologia, 2017. 54(5): p. 693. 4409 232. Artzi, Y., Y. Twig, and A. Blank, Induction-detection electron spin resonance 4410 with spin sensitivity of a few tens of spins. Applied Physics Letters, 2015. 4411 106(8): p. 084104. 4412 233. Bienfait, A., J. Pla, Y. Kubo, M. Stern, X. Zhou, C. Lo, C. Weis, T. Schenkel, 4413 M. Thewalt, and D. Vion, Reaching the quantum limit of sensitivity in electron 4414 spin resonance. Nature nanotechnology, 2016. 11(3): p. 253. 203 4415 234. Mani, R.G., J. Hankinson, C. Berger, and W.A. De Heer, Observation of 4416 resistively detected hole spin resonance and zero-field pseudo-spin splitting in 4417 epitaxial graphene. Nature communications, 2012. 3(1): p. 1-6. 4418 204