ABSTRACT 
 
 
 
 
Title of Document: EVOLUTION OF PATTERNED AND 
UNPATTERNED SURFACES DURING HIGH 
TEMPERATURE ANNEALING AND 
PLASMA ETCHING 
  
 Taesoon Kwon, Doctor of Philosophy, 2007 
  
Directed By: Associate Professor, Raymond J. Phaneuf, 
Department of Materials Science and 
Engineering 
 
 
 
In this thesis we describe experiments designed to probe spontaneous and directed 
surface evolution during annealing and plasma etching of three materials of high 
technological interest: silicon, nanoporous silica and photoresist.           
Vicinal Si(111) surfaces provide a source of steps whose configuration we control 
via the introduction of a topographic pattern; this is done using combination of 
photolithography and reactive ion etching. We study the length scale dependence of self-
organization of step bunches during annealing at ~ 1273 ?C in ultrahigh vacuum (UHV), 
resulting from sublimation and diffusion, and the competition between effects due to the 
intrinsic stiffness of steps and their mutual interactions. We also show the results of 
numerical simulations on these surfaces based upon a simple model of step motion, 
which we compare with our experimental observations.   
  
Nanoporous silica (NPS) is a heterogeneous material which is of potential use in 
micro/nanoelectronic applications requiring an insulator with a small dielectric constant. 
We investigate the stability of the NPS-plasma interface during etching, comparing the 
tendency for spontaneous pattern formation with the persistence of patterned 
perturbations. We study samples with various porosity (0 ~ 50 vol.%) under low pressure 
C4F8/90%Ar plasma etching conditions. Our AFM characterization of unpatterned 
surfaces shows a monotonic increase in RMS roughness with etching time. Annealing 
etched NPS surfaces at temperatures over the range from 300 ~ 900 ?C in UHV as well as 
in non-oxidizing environment produces no significant relaxation of etching-induced 
surface roughness. Statistical analysis using a height-height correlation function reveals 
that NPS surfaces do not show a simple scaling behavior during the technologically-
relevant transient time regime. Etching of patterned surfaces reveals a persistent period of 
approximately 400 nm, which is ~ 4 times that which spontaneously appears during 
etching of unpatterned surfaces. Based upon this observation we investigate the 
possibility of period doubling, and find some evidence for it.    
Lastly, we present preliminary results of surface morphological and compositional 
evolution of model photoresists for lithography at 193 nm and 248 nm wavelengths 
during etching using plasma and ion beam sputtering under a range of conditions. 
Surprisingly, our AFM characterization shows that there is no significant difference in 
roughness evolution between resists whose chemical backbone is qualitatively different, 
i.e. benzene-ring based 248 nm and acrylate-admatane based 193 nm polymers. The 
surface roughening however varies strongly with the position of a methyl group on the 
polymer backbone. Fourier transform infrared spectroscopy (FTIR), Ellipsometry and 
  
XPS characterizations show that the polymers become dense at the early stages of plasma 
/ ion beam exposure, possibly due to graphitization, cross-linking and hydrogen loss. We 
compare these observations with molecular dynamic (MD) simulations of Ar+ ion beam 
sputtering. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
 
EVOLUTION OF PATTERNED AND UNPATTERNED 
SURFACES DURING HIGH TEMPERATURE 
ANNEALING AND PLASMA ETCHING 
 
 
 
By 
 
 
Taesoon Kwon 
 
 
 
 
 
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 
2007 
 
 
 
 
 
 
 
 
 
 
Advisory Committee: 
Professor Raymond J. Phaneuf, Chair 
Professor Ellen D. Williams 
Professor Gottlieb S. Oehrlein 
Professor Lourdes G. Salamanca-Riba 
Professor John Cumings 
 
 
 
 
 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
? Copyright by 
Taesoon Kwon 
2007 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ii 
Dedication 
To my parents, my uncle and aunt (Yoon?s family).  
 iii 
Acknowledgements 
 
First and foremost I would like to thank my advisor, Prof. Raymond J. Phaneuf. 
He has been a constant source of ideas, guidance, and unending critical analysis over the 
years. I would like to thank his scientific enthusiastic and encouragements that he showed 
me. I am grateful for the opportunity to have worked with him.  
I would also like to acknowledge Dr. Hung-chih Kan. I have learned valuable 
scientific insights and scientific way of thinking while I have been working various 
projects with him over the years. 
The work I describe in this thesis was carried out by me in collaboration with a 
number of colleagues whose contributions I acknowledge here. Dr. Hung-Chih Kan 
contributed significantly to the vicinal Si(111) and NPS studies, both in data analysis, and 
in carrying out the numerical simulations described in chapter 2. Xue-Feng Hua and 
Sebastian Engelmann carried out the plasma etching experiments described in chapter 3, 
while Robert Bruce carried out those described in chapter 4. Deborah Cottrill helped the 
annealing experiments described in chapter 3. Sherman Guo helped in the development 
of the nanoscraping codes presented in chapter 4. Dustin Nest carried out ion beam 
sputtering experiments, while Joseph Vegh carried out molecular dynamics simulations 
both from University of California, Berkeley presented in chapter 4. Also Brian Long at 
University of Texas, Austin, performed chemical synthesis of model polymers I 
presented in chapter 4. Particularly, Professor Oehrlein provided plasma etching / 
characterization facilities for the work presented in chapter 3 and 4. I thank each of them 
for their contributions. 
 iv 
The members of my committee, Professor E. Williams, Professor G. Oehrlein, 
Professor L. Salamanca-Riba and Professor J. Cumings, are all inspiring scientists and 
teachers, and it has been my great privilege to talk with them about my research works.  
I would also like to thank the support of NSF, MRSEC at University of Maryland 
and Laboratory for Physical Sciences (LPS) for my research over the years. Especially, I 
am very grateful to LPS clean room staffs: Toby Olver, Russell Frizzell, and Steve 
Brown. They are very wonderful and interesting people.       
Finally I thank all my former and current colleagues in surface physics lab at LPS: 
Sonam Shah, Tabassom Tadayyon, Dominic Britti, Sherman Guo, and Phoebe Tsai for 
their helpful discussion regarding my work and encouragement.   
 v 
Table of contents 
 
 
Dedication .......................................................................................................................... ii 
 
Acknowledgements ..........................................................................................................iii 
 
Table of contents ............................................................................................................... v 
 
List of Tables ................................................................................................................... vii 
 
List of Figures.................................................................................................................viii 
 
Chapter 1 Introduction..................................................................................................... 1 
1.1 Motivation............................................................................................................ 1 
1.2 Ehrlich-Schwoebel effect.................................................................................... 3 
1.3 Introduction to tapping mode AFM.................................................................. 7 
 
Chapter 2 Length-scale dependence of the step bunch self-organization on patterned 
vicinal Si(111) surfaces ................................................................................................... 13 
2.1 Introduction....................................................................................................... 13 
2.2 Experiment ........................................................................................................ 14 
2.2.1 Sample preparation .................................................................................. 14 
2.2.2 High temperature annealing of samples................................................... 18 
2.3 Understanding of the surface evolution .......................................................... 19 
2.4 Results ................................................................................................................ 26 
2.5 Discussion........................................................................................................... 39 
2.6 Summary of Experimental Results.................................................................. 40 
2.7 Numerical simulations on patterned vicinal Si(111) surfaces during high 
temperature annealing............................................................................................ 41 
2.7.1 Introduction.............................................................................................. 41 
2.7.2 Results...................................................................................................... 46 
2.7.3 Discussion................................................................................................ 51 
 
Chapter 3 Evolution of roughness and wavelength selection during fluorocarbon 
plasma etching of Nanoporous Silica ............................................................................ 56 
3.1 Introduction....................................................................................................... 56 
3.2 Experiment ........................................................................................................ 58 
3.3 Results ................................................................................................................ 61 
3.4 Discussion........................................................................................................... 77 
3.5 Conclusions ? Pattern Formation.................................................................... 79 
3.6 Evolution of roughness during annealing of plasma etched NPS................. 80 
3.7 Summary............................................................................................................ 89 
 
 vi 
Chapter 4 Nanotechnological Manufacturing: Nanostructured Polymers Designed 
for Plasma/Energetic Beam Templating of Materials ................................................. 90 
4.1 Morphological and chemical evolution of model polymers during plasma 
etching ...................................................................................................................... 90 
4.1.1 Introduction.............................................................................................. 90 
4.1.2 Experiment............................................................................................... 91 
4.1.3 Results...................................................................................................... 97 
4.1.4 Discussion.............................................................................................. 110 
4.2 Summary.......................................................................................................... 114 
4.3 Appendix: Nanolithography on PS ............................................................... 115 
4.3.1 Introduction............................................................................................ 115 
4.3.2 Experiment............................................................................................. 115 
4.3.3 Results.................................................................................................... 119 
4.3.4 Discussion.............................................................................................. 125 
 
Chapter 5 General conclusions.................................................................................... 128 
 
Chapter 6 Future work................................................................................................. 132 
Chapter 2 Length-scale dependence of the step bunch self-organization on 
patterned vicinal Si(111) surfaces ......................................................................... 132 
Chapter 3 Evolution of roughness and wavelength selection during fluorocarbon 
plasma etching of Nanoporous Silica ................................................................... 133 
Chapter 4 Nanotechnological Manufacturing: Nanostructured Polymers 
Designed for Plasma/Energetic Beam Templating of Materials ......................... 133 
 
Appendix A.................................................................................................................... 134 
Sample cleaning procedures for Si (111) patterned samples:........................... 134 
 
Appendix B .................................................................................................................... 135 
Patterned NPS sample preparation procedure:................................................. 135 
 
Appendix C.................................................................................................................... 136 
Nanometer size square pattern design details for electron beam lithography on 
NPS......................................................................................................................... 136 
 
Appendix D.................................................................................................................... 137 
Roughness evolution of model resist polymers during C4F8/90%Ar plasma 
etching: Effect of trace Al contaminants ............................................................ 137 
 
Bibliography .................................................................................................................. 139 
 
 vii 
List of Tables 
 
 
Table 1.1 Si(111) step parameters proposed at 900 ?C under local mass transport limit in 
Ref. 2.20 and 2.21. Here d is defined by d = Ds / ? where Ds is the adatom diffusion 
rate, and ? is the attachment/detachment rate. q is an effective charge of the adatoms, 
and ? is the step mobility. ? = 2ceqa4? (ceqa2 = 0.2 ML) is used; the step interaction 
parameter g was estimated as approximately 0.015 eV/?2 at 900 ?C....................... 45 
 
Table 1.2 Si step parameters proposed at 1270 ?C in Ref. 2.22. Here Ceq is the 
equilibrium adatom concentration on terraces, a2 is the area of a single atomic cell 
on the surface, and F is the force acting on each adatom (F = qE). Re is the 
sublimation rate, and it is approximately 2 ML/s at 1270 ?C. .................................. 45 
 
 
 
 
 
 
 
 viii 
List of Figures 
 
 
Figure 1.1 Stepped surface with kinks............................................................................... 2 
 
Figure 1.2 Schematic of Ehrlich-Schwoebel potential barrier at step edge. ...................... 3 
 
Figure 1.3 Force vs. tip-to-sample distance in AFM operation. ........................................ 9 
 
Figure 1.4 Schematic of tapping mode Atomic Force Microscopy. ................................ 10 
 
Figure 1.5 Examples of tip-sample convolution: (a) an overestimated convex surface 
feature, and (b) an underestimated concave feature.................................................. 12 
 
 
Figure 2.1 Combinatorial approach: Systematic varying of pit diameters & spacing. .... 15 
 
Figure 2.2 Summary of sample preparation for the cylindrical pit patterned Si(111) 
surfaces. .................................................................................................................... 17 
 
Figure 2.3 Step profile on a patterned vicinal surface, and step motion which would 
result if only sublimation were considered. .............................................................. 20 
 
Figure 2.4 Competing effects acting upon steps on a pit patterned vicinal surface during 
high temperature annealing: Sublimation; Line tension, which is related to the step 
stiffness; Step-step interaction. Here ?
  is the step stiffness, g is the step-step 
interaction coefficient, and l is the separation between steps in the Free E/Area 
equation..................................................................................................................... 22 
 
Figure 2.5 Step stiffness effects vs. pattern length scale after 30 sec. annealing at ~ 
1273 ?C. On the left hand side is an AFM image of 1.4 um diameter ? 2.8 um 
spacing, on the right hand side is an AFM image of 4.0 um diameter ? 8.0 um 
spacing. The smaller period patterned surface shows the nearly straight step bunches 
after annealing, while the larger period patterned surface shows laterally corrugated 
step bunches after same amount of annealing........................................................... 23 
 
Figure 2.6 Step-Step Interaction Effects: Surface plot of AFM image for surface 
patterned with 8 um diameter pits spaced at 16 um.................................................. 25 
 
Figure 2.7 Length scale dependence on the topographical evolution after 15 sec. 
annealing at ~ 1273 ?C.............................................................................................. 27 
 
Figure 2.8 Annealing time effect on evolution. High-pass AFM images for a pit pattern 
of 2.8 ?m diameter x 5.6 ?m spacing at ~ 1273 ?C. The images are for a 20 um x 20 
um field of view. ....................................................................................................... 29 
 ix 
Figure 2.9 Annealing time effect on evolution for a pattern made up of 4 ?m diameter 
pits x 8 ?m spacing at ~ 1273 ?C. The high-pass AFM images are for a 30 ?m x 30 
?m field of view........................................................................................................ 30 
 
Figure 2.10 (Left) In-plane corrugation of pattern relaxation vs. pattern length scale. The 
numbers indicate the initial pit diameter; the center-to-center spacing is twice the 
diameter. (Right) Illustration of determination of in-plane corrugation. .................. 32 
 
Figure 2.11 Relaxation of out of plane corrugation amplitude for a pattern consisting of 
2.8 ?m diameter pits with a 5.6 ?m center-to-center spacing. (a) Profiles measured 
across pit centers, (b) profiles measured between pit centers. (Center) Summary of 
amplitudes vs. anneal time........................................................................................ 34 
 
Figure 2.12 Out of plane corrugation with length scale variation (a) 1.4 um dia. ? 2.8 um 
pitch, (b) 2.0 um dia. ? 4.0 um pitch, (c) 4.0 um dia. ? 8.0 um pitch, and (d) 8.0 um 
dia. ? 16 um pitch...................................................................................................... 36 
 
Figure 2.13 Summary of time constants for decay of in-plane (solid circle) and out-of-
plane (open squares) corrugation amplitudes as a function of initial pit diameter. 
Dashed line shows a best fit to a power law dependence for the in-plane relaxation 
time, with an exponent of 3.86?0.14. ....................................................................... 38 
 
Figure 2.14 Mesoscopic model for step kinetics [1.8]. Here ? is the step mobility, ?
  is 
the step stiffness, g is the step-step interaction coefficient, ?? and ?+ are the kinetic 
coefficients for attachment to the upper and lower terraces, and W1 and W2 are the 
upper terrace and the lower widths, respectably....................................................... 44 
 
Figure 2.15 Two examples of simulations on circular pit patterned Si(111) surface in 
both top-down and cross-sectional views: (a) 0.7 um diameter ? 1.4 um separation, 
and (b) 2.8 um diameter ? 5.6 um separation. Insets are the AFM height images of 
the surface after 30 sec. annealing at ~ 1273 ?C....................................................... 47 
 
Figure 2.16 Summary of experimental results of surface evolutions on effects of length 
scale and annealing time. (a) The top panel shows the three pattern length scales 
from different parts of the surface after 30 sec. annealing at ~ 1273 ? C: 1.4 um pit 
diameter ? 2.8 um separation between pits, 4.0 um pit diameter ? 8.0 um separation 
between pits, and 8.0 um pit diameter ? 16.0 um separation between pits (from left 
to right). The middle column images show the evolution on fixed length scale at 4.0 
um pit diameter ? 8.0 um separation between pits with increased annealing time. (b) 
Log-log plot of decay time constant as a function of pit diameter for both out-of 
plane corrugation (OOP) and in-plane corrugation (IP). .......................................... 49 
 
Figure 2.17 Simulated structures after a 30 second and 65 second anneals. The insets 
show the high pass AFM images that we measure for comparison. The summary 
plots are the extracted simulations of the same in plane and out of plane (OOP) 
corrugation amplitudes we measured in our AFM images. ...................................... 50 
 x 
Figure 2.18 A detailed comparison between the simulated and measured decay times vs. 
pit diameter from both in-plane (IP) and out-of plane (OOP) corrugations analysis. 
Also the characteristic lower and upper bounding periods are estimated by using the 
step kinetic parameters ?, ?
 , and g as 2.2 um and 15.5 um, respectively. Where A is 
the amplitude of the sinusoid, w is the average step spacing, a0  is the miscut angle, d 
is the depth of pit, and L is the period (i.e. twice of pit diameter)............................ 53 
 
Figure 2.19 Step kinetic parameters for simulation [2.12, 2.17 ? 2.19]. The velocity 
equation contains the product of the step mobility and stiffness and the product of 
the mobility and step interaction parameter. For simplicity we used the step mobility 
extrapolated from measurements of step fluctuations at 900 ?C and 1100 ?C by 
Metois [2.12]............................................................................................................. 55 
 
 
Figure 3.1 Processing steps to produce Nanoporous silica films [3.5]............................ 57 
 
Figure 3.2 Schematic drawing of blanket NPS sample structures. .................................. 60 
 
Figure 3.3 Summary of AFM scanning results on blanket samples: Plasma etching 
induced surface roughness vs. plasma etching time as a function of porosity. The 
additional box includes the etching rate of each surface depending on the porosity.63 
 
Figure 3.4 Summary of representative AFM images after plasma etching with 
C4F8/90%Ar at 10 mTorr, 600 W source power, and -125 V self-bias voltage. The 
etching was performed gradually along the long edge of each sample for 0 ~ 70 sec. 
using a Si shutter. The percentage in each image indicates porosity of NPS. SiO2 is 
assumed to be 0 % porosity. ..................................................................................... 64 
 
Figure 3.5 Height correlation functions as a function of plasma etching time for 30 % 
porosity NPS. ............................................................................................................ 67 
 
Figure 3.6 (a) Height-Height correlation function vs. lateral distance (open circles) for an 
unpatterned 15 % NPS sample after etching 43 s in C4F8/90%Ar, calculated from a 2 
um field of view AFM image, and fit to form from reference [3.16] for self-affine 
structure (solid curve). Insert: AFM image of the same surface (0.75 um field of 
view). (b) Asymptotic values of roughness exponent ? (filled circle), RMS 
roughness vs. time exponent ? (closed vertical diamonds), correlation length vs. 
time exponent 1/z (filled square) and ratio of ?/? (open square).vs. porosity. Dashed 
line shows value of 1 predicted by flux re-emission model [3.14] for all exponents.
................................................................................................................................... 68 
 
Figure 3.7 Evidence for wavelength selection during C4F8/90%Ar plasma etching of NPS 
(30 % porosity): (a) AFM image of a blank surface after etching for ~ 47 sec., and 
(b) TEM cross-sectional images after etching from Ref. [3.4]. ................................ 71 
 
 xi 
Figure 3.8 AFM summary of e- beam patterned NPS (30 % porosity) surfaces. We 
pattern the surface with the arrays of square pits with varying in size by maintaining 
a fixed width/spacing ratio of 1:2. And then we etched the ?pre-patterned? surfaces 
at various time periods. ............................................................................................. 73 
 
Figure 3.9 Evolution of height profiles vs. etching time: pattern sizes for (a) 140 nm 
width x 280 nm spacing, (b) 200 nm width x 400 nm spacing, and (c) 560 nm width 
x 1120 nm spacing from the 30 % porosity NPS. In both the smallest and the largest 
pattern periods, the formation of micro-trenches at the side walls of pit bottoms is 
dominant at initial stage of etching........................................................................... 75 
 
Figure 3.10 Summary plot of the amplitude of fundamental Fourier component as a 
function of pattern period. This shows an existence of a persistent length scale at ~ 
400 nm period during Fluorocarbon plasma etching of NPS (30 % porosity), where 
the pattern amplitude persists regardless of etching duration we studied................. 76 
 
Figure 3.11 The mapped images of cross term in height correlation function (g) for the as 
patterned and etched surfaces for the pits with 200 nm width x 400 nm spacing. (a) 
An unpatterned NPS surface is included for the comparison. (b) Starting surface, (c) 
32 s etched surface, and (d) 64 s etched surface. The starting surface shows the nice 
square periodicity, set by initial patterning. In an unpatterned sample, however, there 
is no such periodicity instead only one maxima peak is shown up. After 32 s etching 
the additional maxima appeared, indicating that there are series of stable 
wavelengths. Further etching, 64 s also similarly shows the second periodicity, 
possibly something-like period doubling is going on. ............................................. 78 
 
Figure 3.12 The schematic descriptions of annealing processes performed on NPS (36 % 
porosity) samples. (a) The vacuum chamber is pumped down to approximately 2 x 
10-8 torr. The sample is then heated with a tungsten filament in conjunction with 
electron bombardment; (b) The sample is heated on a Silicon wafer while forming 
gases (H2 and N2) are introduced into the oven in order to prevent oxidation during 
heating. The temperature is controlled by a thermocouple fixed to the base of the 
wafer and an infrared pyrometer............................................................................... 81 
 
Figure 3.13 Summary of AFM scanning on the 36 % porosity NPS surfaces after as Ar+ 
sputtered and after annealing treatments in either UHV chamber or RTA oven in air. 
The inserted captions indicate the sputtering time in RIE and the annealing time and 
temperature in either environment. (a) No or very little changes in surface 
morphologies during low temperature annealing processes, here ? = RMS 
roughness; (b) similar surface morphology changes during high temperature 
annealing processes: 800 ?C vs. 900 ?C.................................................................... 83 
 
Figure 3.14 Examples of height-height correlation functions for the NPS samples (36 % 
porosity) annealed in RTA oven and in UHV chamber. The annealing temperatures 
and durations are noted in the plots. (a) annealed in RTA oven at 700 ?C up to 25 
min., and (b) annealed in UHV chamber at 800 ?C up to 30 min............................. 85 
 xii 
Figure 3.15 Summary of height-height correlation function analysis of annealed NPS 
samples after Ar+ sputtering. The scaling exponents are summarized as a function of 
annealing times and annealing temperatures, especially the results at high 
temperatures are compared with EW theory and we find out the reduction in RMS 
roughness may be due to sublimation....................................................................... 86 
 
Figure 3.16 RTA annealed patterned NPS sample: (a) AFM images of areas with 570 nm 
and 410 nm width square pits after annealing at 900 ?C for 10 min. (b) line profiles 
of 570 nm and 410 nm width square pits. As annealing time increases, the pit depth 
decreases in both pattern sizes. ................................................................................. 88 
 
 
Figure 4.1 Schematic of chemical structures of 248 nm wavelength model polymers (a) ? 
(c), and 193 nm wavelength model polymers (d) and (e). Here Mn = molecular 
weight, DP = degree of polymerization, and OP = Ohnishi Parameter. ................... 94 
 
Figure 4.2 Cross-sectional view of schematic of the inductively coupled plasma chamber 
used in this work. ...................................................................................................... 96 
 
Figure 4.3 Plasma etching using a moving shutter. ......................................................... 96 
 
Figure 4.4 Representative AFM images of five prototypical resists after gradient etched 
with C4F8/90%Ar. The data scale is between 0 and 20 nm for all the images, for ease 
of comparison. The polymers with a methyl group on the aliphatic chain show the 
significant roughening rates than others in the same group...................................... 98 
 
Figure 4.5 RMS roughness vs. thickness removed for 248 nm wavelength model 
polymers after plasma etching with C4F8/90%Ar. P?MS shows much higher RMS 
roughness than PS and P4MS within the same etch duration, 0 ~ 60 s. ................. 100 
 
Figure 4.6 RMS roughness vs. thickness removed for 193 nm wavelength model 
polymers after plasma etching with C4F8/90%Ar. HAMA shows much higher RMS 
roughness than HAdA within the same etch duration, 0 ~ 60 s.............................. 100 
 
Figure 4.7 RMS roughness vs. thickness removed for 248 nm wavelength model 
polymers after pure Ar ion bombardment............................................................... 102 
 
Figure 4.8 RMS roughness vs. thickness removed for 193 nm wavelength model 
polymers after pure Ar ion bombardment............................................................... 102 
 
Figure 4.9 Semi-log plot of RMS roughness vs. etching time for both 248 and 193 nm 
wavelength model polymers after pure Ar ion bombardment. The overall roughening 
trend is repeatable. .................................................................................................. 104 
 
Figure 4.10 Chemical compositional analysis / simulation results for 248 nm model 
resists: (a) IR spectra from PS as a function of etching time, (b) X-ray photoelectron 
 xiii 
spectroscopy (XPS) spectra, (c) Single wavelength ellipsometry (? = 632.8 nm) 
measurements before and after C4F8/90%Ar plasma etching, respectively, and (d) 
Molecular dynamics simulation: cross-sectional view of Ar+ bombardment on PS 
with given conditions.............................................................................................. 107 
 
Figure 4.11 FTIR spectra from 193 nm wavelength model resist, HAMA before and after 
C4F8/90%Ar plasma etching as a function of etching time. For C-H bond stretching 
vibrations are caused both from the adamantane structure and the linear backbone 
chain. CO single bond and CO double bond are also shown clearly...................... 109 
 
Figure 4.12 chemical compositional evolutions with etching time on 193 nm model 
resists after C4F8/90%Ar plasma etching. Both plots show the normalized peak 
height vs. etching time for (a) C-H and C-O stretching, and (b) C-H and C=O 
stretching. ATR-IR spectra clearly show the decrease in CH and CO bonds......... 110 
 
Figure 4.13 Height correlation functions calculated from C4F8/90%Ar etched P?MS as a 
function of etching time. As a reminder I included the definition of height 
correlation function and scaling parameters, ?, ?, and ?. ...................................... 111 
 
Figure 4.14 Roughness exponent, ? estimated by fitting the height correlation functions 
to Sinha?s equation. It approximately equals to 1 for all the samples we study in both 
gas chemistries. ....................................................................................................... 112 
 
Figure 4.15 Estimated scaling exponents, ? and 1/z. Both exponents along with alpha 
approximately equal to 1 from the Monte Carlo (MC) simulation based prediction 
[3.14]. We show one of representative examples of (a) ln ? vs. ln t, where the slope 
is beta, and (b) ln ? vs. ln t, where the slope is 1/z. (c) comparison of calculated 1/z 
and ?/? for 248 nm model resists. The self-affined surface is assumed that 1/z 
should equal to ?/?, however they are not same and are far away from the MC 
simulation predicted value 1 in our experimental results. ...................................... 113 
 
Figure 4.16 A picture of experimental set-up for nanometer patterning, imaging, and 
heating of samples using a DI AFM dimension 5000. An enlarged picture shows the 
details of sample mounting stage............................................................................ 117 
 
Figure 4.17 An AFM image of 2 x 2 diamond patterns drawn by a Si tip on PS surface. 
The scan size is 5 um x 5 um, and the nominal size of the patterns is 1um. Array of 
patterns are made by changing X & Y offset of the piezo tube scanner manually. 119 
 
Figure 4.18 3D AFM images of a nanohole pattern, 90 nm nominal size on PS surface. 
The sequential heating at ~ 70 ?C from 1 min. up to 5 min. shows the array of 
patterns relaxes. Vertical data scale of all the images is 100 nm. The large scale 
scratches at top right are a navigational aid. ........................................................... 121 
 
Figure 4.19 3D AFM images of nanoholes, 30 nm nominal size on PS surface: As 
patterned vs. 1 min. annealed at ~ 70 ?C. We also include the height profiles along 
 xiv 
with 3D height images. Both images show the dramatic relaxation of nanoholes. 
Vertical data scale of all the images is 25 nm......................................................... 122 
 
Figure 4.20 AFM height images of nanometer scale patterns made by Si tips on PS 
surface. The top panel shows the as-patterned surface, and each column for each 
pattern shows the annealed structure at ~ 70 ?C for a minute to 5 min. All the images 
were taken at room temperature after each anneal.................................................. 124 
 
Figure 4.21 Height profiles measured across the center of a row of pits on a patterned PS 
surface. The nominal pattern size is shown bottom of each profile, and the center to 
center spacing of each patter is 3xx larger than pattern size. Different colored lines 
represent different annealing time, and the as-patterned profile means no annealing.
................................................................................................................................. 126 
 
Figure 4.22 Measured pit depth of nanoholes made by AFM tips vs. nominal pit size. 
The patterns with nominal sizes 30 and 50 nm show linear decrease in pit depth with 
annealing time, whereas at the nominal sizes 70, 90, and 220 nm, the pit depths are 
persistent. ................................................................................................................ 127 
 
 
Figure A.1 Optical microscopy image of patterns on NPS films after developing, and a 
detailed schematics of our design for e- beam lithography. For the smaller size pits in 
the rectangular box we varied the e- beam dose, so that we could selectively inspect 
the best patterns....................................................................................................... 136 
 
Figure A.2 Overall summary plots of RMS roughness vs. etching time for (a) 248 nm 
and (b) 193 nm wavelength model polymers after C4F8/90%Ar etching: presence vs. 
absence of Al contaminants. ................................................................................... 138 
 
 
 
 
 
 1 
Chapter 1 Introduction 
 
1.1 Motivation 
 At the microscopic scale, all real crystalline surfaces contain steps and a finite 
density of kinks, producing roughness, as shown in figure 1.1. These defects are 
important in non-equilibrium processes on surfaces such as growth, sublimation and 
etching, all of which have been the subject of considerable technological and scientific 
attention. Each of these processes modifies existing surface roughness in different ways, 
depending on the details of the processing conditions [3.14].  
In this thesis, we discuss the evolution of both nominally flat and lithographically 
patterned surfaces in three technologically important material systems, Si, nanoporous 
silica, and photoresist polymers, during high temperature annealing and plasma etching. 
Surface instabilities during such processes can be considered within the context of a 
moving boundary problem, where the surface protrusion grows with time (i.e. roughens). 
The classic example is the famous Mullins-Sekerka instability [1.1], which results from 
the competition between crystallization and either heat dissipation or the rejection of 
solutes.  
 
 2 
Figure 1.1 Stepped surface with kinks
Step 
Terrace 
Kink 
 3 
1.2 Ehrlich-Schwoebel effect 
One of the best known mechanisms which drives surface instabilities is the 
Ehrlich-Schwoebel barrier. Ehrlich and Hudda [1.2] showed that the attachment of 
adatoms at a descending step-edge can be strongly inhibited by a kinetic barrier (E-S 
barrier) for crossing a descending step as shown in figure 1.2. This asymmetric 
attachment probability to ascending vs. descending step-edges (attachment rates K- > K+), 
illustrated below, has been interpreted as the cause of bunching of steps and formation of 
stacks of islands (?mounds?) during MBE growth at low temperatures [1.3, 1.4].   
 
 
 
 
 
 
 
 
 
 
 
 
 Figure 1.2 Schematic of Ehrlich-Schwoebel potential barrier at step edge.  
v
E-S barrier
K- K+
Adatom
 4 
The E-S barrier tends to stabilize uniform step trains against fluctuations in average 
spacing during sublimation, but as proposed by Bales and Zangwill can lead to a 
roughening of individual step edges [1.6]. 
 Isolated atoms on terraces or at step edges are commonly referred to as ?adatoms? 
(i.e. adsorbed atoms). The evolution of surface structure can be described by the motion 
of adatoms via diffusive motion, attachment from the vapor and sublimation from the 
surface. The diffusion of adatoms in the presence of an incident flux can be described in 
terms of their local concentration c as follows:  
 
                                               2
c cD c F
t ?
? = ? + ?
?                               (1-1) 
 
, where t is time, D is the adatom diffusivity, F is the adatom flux from vapor, and ? is the 
average time that an isolated adatom spends on a terrace before sublimating into the 
vapor. 
As mentioned above, flat terraces are bounded by steps; addition/subtraction of 
adatoms to/from a crystal occurs by attachment/detachment of adatoms at steps. The 
boundary conditions for adatom diffusion equation come from the relationship between 
the adatom flux toward the bounding step edges, the rate of attachment or detachment at 
the step edges, the permeation current of adatoms across the step. These can be described 
as follows:  
 
                 )()()(?  ccPccKcDn eq ?+?=??? ????                             (1-2) 
 5 
, where n?  is the unit normal vector at the step from the upper terrace (-) to the lower 
terrace (+), K+ and K- are the kinetic coefficients for attachment to the lower and upper 
terraces, respectively, and P is the permeability coefficient [1.7]. 
 Alternatively, the evolution of a surface during growth or sublimation can be 
described at a coarser scale via the motion of steps. Weeks and his coworkers [1.8] 
proposed a simple 1+1 dimensional model in which the velocity of a step is written as a 
functional derivative of the individual step Hamiltonian, which includes terms containing 
both the step stiffness, its local curvature, and the step-step interaction free energy. 
Generalizing this to 2+1 dimensions, and including a simple expression describing the 
effect of sublimation yields the following for the velocity of a given point on a step: 
 
         ( )213
2
3
1
3 ?11
~?
wkwknwwghRTkndtSd
B
?+???











 ?+??= +??                             (1-3) 
 
Where S  is the trajectory of the step projected on the terrace plane, n?  is local normal to 
the step edge within this plane, ?  the step mobility, ?~ step stiffness, Bk the Boltzman 
constant, T  the temperature, g the step-step interaction coefficient, +k ( ?k ) is the adatom 
attachment/detachment rate to step edges from/to the step down (up) terrace. Equation (1-
3) basically states that a step moves locally along the direction normal to the step edge 
due to the effect step stiffness ?~ , which is inversely proportional to the local radius of 
curvature R , the step repulsion scaled by g but inversely proportional to the third power 
of  the local distance to nearest neighboring steps 1w ( 2w ), where 1w ( 2w ) is the normal 
distance to nearest neighboring step in the step-up (step-down) direction, and the 
 6 
sublimation of adatom from the neighboring terraces, which is estimated to be 
1wk ?
? (
2wk ?
+ ) (See Fig. 2.14 in chapter 2).   
 
 The organization of the remainder of the thesis is as follows: In the remainder of 
this chapter we describe how our experiments are carried out. In chapter 2 we present 
results on lithographically patterned vicinal Si(111) surfaces, to introduce perturbations at 
well-defined length scales. The pattern allows us to probe the length scale dependence of 
the surface evolution which occurs during our annealing experiments, and to test the 
model described by Eq. (1-3) experimentally. While the above framework is useful for 
considering the evolution of crystalline surfaces during growth and sublimation, it is of 
limited use in describing the evolution of the surface of an amorphous or polymeric film. 
Here continuum models have often been employed, and much of the theoretical interest 
has been in the possibility of universal behavior, as described by scaling. We examine the 
evolution of two non-crystalline materials in the chapter 3 and 4 of this thesis and 
compare to these models. We also look for evidence of pattern formation at a preferred 
wavelength, using patterning once again to perturb the surface at a series of well defined 
lateral length scales.   
 
 
 
 
 
 
 7 
1.3 Introduction to tapping mode AFM 
Most of the characterization experiments I describe in this thesis were carried out 
using tapping mode atomic force microscopy (AFM). Here I briefly review this technique.   
AFM is one of a family of techniques known as scanning probe microscopies 
(SPM) in which the lateral position of a probe is scanned across a surface and the probe - 
sample interaction or interactions are monitored [1.9]. AFM tracks the force or force 
gradient between the probe and sample under study, by measuring the either (1) the 
deflection or (2) the oscillation amplitude, phase or frequency of a flexible cantilever on 
which the probe is mounted [1.9 ? 1.13]. As no current need flow, the technique 
effectively remedies one of the limitations of scanning tunneling microscopy: it can be 
used to characterize insulators. AFM can image conductors, semiconductors and 
insulators in vacuum, atmosphere as well as in liquid.  
There are a number of modes in which an AFM can be operated [1.9 ? 1.13]. Here 
we describe three common modes: contact-, non-contact-, and tapping mode AFM as I 
schematically show the difference in figure 1.3. Early experiments were carried out by 
monitoring the angular deflection of the cantilever to determine the force of interaction 
between the tip and underlying surface, usually adjusting the height of the supported end 
of the cantilever to keep this constant. This is commonly referred to as contact mode, as 
the tip sample separation is generally maintained within the repulsive regime 
corresponding to the short-range exclusion principle-derived force. A second mode, 
referred to as ?non-contact? AFM is based upon application of a small oscillatory 
component to the vertical position of the supported end of the cantilever at a frequency 
close to resonance. In this case either the amplitude of the oscillation of the tip, the phase 
 8 
shift between the tip and supported end oscillations or the resonance frequency is sensed, 
and the average vertical position of the supported end adjusted during lateral scanning to 
maintain this constant, resulting in a constant vertical force gradient. This mode has two 
principle advantages: (1) it is intrinsically less subject to low frequency noise and (2) the 
force of interaction between the tip and sample is typically much smaller than in contact 
mode. The latter is important when probing soft surfaces. A disadvantage is that there is a 
built in instability if the separation is such that the force gradient is equal in magnitude 
but opposite in sign to the spring constant of the cantilever: the tip abruptly jumps into 
contact with the surface. 
Intermittent or ?tapping? mode AFM works very much like non-contact mode, 
except that the trajectory of the tip brings it into intermittent contact with a sample 
surface. The position of the supported end of cantilever is again driven at or near its 
resonance frequency (typically ~ 300 kHz) with an amplitude ranging typically from 
20nm to 100nm. In this case maintaining a constant oscillation amplitude or phase shift 
results in a constant tip-sample force gradient, averaged over one trajectory oscillation. 
The figure 1.4 shows how the tapping mode AFM works schematically. 
   
 
 
 
 
 
 
 9 
 
 
 
 
 
 
 
 
 
 
 
Figure 1.3 Force vs. tip-to-sample distance in AFM operation. 
 
 
Imaging the surface with tapping mode AFM provides some benefits over both 
contact mode and non-contact mode AFM: It gives better lateral resolution than non-
contact mode and produces less damage to the surface than contact mode.  
 
 
 
 
 
 
 
Repulsive force
Attractive force
(tip?to?sample separation)
Distance
Force Intermittent     contact
Contact
Non-
contact
 10 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1.4 Schematic of tapping mode Atomic Force Microscopy. 
 
 
 
Feedback Loop
A B
Oscillating Tip & Cantilever
split p
hotod
iode
detec
tor
Sample
PZT
scanner
La
se
r
 11 
We end this chapter with a brief mention of some issues influencing resolution in 
AFM scanning. In AFM the spatial resolution depends on the shape and size of the tip, as 
well as the separation between the tip and sample [1.9 ? 1.13]. The apparent lateral extent 
of convex surface features is overestimated, and of concave features underestimated, due 
to a convolution of the surface topography with the tip shape as described in Fig. 1.5. 
This becomes important when the radius of the tip, typically approximately 5 ~ 10 nm, is 
greater than that features on the surface being probed, or when the height/width ratio 
approaches or exceeds 1.  
The effective tip shape may change during an image, as the tip may pick up 
impurities as it contacts the surface; this can cause a change in the effective resolution. 
Tips with multiple asperities at the apex can result in multiple superposed images of 
surface features; if these are sufficiently close, the resolution is degraded.  
Other factors influencing resolution are non-linear response of the Piezo materials 
used in the AFM scanner and environmental noise (vibration and electrical interference). 
        
 12 
 
 
              
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1.5 Examples of tip-sample convolution: (a) an overestimated convex surface 
feature, and (b) an underestimated concave feature.  
AFM Tip 
Sample 
(a) 
(b) 
 13 
Chapter 2 Length-scale dependence of the step bunch self-organization 
on patterned vicinal Si(111) surfaces 
 
2.1 Introduction 
There is considerable interest in systems which undergo self-organization, based 
upon a need to fabricate nanometer scale structures, at high densities, on a practical time 
scale. Among the approaches which have been explored for directing self-organization of 
structures at semiconductor surfaces, topographical patterning of a substrate followed by 
epitaxial regrowth, or annealing have received the most attention [2.1 ? 2.4]. However, in 
spite of a number of experimental investigations which have been carried out on such 
systems, the substantial departure from equilibrium, and multiple types of kinetic barriers 
[1.2, 1.6, 2.5 ? 2.7] have thus far prevented a detailed understanding of the evolution of 
topography during these processes.  
In this chapter, we report on an investigation of a simple prototypical system 
which allows for a degree of directed self-organization, that of lithographically patterned 
vicinal Si(111) surfaces during high temperature annealing. We extend the approach 
reported by previous workers [2.1, 2.2] by studying the length-scale dependence of the 
topographical evolution. As discussed below, we observe a qualitative change in the 
nature of this evolution as the pattern length scale is increased, indicating the existence of 
a characteristic length scale in this system. 
 
 
 14 
2.2 Experiment 
 
2.2.1 Sample preparation 
We use vicinal Si(111) wafers, miscut by 0.5?0.25? toward the [2 1 1] azimuth. 
On such surfaces the step density, at least at high temperatures [2.8, 2.9] depends on the 
step height and vicinal angle in a simple manner: specifically tan a0  ~ a0  = h / L, where h 
is the step height, L is the terrace width, and 1/L is the step density. On Si(111) the 
minimum step height is 0.314 nm, corresponding to the separation between (111) 
?double-layers?. We pattern the surface with arrays of cylindrical pits, using 
photolithography followed by reactive ion etching. We effectively adopt a combinatorial 
approach, producing cylindrical pits whose diameters and center-to-center spacing we 
vary systematically with the diameter ranging from 0.7 to 8.0 ?m, and the center-to-
center spacing from 1.4 to 16 ?m. An advantage of this approach is that it allows us to 
investigate the evolution of surface corrugations vs. two different characteristic lateral 
length scales independently. The mask for the photolithography process is shown in 
figure 2.1.  
 
 
 
 
 
 
 
 15 
 
 
 
 
 
 
 
 
 
 
Figure 2.1 Combinatorial approach: Systematic varying of pit diameters & spacing. 
8.0
Pi
t D
iam
ete
r (
????m
)
Center-to-center Spacing (?m)
2 ?
m 
Di
a.
2.8
 ?m
 D
ia.
8 ?m Spac. 5.6 ?m Spac.
16.0 11.2 5.6 4.0 2.8 2.0 1.4
0.7
1.0
1.4
2.0
2.8
4.0
8.0
5.6
Pi
t D
iam
ete
r (
????m
)
Pi
t D
iam
ete
r (
????m
)
2 ?
m 
Di
a.
2.8
 ?m
 D
ia.
 16 
Before patterning we rinse the vicinal Si(111) wafers using a sequence of 
solvents: (1) acetone (2) methanol, and (3) isopropyl alcohol. We next spin coat them 
with the adhesion promoter, HMDS, followed by a positive photoresist (PR), OIR 906-10, 
while spinning at 6000 rpm for 60 sec. This produces a calculated resist thickness of ~ 
0.88 ?m. Next a so-called ?soft bake? of the resist is performed at 90 ?C for 60 s. The 
resist is then exposed to UV light (? = 365 nm) through a mask using a photolithographic 
stepper. The pattern transfer from the mask to the photoresist results from a UV 
exposure-induced solubility change of the resist in aqueous basic solution, i.e. 
?development?. Following this, the developed resist is ?post baked? at 120 ?C for 60 sec.  
We next expose the surfaces to an O2 plasma for 30 sec. in order to remove PR residues 
from the bottom of the pits which remain after development. Next the resist-patterned 
wafers are plasma etched in a reactive ion etching system (Plasmatherm model 790), 
using SF6 gas, at a flow rate of 10 sccm, a pressure of 10 mTorr, and a radio frequency 
source power of 50 W. The depth of the pits after etching is approximately 32 nm, with 
smaller diameter pits showing a very slightly smaller depth. We next remove the 
remaining resist, using cycles of chemical lift-off and oxygen plasma etching.  A few 
such cycles reduce the level of residual resist to below what is detectable in atomic force 
microscopy (AFM) imaging, and produce only very slight changes in the dimensions of 
the pits. The overall sample preparation processes are summarized schematically in figure 
2.2. Finally, the topography of patterned and cleaned samples is characterized using 
tapping mode AFM employing a single crystal Si tip whose diameter is ~ 10 nm. We note 
in passing that the height/diameter ratio is always much less than 1 for our structures. 
 
 17 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.2 Summary of sample preparation for the cylindrical pit patterned Si(111) 
surfaces. 
 
 
 
 
 
 
 
 
 
 
Si(111)
SF6  
Photoresist Si (111)
Spin Coating
Stepper Exposure
UV
Si(111)
PR
Si(111)
32 nm
Post bake & Development
Si(111)
Reactive Ion Etching Remove PRPR Patterning
 18 
2.2.2 High temperature annealing of samples 
 Our high temperature annealing experiments on the patterned Si samples are 
conducted in an ion pumped ultra high vacuum chamber, whose base pressure is 
approximately 2x10-10 mbar. The samples are out-gassed at temperatures between ~ 
550 ?C and 700 ?C for several days to remove loosely bonded impurities after bake out of 
the chamber. Then the samples are heated   to ~ 940 ?C to remove the oxide. Finally each 
sample is heated to a temperature of 1273?5 ?C for a series of periods of time; these 
periods ranged from 15 seconds, to 480 seconds. We increase the temperatures from 
940 ?C to 1273 ?C over a period of several seconds; we find that this heating procedure, 
combined with clamping the sample gently to the holder, produces few line of the defects 
associated with mechanical stress and large temperature gradient on surfaces. We carry 
out our annealing of the samples using a combination of the radiation heating from a 
tungsten filament behind the samples (i.e. opposite the patterned surface) and electron 
bombardment. Temperature was measured with a disappearing-filament pyrometer, 
correcting for the emissivity difference between Si and the W filament. After each 
annealing experiment at ~ 1273 ?C for a given time, we quench cooled the samples to 
minimize changes on surfaces during cooling. Subsequently the samples are transferred 
through atmosphere to a tapping mode AFM (Digital Instruments dimension 3100) and 
the resulting topography measured. Although the surfaces oxidize, previous 
measurements by Tsai, et al. [2.10] indicate that the oxide is conformal to the starting 
surface.   
 
 19 
2.3 Understanding of the surface evolution 
There are numbers of effects that are known to contribute to the evolution of 
surfaces at high temperature, including diffusion in the presence of step-step interactions, 
step stiffness, possibly an Ehrlich-Schwoebel barrier [1.2] as well as sublimation. 
However as yet there is still no detailed quantitative understanding of the combined effect 
of these processes. A major goal of this part of my thesis is to achieve such an 
understanding.  
 Before discussing the results it is useful to introduce some nomenclature. In Fig. 
2.3 we show a schematic of cross section through one of our pit patterned vicinal surfaces. 
There are two main types of steps which occur on these surfaces: (1) The vicinal miscut 
produces nearly straight (but nevertheless meandering [2.11, 2.12]) steps that we refer to 
as ?vicinal steps?. (2) The patterning produce cylindrical pits which are bounded by 
closely spaced nearly circular steps we refer to as ?loop steps?. 
The arrows shown in figure 2.3 represent the motion of steps which would be 
produced if only sublimation were important. If that were so, the vicinal steps would 
always move in up-hill (i.e. step-up) direction under the influence of sublimation, 
whereas the loop steps would move parallel to the vicinal steps on up-hill side, but anti-
parallel to the vicinal steps on down-hill (i.e. step-down) side. This latter effect can result 
in a local ?step annihilation? which is one of the modes by which the patterned structure 
can relax during annealing. 
 
 
 
 20 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.3 Step profile on a patterned vicinal surface, and step motion which would 
result if only sublimation were considered. 
 
 
Vicinal Steps
Step Motion Due to Sublimation
?Up-hill? ?Down-hill?
Loop
Steps
 21 
The above is an incomplete picture of step motion during high temperature 
annealing our patterned vicinal surfaces: we also need to consider diffusion of atoms in 
the presence of chemical potential gradient, including both step-stiffness and step 
interaction effects. The Gibbs-Thomson effect associated with stiffness will oppose the 
outward expansion of loop steps; since the change in chemical potential is inversely 
proportional to the radius of curvature of a circular step (?? ~ 1/r); for small enough 
radius of curvature it will cause the loop steps to collapse, i.e. to move in opposite sense 
on the direction that indicated by short blue arrows in the figure 2.3.   
Next we briefly consider step kinetics on the patterned vicinal surfaces during 
high temperature annealing. As indicated schematically in a figure 2.4, we need to 
include the effects of sublimation, line tension (step-stiffness), and step-step interaction 
on such patterned vicinal surface. We assume that the motion of steps relative to each 
other is restricted by condition that steps of the same sign do not cross; otherwise 
energetically costly overhangs would result. Pointed out by Chui and Weeks [2.13] this 
non-crossing of steps has a consequence on the interaction of steps. The fluctuations of 
the position of a given step are reduced by the presence of neighboring steps. This 
reduces the configurational entropy, and results in a repulsion term in the free energy per 
area which is proportional to the inverse cube of the separation between steps. A second 
mechanism for step interaction is the overlap of subsurface strain fields, which for 
neighboring steps of the same sign again produces a repulsion term in the free energy per 
area which is proportional to the inverse cube of the separation. The sign of this part of 
the interaction is expected to reverse and become attractive if neighboring steps have 
opposite sign, however. 
 22 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.4 Competing effects acting upon steps on a pit patterned vicinal surface during 
high temperature annealing: Sublimation; Line tension, which is related to the step 
stiffness; Step-step interaction. Here ?
  is the step stiffness, g is the step-step interaction 
coefficient, and l is the separation between steps in the Free E/Area equation.   
 
Sublimation
Line 
Tension
Step-Step 
Interaction
Sublimation
Line 
Tension
Step 
Annihilation
At ~ 1273 ?C
0 3
ghf f
l l
?= + +

Free E / Area:
l
 23 
Illustrative examples of influence of step stiffness at different pattern length 
scales are shown in a figure 2.5. It shows the surface plot of AFM Images after annealed 
for 30 sec. at ~ 1273 ?C for the pit size of 1.4 um diameter and 2.8 um center-to-center 
spacing between the pits on the left panel, while the right panel shows part of surface 
patterned with pits of 4.0 um diameter and 8.0 um center-to-center spacing. For smaller 
pattern length scales, the line tension effect dominates, and leads to rapid relaxation to 
nearly straight step bunches. At larger pattern periods effect of line tension is less 
pronounced and the step bunches remain laterally corrugated during relaxation.  
 
 
 
 
 
 
 
 
 
Figure 2.5 Step stiffness effects vs. pattern length scale after 30 sec. annealing at ~ 
1273 ?C. On the left hand side is an AFM image of 1.4 um diameter ? 2.8 um spacing, on 
the right hand side is an AFM image of 4.0 um diameter ? 8.0 um spacing. The smaller 
period patterned surface shows the nearly straight step bunches after annealing, while the 
larger period patterned surface shows laterally corrugated step bunches after same 
amount of annealing. 
 
 
 
1.4 um dia. X 2.8 um spac. 4 um dia. X 8 um spac.
Kink
Surface
Kink
Step
 24 
A second effect which enters into the relaxation of the patterns is the step-step 
interaction. Our AFM images show two different types of indication of interaction, which 
can be seen in figure 2.6. At the up-hill side of the pits the inward relaxation of the 
initially tightly bunched loop steps which form the side-wall provides evidence for 
repulsive step-step interactions between steps of the same sign. By contrast, at the down-
hill side there is a visible bowing-in of the step bunch, which suggests an attractive step-
step interaction of steps with opposite signs. Attractive step-step interactions have been 
suggested theoretically, but as far as we know there has never been any experimental 
evidence to support them previously. As mentioned above, an attractive step-step 
interaction would allow for annihilation of steps locally.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 25 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.6 Step-Step Interaction Effects: Surface plot of AFM image for surface 
patterned with 8 um diameter pits spaced at 16 um. 
 
Bowed downhill wallRelaxed uphill Wall
Attractive Step motion
 26 
2.4 Results 
As illustrated in Fig. 2.5, the topographical evolution varies with the pattern 
length-scales during high-temperature annealing. In these experiments there are three 
quantities which we vary: pit diameter, spacing between the pits, and the annealing time; 
in this thesis we concentrate on patterns for which the initial diameter of the pits is one-
half the center-to-center spacing (corresponding to the diagonal cells in figure 2.1).  
We discuss the dependence on lateral length scale (i.e. pit diameter ? spacing 
between the pits) first. Figure 2.7 shows a summary, in the form of AFM images, of the 
result of a fairly short anneal: ~ 15 sec. at ~ 1273 ?C. The top left panel in the figure 
shows an AFM image from a region of the surface where the initial pattern consisted of 
1.0 ?m -diameter pits, spaced at 2.0 ?m center-to-center. The image has been high-pass 
filtered to allow individual steps and step bunches to be seen, despite the large range of 
heights present in the original image. The pits on this part of the surface have entirely 
disappeared, and been replaced by a set of nearly straight step bunches whose spacing 
matches that of the original pattern, i.e., 2.0 ?m. At the relatively larger period of 
structures atomically flat bottomed circular pits are visible in the image, with step 
bunches wrapping around the sidewalls on the ?uphill? side. In addition, we observe the 
asymmetric intermediate loop shape with more curved step bunches in the periods 5.6 ?m 
diameter ? 11 ?m pitch and 8 ?m diameter ? 16 ?m pitch. The pits are again flat 
bottomed, but bounded by nearly semicircular steps, with flat edges on the uphill side of 
the pits, due to the small depth/diameter ratio for the pits in these cases. We find that the 
general features of the pattern length scale dependence of the surface evolution observed 
in this figure persist for surfaces annealed for longer times.     
 27 
   
  
 
 
 
 
 
 
 
 
 
 
 
Figure 2.7 Length scale dependence on the topographical evolution after 15 sec. 
annealing at ~ 1273 ?C.  
 
1um dia.-2um pitch 1.4um dia.-2.8um pitch 2um dia.-4um pitch
4um dia.-8um pitch 5.6um dia.-11um pitch 8um dia.-16um pitch
 28 
Next, we present results for a fixed lateral pattern period, but increasing annealing 
time. As we continue to anneal the structure, we observe first that the pits completely 
disappear, due both to the annihilation events mentioned above, as well as inward 
collapse of loop steps driven by diffusion in the presence of the Gibb-Thomson effect.  
This disappearance leaves behind step bunches, which for short period structures quickly 
become nearly straight, but for longer period structures remain corrugated laterally. More 
protracted annealing eventually causes the amplitude of the sinusoid to relax. This can be 
seen in figures 2.8 and 2.9, which are for two different pattern length scales. The high-
pass filtered AFM images shown in the figure 2.8 are for a pattern consisting of 2.8 ?m 
diameter pits with a 5.6 ?m center-to-center spacing. All the images are for a 20 ?m x 20 
?m field of view, for ease of comparison. After a relatively short annealing time, ~ 15 s, 
we still see flat-bottomed circular pits, around which step bunches wrap at the up-hill 
edges. This structure subsequently relaxes: first to nearly sinusoidal shaped step bunches 
by 65 s, and then to nearly straight step bunches by 120 s of annealing time. The high-
pass filtered AFM images shown in figure 2.9 are for a larger pattern size: with 4.0 ?m 
diameter pits spaced at 8.0 ?m center-to-center; here the field of view of all the images is 
30 ?m x 30 ?m. The topographical evolution as a function of annealing time shows a 
similar progression as for the smaller period structure. However, the lateral relaxation in 
this case occurs more slowly. Comparing AFM images for surfaces annealed for 30 s in 
figures 2.8 and 2.9, shows that for the 4 ?m diameter ? 8 ?m spacing pits, all of the 
original flat bottomed pits are still present, whereas in the case of smaller 2.8 um 
diameter ? 5.6 um spacing the pits have almost all disappeared, and have been replaced 
by nearly sinusoidal step bunches.               
 29 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.8 Annealing time effect on evolution. High-pass AFM images for a pit pattern 
of 2.8 ?m diameter x 5.6 ?m spacing at ~ 1273 ?C. The images are for a 20 um x 20 um 
field of view.   
 
15 sec. 30 sec.
65 sec. 120 sec.
Uphill Downhill
 30 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.9 Annealing time effect on evolution for a pattern made up of 4 ?m diameter 
pits x 8 ?m spacing at ~ 1273 ?C. The high-pass AFM images are for a 30 ?m x 30 ?m 
field of view.  
 
 
 
 
 
 
 
 
Uphill
120 sec. 480 sec.
30 sec30 sec. 65 sec65 sec.
Downhill
 31 
We next quantify the evolution of the surface topography based on our AFM 
measurements. We consider two different quantities to characterize the relaxation of the 
patterns. The first is the corrugation amplitude of the step bunches measured within the 
average surface plane, which we refer to as in-plane corrugation. In-plane corrugation is 
shown schematically by the dashed lines in the right panel of figure 2.10. To determine 
this, we visually pick out positions of step bunch crests and troughs from our high-pass 
AFM images. As shown in the left panel of figure 2.10, in-plan corrugation relaxes more 
slowly for larger pattern periods; this is qualitatively consistent with a decreasing effect 
of step-stiffness with increasing pit radius and separation.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 32 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.10 (Left) In-plane corrugation of pattern relaxation vs. pattern length scale. The 
numbers indicate the initial pit diameter; the center-to-center spacing is twice the 
diameter. (Right) Illustration of determination of in-plane corrugation. 
 
 
 33 
The second quantity of interest in the relaxation  is the out of plane corrugation 
amplitude  which is the amplitude within a plane defined by the surface normal and the 
azimuth perpendicular to the vicinal steps (i.e. the staircase azimuth). This can be 
measured from height profiles across our AFM images. Based upon symmetry 
considerations there are two obvious choices for the locations of such profiles along the 
vicinal step direction. First, of course, is across the center of neighboring pits; examples, 
for a pattern consisting of 2.8 ?m diameter pits separated by 5.6 ?m, are shown in figure 
2.11 (a). These ?across-center? profiles for small amount of annealing time show 
essentially flat bottoms of (111) orientation, while later ones relax to a nearly sinusoidal 
form. The other symmetric choice of profiles would be the midway between the pits, as 
shown in figure 2.11 (b). Because of the form of the pattern, initially there is no 
corrugation (aside from some very small extrinsic roughness) along this direction. In this 
case the profiles for smaller annealing time, the corrugation amplitude along the profiles 
is quite small. However, annealing drives the initially tightly bunched loop steps apart, 
and these interfere with the vicinal steps. The result is that the pattern spreads across the 
surface, and the corrugation amplitude measured in these ?between pit? profiles 
approaches that measured across pit centers, as seen in the center panel of figure 2.11.  
By approximately 120 sec, the two measures of the out-of-plane corrugation converge 
afterwards relax essentially simultaneously. Based upon physical insight, we expect the 
relaxation of the out of plane corrugation to be driven in large part by the step-step 
interactions. 
We summarize the out of plane corrugations along both directions for the varying 
length scales in a figure 2.12. 
 34 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.11 Relaxation of out of plane corrugation amplitude for a pattern consisting of 
2.8 ?m diameter pits with a 5.6 ?m center-to-center spacing. (a) Profiles measured across 
pit centers, (b) profiles measured between pit centers. (Center) Summary of amplitudes vs. 
anneal time. 
 
 
 
 
 
 
 
 
 
 
60
40
20
0
He
igh
t (
nm
)
20151050
Distance (?m)
30 s
65
240
120
480
60
40
20
0
He
igh
t (
nm
)
20151050
Distance (?m)
30 s
65
120
240
480
2.8 um Dia
5.6 um Pitch 
(a) (b)
 35 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1.4 um Dia
2.8 um Pitch
(a)
2.0 um Dia
4.0 um Pitch
(b)
 36 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.12 Out of plane corrugation with length scale variation (a) 1.4 um dia. ? 2.8 um 
pitch, (b) 2.0 um dia. ? 4.0 um pitch, (c) 4.0 um dia. ? 8.0 um pitch, and (d) 8.0 um dia. ? 
16 um pitch. 
8.0 um Dia
16 um Pitch
(d)
4.0 um Dia
8.0 um Pitch
(c)
 37 
Both the in-plane and out-of-plane/across-pit amplitudes show an approximate 
exponential decay with annealing time. We summarize the relaxation times both in plane 
and out of plane/across pits in the form of a log-log plot in figure 2.13. The slope of the 
logarithm of the out-of-plane time constant increases in this plot throughout the range of 
pattern length scales investigated. The in-plane relaxation time, on the other hand, is well 
fit over the entire range shown by a power law dependence on the lateral length scale, 
with an exponent of 3.86?0.14. Our observations are consistent with an in-plane 
relaxation time which increases approximately as the fourth power of the period of the 
pattern. A ? ~ ?4 is predicted for the case where relaxation is mediated by surface 
diffusion at a temperature above roughening [2.14]. Although the vicinal surfaces studied 
here are logarithmically rough, our observation of such a power law is perhaps surprising 
as the surface is not in equilibrium with a vapor phase, and there is a significant rate of 
sublimation at this temperature, approximately 1.4 bilayers/s [2.12]. The two time 
constants become equal by a pattern period consisting of pits of 8 ?m diameter spaced at 
16 ?m, and there is the suggestion that the out-of-plane relaxation converges to the same 
dependence. However, more measurements at larger length scales are necessary to 
confirm that this is indeed the case. 
 
 38 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.13 Summary of time constants for decay of in-plane (solid circle) and out-of-
plane (open squares) corrugation amplitudes as a function of initial pit diameter. Dashed 
line shows a best fit to a power law dependence for the in-plane relaxation time, with an 
exponent of 3.86?0.14. 
 
 
 39 
2.5 Discussion 
The pronounced difference in the relaxation times in-plane, and out-of-plane 
corrugation amplitudes that we observe at small pattern lengths might be explained by at 
least two possible sources of asymmetry. The first is the difference in the surface stiffness 
along the vicinal direction, where it is determined by step-step interactions, and at right 
angles to this, where it is determined by step stiffness. The second is a difference in the 
diffusivity along steps and across terraces. 
To understand our observations quantitatively and judge the relative contribution 
of these effects requires modeling the motion of steps across the surface including both 
diffusion, which is driven by the effects of step stiffness and step interactions, and 
sublimation. In the following section we present the results of simulations based upon a 
very simple model [1.8, 2.15] describing the velocity of steps in including the first source 
of asymmetry. Here we point out that a strong variation with pattern length in the 
relaxation rate of the in-plane corrugation can be understood qualitatively based upon the 
Gibbs?Thomson effect, which produces a term in the free energy which is inversely 
proportional to the radius of curvature. The size dependence of this effect leads to two 
important differences between the way small-period and long-period structures relax: (1) 
This radius is negative for the loop steps which bound the pits, and thus the Gibbs?
Thomson effect drives diffusion of atoms from the larger loop steps to the smaller ones. 
This curvature-mediated diffusion opposes sublimation, which tends to drive steps in the 
uphill direction. Small pits disappear mainly via diffusion, while large pits instead 
disappear via annihilation with vicinal steps; a much larger in-plane corrugation 
immediately after the pits disappear results in the long-period structure case due to the 
 40 
greater number of ?horseshoe shaped? steps which form during these annihilations. (2) 
Subsequent to the disappearance of the last loop steps, for long-period structures the 
relaxation of the in-plane corrugation is much slower than for small-period structures. We 
expect the characteristic length scale we observe in Fig. 2.10 to depend on temperature, 
and thus it should be possible to vary the pattern period at which the in-plane and out-of-
plane relaxation times coincide by varying the annealing temperature. 
 Finally, we note that the eventual relaxation to a uniform step train suggests that 
diffusion of atoms under the influence of a repulsive step-step interaction for steps of the 
same sense is important; sublimation alone cannot explain this effect. This same 
observation allows us to rule out a strong Ehrlich?Schwoebel barrier [1.2], which would 
result in step bunching. Surprisingly, our observations show that even at a temperature of 
1273 ?C, where sublimation drives our patterned Si surfaces well out of equilibrium, the 
final configuration is consistent with what would be expected based upon relaxation to a 
minimum energy configuration. 
 
 
2.6 Summary of Experimental Results 
In the previous sections we describe the results of a combinatorial approach 
toward controlling the evolution of topography during high-temperature heating of Si. 
Lithographically patterned arrays of cylindrical pits of different diameters and spacings 
on 0.5 ? miscut Si(111) surfaces were annealed at ~ 1273 ?C for times ranging from 
seconds to minutes. Straight steps due to miscut locally annihilate with loop steps at the 
?downhill? side of the pits and partially unwrap, leading to both in plane and out of plane 
 41 
corrugations. Ex-situ AFM observations show the existence of a critical pit separation, set 
by the competition between sublimation pressure on the steps, their intrinsic stiffness and 
their mutual interactions; above it straight steps wrap around pits, leaving a pronounced 
corrugation within the surface plane, beneath it straight step bunches quickly form, with a 
pronounced corrugation perpendicular to the surface plane. Our observations of step 
bowing on the downhill sides of the pits provide evidence of attractive interactions 
between steps of different signs.    
 Most interestingly, we find a pronounced asymmetry in the evolution of the 
pattern within the vicinal plane and perpendicular plane for small lateral spatial periods, 
but a convergence to a symmetric relaxation for lateral periods >~16 ?m for annealing 
carried out at 1273 ?C. 
 
 
2.7 Numerical simulations on patterned vicinal Si(111) surfaces during high 
temperature annealing 
 
2.7.1 Introduction 
 In earlier sections in this chapter we show the experimental results of difference 
in surface evolution between smaller length scale patterns and larger length scale patterns 
on vicinal Si(111) surfaces during annealing at ~ 1273 ?C. There we observe that the 
annealing of smaller length scaled patterns causes a complete disappearance of the 
original pits in fairly short annealing time. In agreement with the earlier work of Ogino 
[2.1], in their place are straight step bunches whose spacing is that of the original 
pattern. A longer anneal causes a relaxation of these straight step bunches to a uniform 
 42 
step train. As we increase the length scale of the pattern both the rate, and the nature of 
the evolution of the surface begin to change. The slower evolution is not so surprising, 
given that it involves transport of atoms across the surface as well as sublimation. Even 
once the pits disappear, the evolution is qualitatively different than at the smallest 
periods. The step bunches remain sinusoidal as the overall structure relaxes. We also 
consider the effects which come into play in determining the characteristic length scale 
which separates the regimes in which bunch waviness relaxes faster than bunch height, 
and that in which they decay together. 
We summarize numerical simulation results on the Si(111) vicinal patterned 
samples to compare it with experimental results [2.16] in this section. As a starting point 
we consider the problem in terms of the contributions to the free energy of a stepped 
surface. As we already considered in experimental parts, the important physical 
parameters in the evolution of such surfaces are the step stiffness and the step-step 
interaction (See in the equation (2-1)).   
                      Free Energy / Area: 0 3ghf f l l?= + +


                                                 (2-1) 
Where 
2
2
?? ?
?
?= +
?

  ( ?
  is the step stiffness), and l is the separation between steps. 
 
Making a step creates additional broken bonds, and bending that step creates more broken 
bonds still. The free energy contains a term which is proportional to the step density, i.e. 
the step creation free energy. This is related to the stiffness. The second important 
contribution, the step-step interaction has both an entropic and elastic contribution, but 
both fall off like 1/ l3 as shown in the equation (2-1). The step-step interaction is 
 43 
repulsive between steps of the same sign both due to the fact that they don?t cross and the 
overlap of the strain fields. It has been suggested that the interaction between steps of 
opposite signs might be attractive, and in fact we see some possible evidence from this 
from the inward bowing of the steps (in Fig. 2.6), and also from our simulations.     
 We have carried out extensive numerical calculations adapting the model 
suggested by John Weeks and his coworkers [1.8]. In this model the local velocity of a 
point on a given step is written as mobility times a functional derivative of a step 
Hamiltonian as described in figure 2.14. It depends explicitly on the step stiffness and 
step-step interactions, and also has a term corresponding to sublimation. If there is an 
asymmetry in the probability of a detatching adatom moving onto the terraces above and 
below the step, the two coefficients are different. Such an asymmetry would result from 
an Ehrlich-Schwoebel barrier, which would be expected to cause step bunching during 
sublimation. Our observations show relaxation to a uniform step-train we see no evidence 
for such a barrier, and thus set the two coefficients equal (i.e. ?+ = ?-). To allow for step 
annihilations we take the interaction between opposite sign steps to be attractive-for 
simplicity we merely reverse the sign of the coefficient.  
The starting values for ?, ?
 , g and ? are extrapolated from the values obtained 
from Metois? experiments [2.12] under near equilibrium conditions at 900 ?C and 
1100 ?C. Step parameters for Si(111) surfaces proposed in previous works at 900 ?C 
[2.20, 2.21] and at 1270 ?C [2.22] under direct current heating are summarized in table 
1.1 and 1.2 for comparison. 
 
 
 44 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.14 Mesoscopic model for step kinetics [1.8]. Here ? is the step mobility, ?
  is 
the step stiffness, g is the step-step interaction coefficient, ?? and ?+ are the kinetic 
coefficients for attachment to the upper and lower terraces, and W1 and W2 are the upper 
terrace and the lower widths, respectably.  
 
 
 
 
 
 
 
 
 
 
 
( ) =
dt
yxd nn , n
wwghRkT ?
111~
3
2
3
1
3 ?











 ??+?? ? ( ) nwkwk ?
12 ??+??
?+
Attraction, g a0 -|g|z
x
x
y
(xn(s),yn(s))
w1 w2
R
n^
+k?k
x
?+ / ?- = 1
No Schwoebel Barrier
Hard Core Step Repulsion
- No Step Crossing
 45 
Parameters d (?) q (e) ? (?3/s) Ds (?2/s) 
A 100000 0.006 3x107 5.2x1011 
B 5000 0.006 4x107 3.4x1010 
C 100 0.03 3x108 5.2x109 
D 10 0.2 2x109 3.5x108 
 
Table 1.1 Si(111) step parameters proposed at 900 ?C under local mass transport limit in 
Ref. 2.20 and 2.21. Here d is defined by d = Ds / ? where Ds is the adatom diffusion rate, 
and ? is the attachment/detachment rate. q is an effective charge of the adatoms, and ? is 
the step mobility. ? = 2ceqa4? (ceqa2 = 0.2 ML) is used; the step interaction parameter g 
was estimated as approximately 0.015 eV/?2 at 900 ?C.  
 
 
Parameters ?
  (meV/ ?) ?ceqa2F / kT q (e) 
 28 6.5 s-1 - Re 0.13 
 
Table 1.2 Si step parameters proposed at 1270 ?C in Ref. 2.22. Here Ceq is the 
equilibrium adatom concentration on terraces, a2 is the area of a single atomic cell on the 
surface, and F is the force acting on each adatom (F = qE). Re is the sublimation rate, and 
it is approximately 2 ML/s at 1270 ?C.   
 
 
 
 
 
 
 
 
 
 
 
 46 
2.7.2 Results 
 We firstly show the results of two different simulations for the smallest period 
structure we have studied, 700 nm diameter pits separated by 1.4 um and for a structure 
4x as large, already in the transition region between the small scale and large scale 
behaviors we see. The figure 2.15 (a) is the simulated starting surface of 0.7 um diameter 
? 1.4 um spacing between the pits, and (b) is the simulated starting surface of 2.8 um 
diameter ? 5.6 um spacing between the pits. Although only a single pit is shown, periodic 
boundary conditions are used, so that the effect of neighboring pits is included. In the 
simulation sequences, we observed that there are two modes by which loop steps 
disappear. The smallest loops collapse due to diffusion driven by the curvature, while the 
large loops annihilate with vicinal steps. We also see a difference in the disturbance of 
the vicinal step spacing midway between pits in the two cases. The overlap of the 
disturbances is much greater in the small period case-this is a significant part of the origin 
of the difference in the subsequent relaxation. As shown in the inserted AFM height 
images in Fig. 2.15, the smallest period structure causes nearly straight step bunches ((a)), 
while the larger period structure causes sinusoidal step bunches due to far more step 
annihilations ((b)) after same amount of annealing, 30 sec. in this case.    
 
       
 
 
 
 
 47 
 
 
 
 
 
 
 
 
   
 
 
 
 
 
 
 
 
 
 
Figure 2.15 Two examples of simulations on circular pit patterned Si(111) surface in 
both top-down and cross-sectional views: (a) 0.7 um diameter ? 1.4 um separation, and 
(b) 2.8 um diameter ? 5.6 um separation. Insets are the AFM height images of the surface 
after 30 sec. annealing at ~ 1273 ?C.    
 
0.7 um
(a) 
2.8 um
(b) 
 48 
In figure 2.16 we show a summary of experimental results, in the form of high-
pass filtered AFM images, as a function of pattern length scale as well as annealing time 
to compare with simulated images of the starting surfaces for the same small period, 
intermediate period and large period structures after a 30 second and 65 second anneals in 
figure 2.17. The insets in Fig. 2.17 show the high pass AFM images that we measure for 
comparison. We can see that the simulation captures all of the qualitative features of the 
evolution, across the entire range of periods. To make a more quantitative comparison, 
we extract from the simulations the same in plane and out of plane corrugation 
amplitudes we measured in our AFM images. These are shown in semi-log plots as 
normalized in-plane (or out-of plane) corrugation vs. time in second in Fig. 2.17. As you 
see the asymptotic behavior is decaying exponential, and the time constants increase with 
spatial period, in qualitative agreement with what we observe experimentally (See Fig. 
2.16 (b)). 
  
 49 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.16 Summary of experimental results of surface evolutions on effects of length 
scale and annealing time. (a) The top panel shows the three pattern length scales from 
different parts of the surface after 30 sec. annealing at ~ 1273 ? C: 1.4 um pit diameter ? 
2.8 um separation between pits, 4.0 um pit diameter ? 8.0 um separation between pits, 
and 8.0 um pit diameter ? 16.0 um separation between pits (from left to right). The 
middle column images show the evolution on fixed length scale at 4.0 um pit diameter ? 
8.0 um separation between pits with increased annealing time. (b) Log-log plot of decay 
time constant as a function of pit diameter for both out-of plane corrugation (OOP) and 
in-plane corrugation (IP).     
 
 
 
 
 
 
(a)
(b)
1.4um dia x 2.8 um spa 4um dia x 8 um spa 8 um dia x 16 um spa
An
ne
ali
ng
 Ti
me
An
ne
ali
ng
 Ti
me
Pattern Length Scale
30 sec. 
@ 1273 C
8 min. 
65 sec
1
10
100
1000
7 8 9
1
2 3 4 5 6 7 8
Pit Diameter (um)
De
ca
y T
im
e C
on
sta
nt
OOP
IP
De
ca
y T
im
e C
on
sta
nt
 50 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.17 Simulated structures after a 30 second and 65 second anneals. The insets 
show the high pass AFM images that we measure for comparison. The summary plots are 
the extracted simulations of the same in plane and out of plane (OOP) corrugation 
amplitudes we measured in our AFM images.     
 
 
 
 
 
 
 
30s
65s
4.0 um 8.0 um
t=0s
10-5
10-4
10-3
10-2
10-1
100
100806040200
Time (sec)
No
rm
. In
 P
lan
e C
or
ru
ga
tio
n
2
3
4
5
6
7
0.1
2
3
4
5
6
7
1
100806040200 Time (sec)
No
rm
. O
OP
 C
or
ru
ga
tio
n
0.7 um
1.0 um
1.4 um
2.0 um
2.8 um
4.0 um
5.6 um
8.0 um
No
rm
. In
 P
lan
e C
or
ru
ga
tio
n
No
rm
. In
 P
lan
e C
or
ru
ga
tio
n
No
rm
. O
OP
 C
or
ru
ga
tio
n
No
rm
. O
OP
 C
or
ru
ga
tio
n
1.4 um
 51 
2.7.3 Discussion 
In this section we interpret our simulation results qualitatively in terms of in-plane 
(IP) and out-of plane (OOP) corrugations by comparing our experimental results. In 
figure 2.18 we show a detailed comparison between the simulated and measured decay 
times vs. length scale. The model successfully captures the different dependences of the 
two decay times for the smallest structures, as well as their convergence for the larger 
period structures. It underestimates the exponent for the asymptotic dependence, giving ~ 
2.8 rather than 4. 
In the simulations, the difference between regimes can be understood qualitatively 
as follows: Shortly after beginning the anneal the step-step interaction drives the closely 
bunched loop steps outward in a shock wave, propagating the original shape of the 
pits. The larger overlap of shock waves for the smaller period structure results in a 
disturbance in the step spacing which extends all the way out to the mid-plane between 
pits, while for the larger period structures the step spacing is uniform here. At the uphill 
apices of the pits where the steps are closely bunched a given step is effectively pinned 
by its neighbors. The driving force for the change in step position comes largely from the 
curvature of the steps away from these apices, where its motion is relatively unhindered 
due to the larger step separation in the disturbed regions between pits. 
We can also make rough approximations as to the characteristic length scales 
bounding the small period, transitional and large period behaviors. For the small period 
structure the step stiffness term in the velocity equation dominates the step interaction 
term. Once the pit disappears the steps in the bunch take on an approximately sinusoidal 
shape. An inspection of the simulation and a little insight suggest that the small period 
 52 
regime corresponds to amplitude A ~ w, the average step spacing. This gives a 
characteristic lower bounding period of ~ 2.2 um-close to what we observe. In the 
opposite limit, it is the step-step interactions which dominate. The appropriate 
characteristic amplitude is related to the shape of the pit, specifically the pit depth divided 
by the sine of the vicinal angle. This gives a characteristic upper spatial period of 15 um, 
again close to what we observe. 
 53 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.18 A detailed comparison between the simulated and measured decay times vs. 
pit diameter from both in-plane (IP) and out-of plane (OOP) corrugations analysis. Also 
the characteristic lower and upper bounding periods are estimated by using the step 
kinetic parameters ?, ?
 , and g as 2.2 um and 15.5 um, respectively. Where A is the 
amplitude of the sinusoid, w is the average step spacing, a0  is the miscut angle, d is the 
depth of pit, and L is the period (i.e. twice of pit diameter).       
 
 
 
 
1
10
100
1000
Tim
e c
on
sta
nt 
(se
c)
7 8 9 1 2 3 4 5 6 7 8
Pit Diameter (?m)
          OOP      IP
Exp      
Sim       
 
?=9x109 A3/s; ? = 8.35x10-2 meV/A; g = 3.563 meV/A2~
0.7 um 5.6um
mghL
wALAr
w
h
w
hg
r
???pi
pi
???
2.2
~2
,21
tan,
~
2
2
3
3
???<
?




??
?=?>
mg dL
dA
LAr
w
hg
r
???pi
?
pi
?
5.15
~2
sin2
1,21
,
~
2
2
3
3
???>
??




??
?<
)2sin( yLAx ??= pi
 54 
Finally we consider the size of the parameters which give optimum agreement 
with the experiment as shown in figure 2.19. The velocity equation contains the product 
of the step mobility and stiffness and the product of the mobility and step interaction 
parameter. For simplicity we used the step mobility extrapolated from measurements of 
step fluctuations at 900 ?C and 1100 ?C by Metois [2.12]. We fit to the step relaxation 
times and last loop step disappearance times to get the step interaction parameter and step 
stiffness. Both values (black filled markers with a dotted circle in Fig. 2.19) are very low 
compared to the extrapolated values: approximately two orders of magnitude 
lower. Seemingly this discrepancy should be attributed to the nonequilibrium conditions 
under which we did our annealing. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 55 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.19 Step kinetic parameters for simulation [2.12, 2.17 ? 2.19]. The velocity 
equation contains the product of the step mobility and stiffness and the product of the 
mobility and step interaction parameter. For simplicity we used the step mobility 
extrapolated from measurements of step fluctuations at 900 ?C and 1100 ?C by Metois 
[2.12].  
 
 
One last point is that although the step-step interaction is apparently very small, it 
is necessary to get agreement with our experiments. Turning it off causes a very large 
increase in the out of plane relaxation times-well out of the range observed in our 
experiments. 
108
109
1010
? 
(A3
/se
c)
160015001400130012001100
T (?K)
? 
(A3
/se
c)
? 
(A3
/se
c)
(m
eV
/A
)
0.1
1
10
160015001400130012001100
T (?K)
?~ ?~ g (
me
V/
A2 )
200
150
100
50
0
160015001400130012001100
T (?K)
( ) =
dt
yxd nn , n
wwghRkT ?
111~
3
2
3
1
3 ?











 ??+?? ? ( ) nwkwk ?
12 ??+??
?+
dt
Step Mobility Step Stiffness Step-Step Interaction
[1] N.C. Bartelt et. al., PRB 48, 15453 (1993)
[2] S.D. Cohen et. al., PRB 66, 115310 (2002)
[3] J.M. Bermond, et. al. Surf. Sci. 416, 430 (1998)
[4] J.J. Metois et. al. Surf. Sci. 486, 95 (2001) k+ k-= = 1.25 BL/s * 1/2
( )
( )
2
23
2 ~4
11~24



	






++= kTAhkTg ??pi
 56 
Chapter 3 Evolution of roughness and wavelength selection during 
fluorocarbon plasma etching of Nanoporous Silica 
 
3.1 Introduction 
There is considerable interest in the development of low-k dielectrics for high 
speed devices for which the RC time constant is rate limiting [3.1]. While integrating 
copper metallurgy in place of traditional aluminum has reduced the resistance component 
of the RC time delay, reducing the capacitance component will involve integration of a 
new insulating material with a lower dielectric constant (k) than the incumbent silicon 
dioxide dielectric materials [3.2]. The low-k dielectric material can either be inorganic, 
organic, or a hybrid combination, and are deposited by chemical vapor deposition (CVD) 
or by spin coating [3.2, 3.3].  
An appealing candidate for these applications is a nanoporous silica (NPS), 
consisting of a SiO2 matrix into which gas-filled pores are dispersed. Introduction of the 
pores lowers the dielectric constant of the nanoporous film since the dielectric constant of 
air is 1.0. One of the unique features of a porous material is the ability to control porosity 
by varying the volume density of pores, with a value of k ~ 1.9 is achievable at a porosity 
of 50 % and hence tailor the performance of the material to meet the requirements of 
successive generations of future integrated circuits [3.4]. The porosity is tuned by 
changing the amount of sacrificial copolymers called porogens into the low-k matrix 
resin. The porogens volatilize during thermal curing (> 400 ?C) of a NPS film leaving 
nano-size pores. Figure 3.1 shows a summary of how NPS film can be produced.   
 
 57 
   
 
 
 
       
 
Figure 3.1 Processing steps to produce Nanoporous silica films [3.5].   
 
 
Defining the location and extents of insulator regions on a device requires 
patterning, with lithography followed by plasma-based etching being the standard 
approach for contiguous SiO2 [3.6], and also resist stripping and post-etch cleaning 
processes commonly utilize the plasma. An issue of some concern is thus the stability of 
the NPS/plasma interface during plasma etching. A roughening of the etch front will 
result in unwanted variations in the thickness of the insulator making it difficult to control 
critical dimensions. Therefore, we set out to study the evolution of surface roughness 
during plasma etching of NPS and contiguous pattern formation during etching of NPS. 
Recently Hua et al. reported on the results of etching methyl-silsesquioxane 
(MSQ) derived NPS with C4F8-based plasmas under both ion-poor and ion-rich 
conditions [3.4]. They found that in the former case a relatively thick fluorocarbon 
polymer layer builds up on the NPS surface, and that the pores in the top ~ 200 nm of the 
NPS are infiltrated, increasing its dielectric constant. In contrast, for an ion-rich plasma 
containing C4F8/90%Ar TEM images showed no obvious infiltration of the pores and 
most importantly the dielectric constant maintained its low value after etching. These 
 58 
latter conditions however produced much rougher etch-fronts. Controlled generation of 
nanoscale roughness has the potential for great technological impact in the development 
of nonwetting surfaces [3.7, 3.8], low friction coatings [3.7, 3.8], wafer bonding [3.8, 3.9] 
and light-trapping films for high-efficiency solar cells [3.10]. There is thus considerable 
interest in the development of materials and processes for which surface roughness of a 
controllable amplitude and spatial period can be easily achieved. Interestingly, 
transmission electron microscopy images of etched NPS show some indication of 
spontaneous pattern formation [3.4]. Such an effect is potentially useful as a means of 
self organization of a rippled structure at a preferred wavelength.  
In this chapter we describe a series of experiments on plasma etching of both 
pristine and patterned NPS, designed to both characterize the lateral size dependence of 
the roughening which occurs, and to probe this system for instability to spontaneous 
pattern formation. We first describe our experimental procedures. We then present 
experimental results for unpatterned surfaces, and then for lithographically patterned 
surfaces. 
 
 
3.2 Experiment 
Our MSQ-derived NPS films, for which the empirical formula is (CH3-SiO3/2)n, 
are 400 nm in thickness, with pore sizes of between 2-3 nm. A schematic of our sample, 
which has a layer of NPS deposited on a Si substrate with sandwiched structures, is 
shown in figure 3.2. The surfaces are etched in a reaction chamber employing inductively 
coupled plasma (ICP) geometry with Ar-rich Fluorocarbon plasma [3.4, 3.11]. A low 
 59 
pressure of 10 mTorr is used, so that the ion mean free path is large relative to the 
characteristic size of features on the surface. The self bias voltage is set at -125 V, gas 
flow rate at 50 sccm, and an RF source power at 600 W. To improve our understanding 
of plasma-surface interactions, we employ a shutter approach [3.12] where a sample is 
etched for a time period which increases progressively along the sample (gradient etch) 
using a moving shutter. Using this shutter approach we can obtain the entire etching 
history along the sample in a highly controlled fashion. Both prior to and after each 
etching experiment we characterize the topography of the NPS surface using the tapping 
mode AFM (DI dimension 3100) described in chapter 1. In addition, at each stage of our 
experiments we measure the NPS film thickness using a single wavelength (632.8 nm) 
ellipsometry; this allows us to determine both the etching rate, and the depth of the 
modified surface layer. We use NPS films with the porosities 10 %, 15 %, 30 %, and 
50 % for ?blanket etch? experiments. And for comparison, we perform the same 
experiments to the conventional SiO2 film, which is assumed as 0 % porosity, and 
organosilicate glass (OSG), which contains relatively low porosity of ~ 7 %. 
  
 
 
 
 
 
 
 
 60 
 
 
 
 
 
 
 
 
 
Figure 3.2 Schematic drawing of blanket NPS sample structures. 
  
 
We also investigate experiments on lithographically patterned surfaces, in order to 
probe the possibility of presence of a preferred length scale set by the system during 
etching. We produce our patterns, consisting of a series of various nm-sized/spaced 
square pits by using electron beam lithography followed by plasma etching; the 
lithography is done using a scanning electron microscope (SEM, JEOL Model 6500F) 
controlled by lithography software (Nabity NPGS). We vary both pit size and spacing 
between the pits (Pattern design details are shown in Appendix C). Due to proximity 
effects, the minimum pattern size we could reliably produce was ~ 140 nm. Here we only 
focus on results for NPS samples with 30 % porosity. The plasma etching conditions 
were held fixed, using the parameters described above for the blanket etch surface 
experiments. An initial 16 second etch was used for patterning we define as a starting 
surface, which depth is about 33 nm. Having multiple patterns on a single wafer 
NPS
SiO2
Si sub.
SiCN
C4F8 / 90%Ar Plasma Etching: 
10 mTorr, 50 sccm gas flow, 600 W RF 
source power, and -125 V bias voltage
400 nm
100 nm
550 nm
NPS
Si sub.
SiO2
SiCN
 61 
minimizes the nearly inevitable etching variation from sample to sample and allows 
collecting accumulated surface information from the staring surface. Subsequently the 
patterned surfaces were cleaned, and their topography measured. Finally, additional 
plasma etching of the samples was carried out for steps of 32 seconds; we performed 
sequential etches on the same samples, using the pattern to navigate to particular 
individual features on the surface after each etching step.  
 
 
3.3 Results 
Plasma etching NPS under the conditions described above results in a very rough 
surface; the overall rate at which the surface roughens increases monotonically with 
porosity as showed in figure 3.3, and at a rate at least an order of magnitude faster than 
either contiguous SiO2 or organosilicate glass [3.4]. Lazzeri et al. [3.13] reported that 
surface roughness strongly increases with NPS porosity, however no surface roughness 
develops on OSG and bulk SiO2 even after prolonged C4F8/90%Ar plasma treatment. The 
threshold porosity for excess roughening is about 10 %, meaning that the porosity values 
above 10 %, significant bulk and surface modifications including roughness of NPS 
dielectrics are observed [3.13]. These results are consistent with our experimental results 
summarized in figure 3.3. It is known that porous materials are etched faster than non-
porous materials like SiO2 because of their intrinsic sponge-like fragile structures (i.e. 
less mass density), so that higher porosity yields higher etching rate. 
In figure 3.4 we show representative AFM images for the etched surfaces. The 
size of each image is 2 ?m x 2 ?m; the vertical scale extends for 0 - 40 nm for all the 
 62 
images, for ease of comparison. Dramatic surface morphological changes can be 
observed as both etching time and porosity are increased. By contrast, only a very slight 
change in surface morphology during etching of bulk SiO2 (0 % porosity) was observed 
over the etching time range we studied. 
 63 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.3 Summary of AFM scanning results on blanket samples: Plasma etching 
induced surface roughness vs. plasma etching time as a function of porosity. The 
additional box includes the etching rate of each surface depending on the porosity. 
Etch Rate:
SiO2 (0% Porosity) = 120 nm/min
OSG (7% Porosity) = 130nm/min
NPS 10% porosity = 200 nm/min
NPS 15% porosity = 220 nm/min
NPS 30% porosity = 250 nm/min
NPS 50% porosity = 270 nm/min
Po
ro
sit
y
Po
ro
sit
y
10%
15%
30%
50%
0 %
7 %
 64 
   
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.4 Summary of representative AFM images after plasma etching with 
C4F8/90%Ar at 10 mTorr, 600 W source power, and -125 V self-bias voltage. The etching 
was performed gradually along the long edge of each sample for 0 ~ 70 sec. using a Si 
shutter. The percentage in each image indicates porosity of NPS. SiO2 is assumed to be 
0 % porosity.  
 
0 %: ~69s0 %: ~37s0 %: ~13s 
15%: ~59s
10%: ~ 9s 10%: ~29s 10%: ~69s
15%: ~12s 15%: ~33s
30%: ~12s 30%: ~28s 30%: ~59s
Scan size:
2um x 2um
50%: ~ 9s 50%: ~31s 50%: ~60s
 65 
Conventionally, the roughness of such films is characterized by calculated the 
height-height correlation function: 
 
                                                    ( )2( ) ( ) ( )G R h r h r R= ? +                             (3-1) 
 
where h is the local height of the surface, r  and R  are two dimensional translation 
vectors lying within the average surface plane, and the average is over the entire image. 
G measures how the correlation in height between different parts of the surface falls off 
with distance due to roughness. It is frequently assumed that the structure of rough 
surfaces result is self-affine [3.14, 3.15]. Based on this assumption, scaling theory would 
predict that the height-height correlation function should show a power-law dependence 
on distance, G ~ R2?, for R much smaller than a characteristic value called the correlation 
length ?. For R >> ?, G is predicted to saturate at a value of 2w2, i. e. twice the square of 
the RMS roughness. In addition, if scaling theory applies both the RMS roughness and 
the correlation length should show power law dependences on the etching time: w ~ t? 
and ? ~ t1/z, where the three exponents should be related according to ?/? = 1/z [3.15].   
It is not obvious that simple scaling theory should describe the structure resulting 
from the etching of a heterogeneous material like NPS. To determine to whether models 
based upon this theory are applicable to this complex process we calculated the height-
height correlation function for samples of different porosities over a series of etch times. 
We show the examples of height correlation functions as a function of etching time 
calculated from 30 % porosity NPS in figure 3.5. In the plots, the level of saturation (i. e. 
 66 
twice the square of the RMS roughness) as well as correlation length (a0 ) increase with 
time. Similarly, we measured the height correlation functions for the samples with 
different porosities. In figure 3.6 (a) we show another example of the measured height-
height correlation function, for a 15 % porosity sample after etching for 43 s. The solid 
line shows a best fit to the functional form suggested by Sinha, et al. [3.16]  
 
                                               













??= ?
?
2
2 exp12)( RwRG                            (3-2) 
 
which has the proper behavior in the limiting cases. The fit of this form to our calculated 
values is generally good, although the data show a more rapid fall off than the fit for the 
smallest separations. This could be an effect due to the finite AFM probe radius, which 
should smear out roughness on very short length-scales. The data also show a damped 
oscillation about the saturation value, which is not predicted by simple scaling theory. 
The first minimum is for R ~ 100 nm. 
 67 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.5 Height correlation functions as a function of plasma etching time for 30 % 
porosity NPS. 
 
1
2
3
4
5
6
7
8
9
10
2

G
 (n
m)
 
4 5 6 7 8 9
10
2 3 4 5 6 7 8 9
100
2 3 4 5 6 7 8 9
1000
r (nm)
5s
12s
20s
28s
36s
43s
51s
59s
66s

G
 (n
m)
 
a0 (correlation length)a0
a1
2 w
a1
2 w
Slope (2a2 )
less than 10nm !!
~ 5 sec
~ 66 sec~ 36 sec
~ 12 sec
r
 68 
 
 
 
 
 
 
 
 
 
Figure 3.6 (a) Height-Height correlation function vs. lateral distance (open circles) for an 
unpatterned 15 % NPS sample after etching 43 s in C4F8/90%Ar, calculated from a 2 um 
field of view AFM image, and fit to form from reference [3.16] for self-affine structure 
(solid curve). Insert: AFM image of the same surface (0.75 um field of view). (b) 
Asymptotic values of roughness exponent ? (filled circle), RMS roughness vs. time 
exponent ? (closed vertical diamonds), correlation length vs. time exponent 1/z (filled 
square) and ratio of ?/? (open square).vs. porosity. Dashed line shows value of 1 
predicted by flux re-emission model [3.14] for all exponents. 
 
 
From fits like that shown in Fig. 3.6 (a) we have determined the apparent value of the 
roughness exponent ?. Aside from some scatter ? is approximately equal to 1, 
independent of porosity, as shown by the filled circle in Fig. 3.6 (b). This corresponds to 
the maximum value predicted by self-affine theory, and to a very rough surface [3.15].  
Interestingly, Monte Carlo simulations based on the recently proposed ?flux reemission 
model? [3.14] for the evolution of a generic surface during reactive ion etching, predict a 
value of ? ~ 1, in agreement with our observations. This is a non-local model, in which a 
radical or ion which is incident upon a surface either reacts with the surface, etching it, or 
(b)(a)
15% ~43 s
 69 
is re-emitted, possibly interacting with the surface multiple times, leading to the 
following height equation: 
   
 ( ) ( ) ??? +++?+????=
?
? ...),(),(1
1100
242 trFStrFShhh
t
h          (3-3) 
 
 
 
 
 
 
 
 
 
Here the first term corresponds to evaporation and condensation induced smoothing 
(n>0), the second term to surface diffusion, the third, nonlinear term to etching, and the 
last term to stochastic noise [3.14]. The Monte Carlo simulations further predicted that 
both the RMS vs. time exponent ? and the correlation length vs. time exponent 1/z should 
also be approximately equal to 1 [3.14]. This prediction however is in pronounced 
disagreement with our results: the apparent asymptotic values that we extract for both 
these exponents decrease with increasing porosity, with values dropping to well below 1 
for the most porous samples. Furthermore, as seen by comparing the measured values of 
1/z (filled square) with the measured ratios of ?/? (open square) in Fig. 3.6 (b) we find 
that the more general prediction for self affine structures, that ?/? = 1/z, is not 
Incident Particle 
(Radical, Ion)
F0
'?n
n?
'?rrn
'r
r
The incoming particle 
can be reemitted
 70 
reproduced over the range of etching times that we have studied. It may be that our 
measurements reflect the transient, rather than steady state behavior. For our films, it is 
not possible to extend the etching experiments substantially; by 64 s we have etched more 
than half way through the 400 nm thick NPS film for the highest porosity. Further, it is 
likely to be the transient response which is of most interest in device fabrication using 
NPS.  
In summary, our results show that the time-evolution of the roughness of NPS 
during plasma etching for etch depths of up to a few hundred nm is not well explained 
either by the flux reemission model [3.14] or more generally by models which assume 
self-affine behavior [3.15]. 
 
We now turn to the question of spontaneous pattern formation during plasma 
etching of NPS, which was suggested both by the TEM images in ref. [3.4] and by the 
damped oscillation in the height-correlation function in Fig. 3.6 (a). The figure 3.7 shows 
the AFM image vs. TEM cross-sectional image from the blanket 30 % porosity NPS 
surfaces after etching. A TEM image of an etched NPS indicates a preferred wavelength 
as about 100 nm. However, the cross sectional TEM images in ref. [3.4] did not allow for 
full 2 + 1 dimensional mapping of the topography of the etched surface, and with an 
AFM image it is hard to determine the preferred wavelength. Also, it is not possible 
based upon them whether in fact wavelength selection takes place. 
 
 
 
 71 
 
 
 
 
 
 
 
 
 
 
Figure 3.7 Evidence for wavelength selection during C4F8/90%Ar plasma etching of NPS 
(30 % porosity): (a) AFM image of a blank surface after etching for ~ 47 sec., and (b) 
TEM cross-sectional images after etching from Ref. [3.4].    
 
 
To investigate this intriguing possibility, we have used a combination of 
lithographic patterning and atomic force microscopy imaging to examine the evolution of 
the NPS surfaces during C4F8/90%Ar plasma etching, as a function of lateral length scale. 
For this we adopt the technique of pre-patterning to introduce perturbations at a series of 
well defined wavelengths [2.3, 2.4]. This approach is particularly well suited to probing 
the tendency of moving interfaces toward pattern formation, a phenomenon which has 
been reported during both plasma etching of Si(001) [3.17] and in ion sputtering of 
semiconductor [3.18] and insulator surfaces [3.19]. We pattern the NPS surfaces using 
electron beam lithography followed by etching in ICP chamber, creating arrays of square 
pits on the surface whose width and spacing we vary from cell to cell, but maintaining a 
2 um X 2 um
Etch for ~ 47 sec. 
Tapping mode AFM
30% Nanoporous Silica
TEM Cross-Section
Partially etched NPS
SiCN
~ 100 nm
(a) (b)
 72 
fixed width/spacing ratio of 1:2 and an initial depth of ~ 33 nm as described in Fig. A.1. 
Some of AFM images of a patterned area, subsequent to removal of the resist are shown 
in figure 3.8. These are 30 % porosity surfaces, containing 140 nm wide pits, spaced at 
280 nm center to center; due to proximity effects this was the smallest pattern we 
successfully produced. We also include the AFM images from 280 nm width ? 560 nm 
center to center spacing and from 400 nm width ? 800 nm center to center spacing. In Fig. 
3.8 we summarize the patterned surface evolution after additional etch durations of 32 s, 
64 s, and 96 s in vertical direction for each patterned surfaces. The induced roughness 
visibly increases with time. For 140/280 nm pits after 96 sec. we noticed AFM tip effects, 
so the image is excluded in the summary.  
 
 
 
 
 
  
 
 
 
 
 
 
 
 73 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.8 AFM summary of e- beam patterned NPS (30 % porosity) surfaces. We 
pattern the surface with the arrays of square pits with varying in size by maintaining a 
fixed width/spacing ratio of 1:2. And then we etched the ?pre-patterned? surfaces at 
various time periods.  
 
 
In figure 3.9 we show the evolution of height profiles measured across a row of 
pits for the same series of etching times for the various pit sizes. An advantage of this 
patterning-based approach is that it allows us to return to the same part of the surface 
after each etch step, and thus follow the evolution of individual structures. As seen in the 
profiles, etching produces profound changes in the topography. For the smallest structure, 
400/800 nm
Surface 
evolution 
during 
C4F8/90%Ar 
Plasma etch
140/280 nm
32 sec Etch
64 sec Etch
96 sec Etch
As 
Patterned
280/560 nm
33 nm
NPS (30%)
 74 
140 nm wide x 280 nm spacing (Fig 3.9 (a)), deep trenches form at the edges of the pits 
by 32 s. The dominant effect for increased etching time is an inward motion of the 
sidewalls which coalesce to single downward pointing cusps by an etching time of 64 s. 
Figs. 3.9 (b), and (c) show sequences of profiles for larger patterns: 200 nm width x 400 
nm spacing, and 560 nm width x 1120 nm spacing. For the largest period structure, 
trenches again form initially at the sidewalls; in this case additional etching produces a 
different mode of evolution, with downward pointing spikes forming between pits and 
nearly obscuring the initial pattern by 64 s. For the 400 nm period structure, the mode of 
evolution of the structure is evidently intermediate between the two extreme cases, and 
results in persistence of the amplitude. This can be seen even more clearly in figure 3.10, 
where we plot the amplitude of the fundamental Fourier component as a function of the 
pattern period, for the initial surface and three additional etch steps. The initial patterning 
produces some variation with period, with an ~ 30 % increase in the amplitude of the 
shortest period structure. Subsequently, for the smallest period structure amplitude falls 
off approximately linearly, to approximately 2/3 of its initial value by an etch time of 64 s. 
For the longest period structure the decay is more abrupt, saturating at a value 
approximately 20 % of the initial amplitude by 32 s. In striking contrast is the behavior 
for the 400 nm period structure: the amplitude remains constant up to the longest etch 
time studied. 
 
 
 
 
 
 
 75 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.9 Evolution of height profiles vs. etching time: pattern sizes for (a) 140 nm 
width x 280 nm spacing, (b) 200 nm width x 400 nm spacing, and (c) 560 nm width x 
1120 nm spacing from the 30 % porosity NPS. In both the smallest and the largest pattern 
periods, the formation of micro-trenches at the side walls of pit bottoms is dominant at 
initial stage of etching.   
 
(c) 
200
150
100
50
0
x1
0-9
 
1086420
x10 -6  
Starting surface
32 sec Etch
64 sec Etch
96 sec Etch
560 X 1120 nm
As Patterned
32 s
64 s
96 s
x1
0-9
 
x1
0-9
 
tEtch
(a) (b) 
tEtch
140 X 280 nm
As Patterned
200
150
100
50
0
x1
0-
9
3.02.52.01.51.00.50.0
x10 -6
Starting surface
64 s
As Patterned
32 s
x1
0-
9
32 s
64 s
96 s
200 X 400 nm
As Patterned
 76 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.10 Summary plot of the amplitude of fundamental Fourier component as a 
function of pattern period. This shows an existence of a persistent length scale at ~ 400 
nm period during Fluorocarbon plasma etching of NPS (30 % porosity), where the pattern 
amplitude persists regardless of etching duration we studied. 
 
 77 
3.4 Discussion 
A question which arises concerns the value of this persistent wavelength; it is 
approximately 4 times that of the first minimum in the height-height correlation function 
shown in Fig. 3.6 (a). An interesting possibility is that there is a series of (meta)stable 
wavelengths, and that period doubling can occur. We in fact see some evidence for this, 
as illustrated in figure 3.11 (b) ~ 3.11 (d). These are gray scale representations of a 
second height correlation function, defined as 
 
                                              ( ) ( ) 2)( hrhRrhRg ??+= 

                       (3-4) 
 
Where ( )rh   is the local surface height and represents the ensemble average over r . 
They are for the 400 nm period-patterned NPS region, i.e. that which shows a persistent 
amplitude. We also add an unpatterned NPS surface for the comparison. The periodicity 
in the square array of spots seen in Fig. 3.11 (b) reflects that of the initial pattern. In an 
unpatterned sample (Fig. 3.11 (a)), however, there is no such periodicity instead only one 
maxima peak is shown up. After certain amounts of etching the correlation map looks 
quite different. A striking change occurs after 32 sec of etching (Fig. 3.11 (c)): a second 
set of spots has appeared between those for the patterned surface. This second periodicity 
is induced by the etching; further etching (64 s, Fig. 3.11 (d)) shows that this second 
periodicity is persistent as well. 
 78 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.11 The mapped images of cross term in height correlation function (g) for the as 
patterned and etched surfaces for the pits with 200 nm width x 400 nm spacing. (a) An 
unpatterned NPS surface is included for the comparison. (b) Starting surface, (c) 32 s 
etched surface, and (d) 64 s etched surface. The starting surface shows the nice square 
periodicity, set by initial patterning. In an unpatterned sample, however, there is no such 
periodicity instead only one maxima peak is shown up. After 32 s etching the additional 
maxima appeared, indicating that there are series of stable wavelengths. Further etching, 
64 s also similarly shows the second periodicity, possibly something-like period doubling 
is going on. 
 
 
Pattern formation generally requires the competition of at least two effects, one of 
which destabilizes the interface and the second of which smoothes it out over short 
distances [1.1]. The profiles shown in Fig. 3.9 suggest that such a competition exists 
during the plasma etching of NPS. We now consider what these effects might be. It has 
been suggested [3.14] that smoothing during reactive ion etching could be mediated by 
(a)
Unpatterned sample Starting Surface
Cross term in G:
32s Etch
200nm
(C)
64s Etch
(d)
(g
( ) ( ) 2)( hrhRrhRg ??+= 
 79 
evaporation-condensation, surface diffusion or a combination of the two. In the related 
case of room temperature sputtering of amorphous surfaces it is thought that viscous flow 
might be promoted by ion impact [3.20]. We expect that a combination of these effects 
might be important in the evolution of the shortest period structures seen here. The 
etching induced roughening which destabilizes the interface is likely to be more complex 
than for the ion sputtering case, as evidenced by the qualitatively different topography 
which evolves. The linear height equation suggested for the latter case [1.1, 3.20] cannot 
explain the downward pointing cusps, which indicate a breaking in the up-down 
symmetry [3.21] of the system, and require a nonlinear term like that included in the flux 
re-emission model [3.14]. The lack of agreement between our observations and the 
predicted time dependence in that model, and most importantly the dramatic proliferation 
of spikes in the AFM profiles suggest that the nanopores play an important role. An 
intriguing possibility is that the pores might act as nucleation sites for the formation of 
nanotrenches which percolate through the matrix, and then spread outward, with the 
shape of the trenches setting a preferred spacing. Numerical simulations of the etching of 
NPS are needed to see if such an effect indeed explains the observed profound 
roughening of this technologically important material during plasma etching. 
 
 
3.5 Conclusions ? Pattern Formation 
Finally we consider the difference between the persistent pattern length of 400 nm 
seen in Fig. 3.10, and the value of ~ 100 nm suggested by the dip in the height-height 
correlation function. One possibility is that there are more than two competing effects, as 
 80 
discussed above, resulting in more than one maximum in the evolution rate with size. A 
second interesting possibility is that multiples of a stable period show transient stability, 
and that further etching might result in multiple period doubling. Further investigations to 
distinguish between these possibilities are in progress. 
 
 
3.6 Evolution of roughness during annealing of plasma etched NPS 
 Above we have shown that the surface of nanoporous silica roughens strongly, 
and monotonically with plasma etching. This conclusion poses challenges to the possible 
application of this material into nanoscale electronics. It would be desirable to find a way 
to cure the roughness created by the plasma etching. In this section we describe our 
investigations of the possibility of relaxing the roughness on NPS surfaces induced by 
plasma etching by subsequent annealing.  
For these experiments we worked with NPS samples with the porosity of ~ 36 %, 
whose starting thickness is approximately 230 nm, deposited by spin casting on Si(100) 
wafer. We also perform similar annealing experiments on e- beam patterned NPS (36 % 
porosity).   
Both unpatterned and patterned samples were prepared using Ar+ sputtering in a 
reactive ion etching (RIE) chamber to roughen the surface for annealing. Then annealing 
experiments were conducted in both an UHV (ultra high vacuum) chamber and in a rapid 
thermal annealing (RTA) oven in air. The annealing processes in both environments are 
schematically shown in figure 3.12.  
 81 
We investigated the effect of annealing at temperatures ranging from ~ 300 ?C to 
~ 900 ?C, and annealing times ranging from minutes to tens of minutes. Temperatures 
were measured using a calibrated thermocouple below 500 ?C and by IR Pyrometer 
above 500 ?C. After each annealing step we measured the topography of the resulting 
surfaces with AFM.  
 
    
 
 
 
 
 
 
 
 
 
Figure 3.12 The schematic descriptions of annealing processes performed on NPS (36 % 
porosity) samples. (a) The vacuum chamber is pumped down to approximately 2 x 10-8 
torr. The sample is then heated with a tungsten filament in conjunction with electron 
bombardment; (b) The sample is heated on a Silicon wafer while forming gases (H2 and 
N2) are introduced into the oven in order to prevent oxidation during heating. The 
temperature is controlled by a thermocouple fixed to the base of the wafer and an infrared 
pyrometer.   
 
 
Ultra High Vacuum (UHV)
A turbo pump and ion 
pump were used to 
achieve and maintain 
high vacuumNPS Sample
Tungsten 
Filament
a0a1
(a) 
Rapid Thermal Annealing (RTA)
H2
N2
Si wafer
NPS Sample
(b) 
 82 
We summarize some of representative AFM images of as Ar+ sputtered and 
annealed surfaces in both UHV chamber and RTA oven in figure 3.13. We divide AFM 
images depending on their annealing temperatures, so that we summarize relatively lower 
temperature (300 ~ 700 ?C) in Fig. 3.13 (a) and relatively higher temperature (800 ~ 
900 ?C) in Fig. 3.13 (b). During low temperature annealing there is little to no change in 
RMS roughness or surface morphology. While the high temperature annealing, the two 
annealing processes appear to similarly modify the NPS surface under corresponding 
conditions.  
 
 83 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.13 Summary of AFM scanning on the 36 % porosity NPS surfaces after as Ar+ 
sputtered and after annealing treatments in either UHV chamber or RTA oven in air. The 
inserted captions indicate the sputtering time in RIE and the annealing time and 
temperature in either environment. (a) No or very little changes in surface morphologies 
during low temperature annealing processes, here ? = RMS roughness; (b) similar 
surface morphology changes during high temperature annealing processes: 800 ?C vs. 
900 ?C.   
High Temperature Annealing (800?C - 900?C)
De
cr
ea
sin
g R
MS
 ro
ug
hn
es
s
Inc
re
as
ing
 w
eb
be
d n
etw
or
k
UHV: 15min, 800C
UHV: 30min, 800C
6min Ar+ etched 6min Ar+ etched
RTA: 15min, 800C
RTA: 30min, 800C
6min Ar+ etched
UHV: 5min, 900C
UHV: 10min, 900C
6min Ar+ etched
RTA: 5min, 900C
RTA: 10min, 900C
0.5a0 m 0.5 a0 m
(b) 
(a) 
Low Temperature Annealing (300?C - 700?C)
108s Ar+ etched UHV: 25min, 700C 6min Ar+ etched RTA: 25min, 700C
a1 = 4.21nm a1 = 3.81nm a1 = 10.50nm           a1 = 9.90nm 
0.5a2 m
 84 
To confirm this observation, the height-height correlation functions were 
calculated from our images to statistically characterize other parameters which might 
indicate a change in the surface. In figure 3.14 we show some examples of measured 
height-height correlation functions from the surfaces before and after annealing at 700 ?C 
in RTA oven and at 800 ?C in UHV chamber. We extracted roughness parameters 
including such as ?, ?, and ? from the correlation plots; an example is shown in Fig. 3.14. 
These are summarized as a function of annealing time in figure 3.15. From the figures 
3.14 and 3.15 we see that the RMS roughness (?) and correlation length, a0 , decrease, 
while the roughness exponent, a1 , remains about the same. We also perform the numerical 
simulations on the high temperature annealed surfaces as shown in Fig. 3.15 as gray and 
black dotted / solid lines. We compare our results with the predictions of the quasi-
phenomenological Edward-Wilkinson continuum equation (Equation (3-5)), which has a 
diffusion-like form, but is identified with smoothing due to sublimation and 
recondensation [3.22]: 
                                    2/h t V h? ?? ? = + ? +                                          (3-5) 
 
where ? is the surface tension term, ? is the space- and time-dependent stochastic noise, 
and V is the constant average velocity of the propagating surface.    
Numerical simulations using the Edward-Wilkinson equation for sublimation, and that 
for surface diffusion predict reduction in the RMS roughness, however the simulations 
predict an increase in the correlation length and roughness exponent which are not 
consistent with the experimental results.  
    
 85 
   
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.14 Examples of height-height correlation functions for the NPS samples (36 % 
porosity) annealed in RTA oven and in UHV chamber. The annealing temperatures and 
durations are noted in the plots. (a) annealed in RTA oven at 700 ?C up to 25 min., and 
(b) annealed in UHV chamber at 800 ?C up to 30 min. 
Slope = 2a0
2a1 2
a2 ? correlation length
a3 = root mean square 
roughness
a4 = roughness exponent
0 (rough) ? 1 (smooth)
Initial surface
RTA: 25min, 700C
8
1
2
4
6
8
10
2
4
6
8
100
2
4
G 
(n
m
2 )
G 
(n
m
2 )
2 3 4 5 6 7 8 910 2 3 4 5 6 7 8 9100 2 3 4 5 6 7 8 91000
r (nm)
Initial surface
UHV: 30min, 800C
UHV: 15min, 800C
6
8
1
2
4
6
8
10
2
4
6
8
100
2
G 
(n
m2
)
G 
(n
m2
)
2 3 4 5 6 7 8 910 2 3 4 5 6 7 8 9100 2 3 4 5 6 7 8 91000
r (nm)
(a) 
(b) 
RTA: 10min, 700C 
 86 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.15 Summary of height-height correlation function analysis of annealed NPS 
samples after Ar+ sputtering. The scaling exponents are summarized as a function of 
annealing times and annealing temperatures, especially the results at high temperatures 
are compared with EW theory and we find out the reduction in RMS roughness may be 
due to sublimation.  
(a) 
Lo
w 
tem
pe
ra
tu
re
 an
ne
ali
ng
    
  
H-
H 
co
rre
lat
ion
 pa
ra
me
ter
s
0.92
0.90
0.88
0.86
302520151050
Annealing Time (min)

RTA: 700C
UHV: 500C
UHV: 700C
60
40
20
0
3 02 520151 050 Annealing Tim e (m in)
RTA: 700C
UHV: 500C
UHV: 700C
(
nm
)

(n
m)
(
nm
)

(n
m)
a0
a1
a0
(b) 
60
40
20
0
35302520151050
Annealing Time (min)
RTA: 900C
UHV: 800C
RTA: 800C
UHV: 900C
Sublimation 
simulation
Diffusion 
simulation
Hi
gh
 te
mp
er
atu
re
 an
ne
ali
ng
H-
H 
co
rre
lat
ion
 p
ar
am
et
er
s
UHV: 900C
a2
a3
a2
0 .90
0 .85
0 .80
0 .75
3 5302 52 0151 050
Ann ealin g T im e (m in)

UHV: 800C RTA: 800CRTA: 900C
Sublimation 
simulation
Diffusion 
simulation
(
nm
)

(n
m)
(
nm
)

(n
m)
 87 
We also carry annealing experiments on e- beam patterned NPS sample with the 
same porosity of 36 % for comparison with blank ones. Patterned samples allow for the 
characterization of identical areas on one sample. This e- beam patterned sample is 
annealed with RTA at 900 ?C for two consecutive runs of 5 minutes each as summarized 
in figure 3.16. The major changes seen here is the reduction in pit depth and the changing 
morphology at the pit edge. These changes may be again due to sublimation of the NPS 
surface during annealing.   
 
In summary, our experimental results show that a simple annealing procedure is 
of limited effectiveness in relaxing etching induced roughness on NPS. Our results show 
however that the morphology of NPS is a very stable material at high temperatures, 
which may prove useful in high temperature applications.  
 
  
 
 
 88 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.16 RTA annealed patterned NPS sample: (a) AFM images of areas with 570 nm 
and 410 nm width square pits after annealing at 900 ?C for 10 min. (b) line profiles of 
570 nm and 410 nm width square pits. As annealing time increases, the pit depth 
decreases in both pattern sizes.   
 
 
570nm pattern RTA: 10min, 900C 410nm pattern RTA: 10min, 900C
1 a0 m 1 a0 m
(a) 
120
100
80
60
40
20
0
-20
x1
0-9
6543210
x10-6
x1
0-9
570nm pattern profiles
10min
5min
Initial 
surface Dec
re
as
ing
pit
 de
pt
h
100
80
60
40
20
0
-20
x1
0-9
43210
x10-6
410nm pattern profiles
10min
5min
Initial 
surface
x1
0-9
x1
0-9
De
cr
ea
sin
g
pit
 de
pt
h
De
cr
ea
sin
g
pit
 de
pt
h
(b) 
 89 
3.7 Summary 
Here we summarize the important results and conclusions of this part of thesis.  
Firstly, we observe the NPS roughens monotonically with time and porosity 
during plasma etching. And the scaling theory does not describe the etched NPS surfaces 
well at least over the time range we investigated.     
Our pattering and etching experiments reveal the evidence of a persistent 
wavelength at ~ 400 nm. It is not so clear what mechanism is involved for this. One 
possibility could be the preferred periodicity set by nanotrenches, nucleate at pores 
during plasma etching and have a preferred spacing.      
A most interesting result is an indication of period doubling even at persistent 
wavelength (400 nm). In order to clarify this issue, we need to investigate the smaller 
periodicities.  
Annealing in vacuum and in non-oxidizing environment produces similar changes 
in the surface morphology of NPS during annealing. Low temperature annealing (300 ?C 
~ 700 ?C) shows no obvious signs of curing the surface roughness caused by plasma 
etching processes, while high temperature annealing (800 ?C ~ 900 ?C) does reduce the 
surface roughness of the NPS surface, potentially due to sublimation of the material.  
 90 
Chapter 4 Nanotechnological Manufacturing: Nanostructured Polymers 
Designed for Plasma/Energetic Beam Templating of Materials  
 
 The third major part of this thesis concerns the morphological stability of the 
surface of model resists during plasma etching. Here we describe our preliminary results, 
investigating the morphological and chemical evolution of unpatterned resist surfaces.   I 
also present as an appendix our first attempts at creating patterns on the surface of one of 
these films, polystyrene, use AFM-based nanolithography; this process will serve as an 
enabler for further investigations of the length scale dependence of morphological 
evolution of resist during both etching and annealing, in analogy to the work I presented 
in Chapters 2 and 3.   
 
 
4.1 Morphological and chemical evolution of model polymers during plasma etching 
  
4.1.1 Introduction 
 Controlled patterning of materials at the nanometer scale will be one of the 
fundamentals of future nanotechnological manufacturing. The current demand for making 
devices with decreasing dimensions drives the development of photolithography with 
shorter wavelength light sources, novel techniques such as nanostamping, and new 
photoresist materials. One of the least understood elements for nanoscale patterning is the 
interaction of the plasma species and the organic molecules during pattern transfer.  In 
particular, it would be desirable to understand the chemical, morphological and 
 91 
topographic changes induced by these interactions in the macromolecules themselves and 
macromolecule-defined nanoscale features.  
A crucial consideration in the development of resists of next-generation 
lithography is the stability of the resist-plasma interface during plasma etching. 
Roughening of the interface leads to line edge roughness, which ultimately will limit the 
minimum feature size achievable. In this work we seek to understand the relationship 
between the rate at which model resists roughen during etching and their chemical 
structure. In addition, we explore how roughening relates to the tendency of a resist to 
undergo cross-linking vs. chain-scission in the presence of ionizing radiation. 
 
 4.1.2 Experiment 
We investigate the evolution of the surface roughness and of chemical 
composition of five prototypical model resists. This is a collaborative investigation, with 
synthesis carried out by Professor C. Grant Willson?s group at University of Texas, 
inductively coupled plasma (ICP) etching done in a special homebuilt and well-
characterized reactor by Professor Gottlieb Oehrlein?s group at University of Maryland 
[4.1], Ar ion bombardment studies carried out by Professor David Graves? group at the 
University of California at Berkeley, and characterization carried out by our group. In 
figure 4.1 we show the chemical structures of the five model polymers we study: 
polystyrene (PS), Poly(4-Methyl Styrene) (P4MS), poly(a0 -Methyl Styrene) (P?MS), 
poly(3-hydroxy-1-adamantyl methacrylate) (HAMA), and poly(3-hydroxy-1-adamantyl 
acrylate) (HAdA). Parallel studies of the effect of pure ion sputtering are carried out 
using a high vacuum system and employing a noble gas beam to sputter the films over a 
 92 
range of incident angles. We characterize the topography, density and composition of the 
surfaces of these resists using a combination of atomic force microscopy (AFM), 
ellipsometry, x-ray photoelectron spectroscopy (XPS) and infrared fourier transform 
microscopy (IRFTM) is done before and after etching.  
In our first investigations we have studied plasma etching of two groups of resists: 
aromatic ring (polystyrene)-based and adamantine-based polymers, which are model 
structures for photolithography using light at a wavelength of 248 nm and 193 nm, 
respectively. Each group has the nearly same Ohnishi parameter [4.2], which is a 
common measure of the resistance of the polymers during plasma etching, defined below.  
                                          
                                                                                                                            (4-1) 
 
 
, where N = total # of atoms in a monomer unit, NC = total # of carbon atoms in a 
monomer unit, and NO = total # of oxygen atoms in a monomer unit.  
Figs. 4.1 (a) - 4.1 (c) show the chemical structure of polystyrene and its derivates; 
their monomeric structure consists of a simple aliphatic chain (i.e. carbon-carbon 
backbone) and an aromatic ring. The main difference among the three variants shown is 
the presence or absence of a methyl group (CH3-), and its position relative to the aromatic 
ring. We chose these variants, as it is known that the addition/positioning of the CH3 
group to the aliphatic chain can be used to change the tendency of polymer upon 
exposure to ultraviolet radiation from cross-linking (which is the case for the PS and 
P4MS) to chain-scission (for P?MS).  
Ohnishi Parameter
= ?NN N
C O
? Etch Rate
(OP) 
 93 
Figs. 4.1 (d) and 4.1 (e) on the other hand show the chemical structure of HAMA 
and HAdA. Once again in this case the addition of the CH3 group changes the response of 
the polymer to UV radiation, from cross-linking for HAdA to chain-scission for HAMA.  
Polymers with similar structure have the nearly same values of Ohnishi parameter, 
and based upon a simple phenomenological model, they should have similar resistance to 
plasma etching. A crucial, but unresolved question involves how the rate of roughening 
during etching depends on the structure of the polymer, and whether the Ohnishi 
parameter is useful in this regard. A related question involves the effect of the methyl 
group on the tendency to roughen. 
 
 94 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.1 Schematic of chemical structures of 248 nm wavelength model polymers (a) ? 
(c), and 193 nm wavelength model polymers (d) and (e). Here Mn = molecular weight, 
DP = degree of polymerization, and OP = Ohnishi Parameter.   
 
Poly(3-hydroxy-1-adamantyl methacrylate)
HAMA
Mn = 18000
Poly(3-hydroxy-1-adamantyl acrylate)
HAdA
Mn = 12000
OH
O
O
OH
O
O
193nm (d) (e)
OPHAdA = 3.4OPHAMA = 3.36
nnn
Polystyrene (PS)
Mn = 21000
DP = 201
Poly(4-methylstyrene) (P4MS)
Mn = 23000
DP = 195
Poly(-methylstyrene) (PMS)
Mn = 30000
DP = 254
248nm
(a) (b) (c)
OPPS = 2 OPP4MS = OPP?MS = 2.11
 95 
Our model polymers are spun onto a Si substrate with an average starting 
thickness of ~ 400 nm, and then plasma etched with various gas combinations in an ICP 
reactor. Most of our results are for either C4F8/90%Ar or pure Ar. For both plasma gas 
chemistries we set the gas flow rate at 50 sccm, the operating pressure at 10 mTorr, and 
the self-bias voltage at -100 V. For C4F8/90%Ar plasma, we use a RF source power 800 
W. For pure Ar ion sputtering instead we use a source power 400 W in order to maintain 
the etching rate below 100 nm/ min.   
Figure 4.2 shows the schematic of the ICP chamber used in our experiments. The 
etching time normally ranged between 0 ~ 60 seconds. In some cases we etched the 
surface uniformly for a given time, while in others we used a moving Si shutter to vary 
the etching time across the surface of a resist film [3.12]; This latter approach allows for 
ease of following the evolution of the film vs. etching time under controlled conditions. 
In this shutter approach, we gradually expose part of the sample along its long side as 
shown in figure 4.3.   
 
 96 
            
B-fieldsE-field
Induction
coil
Quartz
coupling
window
Source Power
1400 W, 13.56 MHz
Bias Power
0-1000 W, 13.56 MHz
 
Figure 4.2 Cross-sectional view of schematic of the inductively coupled plasma chamber 
used in this work.   
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.3 Plasma etching using a moving shutter. 
 
60 sec
shutter
sample
substrate stage
gradient sample
60 sec
thickness
 97 
4.1.3 Results 
The etched model polymers were characterized with tapping mode AFM to follow 
their morphological evolution. In figure 4.4 we show example results of the surface 
evolution of model polymers under C4F8/90%Ar plasma etching. Comparing the etching 
rates (in nm/min.), the Ohnishi model seems to hold more or less for the polymers with 
similar structures. An exception is that while P4MS and P?MS have the same chemical 
composition and Ohnishi Parameters, they show quite different etching rates. The strong 
effect of the chemical structure on its response to the plasma can be also seen in the AFM 
images in Fig. 4.4. While all of the surfaces get rougher with increasing etching time, 
however, when the methyl group is positioned at the aliphatic chain (i.e. for the cases of 
P?MS and HAMA), the surface roughens significantly faster. 
 
 
 
 
 
 
 
 
 
 
 
 
 98 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.4 Representative AFM images of five prototypical resists after gradient etched 
with C4F8/90%Ar. The data scale is between 0 and 20 nm for all the images, for ease of 
comparison. The polymers with a methyl group on the aliphatic chain show the 
significant roughening rates than others in the same group. 
 
 
 
2um x 2um
Etched @ 800W, -100V 
PS
n
~ 17s etch
~ 58s etch
Etch rate:
38.11 a02.63 nm/min
P4MS
n
~ 13s etch
~ 60s etch
33.43 a02.61 43.55 a00.62
~ 17s etch
~ 59s etch
P?MS
n
193nm wavelength
model resists
OH
O
O
HAMA
~ 13s etch
~ 59s etch
58.23 a04.99
OH
O
O
HAdA
~ 17s etch
~ 55s etch
53.76 a05.75
248nm wavelength
model resists
 99 
This is confirmed by our quantitative analysis of the AFM images. We show the 
RMS roughness as a function of etching time in Fig. 4.5 and 4.6. In the summary plots, 
we show that for both P?MS and HAMA, the addition of a CH3 group to the ? position 
of the aliphatic chain results in a significant increase in the rate of roughening during 
etching as compared to the other polymers. 
 
 
 
 
 
 
 
 
 
 
 
 
\ 
 
 
 
 
 
 100 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.5 RMS roughness vs. thickness removed for 248 nm wavelength model 
polymers after plasma etching with C4F8/90%Ar. P?MS shows much higher RMS 
roughness than PS and P4MS within the same etch duration, 0 ~ 60 s. 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.6 RMS roughness vs. thickness removed for 193 nm wavelength model 
polymers after plasma etching with C4F8/90%Ar. HAMA shows much higher RMS 
roughness than HAdA within the same etch duration, 0 ~ 60 s. 
PMS
n
PS
n
P4MS
n
248nm PR
OH
O
O
HAdA
OH
O
O
HAMA
193nm PR
 101 
This trend, of increased roughening for a structure including a methyl group at the 
? position, also holds during pure Ar etching, although the absolute surface roughnesses 
are smaller for a given amount of etching (See Fig. 4.7 and 4.8). This is perhaps 
surprising: it is frequently observed that ion bombardment of surfaces results in material 
in a rough or ?rippled? surface. Interestingly, we observe that increasing the ion fraction 
of the etching gas for these model polymers results in smoother surfaces.   
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 102 
 
 
 
 
 
 
 
 
 
Figure 4.7 RMS roughness vs. thickness removed for 248 nm wavelength model 
polymers after pure Ar ion bombardment. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.8 RMS roughness vs. thickness removed for 193 nm wavelength model 
polymers after pure Ar ion bombardment. 
 
PMS
n
PS
n
P4MS
n
248nm PR
193nm PR
OH
O
O
HAdA
OH
O
O
HAMA
 103 
A complicating issue in plasma etching involves the effect of trace contaminants. 
In particular, ion discharges tend to sputter material from remote regions of the reaction 
chamber. Our XPS analysis for early studies revealed Al and O2 contamination, 
presumably from inadvertent ion bombardment of the Al anode and quartz coupling 
window. In subsequent experiments we essentially eliminate these contaminants by 
covering the electrode and quartz window with a Si wafer and Kapton tape, respectively. 
We find that this reduces the contamination levels to beneath what is detectable in XPS. 
This also allows us to test the sensibility of both the etching, and roughening rates to the 
presence of these elements (See Appendix D for C4F8/90%Ar etching case). As shown in 
a summary plot in figure 4.9, the roughness trend is qualitatively reproducible, i.e. P?MS 
shows higher roughening rate than PS and P4MS, and HAMA shows higher roughening 
rate than HAdA. But the overall roughening rates for 248 nm wavelength model 
polymers are lower than the values shown in Fig. 4.7. We caution that this latter result 
might be caused by other factors, as the investigation carried out here was not systematic. 
The 248 nm wavelength model polymers shown in Fig. 4.7 were etched on a different 
day than the 193 nm wavelength model polymers shown in Fig. 4.8, and we cannot 
completely exclude other trace contaminants which might have been present during one 
of these experiments. However, the later results summarized in Fig. 4.9 are based on 
etching experiments performed on the same day. We conclude that the qualitative 
difference, of the effect of the presence or absence of an ? methyl group on rate of 
roughening is robust in the presence of at least trace Al and O impurities.         
  
 104 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.9 Semi-log plot of RMS roughness vs. etching time for both 248 and 193 nm 
wavelength model polymers after pure Ar ion bombardment. The overall roughening 
trend is repeatable. 
 
 
Our preliminary results clearly show that the chemical structures of the polymers 
strongly affect their performance as resists. In particular, the position of the CH3 group 
clearly affects the rate at which the surface roughens under plasma etching. 
  
Besides the morphological evolution of the polymer surfaces, we have 
investigated the evolution of the chemical composition of our model polymers during 
plasma etching using the ATR (Attenuated total internal reflection) mode FTIR 
spectroscopy. ATR-IR spectroscopy allows identifying chemical elements and chemical 
structures by using an attenuated total internal reflection, which penetrates through the 
 105 
thin film in a range of a few microns. The chemical bonds can be vibrated as a result of 
infrared absorption, and different elements compose the chemical bonds are assigned to 
unique wave-numbers.        
 Our preliminary ATR-IR spectroscopic observations on model polymers etched 
with C4F8/90%Ar show the decreased CH bond concentration in all 248 nm model 
polymers. This is also observed in Ar+ sputtered model polymers. This result is consistent 
with ellipsometry and XPS measurements, and molecular dynamics (MD) simulation 
(MD simulation was done by professor Graves?s group at University of California, 
Berkeley) as shown in figure 4.10. In our IR spectroscopy analysis, we have monitored 
the intensity of C-H peaks as a function of etching time. In addition to the common peaks 
from the aromatic ring and the linear backbone chain, there peaks from the methyl group 
are also present in the spectra obtained from P4MS and P?MS. We can also see decrease 
in C-H peak heights both at linear chain and pendant of PS-based polymers from XPS 
analysis (Fig. 4.10 (b)), and increase in index of refraction at the early stage of plasma 
etching (indicated by blue dotted line in Fig. 4.10 (c)) from ellipsometry measurements 
for all three materials. In Fig. 4.10 (d) we observed significant decrease of hydrogen near 
PS surface from the depth profile as a result of more than thousand Ar ion impacts with 
100 eV. Near surface region of a simulated image after Ar ion bombardment also showed 
very dense graphite-like layers. Here we can draw one common conclusion: the plasma / 
ion beam exposures result in hydrogen loss and material densification possibly due to 
cross-linking of polymers, graphitization, etc. Further investigation is needed to correlate 
the chemical evolution to the different morphological evolution in chain-scission from 
cross-link polymers.  
 106 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
 
 
C-H Aromatic 
out-of-plane bending
PS
CH2 C( )
H
Crosslink
CH stretching 
vibration bands
CH2 CH( )
(a) 
0 10 20 30
F2s
O2s
C2s
?(pendant C-H), C2s
?(pendant C-H)
?(pendant C-H, C-C)
?(chain C-H),
   pi orbitals
pi orbitals  
XP
S 
Int
en
sit
y (
a.u
.)
Binding Energy (eV)
 PS
 PVT
 P?MS
  
 
 
(b)
 
XP
S 
Int
en
sit
y (
a.u
.)
 
 
0 10 20 30 40 50 60
0.000
0.005
0.010
0.015
0.020
0.025
0.030
 
 
Ind
ex
 C
ha
ng
e
Etching Time (sec)
 PS
 P4MS
 P?MS
800W, -100V
(c)
 
Ind
ex
 C
ha
ng
e
 
Ind
ex
 C
ha
ng
e
Etching 
 107 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.10 Chemical compositional analysis / simulation results for 248 nm model 
resists: (a) IR spectra from PS as a function of etching time, (b) X-ray photoelectron 
spectroscopy (XPS) spectra, (c) Single wavelength ellipsometry (? = 632.8 nm) 
measurements before and after C4F8/90%Ar plasma etching, respectively, and (d) 
Molecular dynamics simulation: cross-sectional view of Ar+ bombardment on PS with 
given conditions. 
 
 
 
 
 
 
 
 
0
5
10
15
20
25
30
35
40
45
50
0 50 100 150
Species Density (arb)
De
pt
h (
?)
C
H
Depth Profiles
100eV Ar+, after 1198 impacts
(~ 2.2x1016 cm-2)
0
5
10
15
20
25
30
35
40
45
50
0 50 100 150
Species Density (arb)
De
pt
h (
?)
C
H
Depth Profile
: Starting cell
Dehydrogenation
C ? Blue, H ? Yellow
(d)
De
pt
h (
?)
De
pt
h (
?)
 108 
Figure 4.11 shows FTIR spectra for HAMA before and after C4F8/90%Ar plasma 
etching as a function of etching time. We recognize in these spectra peaks from the C-H 
stretching from both the C-C backbone and the adamantane structure. The other feature 
that is as easily recognizable is the CO single bond and CO double bond stretching. Here 
we monitor those peak heights as a function of etching time for both HAMA and HAdA. 
And then we normalize the peak heights with the initial values before etching. The 
summary plots are shown in figure 4.12. Both plots in Fig. 4.12 we compare the CO 
intensities to that of the C-H stretching from CH2 bonds. The main difference between 
HAMA and HAdA, based on these two plots, seems to be that for HAdA the signal from 
both the CO double bond and CO single bond seem to higher compare to the signal from 
the CH stretching with etching time. It may imply that the C-O and C=O bonds were 
etched less than the C-H bonds. And for HAMA, the C=O bond signal evolves almost the 
way the CH signal does (Fig. 4.12 (b)), and the C-O bond seems to decay slightly faster 
at the beginning of etching than that of C=O bond. Lastly, there are no differences in the 
rate of decreasing between CH stretching from symmetric and asymmetric CH2 
vibrations. Still remaining to be done is to tie these differences to what we observed from 
the roughness evolution of these two polymers. 
 109 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.11 FTIR spectra from 193 nm wavelength model resist, HAMA before and after 
C4F8/90%Ar plasma etching as a function of etching time. For C-H bond stretching 
vibrations are caused both from the adamantane structure and the linear backbone chain. 
CO single bond and CO double bond are also shown clearly.  
 
 
 
 
 
 
C=O
CCH2( )
a0400nm thick.
a0389nm
a0379nm
a0370nm
a0358nm
a0349nm
O
OH
O
HAMA
C-O
OH OR
C-
H 
 110 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.12 chemical compositional evolutions with etching time on 193 nm model 
resists after C4F8/90%Ar plasma etching. Both plots show the normalized peak height vs. 
etching time for (a) C-H and C-O stretching, and (b) C-H and C=O stretching. ATR-IR 
spectra clearly show the decrease in CH and CO bonds. 
 
 
4.1.4 Discussion 
 We analyze AFM images from etched model polymers using the height-height 
correlation function. In addition to providing information about the lateral length scale of 
roughness from surfaces, this statistical analysis allows us to compare the detailed 
evolution of the surface roughness with models based on simple scaling theories for 
kinetic roughening. The typical shape of the correlation function we obtain is shown in 
Fig. 4.13; this was from an AFM image obtained after fluorocarbon plasma etching of 
P?MS. It generally follows the shape predicted by theories for self-affine roughness: 
vs.
C4F8/90%Ar plasma
HAdA OH
O O
H
CH2 C( )
HAMA OH
O O
CH3
CH2 C( )
Chain scission Cross link
C4F8/90%Ar plasma
No
rm
ali
ze
d a
bs
or
ba
nc
e
No
rm
ali
ze
d a
bs
or
ba
nc
e
Etching time (s) Etching time (s)
(a) (b) 
 111 
there is a power law regime at smaller lateral distances, but it flattens out at larger 
distance. As for the etched NPS surface presented in Ch. 3, we have fitted these 
calculated height correlation functions to empirical formula suggested by Sinha et al. 
[3.16] in order to extract the scaling exponents ?, ?, and 1/z. The value ? is estimated to 
be approximately 1 for all the samples after etching with both pure Ar and C4F8/90%Ar 
discharges indicating surfaces are very rough (See Fig. 4.14).. 
 
 
 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.13 Height correlation functions calculated from C4F8/90%Ar etched P?MS as a 
function of etching time. As a reminder I included the definition of height correlation 
function and scaling parameters, ?, ?, and ?.   
 
17s
29s
41s
59s
2?
? (correlation length)
RMS roug. = g7542 g595 11s
[ ]
[ ] 





?
?+?
)()(2),(
),'(),'(),(
2
2
t
rftwtrG
trhtrrhtrG
?

1)(,1))((
1~,1)(,))(())(( 2
>>=
<<=
t
r
t
rf
t
r
t
r
t
rf
??
???? ?
 112 
  
 
 
 
 
 
 
 
 
 
Figure 4.14 Roughness exponent, ? estimated by fitting the height correlation functions 
to Sinha?s equation. It approximately equals to 1 for all the samples we study in both gas 
chemistries.  
 
 
As shown in Fig. 4.15 the ?growth? exponent, ?, is extracted from the power-law 
dependence of the RMS roughness with etching time ((a)). Similarly, the dynamic 
exponent, 1/z, is extracted from the power-law dependence of the correlation length with 
etching time ((b)). Even though they both show power law dependences with time, they 
do not follow the prediction of the scaling theory, i.e. 1/z is not equal to ?/?. This lack of 
agreement is shown in Fig. 4.15 (c). The results imply that the simple scaling theory does 
not apply to the surface evolution we observed over the time we etched.  
? g759 1
 113 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.15 Estimated scaling exponents, ? and 1/z. Both exponents along with alpha 
approximately equal to 1 from the Monte Carlo (MC) simulation based prediction [3.14]. 
We show one of representative examples of (a) ln ? vs. ln t, where the slope is beta, and 
(b) ln ? vs. ln t, where the slope is 1/z. (c) comparison of calculated 1/z and ?/? for 248 
nm model resists. The self-affined surface is assumed that 1/z should equal to ?/?, 
however they are not same and are far away from the MC simulation predicted value 1 in 
our experimental results.    
 
1/z & ?/?_C4F8/90%Ar plasma
1/z
PS
?/?
PS
1/z
PaMS
?/?
PaMS
1/z
P4MS
?/?
P4MS
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1/z
 an
d ?
/??/??/??/?
1/z & ?/?_C4F8/90%Ar plasma
1/z
 an
d ?
/??/??/??/?
1/z
?/?
1/z
?/?
?/?
1/z
     P P?MS P?MS P S P4MS
1/z
 an
d ?
/??/??/??/?
1/z
 an
d ?
/??/??/??/?
1/z
 an
d ?
/??/??/??/?
(c)
1/z
 an
d ?
/??/??/??/?
1/z
 an
d ?
/??/??/??/?
1/z
 an
d ?
/??/??/??/?
1/z
 an
d ?
/??/??/??/?
1/z
 an
d ?
/??/??/??/?
1/z
 an
d ?
/??/??/??/?
1/z
 an
d ?
/??/??/??/?
1/z
 an
d ?
/??/??/??/?
1/z
 an
d ?
/??/??/??/?
1/z
 an
d ?
/??/??/??/?
Slope = ? Slope = 1/z
(a) (b)
???? ?? //1,~,~,~),( 12 =zandttrtxG z
1/1 ??? z??MC simulation prediction: 
 114 
4.2 Summary 
 We have reported that during etching in C4F8/90%Ar the presence vs. absence of 
substitutional methyl groups and their position relative to the aromatic ring in polystyrene 
derivatives has a pronounced effect on the rate of roughening. In particular poly-a0 -
styrene (Pa0 MS) roughens fastest, un-substituted polystyrene (PS) at an intermediate rate, 
and poly(4-methylstyrene) (P4MS) most slowly in 248 nm wavelength model resists. 
Similarly, poly(3-hydroxy-1-adamantyl methacrylate) (HAMA), where the methyl group 
is added to the backbone, shows the higher roughness than HAdA, which has no methyl 
group added to either the admantane pendent or the backbone. Interestingly, the trends 
were similar in pure Ar+ sputtering: polymers with a methyl group added to the alpha 
position of the aromatic ring showed again higher RMS roughness than other polymers. 
 In addition to the morphological evolution of 5 model polymers, we have 
investigated chemical evolution of these materials during etching via ATR-IR 
spectroscopy, ellipsometry, XPS and molecular dynamics simulations. And we have 
found out that these materials become dense after energetic ion beam or plasma exposure 
and that could be graphitization, hydrogen loss and/or cross-linking of polymers.     
For more quantitative analysis of roughened surfaces using both gas chemistries 
we have used height-correlation function analysis. Our analysis results turned out that 
these etched model polymers do not follow scaling behavior within the time scale we 
explored.    
 
 
 115 
4.3 Appendix: Nanolithography on PS 
4.3.1 Introduction  
 As we mentioned in section 4.1 the consideration of line edge roughness (LER) is 
significantly important in developing new resist materials, since it will directly affect the 
performance of devices by transferring the LER from the resist mask to the underlying 
active layer. Thus, we consider making nanometer scale patterns to extend our 
understanding from our studies in blank samples. As a starting point we have attempted 
to pattern polystyrene (PS) samples by using an AFM. We will discuss the detailed 
procedures in experimental part.  
 Similar to earlier two chapters here we seek to determine whether a characteristic 
length scale exists during heating, by prepatterning a polymer surface. This is inspired by 
the observation that etched unpatterned surfaces show a damped oscillation in height-
height correlation function (see Fig. 4.13), which is not predicted in conventional 
correlation function. In these first attempts we perturb the nominally flat topography of a 
PS surface with well defined pattern periods using an AFM tip.  
 
4.3.2 Experiment 
Due to limited resolution in pattering down to ~ 140 nm using our e- beam 
lithography facility, we have considered to do AFM-based nanolithography. AFM-based 
nanopatterning has a distinct advantage over the STM because AFM as fabricating and 
imaging tool can be used for insulating as well as conducting materials. 
In this preliminary study, we have designed and fabricated a sample mounting 
stage which allows heating and it is shown in figure 4.16. A homemade resistive heater is 
 116 
sandwiched between the PS sample and an aluminum heat sink. The Al heat sink was 
designed for insuring effective heating and cooling. Also four tantalum-tungsten (TaW) 
spring tabs are used to hold the sample firmly. The overall height of the sample mounting 
stage is 1.2 cm, the width of the stage is 4 cm x 4 cm, and the dimension of resistive 
heater is ~ 2 cm x 2 cm. The heating is done by a DC power supply with maximum 
voltage of 20 V and maximum current of 3 A. We measure the temperature by using a 
thermocouple, which is mounted directly onto the sample surface. The temperature 
accuracy based on our measurements is about 70?6 ?C. However, center of the sample 
surface should be hotter than the thermocouple reading because the thermocouple was 
placed at the edge of the sample and there must be temperature gradient along the sample.   
 117 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.16 A picture of experimental set-up for nanometer patterning, imaging, and 
heating of samples using a DI AFM dimension 5000. An enlarged picture shows the 
details of sample mounting stage.    
 
 
Resistive heater
Al heat sink
PS
Thermocouple 
Digital thermometer 
 118 
The nanolithography was done by a commercial AFM (digital instruments (DI) 
Dimension 5000) by adopting the NanoScriptTM macro language. Lithography uses C++ 
program along with NanoScriptTM macro Litho functions to manipulate the tip relative to 
the sample surface [4.3]. All the patterning was conducted at room temperature in the air, 
and regular Si tips with tip radius 10 nm, cantilever length 125 um, force constant 40 N/m, 
and resonant frequency 300 kHz were used for both patterning and imaging the surfaces 
in tapping mode. The lithography programs direct the microscope to inscribe or move 
items on the sample surface [4.3]. This function is designed for a closed loop XY scanner, 
and standard contact mode tips (Silicone Nitride tips) are recommended by manufacture, 
Veeco. However, we have performed our experiments using an open loop XY scanner, 
which causes significant piezo drift effects during patterning. After several trials we were 
able to successfully make arrays of diamond-shaped trench patterns. Figure 4.17 shows 
an AFM image of our first successful patterns where the field of view is 5 um x 5 um and 
the nominal size of the diamond is 1 um.   
For more effective and practical patterning we have developed C++ complier for 
this purpose by using an industry standard complier supplied by Veeco, so that we can 
make arrays of patterns easily and quickly.        
 
 
 
 
 
 
 119 
 
 
 
 
 
 
 
 
Figure 4.17 An AFM image of 2 x 2 diamond patterns drawn by a Si tip on PS surface. 
The scan size is 5 um x 5 um, and the nominal size of the patterns is 1um. Array of 
patterns are made by changing X & Y offset of the piezo tube scanner manually. 
 
 
 
4.3.3 Results 
Figs. 4.18 and 4.19 show patterns consisting of 4 x 4 arrays of roughly cylindrical 
nano-holes at the nominal sizes of 90 and 30, respectively created on PS. We have also 
created patterns consisting of arrays of holes of other diameters: 50, 70, 110, and 220 nm. 
Since the patterning is done by indenting the tip to the surface and scratching out defined 
area by moving the tip back and forth several times, it causes material piles up in both 
shoulders ? not necessarily symmetric ? of the nanohole. In our first attempts we set the 
center-to-center spacing between the holes by 3x larger than the nominal size of the hole, 
to reduce overlap of disturbance between neighboring pits. We have in addition 
investigated the optimal indentation depth of the tip. We recycle the sample for additional 
processes and collect accumulated information from same areas, so that we can observe 
 120 
evolution of patterns qualitatively. A third important issue is the temperature during 
lithography; for the pattern shown in figure 4.18, the surface was heated to ~ 70 ?C, 
beneath the glass temperature of ~ 95 ?C for PS. Annealing of the surface may help to 
define better shape of the holes leading to sinusoidal periodic structures. We find indeed 
that annealing the surfaces at ~ 70 ?C causes partial relaxation of the patterns. The 
changes during annealing are more dramatic at the smallest patterns we study, nominal 
size of 30 nm as shown in figure 4.19; this is expected based on diffusion mediated 
relaxation. In Fig. 4.19 we show both height profiles (Red circled areas) and 3D height 
images; as seen from the figure these shallower and smaller nanoholes relax to nearly 
smooth surface.                     
 121 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.18 3D AFM images of a nanohole pattern, 90 nm nominal size on PS surface. 
The sequential heating at ~ 70 ?C from 1 min. up to 5 min. shows the array of patterns 
relaxes. Vertical data scale of all the images is 100 nm. The large scale scratches at top 
right are a navigational aid.     
90nm_As patterned
90nm_70 ?C, 1 min. 90nm_70 ?C, 5 min.
 122 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.19 3D AFM images of nanoholes, 30 nm nominal size on PS surface: As 
patterned vs. 1 min. annealed at ~ 70 ?C. We also include the height profiles along with 
3D height images. Both images show the dramatic relaxation of nanoholes. Vertical data 
scale of all the images is 25 nm.  
 
 
 
 
30nm_As patterned
30nm_70 ?C, 1min.
 123 
 We summarize our early attempts at AFM-based nanolithography on PS and 
annealing in figure 4.20. Results are for as patterned, after a first annealing step at ~ 
70 ?C for 1 min., subsequent annealing for 2 more minutes at same temperature and then 
a final anneal of 2 more minutes. After each anneal we shut off power for fastest cooling; 
all of the images were taken at room temperature. The 30 nm nominal size holes almost 
disappeared by 5 min. The 50 nm nominal size holes also were relaxed, but the patterns 
are still visible, while the larger holes seemed to show little or no change within 5 min. 
annealing except 110 nm holes. We are using the standard Si tip for tapping mode AFM, 
and its radius is less than 10 nm, so the nominal pattern size 110 nm should be made 
easily. Our result might be caused by a blunt tip, which may be adhered by more material 
? more adhesive force ? due to its larger surface area than a sharp tip. Another possible 
explanation for this might be the combination of tip and surface defects such as scratches 
or impurities in the area we patterned.                      
 124 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.20 AFM height images of nanometer scale patterns made by Si tips on PS 
surface. The top panel shows the as-patterned surface, and each column for each pattern 
shows the annealed structure at ~ 70 ?C for a minute to 5 min. All the images were taken 
at room temperature after each anneal.     
 
 
 
 
50nm 70nm 90nm 110nm 220nm
As patterned
70 ?C, 1min.
70 ?C, 2min.
(total of 3 min.)
Nominal size
30nm
70 ?C, 2min.
(total of 5 min.)
t = 0
time 
 125 
4.3.4 Discussion 
For quantitative understanding of our AFM images shown in previous section we 
obtained line profiles of each pattern by drawing a line across the center of the holes. The 
measured line profiles as a function annealing time for each pattern is shown in Fig. 4.21. 
The nominal pattern size is shown bottom of each profile. The smallest hole, nominal size 
30 nm, relaxes quickly within one minute annealing from the ripple like shape to much 
less corrugated surface. However, for the larger sizes 70, 90, and 220 nm we observe 
very little change in depth with annealing. This is summarized in figure 4.22. There the 
patterns with nominal sizes 30 and 50 nm show linear decrease in pit depth with 
annealing time, whereas the pit depths are persistent at the nominal sizes 70, 90, and 220 
nm. Further investigations are required to quantify the relation between the characteristic 
relaxation time and spatial period. 
       
 126 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.21 Height profiles measured across the center of a row of pits on a patterned PS 
surface. The nominal pattern size is shown bottom of each profile, and the center to 
center spacing of each patter is 3xx larger than pattern size. Different colored lines 
represent different annealing time, and the as-patterned profile means no annealing.  
 
 
 
 
30 nm 50 nm 70 nm
90 nm 110 nm 220 nm
As patterned
70 ?C, 1 min.
70 ?C, 3 min.
70 ?C, 5 min.
 127 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.22 Measured pit depth of nanoholes made by AFM tips vs. nominal pit size. 
The patterns with nominal sizes 30 and 50 nm show linear decrease in pit depth with 
annealing time, whereas at the nominal sizes 70, 90, and 220 nm, the pit depths are 
persistent. 
 
 128 
Chapter 5 General conclusions 
 
 In this chapter we summarize general conclusions from three major works 
presented in this thesis. We have studied 3 technologically important materials: Si, 
Nanoporous Silica (NPS), and Resist polymers. In each case, we explored the length 
scale dependence of the evolution of the surface during etching or annealing. Our general 
approach in this work has been comparing observations of apparent characteristic length 
scales on unpatterned surface with systematic observations on patterned surfaces across 
these scales. We find that the interpretation of the length scale dependence of the 
evolution of the surface is aided considerably by this approach. A general remark is that 
the observation of a characteristic length scale in each of these systems points to 
competition between at least two effects; in the annealing experiments these are different 
terms in the free energy of a stepped surface, while in the etching experiments the effects 
are kinetic, with one effect destabilizing the flat surface, and the second smoothing it at 
short length scales.   
  
 In chapter 2, we described that the length scale dependence on the evolution of 
cylindrical pit patterned vicinal Si(111) surfaces during high temperature annealing at ~ 
1273 ?C for varying amounts of time. The smaller pit structures consist of nearly straight 
step bunches within a short annealing, while the larger pit structures consist of nearly 
sinusoidal step bunches even longer annealing. In order to understand our observations 
quantitatively we considered two step kinetic effects which require modeling the motion 
of steps across the surface including both diffusion, which is driven by the effects of step 
 129 
stiffness and step interactions, and sublimation. For the smaller pit structures diffusion 
driven by curvature governs the evolution, i.e. straighten out as soon as the annealing 
begins due to inward collapse of loop steps resulted in Gibbs-Thompson effect; whereas 
the repulsive step-step interaction effect governs the evolution of larger pit structures 
during high temperature annealing. And the larger pit structures are relaxed mainly by 
step annihilation of the steps with opposite signs in down-hill side. These observations of 
length scale dependence on the evolution agreed semi-quantitatively with the numerical 
simulations based on the mesoscopic step kinetics model. Finally, we note that the 
eventual relaxation to a uniform step train suggests that diffusion of atoms under the 
influence of a repulsive step-step interaction for steps of the same sense is important; 
sublimation alone cannot explain this effect. This same observation allows us to rule out 
a strong Ehrlich?Schwoebel barrier [1.2], which would result in step bunching during 
sublimation. Surprisingly, our observations show that even at a temperature of 1273 ?C, 
where sublimation drives our patterned Si surfaces well out of equilibrium, the final 
configuration is consistent with what would be expected based upon relaxation to a 
minimum energy configuration.   
 
 In chapter 3, we investigated the roughness evolution of blanket NPS samples and 
the wavelength selection in nanometer scale patterned NPS samples both during ion-rich 
fluorocarbon plasma etching. We found that NPS roughens dramatically during plasma 
etching under ion rich conditions. And the scaling theory does not describe the etched 
NPS surfaces well at least over the time range we investigated probably we are at 
transient regime. In addition, we found the evidence from our patterning experiments of 
 130 
wavelength selection at 400 nm, while our correlation function analysis and cross-
sectional TEM image suggest a persistent wavelength at approximately 100 nm. 
Although the continuum model which has been applied to explain rippling during ion 
sputtering might be applicable here, it does not obviously include the effect of micro-
trenching, which seems to be the dominant effect during plasma etching of NPS. An 
intriguing speculation is that the nanopores might actually nucleate micro-trenches. Most 
interestingly we found an indication of period doubling even at persistent wavelength 
(400 nm). In order to clarify this issue, we need to investigate the smaller periodicities. A 
further interesting speculation is that patterning the surface at a persistent wavelength 
might stabilize it against fluctuations at other length scales, in analogy with driven 
?chaotic? systems. 
 
In chapter 4, we studied how the chemical structures of model resist polymers 
affect the surface evolution during C4F8/90%Ar plasma etching and Ar ion sputtering. 
We found that the polymers with the methyl group positioned on ? position of the 
aliphatic chain roughen at much faster rate than the other cases under both gas 
chemistries. Our unpatterned polystyrene surfaces show some sign of a preferred 
modulation at ~ 70 nm; we anticipate that surfaces patterned at a wavelength near this 
might show persistence in topographical amplitude. We expect that this will have 
implications on line edge roughness, and the stability of patterned features during plasma 
etch based pattern transfer. It may well dictate an optimum length scale for such features.  
As a first attempt we have also patterned polystyrene surfaces with the arrays of holes, 
 131 
which ranges from a few tens nanometers to a few hundreds nanometers, using 
nanoscraping method with an AFM.  
 132 
Chapter 6 Future work 
 
 In this chapter we mention possible future work which would extend our current 
understanding regarding the three systems I described in earlier chapters. 
 
Chapter 2 Length-scale dependence of the step bunch self-organization on patterned 
vicinal Si(111) surfaces 
 Firstly, we can test our insights as to what sets the lower- and upper limits of 
ranges of length scale dependence of the self-organization of step bunches on patterned 
vicinal Si(111). Two relatively easy experiments would involve varying the vicinal angle 
(a0 ) and pit depth (d). By increasing the vicinal angle of the surface, we expect the lower 
bounding limit to move to left in Fig. 2.18. While if we increase the pit depth, we expect 
the upper bounding limit to move to right in Fig. 2.18. 
 We could also perform same experiments on singular Si(111) wafers in order to 
understand the role of nominally straight steps during evolution. The permeability of 
adatoms might be possible on surface during annealing. 
 It would be of considerable interest to carry out annealing experiments over a 
range of different temperatures. This would allow us to probe the temperature 
dependence of the effective step stiffness and step interactions. A limitation is that if we 
anneal such a patterned vicinal surface much lower than 1200 ?C, we expect to see high 
density of SiC pinning sites, which hinder the motion of steps, due to not sufficiently 
clean surface, while we if we anneal the surface at much higher temperature void island 
 133 
growth will compete with step flow, so that the voids act as sink of adatoms and may 
change overall evolution we observed. 
 
Chapter 3 Evolution of roughness and wavelength selection during fluorocarbon 
plasma etching of Nanoporous Silica          
 From our etched surface characterization using a cross term in height correlation 
function (G2) analysis clearly showed that we need to try smaller length scales for 
preferred wavelength selection during C4F8/90%Ar plasma etching. An alternating 
technique such as nanoscraping using an AFM, described in section 4.3 in chapter 4 
allows us to test smaller pattern length scales on such surfaces.   
 
Chapter 4 Nanotechnological Manufacturing: Nanostructured Polymers Designed for 
Plasma/Energetic Beam Templating of Materials 
 Even more so than surface roughness, line edge roughness significantly affects the 
possibility of dramatic decreases in critical dimensions we can achieve; furthermore the 
performance of microelectronic devices as the roughness value is comparable to the 
intrinsic roughness of polymer molecules. The nano-patterning techniques described in 
section 4.3 in chapter 4 should allow us to test the length scale dependence of line edge 
roughness, and the persistence of patterned features at the scale of 10?s of nm. We expect 
that the studies begun in this thesis will have considerable impact in the optimization of 
resist chemistries and etching parameters for extending critical length scales downward. 
 134 
Appendix A 
 
Sample cleaning procedures for Si (111) patterned samples: 
1) Acetone jet (i.e. pressurized Acetone gun) cleaning a0  Acetone soak cleaning in an 
ultrasonic cleaner for ~ 30 min. 
2) NMP (N-Methyl-2-Pyrrolidone = C5H9NO) solution soaking @ 80 ?C for 30 min. a0   
Rinse the samples with Acetone - Methanol - IPA - DI water 
3) Asher (O2 plasma, Pressure 5 Torr, RF power 500 W): 
(i) Conditioning. ? STRIP recipe for 2 ~3 min. using a Si sacrificial piece  
(ii) Ashing ? STRIP recipe for 1 ~ 6 min.  
4) Acetone soak cleaning in the ultrasonic cleaner for 2 ~3 min. a0  Rinse the samples 
with DI water 
 
 135 
Appendix B 
 
Patterned NPS sample preparation procedure: 
1. Spin casting (positive e- beam resist, 950 PMMA A4) on the sample at 5000 rpm, 
60 seconds. a0  PMMA thickness is ~ 110 nm 
2. Soft bake at 180 ?C for 5 minutes 
3. Deposit ~ 10 nm of Al layer using thermal evaporation  
4. Perform e- beam lithography (SEM, JEOL Model 6500F)  
5. Remove Al layer using OPD 4262 (Basic solution for positive resist development) 
for 1 minute a0  DI water rinse 
6. Develop PMMA layer by MIBK/IPA (1:3 vol. ratio) for 20 seconds and then rinse 
the sample in IPA for ~ 20 seconds 
7. Plasma cleaning to remove PMMA residues near the patterns: dandescum recipe ? 
O2 plasma for 15 seconds 
8. Plasma Etching for pattern transfer: SiO2pt recipe ? CHF3 + O2 for 30 seconds. 
9. Lift-off with NMP (1-methyl-2-pyrrolidinone, C5H9NO) 
 136 
Appendix C 
 
Nanometer size square pattern design details for electron beam lithography on NPS 
 
 
 
 
 
 
 
 
 
 
Figure A.1 Optical microscopy image of patterns on NPS films after developing, and a 
detailed schematics of our design for e- beam lithography. For the smaller size pits in the 
rectangular box we varied the e- beam dose, so that we could selectively inspect the best 
patterns.    
 
 
We vary both pit size and spacing between the pits. We attempted to produce a minimum 
square size of 50 nm as shown in figure A.1, however, the minimum pattern size we 
could produce was ~ 140 nm due to proximity effect. 
e- beam dose 
[Current/Area]
40  45  50  55  60  65  70  75   80   85 Nominal pit size (nm)
450 ?C/cm2
500 ?C/cm2
550 ?C/cm2
600 ?C/cm2
650 ?C/cm2
100 nm / 200 nm
140 / 280
200 / 400
280 / 560
400 / 800
560 / 1120
Nominal pit size:
Diameter / center to center spacing
 137 
Appendix D 
 
Roughness evolution of model resist polymers during C4F8/90%Ar plasma etching: 
Effect of trace Al contaminants 
 
      As we discussed in section 4.1.3 in chapter 4 we have tested the sensibility of 
both the etching, and roughening rates to the presence of Al contaminants during 
C4F8/90%Ar plasma etching (there is no significant evidence of quartz window erosion in 
this case as seen in pure Ar ion sputtering case.). Figure A.2 shows that the roughness 
trend is qualitatively reproducible in both groups of model polymers, i.e. P?MS shows 
higher roughening rate than PS and P4MS, and HAMA shows higher roughening rate 
than HAdA. And both 248 nm and 193 nm wavelength model polymers get roughen 
nearly the same range from about 0.4 nm up to about 7.4 nm in this case. Thus, the trace 
of Al contaminants during C4F8/90%Ar plasma etching on these model polymers does not 
hold significant effect in surface roughness evolution.       
 
 
 
 
 
 
 
 
 138 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure A.2 Overall summary plots of RMS roughness vs. etching time for (a) 248 nm 
and (b) 193 nm wavelength model polymers after C4F8/90%Ar etching: presence vs. 
absence of Al contaminants. 
(b) 
(a) 
 139 
Bibliography 
 
Chapter 1 
1.1 D. G. Cahill, J. Vac. Sci Technol. 21, S110 (2003). 
1.2 G. Ehrich and F. J. Hudda, J. Chem. Phys. 44, 1099 (1996); R. L. Schwoebel and E. J. 
Shipsey, J. Appl. Phys. 37, 3682 (1966).  
1.3 T. Frisch, and A. Verga, Condensed matter, Jul 2006. 
1.4 T. Tadayyon-Eslami, Thesis, University of Maryland (2006). 
1.5 J. Villain, J. Phys. I 1, 19 (1991). 
1.6 G. S. Bales and A. Zangwill, Phys. Rev. B 41, 5500 (1990). 
1.7 M. Ozdemir and A. Zangwill, Phys. Rev. B 45, 3718 (1992). 
1.8 J. D. Weeks, D.-J. Lui, and H.-C. Jeong, in Dynamics of Crystal Surfaces and 
Interfaces, edited by P. M. Duxbury and T. J. Pence (Plenum, New York, 1997), pp. 
199 ? 216. 
1.9 Veeco Metrology Group, Digital Instruments SPM training notebook. 
1.10 NanoScience Instruments: Atomic Focre Microscopy Overview. 
1.11 Roberto Lazzaroni, LAMINATE short course on Scanning Probes Microscopies, 
Mons, Sept 11 2001. 
1.12 The Colvin Group TM-AFM Manual at Rice University (http://nanonet.rice.edu). 
1.13 Atomic Force Microscopy: lecture note from ENMA489T/698T 
NanoCharacterization course by Professor R. Phaneuf in University of Maryland. 
 
 
 140 
Chapter 2 
2.1 T. Ogino, Surf. Sci. 386, 137 (1997).  
2.2 S. Tanaka, N. C. Bartelt, C. C. Umbach, R. M. Tromp, and J. M. Blakely, Phys. Rev. 
Lett. 78, 3342 (1997); S. Tanaka, C. C. Umbach, J. M. Blakely, R. M. Tromp, and M. 
Mankos, J. Vac. Sci. Technol. A 15, 1345 (1997).  
2.3 H.-C. Kan, S. Shah, T. T. Tadyyon-Eslami, and R. J. Phaneuf, Phys. Rev. Lett. 92, 
146101 (2004).  
2.4 S. Shah, T. J. Garrett, K. Limpaphayom, T. Tadayyon-Eslami, H. C. Kan, and R. J. 
Phaneuf, Appl. Phys. Lett. 83, 4330 (2003).  
2.5 M. D. Johnson, C. Orme, A. W. Hunt, D. Graff, J. Sudijono, L. M. Sander, and B. G. 
Orr, Phys. Rev. Lett. 72, 116 (1994).  
2.6 J. Kallunki, J. Krug, and M. Kotrla, Phys. Rev. B 65, 205411 (2002).  
2.7 O. Pierre-Louis, M. R. D'Orsogna, and T. L. Einstein, Phys. Rev. Lett. 82, 3661 
(1999). 
2.8 R. J. Phaneuf and E. D. Williams, Phys. Rev. Lett. 58, 2563 (1987). 
2.9  R. J. Phaneuf, E. D. Williams, and N. C. Bartelt, Phys. Rev. B 38, 1984 (1988). 
2.10 Y. Tsai and Y. Shapir, Phys. Rev. E 50, 3546 (1994). 
2.11 Pierre-Louis, M. R. D?Orsogna, and T. L. Einstein, Phys. Rev. Lett. 82, 3661 
(1999). 
2.12 J. J. Metois, J. C. Heyraud, and S. Stoyanov, Surf. Sci. 486, 95 (2001). 
2.13 S. T. Chui and J. D. Weeks, Phys. Rev. B 23, 2438 - 2441 (1981). 
2.14 W. W. Mullins, J. Appl. Phys. 30, 77 (1959). 
2.15 D. Kandel and J. D. Weeks, PRL 74, 3632 (1995). 
 141 
2.16 H. Kan, T. Kwon, and R. Phaneuf, in preparation (2007). 
2.17 N. C. Bartelt et al., Phys. Rev. B 48, 15453 (1993). 
2.18 S. D. Cohen et al., Phys. Rev. B 66, 115310 (2002). 
2.19 J. M. Bermond et al., Surf. Sci. 416, 430 (1998).  
2.20 D. Liu and J. Weeks, Phys. Rev. B 57, 14891 (1998). 
2.21 E. Williams, Surf. Sci. 299/300, 502 (1994). 
2.22 K. Thurmer, D. Liu, E. Williams, and J. Weeks, Phys. Rev. Lett. 83, 5531 (1999). 
 
Chapter 3 
3.1 S. Sivoththaman,  R. Jeyakumar, L. Ren, and A. Nathan, J. Vac. Sci. Technol. A 20, 
1149 (2002).  
3.2 J.N. Bremmer, SolidState Technology, September 2001. 
3.3 M.V. Bavel, F. Iacopi. M. Baklanov, and K. Maex, FUTURE FAB International, 
Issue 17, Section 6. 
3.4 X. Hua, et al, J. Vac. Sci Technol. A 23, 151 (2005). 
3.5 http://fcs.itc.it/MAME/download/low-k%20dielectrics.pdf 
3.6  D. R. Allee, C. P. Umbach and A. R. Broers, J. Vac Sci Technol. B 9, 2838 (1991). 
3.7 J. Bico, C. Marzolin and D. Quere, Europhys. Lett. 47, 220 (1999). 
3.8 B.N.J. Persson, O. Albohr, U. Tartaglino, A.V. Volokitin and E. Tosatti, J. Phys.: 
Condens. Matter 17, R1 (2005). 
3.9 C. Gui, M. Elwenspoek, N. Tas and J.G.E. Gardeniers, J. Appl. Phys. 85, 7448 (1999). 
3.10 J. Krc,, M. Zeman, F. Smole, J.W. Metselaar and M. Topic, Sol. En. Mat. Sol. 
Cells 74, 401 (2002). 
 142 
3.11 X. Hua, X. Wang, D. Fuentevilla, G. S. Oehrlein, F. G. Celii and K. H. R. Kirmse, 
J. Vac. Sci. Technol. A 21, 1708 (2003). 
3.12 X. Hua et al, J. Vac. Sci. Technol. B 24, 1850, (2006). 
3.13 P. Lazzeri, X. Hua, G. S. Oehrlein, M. Barozzi, E. Iacob, and M. Anderle, J. Vac. 
Sci. Technol. B 23, 1491, (2005). 
3.14 J. T. Drotar, Y.P. Zhao, T.M. Lu and G.C. Wang, Phys. Rev. B 61, 3012 (2000). 
3.15 ?Dynamics of Fractal Surfaces?, ed. F. Family and T. Vicsek (World Scientific, 
Singapore, 1991). 
3.16 S.K. Sinha, E.B. Sirota, S. Garoffi and H.B. Stanley, Phys. Rev. B 38, 2297 
(1988). 
3.17 Y.P. Zhao, J.T. Drotar, G.C. Wang and T.M. Lu, Phys. Rev. Lett. 82, 4882 (1999). 
3.18 S. Facsko, et al., Appl. Phys. Lett. 80, 130 (2002). 
3.19 C.C. Umbach, R.L. Headrick, and K. C. Chang, Phys. Rev. Lett. 87, 246104 
(2001). 
3.20 T. M. Mayer, E. Chason, and A. J. Howard, J. Appl. Phys. 76, 1633 (1994); E. 
Chason, T. M. Mayer, B. K. Kellerman, D. T. McIlroy, and A. J. Howard, Phys. Rev. 
Lett. 72, 3040 (1994). 
3.21 P. Politi, J. Japan. Assoc. Cryst. Growth 29, 3 (2002). 
3.22 S.F.Edwards and D.R.Wilkinson, Proc. R. Soc. London A 381, 17 (1982). 
 
Chapter 4 
4.1 X. Li et al., J. Vac. Sci. Technol. A 21, 284 (2003). 
4.2 H. Gokan, S. Esho, and Y. Ohnishi, J. Electrochem. Soc 130 143 (1983). 
 143 
4.3 Veeco, ?Nanolithography ?, Digital Instruments user manual, Software Version 5.12.