ABSTRACT
Title of thesis: STRESS CHARACTERIZATION
OF STRETCHABLE CRYSTALLINE
SEMICONDUCTORS
Sabrina M. Curtis, Master of Science, 2018
Thesis directed by: Professor Marina S. Leite
Department of Materials Science
Thesis co-advised by: Dr. Nathan Lazarus and Dr. Randy Tompkins
Special Members of the Graduate Committee
Stretchable crystalline semiconductors are the key to enable wearable high
power and energy devices. The work presented in this thesis evaluates the non-
uniform surface stress distribution of stretchable Si and GaN serpentine geometries
and has yielded the following contributions: (i.) 2D and 3D numerical analyses of the
effect of mechanical anisotropy in (100) Si on crystalline stretchable behavior, reveal-
ing the <100>direction can be up to 36% more stretchable than the <110>direction,
and (0001) GaN has no anisotropic dependence. (ii.) A micro-fabrication procedure
which allows for the fabrication and release of stretchable Si into serpentine me-
chanical test structures which demonstrated an experimental strain-to-rupture of
84%. (iii.) In-situ characterization of the non-uniform surface stress distribution
in stretchable Si, while applying external strain, using micro-Raman spectroscopy.
(iv.) A micro-scale imaging technique to spatially resolve the local surface stress
distribution in stretchable AlGaN/ GaN high electron mobility transistor devices.
STRESS CHARACTERIZATION OF STRETCHABLE
CRYSTALLINE SEMICONDUCTORS
by
Sabrina M. Curtis
Thesis 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
Master of Science
2018
Advisory Committee:
Professor Marina S. Leite, Chair
Dr. Randy Tompkins, Co-Advisor
Dr. Nathan Lazarus, Co-Advisor
Professor Gary Rubloff, Committee Member
©c Copyright by
Sabrina M. Curtis
2018
Acknowledgments
I would like to dedicate my Master’s thesis to everyone who has supported
me along this M.S/B.S journey. To start, I would like express my gratitude for my
advisers Dr. Nathan Lazarus and Dr. Randy Tompkins. Their outstanding mentor-
ship has taught me numerous useful research skills and how to truly critically think
like a scientist. They gave me the personal freedom and confidence to successfully
chase ideas of my own, furthering my love for science. In addition to the guidance
I received in the lab, they have both provided me with important life advice. I
am a better scientist, writer, critical thinker, researcher, and presenter because of
them, and for that I am forever grateful. I’d also like to thank my other committee
members Prof. Marina Leite and Prof. Gary Rubloff for always believing in me and
motivating me to do better. I owe my decision to obtain a Ph.D. after my masters
to the unbelievable support I have received over the years from this committee.
To my Army Research Lab (ARL) members/collaborators/friends: Dr. Bar-
bara Nichols and Dr. Sina Najamaei for their expertise with Raman spectroscopy,
and patience with my many questions. Dr. Milena Graziano, Yomery Espinal, and
Dr. Manuel Rivas for their positivity, being the best writing buddies, and helping me
keep my sanity during the long work nights and weekends. I definitely couldn’t have
gotten through this without you three. Gabe Smith for his knowledge in mechan-
ics, mentorship during the Collegiate Inventor Competition (FlexSi!), excitement to
pursue additional projects with me, and for being an awesome study buddy. Thank
you to everyone else at ARL that have helped shaped my project in some shape or
form: Dr. Ken Jones, Iain Kierzewski, Cory Knick, Dr. Darin Sharar, Dr. Adam
Wilson, Dr. Brendan Hanrahan, Dr. Sarah Bedair, Elad Siman-Tov, Mike Derange,
Franklin Nouketcha, Dr. Lauren Boteler, Dr. Aivars Lelis, and Claude Pullen.
ii
To Leite Lab members/friends: Dr. Elizabeth Tennyson, Dr. Chen Gong,
John Howard, Zack Benson, Prof. Bernardo Neves, Alan Kaplan, and Erica Lee.
Thank you for the many discussions about my research and teaching me all about
solar cells! In particular, thank you to Beth for guiding me throughout the grad
school process, help with LATex, and for your advice / friendship.
To my MSE Stretchable Solar Cell Capstone team: Haotian Wang, Gabriel
Anfinrud, Alex Randolph, Gabe Vostal, Kelvin Chang, Maria Pascale, Julia Down-
ing, and Joe Auyob. I will never be able to fully express how much I appreciate each
and every one of you for putting in 100% effort into this project. I especially want
to thank Haotian and Gabriel for always stepping up to any challenge that faced us
along the way. We would not be Collegiate Inventors without the tremendous work
these folks put in. I also want to give a special thanks to Prof. Ray Phaneuf for his
guidance along every step of the journey.
I also want to express my gratitude to technical staff members at the University
of Maryland for their assistance through many research challenges. In particular,
thank you to Tom Loughran, Mark Lecates, Jon Hummel, John Abrahams, and Dr.
Jim O’Connor at the Nanocenter. Without all of your support (and leniency with
the rules) we would have never fabricated anything close to a solar cell! I owe 90% of
my micro-processing knowledge to guidance received from these outstanding guys.
I also owe a huge thanks to the many technical staff members at ARL that
have advanced my micro-processing knowledge: Dr. Madhumita Roy, Raymundo
Prieto, Nelson Mark, Nick Strnad, Joel Martin, Stephan Kelley, Brian Power, Brian
Isaacson, Dr. Paul Sunal, and James Mulcahy.
To our collaborators at the College of Nanoscale Science and Engineering at
SUNY Polytechnic Institute: Dr. Shadi Shahedipour-Sandvik, Isra Mahaboob, and
Kasey Hogan. Thank you for the enthusiastic bi-weekly discussions, the bottom-up
GaN samples, and research guidance.
It is also extremely important to me that I properly thank and acknowledge
all of my previous research mentors: Dr. Don Schmadel, Prof. Kelsey Hatzell,
Prof. Jeffery Davis, Dr. Gretchen Peters, Dr. Taylor Plank, Dr. Myung Jung, and
iii
Prof. Brajendra Mishra. Thank you to everyone for your patience, guidance, and
mentorship over the years. You all have shaped me into the research scientist that
I am today, and directly impacted my decision to obtain a Ph.D.
The love, encouragement, and support I have received from my family is truly
invaluable. First to James: You have been my rock every step of the way during this
master’s, and I know I can count on you for absolutely anything. To my siblings:
Kaleigh, Chesi, Cade, Marques, Valerie and Jada and cousins: Emily, Maya, Mark,
Casey, Janine, Shawn, Dean, Vincent, Kalynn, Zander, Damien, Gavin, and Corrine
this thesis is really for all of you. I hope you all chase your dreams, and I know you
will all be very successful in life. To Uncle John: thank you for always being a phone
call away whenever I needed someone to vent or brag about my accomplishments to!
To Aunt Nichole: for being my second mom, 14er buddy, and for your hundreds of
edits on my papers/documents over the years. I am a better person and definitely a
better writer because of you. To my other parents: Jeff, Tony, and Tiffani, thank you
all for stepping up and parenting me in all different ways. I am the responsible, fun,
witty, and disciplined person that I am today because of my well-rounded upbringing
between my 4 (or 6?) parents. To my Curtis, Bailey, Daigle, Cowen, and Williams
grandparents thank you all for always staying interested in my research and pushing
me to accomplish my goals. My gratitude also extends to all of my other cousins,
aunts, uncles, and step family members that would take two more pages to list!
Finally, to my best friend, the one constant in my life, my mom Jennifer.
Thank you for always believing in me even when I didn’t. You are the reason I came
to Maryland in the first place and you led me to engineering. You have worked so
hard and sacrificed so much to give Kaleigh and I everything we wanted and needed.
You are truly an inspiration, I love you mama.
Sabrina M. Curtis
April 2018
College Park, MD
iv
Table of Contents v
List of Figures viii
1 Introduction and Research Objectives 1
1.1 The Need for Stretchable Crystalline Materials . . . . . . . . . . . . . 1
1.2 Master’s Thesis Research Contributions . . . . . . . . . . . . . . . . . 3
1.3 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Silicon and Gallium Nitride for Stretchable Electronics 7
2.1 Stretchable Materials, Methods and Devices . . . . . . . . . . . . . . 8
2.1.1 Requirements for Wearable Electronics . . . . . . . . . . . . . 8
2.1.2 Stretchable Inorganic Materials, Methods, and Devices . . . . 8
2.2 The Need for Stretchable Crystalline Materials for Power and Energy
Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Anisotropic Effects of Silicon and Gallium Nitride . . . . . . . . . . . 12
2.3.1 Mechanics of (100) and (111) Silicon . . . . . . . . . . . . . . 12
2.3.2 (0001) Gallium Nitride . . . . . . . . . . . . . . . . . . . . . . 13
2.3.3 Effect of Anisotropy on the Stiffness Tensor of Si and GaN . . 14
3 Numerical Modeling of Stress and Strain in Stretchable Crystalline
Materials 19
3.1 Numerical Evaluations of Stretchable Systems . . . . . . . . . . . . . 20
3.2 (2D) Stationary Linear Elastic Model . . . . . . . . . . . . . . . . . . 23
3.2.1 Numerical Model Input Parameters to Evaluate the von Mises
Peak Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.2 Effect of Serpentine Geometry on Stretchable Behavior of (100)
Silicon and (0001) Gallium Nitride . . . . . . . . . . . . . . . 29
3.2.3 In-Plane Rotation Dependence of (0001) GaN and (100) Si . . 32
3.2.4 Stretchability of (100) Silicon in the <100> and <110> di-
rections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 (3D) Stationary Linear Elastic Model . . . . . . . . . . . . . . . . . . 37
3.4 Modeling Crystalline Stretchable Behavior Summary and Conclusions 40
v
4 Microfabrication of Stretchable Crystalline Serpentine Structures 43
4.1 State of the Art Fabrication Approaches to Enable Flexible and Stretch-
able Si and GaN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.1.1 Methods to Enable Flexible / Stretchable Si . . . . . . . . . . 44
4.1.2 Methods to Enable Flexible / Stretchable GaN . . . . . . . . 45
4.2 Fabrication Process of <100> and <110> Serpentines from (100)
Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3 Fabrication Process of Serpentines from (0001) Gallium Nitride . . . 55
4.4 Fabrication and Release Summary and Conclusions . . . . . . . . . . 57
5 In-Situ Stress Measurements on Stretchable Crystalline Si using
micro-Raman Spectroscopy 58
5.1 Raman Spectroscopy as a Stress Measurement Technique . . . . . . . 59
5.2 General Theory of Raman Spectroscopy . . . . . . . . . . . . . . . . 61
5.2.1 Raman To Measure Stress in Silicon . . . . . . . . . . . . . . . 64
5.3 Experimental Modification to Allow Application of External Strain
during µRS Measurements . . . . . . . . . . . . . . . . . . . . . . . . 69
5.3.1 3D Printed Sample Holder Design . . . . . . . . . . . . . . . . 69
5.3.2 Optical Straining Images of Stretchable <110> Si . . . . . . . 71
5.4 Optical Tensile Testing and FEM Result Comparison . . . . . . . . . 74
5.5 Stress Measurements on Released <100> Si Curved Corner Serpen-
tines: Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . 75
5.5.1 Stress Measurement Collection Techniques Using Raman . . . 75
5.5.2 Raman Stress Characterization on Stretchable Si Curved Cor-
ner Serpentines . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.6 Low-Cycle Fatigue Evaluation on Stretchable <100> Si using Raman
Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.7 Raman Spectroscopy to Measure Stress in Stretchable Si Summary
and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6 Ex Situ Stress Measurements of Stretchable AlGaN/ GaN HEMT
Devices 84
6.1 AlGaN/ GaN HEMT Overview . . . . . . . . . . . . . . . . . . . . . 86
6.1.1 Stretchable AlGaN/ GaN HEMT Motivation . . . . . . . . . . 86
6.1.2 AlGaN / GaN HEMT Hetero-Structure . . . . . . . . . . . . . 87
6.1.3 Built-In Stress within HEMT Structure . . . . . . . . . . . . . 88
6.2 Raman to Measure Stress in GaN . . . . . . . . . . . . . . . . . . . . 90
6.2.1 Stress Measurement Methodology . . . . . . . . . . . . . . . . 92
6.3 Stress Measurements on Bottom-Up AlGaN/GaN HEMTs: Results
and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.3.1 Bottom-Up Approach Background . . . . . . . . . . . . . . . . 94
6.3.2 Selective Area Growth with SiO2 Mask . . . . . . . . . . . . . 95
6.3.3 Selective Area Growth with Tungsten (W) Mask . . . . . . . . 96
6.4 Stress Measurements on Top-Down AlGaN/GaN HEMTs: Results
and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
vi
6.4.1 Top-Down Approach Background . . . . . . . . . . . . . . . . 98
6.4.2 Stress in AlGaN/ GaN HEMT on the wafer . . . . . . . . . . 99
6.4.3 Stress in AlGaN/GaN HEMT when Released and Embedded
into a Stretchable Substrate . . . . . . . . . . . . . . . . . . . 100
6.5 Stress Measurements in AlGaN/GaN HEMTs Conclusions . . . . . . 101
7 Outlook for Stretchable Crystalline Materials 104
7.1 Conclusions and Summary of Contributions . . . . . . . . . . . . . . 104
7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
7.3 Products of this Research . . . . . . . . . . . . . . . . . . . . . . . . 110
7.3.1 Honors and Awards . . . . . . . . . . . . . . . . . . . . . . . . 110
7.3.2 Oral Presentations . . . . . . . . . . . . . . . . . . . . . . . . 110
7.3.3 Posters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
7.3.4 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Bibliography 112
vii
List of Figures
2.1 Diamond cubic crystal structure of single crystal silicon. . . . . . . . 13
2.2 Wurtizite hexagonal closed packed crystal structure of single crystal
GaN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 C11 stiffness coefficient of in-plane rotations on (100) Si and (0001)
GaN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1 Serpentine geometries analyzed in this work . . . . . . . . . . . . . . 24
3.2 Material properties used to model anisotropy in the linear elastic model 25
3.3 2D COMSOL simulation of a 10 period Si or GaN serpentine trace
embedded within a Sylgard 184 elastomer substrate after an applied
30% global strain parallel to the trace . . . . . . . . . . . . . . . . . . 26
3.4 2D COMSOL Mesh Convergence Plot . . . . . . . . . . . . . . . . . . 28
3.5 Meshing conditions and COMSOL Multiphysics stress output of Curved
Corner s erpentine . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.6 Von Mises peak stress distribution on four tested serpentine geometries 30
3.7 Effect of serpentine geometry on the reduction of peak stress after
applying a 30% strain parallel to the trace for single crystal Si and
GaN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.8 Maximum von mises peak stress value for all serpentine geometries
as a function of in-plane rotations on (0001) GaN serpentines after
applying a 30% strain. . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.9 Maximum von Mises peak stress as a function of in-plane rotations
on (100) Si serpentines after applying a 30% strain. . . . . . . . . . . 34
3.10 Width-to-radius (w/r) ratios analyzed . . . . . . . . . . . . . . . . . . 35
3.11 Effect of anisotropy and width-to-radius ratio in Si on stretchable
behavior for Curved Corner and Rectangular serpentines. . . . . . . . 36
3.12 3D mesh convergence test . . . . . . . . . . . . . . . . . . . . . . . . 38
3.13 3D COMSOL model of a free standing 5 period <100> Si Curved
Corner serpntine trace stretching to a maximum global strain of 84%. 39
3.14 3D FEA modeling results demonstrating the fracture location of<110>
and <100> Si Curved Corner serpentines. . . . . . . . . . . . . . . . 40
3.15 2D and 3D FEA modeling results comparison of the maximum end-to-
end displacement (tensile strain) of <110> and <100> Si serpentines. 40
4.1 Diagram labeling the angle and family of directions on a (100) Si wafer. 48
viii
4.2 Procedure developed to fabricate and release Si serpentines from an
SOI Wafer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3 Scanning electron microscopy (SEM) imagess of the other serpentine
geometries tested though DRIE . . . . . . . . . . . . . . . . . . . . . 54
4.4 Fabricated Curved Corner Si serpentine released and mounted into
the 3D printed sample holder, ready for Raman Spectroscopy char-
acterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.5 Simplified process flow chart showing the major steps required to
fabricate and release a GaN serpentine. . . . . . . . . . . . . . . . . 56
5.1 Location of the Amplitude, Bend, and Straight part of a Si Curved
Corner serpentine trace. . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2 Jablonksi energy diagram of quantum energy transitons between Ra-
man and Rayleigh scattering. . . . . . . . . . . . . . . . . . . . . . . 62
5.3 Raman Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . 63
5.4 Raman Spectra and stress relation in unstrained bulk (100) Si. . . . . 67
5.5 Micro-Raman wavenumber position map of reference SOI wafer . . . 68
5.6 Solidworks engineering drawing of the designed assembled sample
holder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.7 Custom built sample holder for the Raman Microscope. . . . . . . . . 71
5.8 Optical images of compressive strain testing of a <110> Curved Cor-
ner Si serpentine surviving a global strain of -24% compression . . . . 72
5.9 Optical images of global tensile strain testing of a <110> Curved
Corner Si serpentine to a maximum of 84%. . . . . . . . . . . . . . . 73
5.10 Experiment and model strain comparison of the <110> Si Curved
Corner serpentine stretching to 84%. . . . . . . . . . . . . . . . . . . 74
5.11 Images demonstrating the locations on the serpentine measured with
Raman. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.12 Raman measured stress distribution for all positions after applying a
30% global strain global parallel to the trace. . . . . . . . . . . . . . . 78
5.13 Raman measured stress distribution across the Amplitude, Bend, and
Straight part of the serpentine trace as a function of applied strain. . 79
5.14 Low-cycle fatigue testing of a <100> Curved Corner serpentine from
0% to 30% applied global strain for 15 cycles. . . . . . . . . . . . . . 80
5.15 Low-cycle stress and fatigue evaluation on the Amplitude, Bend, and
Straight of the <100> Si Curved Corner serpentine after applying a
global strain of 30% for 0-15 cycles. . . . . . . . . . . . . . . . . . . . 81
6.1 Scanning electron microscopy (SEM) images of a stretchable AlGaN/
GaN HEMT devices grown through the top-down and bottom-up
approaches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.2 Cross section of a AlGAN/ GaN HEMT device showing the electric
field lines that form the 2DEG. . . . . . . . . . . . . . . . . . . . . . 88
ix
6.3 Table showing GaN, AlN, and common substrate materials Si, SiC,
and Sapphire lattice constant and coefficient of thermal expanion
(CTE) mismatch, and dislocation density values . . . . . . . . . . . 89
6.4 Raman Spectra of µm GaN in the (0001) back scattered geometry on
a bulk sapphire substrate. . . . . . . . . . . . . . . . . . . . . . . . . 92
6.5 A 70 µm x 70 µm Raman position map of E2 (high) phonon mode in
the as-grown AlGaN/ GaN on Si wafer . . . . . . . . . . . . . . . . . 93
6.6 Diagram aemonstrating the bottom-up fabrication approach to build
a stretchable AlGaN / GaN HEMT using selective area growth. . . . 94
6.7 2D Raman stress maps of bottom-up SAG AlGaN/ GaN HEMTs
with the SiO2 Mask. . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.8 2D Raman stress map of bottom-up SAG AlGaN/ GaN HEMT fab-
ricated with the tungsten metal mask. . . . . . . . . . . . . . . . . . 97
6.9 Top-down fabrication approach for stretchable AlGaN/GaN HEMTs. 98
6.10 2D Raman stress map of a top-down stretchable AlGaN/ GaN HEMT
on the Si wafer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.11 2D Raman stress map of a top-down stretchable AlGaN/ GaN HEMT
released from the Si wafer and encapsulated in silicone. . . . . . . . . 101
7.1 Fabricated stetchable silicon photovoltaic devices. . . . . . . . . . . . 109
x
Chapter 1: Introduction and Research Objectives
1.1 The Need for Stretchable Crystalline Materials
The motivation for this research lies in the need for stretchable high power and
high energy systems that can elastically bend, flex, and stretch by a minimum of
30% strain for integration into the soldiers’ uniform or onto their skin. Crystalline
semiconductors (such as Si and GaN) are brittle materials used in a number of power
and energy applications, and are intrinsically not stretchable or flexible; however
they can reach unprecedented end-to-end displacements (10s - 100s % global strain)
if patterned into unconventional micro-structured serpentine geometries (1). Our
Wide Band Gap Semiconductors research group in the Energy and Power Division at
United States Army Research Laboratory (ARL) is pursuing the development of the
first stretchable aluminum gallium nitride / gallium nitride high electron mobility
transistor (AlGaN/ GaN HEMT) (2; 3) for highly efficient power management (>
100 watts) of wearable systems which could serve in applications such as the DARPA
Warrior Web soft exoskeleton (4; 5). The research described in this thesis is a
numerical and experimental evaluation of the non-uniform surface stress distribution
of crystalline semiconductors (Si and GaN) patterned into stretchable serpentine
geometries. Modeling and experimental techniques are presented to examine the
influence of stretchable serpentine geometry and crystalline anisotropy on the non-
uniform stress distribution under applied external strain.
Si has a low-band gap of 1.12 eV and is used in a variety of low power-
output sensor and actuator devices due to its low manufacturing cost, matured
fabrication processes, and its abundance which also makes it the most common
substrate material for MEMS devices (6). Si is reaching its limits of power density
1
due to limitations in the material properties such as a low critical electric field
and thus a high specific on-resistance, and high rectifying losses (7). Rectifying
and resistive losses are one of the largest sources of power loss in wireless power
systems and result in the generation and dissipation of heat which could cause
discomfort to a user if integrated onto human skin (8) or a soft substrate that could
be worn. As an alternative to Si devices, wide band gap materials such as 6H-
SiC (2.86 eV), GaN (3.4 eV), and C (diamond) (5.6 eV) have high critical electric
fields, low specific on resistances, and low resistive losses which can allow for higher
power, higher frequency, faster-switching, and overall more efficient wearable device
technologies (7; 9). High electron mobility transistor (HEMTs) are a type of field
effect transistor used to provide high power at microwave frequencies in applications
such as low noise small signal amplifiers, power amplifiers, and oscillators (9; 10).
An AlGaN/ GaN heterostructure is an ideal candidate for HEMT devices since the
band gap is 3x higher than Si it can achieve higher voltages, electron mobility, break
down fields and power efficiencies, while maintaining lower rectifying losses (7). In
addition the specific on-resistance of GaN is 1000X lower than Si, meaning it can
mitigate the heat loss significantly better, which is desired for wearable systems (2).
These advantages are the reasons why our research group is exploring stretchable
crystalline materials to fabricate the first stretchable AlGaN/ GaN HEMT device,
for stretchable wireless high power management.
When designing devices intended for wearable applications, it is important to
understand and predict the failure strain value and stress concentration locations of
the device. This work proposes a simple theoretical and in-situ experimental stress
mapping and monitoring technique of Si and GaN serpentines under applied strain.
2D and 3D finite element analysis (FEA) numerical simulations are used to model
the non-uniform local stress distribution of multiple stretchable serpentine structures
under applied external strain. This allows for the prediction of the maximum surface
stress on the structure and its likely failure location. The model also provides
insight for promising stretchable geometries, which are then fabricated from Si and
GaN. The modeled local stress distribution along the serpentine geometry after
2
an applied external strain is then experimentally verified using the non-destructive
characterization technique micro-Raman spectroscopy. Finally, further experimental
verification is presented through low-cycle stress monitoring experiments and optical
imaging. Adapting widely used theoretical modeling and experimental techniques of
localized stress concentrations within crystalline semiconductors can provide insight
into predictive failure analysis of stretchable crystalline integrated circuits.
1.2 Master’s Thesis Research Contributions
I accomplish the following research objectives by modeling, fabricating and ex-
perimentally characterizing the non-uniform stress distribution of stretchable crys-
talline materials. From these contributions, I foresee the methods developed in this
thesis to be widely implemented during future stretchable crystalline device design,
fabrication process monitoring, and performance testing.
(i.) Stretchable anisotropic modeling of crystalline semiconductors.
Using COMSOL Multiphysics 5.2, I perform a refined 2D model and the first 3D
finite element model (FEM) investigating the influence of serpentine geometry and
mechanical anisotropy on the stress/ strain behavior of (100) Si and (0001) GaN. To
our knowledge, this is the first 3D anisotropic FEM model of any stretchable crys-
talline semiconductor. In agreement with prior results (2), our results show serpen-
tine geometries can reduce peak stress by 20-98%, and geometries with curved edges
(Curved Corner and Horseshoe) mitigate stress under strain better than those with
sharp corners. Upon performing in-plane rotations to study crystalline anisotropic
stretchable dependence it was demonstrated (0001) GaN behaves isotropically within
the c-plane used for GaN power device fabrication which is ideal for stretchable elec-
tronics. (100) Si behaves anisotropically, revealing the <100> direction can be up
to 12-30% more stretchable than the <110> direction.
(ii.) Stretchable fabrication and release process of crystalline ma-
terials. I develop and optimize a reliable micro-fabrication process which allows
for the fabrication and release of free standing stretchable crystalline Si serpentine
3
mechanical testing structures. This procedure uses standard micro-machining and
photolithography techniques, that can easily be repeated in a standard clean room,
allowing fabrication of serpentines with varying thicknesses, widths, and amplitudes
ranging from a few nanometers to hundreds of microns. This process could be
adapted to allow for the release of other stretchable thin-film crystalline materials
epitaxially grown onto a silicon substrate, such as III-V materials (GaN, AlGaN,
InGaN). Furthermore, this fabrication and release process is compatible with dielec-
tric and metal deposition processes which are crucial steps during stretchable device
fabrication.
(iii.) In-situ stress characterization and fatigue evaluation of stretch-
able Si with micro-Raman Spectroscopy. For the first time, I experiemntally
characterize the non-uniform local surface stress distribution on a stretchable <100>
Curved Corner Si serpentine while applying global external strains of 0 - 72%. To
achieve this, I custom-built a 3D printed sample holder that allows for static micro-
Raman stress measurements to within 50 MPa, while applying external strain on
the serpentine structure. Due to a small width-to-radius ratio (w/r = 0.2), the
tested <100> Curved Corner serpentine buckles out of plane to relieve stress un-
der applied external strain, non-uniformly concentrating the maximum stress in the
buckled regions called the Bend. This is the location of fracture predicted by the
3D anisotropic model. Additionally, tensile testing on the <110> Curved Corner
Si serpentine revealed a global strain-to-rupture of 84%, which is in excellent agree-
ment with the 2D model. However, the local strain within the individual period
could displace by larger amounts than the global strains, which was predicted in
the 3D model. I also show micro-Raman spectroscopy can be used to study the
reversible elastic behavior of stretchable crystalline serpentines by performing low-
number cycle fatigue characterization for 15 cycles from 0 - 40% strain, showing no
appreciable change in the stress.
(iv.) Stress monitoring of stretchable AlGaN / GaN HEMT device
fabrication using micro-Raman spectroscopy. A variant of micro-Raman spec-
troscopy is used to spectrally and spatially resolve the local surface stress distribu-
4
tion within GaN devices, into 2D stress maps. With my collaborators at ARL and
the College of Nanoscale Science at SUNY Polytechnic Institute, I study the stress
changes induced in stretchable AlGaN/ GaN HEMT devices, fabricated through two
different approaches (bottom-up vs top-down). I show that selective area growth
(bottom-up approach) of AlGaN/ GaN HEMT devices onto a sapphire substrate
induces a strong compressive stress (-1.7 GPa). I also show that etching AlGaN/
GaN into a stretchable HEMT device on a silicon substrate through the top-down
approach induces tensile stress (+0.5 GPa). Finally, I demonstrate removing the Si
substrate and encapsulating the stretchable device within a soft silicone elastomer
induces additional tensile stress (+0.8 GPa).
1.3 Thesis Organization
This thesis is organized into seven main chapters. Chapter 1 stated the re-
search problem and the contributions of the thesis. Chapter 2 sets the motivation
to use Si and GaN in stretchable electronic applications, covers necessary back-
ground information of materials and reviews the mechanical concepts that enable
traditionally brittle and rigid materials to stretch. Additionally, the influence of
crystalline anisotropy in Si and GaN is reviewed. Chapter 3 discusses the 2D and
3D finite element models developed to evaluate the mechanical behavior of Si and
GaN stretchable structures under applied strain. This includes evaluation of the
anisotropic behavior of (100) Si in serpentine structures, prediction of failure loca-
tion, and determination of the maximum tensile strain on two serpentine geometries,
as a function of the width-to-radius ratio. Chapter 4 describes the details of the novel
micro-fabrication and release process developed that allowed for the development
of single crystal Si and GaN into stretchable mechanical test structures. Chapter
5 presents the experimental procedure, results, and analysis of micro-Raman spec-
troscopy data for measuring the non-uniform stress distribution of Si mechanical test
structures to validate the model. Additionally, I present using using micro-Raman
as a low-cycle fatigue characterization technique. Chapter 6 presents methodology
5
to use micro-Raman spectroscopy as a stress monitoring technique during the fabri-
cation of stretchable AlGaN/ GaN HEMTs. Finally, Chapter 7 provides conclusions,
recommendations for future work, and the research contributions of this work to the
greater academic community.
6
Chapter 2: Silicon and Gallium Nitride for Stretchable Elec-
tronics
Stretchable electronics is the integration of highly deformable electrical con-
ducting components onto soft stretchable substrates. Fabrication and transfer pro-
cesses are well established for stretchable conductor systems that embed metal traces
into elastomers for metal interconnection of circuit components, often through a
wavy serpentine method (1; 11; 12). However, research on semiconductor stretch-
able devices is less reported (13; 14; 15). Inorganic materials such as crystalline
semiconductors, metals, dielectric oxides and nitrides are required to develop high-
performance stretchable circuits for wearable electronic applications (16). To en-
able a stretchable device, all circuit components must be architecturally reconfig-
ured into compliant geometries, or replaced with intrinsically high strain materials
(17). Chapter 2 is intended to review the current status of research efforts toward
stretchable materials, components, and devices. This chapter also motivates why
the crystalline semiconductors silicon (Si) and gallium nitride (GaN) are particularly
interesting materials to study for applications in stretchable power management and
future stretchable energy devices. Finally, an overview of the basic materials prop-
erties, and the effect of crystalline anisotropy of Si and GaN on their mechanical
behavior is presented.
7
2.1 Stretchable Materials, Methods and Devices
2.1.1 Requirements for Wearable Electronics
Wearable smart electronics are becoming increasingly popular among con-
sumers and military personnel because they offer a more convenient solution to
portable electronics. Wearable electronics can be achieved by micro-fabricating and
implementing stretchable electrical devices directly onto human skin (18), or a sub-
strate that can be worn (19; 20; 21). Any device intended to be used for wearable
applications must elastically survive cycled deformation such as bending, flexing,
twisting and stretching by a minimum of 20% strain (16) to 30% strain, to match
the elastic performance of human skin (18). Some locations of the body are reported
to require even higher strain levels up to a 100%, such as behind the kneecap (8).
To meet these demands, high performance wearable electronic systems require all
active circuit components to be elastically deformable, and thus stretchable.
Early efforts to build stretchable conducting circuits exploited the use of semi-
conducting organic materials due to their intrinsic hyperelastic (high strain) mechan-
ical properties (22; 23; 24). Many organic flexible and stretchable devices have been
demonstrated included organic stretchable solar cells (25), organic light-emitting
diode (OLED) displays (26), flexible artificial electronic skin (27), and organic pho-
todiodes (OPD) for non-invasive medical sensors (28). However, with the growing
complexity of wearable technologies requiring high power and high energy output,
the low carrier mobilities and resulting low efficiencies of organic materials are not
suited for these applications (29). As a result, vast efforts have been made to de-
velop methods and compliant geometries to enable stretchability within inorganic
materials, which are traditionally low-strain materials (13; 14; 15; 30).
2.1.2 Stretchable Inorganic Materials, Methods, and Devices
Metal conductors, like most inorganic materials, are intrinsically stiff and un-
able to stretch significantly (< < 1%); however, they can bend if their cross section
8
is sufficiently thin (11). One of the first techniques to develop a stretchable cir-
cuit system with thin-film metal is referred to as the pre-strained substrate method
(31; 32). In this method, a stretchable substrate such as silicone or polyurethane
is held under tension, and evaporation or sputtering is used to deposit the metal
directly onto the substrate. When the tension is released from the substrate, the
system is allowed to relax which buckles the metal forming compliant out-of-plane
wavy structures. These highly deformable metallic nanoribbons are heavily used
as stretchable inter-connectors, because they can regain mechanical and electrical
continuity upon cycling strain (31).
A second method to create stretchable metal uses standard photolithography
and micro-machining techniques to pattern materials into 2D structures comprised
of kinks and waves, referred to as serpentines. These structures can elastically
cycle large end-to-end displacements, reversibly, behaving similar to a spring. The
amplitude and wavelength of the wavy serpentine geometry undergo a geometrical
reconfiguration to relieve stress in response to the physical deformations (11; 12; 33).
For example, Gray et al. explored the buckling mechanics and stretchable behavior
of gold (Au) patterned into 2D spring-like serpentine structures. They showed
that by reducing the thickness and width of the serpentine traces, the structure
becomes mechanically more reconfigurable and could reach higher tensile strains.
They demonstrated the gold metal wires could stretch and compressive reversibly
by 54% several times, while maintaining stable electrical conductivity (11).
The mechanical performance of the serpentine can be further improved upon
by embedding the serpentine components within a soft elastomer support, such as
polydimethylsiloxane (PDMS) (34). The soft substrate offers both more deformable
regions and mechanical protection, which helps prevent damage to the circuit and
can improve device performance, life-time, and fatigue characteristics (35; 36; 37).
The effective stiffness, and thus strain-to-rupture of the serpentine/ elastomer sys-
tem is tunable, dependent on the geometrical parameters: arc length, amplitude,
height, width and Youngs modulus of the materials. Using an elastomer as the
stretchable substrate is advantageous because the modulus of elasticity is at least
9
three orders of magnitude lower than the wavy material conductive material em-
bed within. This means when the material is stress/strained, the majority of the
peak stresses are concentrated in the elastomer rather the conductor components,
(11; 38; 39). Thin copper wires were demonstrated to reach strains beyond < 50%,
when well-bonded to an elastomeric substrate, however, it was reported that metals
undergo irreversible plastic deformation, which would cause a degradation in the
mechanical and electrical performance of the stretchable device (40).
2.2 The Need for Stretchable Crystalline Materials for Power
and Energy Devices
Currently, the most efficient power and energy devices utilize crystalline inor-
ganic semiconductor materials, which have a tensile strain of < 1%, far below the
30% tensile strain requirement for wearable systems. While there are significant
research advances in the development of flexible high power and high energy devices
from inorganic materials (41), these technologies are insufficient for stretchable elec-
tronic applications, due to structural limitations. As a result, great efforts have been
made to enable stretchable lithium ion batteries (42), stretchable super capacitors
(43; 44), stretchable crystalline solar cells (30; 45), stretchable inductors (46; 47)
and other stretchable wireless power transfer technologies (48; 49). Development of
stretchable single crystalline semiconductor devices made of silicon (Si) and gallium
nitride (GaN) are of particular interest because they could be the solution to high
power energy generation and energy storage wearable devices.
One of the first techniques used to enable stretchable systems which contain
rigid or brittle circuit components is referred to as an ”island plus bridge” layout,
where the functional inorganic material is a rigid micro-scale ”island” connected
by stretchable metal interconnect ”bridges” (50). The bridges must have a low ef-
fective stiffness to tolerate large deformations. Through selective gas and chemical
etch processes, these island structures can be released (de-bonded) from their tra-
ditional rigid substrate, and transferred to a stretchable substrate, (42; 45). Under
10
deformation, if the peak stresses present in the island are smaller than yield stress
(7 GPa for silicon) of the material, the system can survive cycling tension and com-
pression, and is considered to be a highly elastic reversible system. The serpentine
geometries are suitable to serve as the structure for both the device ”island”, and
the stretchable metal interconnect ”bridge” (18).
Single crystal silicon is a narrow band gap material (1.1 eV), widely used
as various components in various microelectromechanical systems (MEMS), due to
well-studied materials properties, and matured fabrication procedures which leads
to low manufacture cost. Well known deposition, etching, and photolithography
techniques have led to highly efficient flexible Si solar cell devices, super junction
MOSFETs, and other high performance integrated silicon circuits. While Si is a an
excellent semiconductor material, Si-based transistor devices are reaching their lim-
its of power density, breakdown voltage, operation frequency, and temperature (7).
In search of devices with higher power and energy densities, wide-band gap (WGB)
semiconductors (< 2 eV) may be able to overcome these challenges demonstrating
power electronic devices that are faster, more efficient, and can withstand higher
voltages and higher temperatures than Si. As a result, Si has transitioned into serv-
ing as a cost-effective substrate to support epitaxial growth of high performing wide
band gap materials.
Gallium Nitride (GaN) is a an ideal candidate for highly efficient power conver-
sion electronics due to its wide direct electronic band gap (3.4 eV at room temper-
ature), which results in a high electronic breakdown field, large electron saturation
field, and unusually large electron mobility, allowing it to be used in high tempera-
ture, high voltage, and high frequency applications (51). One of the advantages of
using GaN for power electronics is the magnitude of the band gap can be altered,
ranging as high as AlN (6.2 eV) and as low as InN (0.64 eV), because GaN forms
solid solutions (AlGaN, InGaN, AlInGaN) with its III-Nitride counterparts. The
advantage of these properties for high electron mobility transistor devices will be
further discussed in Section 6.1.
11
2.3 Anisotropic Effects of Silicon and Gallium Nitride
Single crystal (or monocrystalline) materials, are composed of repeating pe-
riodically arrayed atoms that form crystal lattices. Simple cubic materials behave
isotropically, meaning their mechanical, optical, and electronic properties have no
directional dependence due to rotational symmetry. Silicon and gallium nitride have
anisotropic crystal structures which means their properties are dependent on crys-
tallographic orientation. The concept of mechanical anisotropy in Si and GaN are
reviewed below.
2.3.1 Mechanics of (100) and (111) Silicon
The crystal structure of single crystal Si is a face-centered-diamond cubic,
which consist of two interpenetrating face centered cubic (FCC) crystal structures,
offset by an amount of x = y = z = a0 , where a0 is the lattice constant of Si. The4
elastic properties, stiffness and compliance matrix, of silicon can be described using
three independent elements due to the cubic symmetry in silicon. Due to mechanical
anisotropy, if one were to fabricate identical MEMS devices on the isotropic (111)
Si plane and anisotropic (100) Si plane the properties of the device are expected to
behave quite differently depending on local atomic arrangement. Here, I evaluate
(100) Si since this is the most common plane for MEMS device fabrication. (111) Si
is also shown since it’s a common substrate for III-V materials, due to the in-plane
isotropic properties which promotes lattice matching along the closed packed planes
of the basal (0001) plane of the hexagonal wurtzite crystal structure. The crystal
structure of Si highlighting the (100) and (111) planes are shown in Figure 2.1.
12
Figure 2.1: Diamond cubic crystal structure of single crystal silicon. A.) (100) anisotropic
plane and B.) (111) isotropic plane.
2.3.2 (0001) Gallium Nitride
Gallium Nitride is composed of a group III element (Ga), and a group V ele-
ment (N). It owes its interesting material properties due to the bonding nature of the
Ga and N ions. GaN, AlN, and AlGaN all have a wurtzite crystal structure, which
is a thermodynamically stable crystal structure composed of two interpenetrating
hexagonal closed packed lattices (52). All group III metals bonded to nitrogen ex-
perience a large difference in electronegativity, creating strong ionic bonds between
the molecules. Since ionic bonds are the strongest bonds to break, the energy that
it takes to excite an electron from the valence band to the conduction band is ex-
tremely large, therefore, the material has a wide band gap. The material properties
of GaN enable advanced performance of high-electron mobility transistors (HEMT),
monolithic microwave integrated circuits (MMICs) for RF applications, solar cells,
and light emitting diodes (LEDs). The wurtzite crystal structure of GaN is shown
in Figure 2.2.
13
Figure 2.2: Wurtizite hexagonal closed packed crystal structure of single crystal GaN.
Herem a is the lattice constant which is interatomic spacing between two Ga ions. The blue
highlighted plane is the (0001) growth plane analyzed in this work.
2.3.3 Effect of Anisotropy on the Stiffness Tensor of Si and GaN
The Young’s modulus E is a material property that describes the relationship
between stress and strain for an out-of-plane deflection of a square plate, and is
anisotropically dependent on crystal axis orientation. For Si, the Young’s modulus
ranges from 130 - 188 GPa which could present up to a 45% variation in stress
within traditional MEMS devices, or stretchable crystalline serpentines. The effect
of mechanical anisotropy along various crystallographic orientations of a material
is described by the material’s elastic coefficients related through the fourth ranked
stiffness and compliance tensors. Due to crystal symmetry, the generalized stiffness
and compliance coefficients can be reduced to a simplified 6 x 6 matrix, as shown
in Equation 2.1.
14
   C11 C12 C13 
 S11 S12 S13
C21 C22 C23   
 

S21 S22 S23 


C31 C32 C33  S31 S32 S33 Cijkl =  S ijkl = C44  

S44 
C55 S55 
C66 S66
(2.1)
where C11 = Ciiii, C12 = Ciiji, C44 = Cijij, S11 = Ciiii, S12 = Siiji, S44 = 4Sijij
The stiffness coefficients can then be used to calculate the compliance coeffi-
cients, at a particular orientation using Equation 2.2. For isotropic materials the
stiffness tensor Cijkl is simply expressed as the single coefficient E of the Young’s
modulus (53).
C11 + C12 −C12 1
S11 = , S12 = , S44 = (2.2)
(C11 − C12)(C11 + 2C12) (C11 − C12)(C11 + 2C12) C44
The stiffness and compliance tensors are also related to stress and strain in a
crystal through Equation 2.3.
Hooke’s Laws: σij = Cijklkl, ij = Sijklσkl (2.3)
where σijkl and ijkl are the stress and strain components respectively.
Through well-established calculations, the generalized Hookes Law can be used
to resolve the stress components along a crystal axis Equation 2.3. Through multi-
plication of the direction cosine matrix by a known tensor reference frame, one can
perform a tensor transformation to determine the elastic coefficients for any crys-
tallographic orientation. These calculations are well established and are reported in
detail elsewhere for Si (53; 54; 55) and for GaN (56; 57). After performing these
rotations, the Youngs Modulus can then be calculated for the [100], [110], and [111]
crystallographic directions of Si as shown in Equation 2.4 and are found to be E110
= 169 GPa, E100 = 130 GPa, E111 = 188 GPa.
15
1 1
= S11 = GPa
−1
E100 130
1 1 1 1 (2.4)
= S11 − [(S11 − S12) − S44] = GPa−1
E110 2 2 169
1 2 1 1
= S11 − [(S −111 − S12) − S44] = GPa
E111 3 2 188
In the case of a (100) Si plane, the wafer flat is aligned in the [110] direction,
and has a Young’s modulus of E110 = 169 GPa. The bracket notation of [110]
indicates this direction is a member of the <110> family of directions which lie
parallel or perpendicular (”X” or ”Y” axis) to the wafer flat. The lowest Young’s
modulus (E100 = 130 GPa) occurs along the [100] direction, in the <100> family
occurs at a 45◦ rotation from the ”X” or ”Y” axis. The highest Young’s modulus
(E111 = 188 GPa) is along the <111>family of directions on the (111) Si plane (53).
The studies performed in this thesis investigate the effect of mechanical anisotropy
on the stretchable behavior of crystalline serpentines on (100) Si and (0001) GaN.
To do this, we performed in-plane rotations in 10◦ increments on (100) Si from the
[100] direction, and 10◦ increments on the (0001) GaN from the [0001] direction, and
then evaluated the stress behavior of identical serpentine geometries. The elastic
stiffness tensors [100] Si, [110] Si, and [0001] GaN used in this thesis are shown in
Equation 2.5, 2.6, and 2.7.
 
165.7 63.9 63.9   63.9 165.7 63.9 

 63.9 63.9 165.7 C 9[100]Si =  x10 Pa, (2.5)
79.6 
79.6 
79.6
16
 
165.7 63.9 63.9  63.9 165.7 63.9    63.9 63.9 165.7C[110]Si =  79.6 
x10
9Pa (2.6)
 79.6 
 79.6


390 145 106
  145 390 106 
C [0001]GaN = 
106 106 398 
9
x10 Pa (2.7) 105 105 
122.5
The stiffness tensor for 0◦ - 90◦ in-plane rotations on (100) Si and (0001) GaN
was calculated to be used in future modeling steps. The first elastic coefficient (C11)
is representative of the anisotropic behavior of the material as a function of crystal
rotation along the xyz axes, and is shown for both Si and GaN in Figure 2.3.
Figure 2.3: C11 stiffness coefficient of in-plane rotations on (100) Si and
(0001) GaN Variations in the C11 coefficient in Si indicate strong anisotropic be-
havior in the (100) plane. The lack of variations in the C11 coefficient indicates
isotropic behavior
Silicon is shown to have the highest C11 value along the <110> direction while
17
the lowest C11 value occurs at the 45
◦ rotation along the <100> direction. This leads
me to hypothesize that the <100> direction in Si would have improved stretchable
behavior over the <110>. Additionally there is no variation in the C11 value on the
(0001) GaN plane, as a function of rotation angle which indicates this plane of GaN
would display isotropic stretchable behavior along all crystallographic directions.
Mechanical anisotropy plays a significant role in predicting the failure of crys-
talline devices. To the best of our knowledge, this issue has not been addressed in
stretchable crystalline devices. Generally the anisotropic mechanical dependence in
devices with rectangular shapes is shown to be small, however, it is expected that
this dependence will become significant when we evaluate serpentine geometries with
curved edges and angled members (53). This influence will be investigated using
finite element modeling methods and by experimentally fabricating and character-
izing crystalline serpentine devices.
18
Chapter 3: Numerical Modeling of Stress and Strain in
Stretchable Crystalline Materials
Finite element analysis is used in Chapter 3 to examine the mechanical behav-
ior of stretchable single crystal semiconductors. 2D and 3D models are performed
using the comprehensive numerical solver COMSOL Multiphysics 5.2 to evaluate
the effect of serpentine geometry and mechanical anisotropy on crystalline stretch-
able behavior of (100) Si and (0001) GaN. To do this I first refine a 2D model to
evaluate the non-uniform von Mises peak stress distribution after applying a 30%
strain parallel to the trace on a number of common serpentine geometries (curved
corner rectangle, rectangle, horseshoe, triangle, and trapezoid) (2; 47). It was found
that serpentine geometries with a more gradual change in direction (i.e Curved Cor-
ner and Horseshoe) distribute the local strain fields over the trace more uniformly,
and are ideal candidates for stretchable geometries of crystalline devices. Next, in-
plane rotations are applied on (100) Si and (0001) GaN to investigate the influence
of crystallographic orientation on the von Mises peak stress distribution showing
(0001) GaN behaves isotropically, displaying 6-fold rotation symmetry, while (100)
Si has a strong anisotropic dependence due to 4-fold rotation symmetry. To fur-
ther study the anisotropic dependence in Si, I then determine the maximum global
tensile strain of the Curved Corner and Rectangular geometries as a function of
the width-to-radius (w/r) ratio. Si serpentines with a low w/r ratio (< 0.1) were
demonstrated to reach end-to-end displacements as high as 276% (2.76X its original
length), while w/r ratios of up to 0.6 could reach global end-to-end displacements
of > 20%. Additionally, serpentines patterned in the <100> direction on the (100)
Si plane were found to be up to 17 - 32% more stretchable than those patterned
19
in the <110> direction. Finally, a 3D FEA moel is used to further investigate the
effect of mechanical anisotropy in the Si Curved Corner structure with w/r = 0.2,
predicting a maximum global tensile strain of 84% in the <100> direction and 76%
in the <110> direction. Stress measurements using micro-Raman spectroscopy with
be used to experimental verify these results in Chapter 5.
3.1 Numerical Evaluations of Stretchable Systems
Finite Element Analysis (FEA) is a popular tool researchers use to analyze
material mechanical behavior and extract important parameters such as the von
Mises peak stress distribution, tensile strain, principal stress/ strain coefficients,
and device failure location in many microelectromechanical systems (MEMS). FEA
has played a pivotal role in the rapid expansion of the stretchable electronics field, by
providing great insight on the ideal architectures for stretchable device fabrication
and evaluation of the mechanical and electrical performance under strain. Early
efforts used FEA techniques to examine the mechanical behavior of free standing
serpentine metallic traces (Au, Cu, Pt), and metalic traces bonded to elastomer sup-
ports for use as stretchable interconnects in ”island-bridge” device layouts. These
studies show that serpentine structures can strongly relieve stress under strain, in-
creasing intrinsic metallic strain-to-rupture from (< 5%) to 25 - 1600%, depending
on geometrical parameters such as the ratio between the trace width (w) and arc
radius (r), and the serpentines length (l) (11; 33; 37; 38; 39; 58; 59). These stud-
ies demonstrated curved structures experience smaller stress concentrations than
structures with sharp corners (58). (11; 33; 37; 38; 39; 59)
Often times fabricated stretchable devices are encapsulated within an elas-
tomeric substrate to provide protection and additional stretchable support. FEA
has previously been used to examine the effect of film thickness and grain size on the
mechanical performance of metallic 2D serpentines supported by polymer substrates.
Through simulation and optical imaging it has been shown that as film thickness
decreases, crack density increases which subsequently causes an increase in the yield
20
strength (and effective stiffness) in the material, due to an increase in grain sizes
(37). Another study looked at the influence of serpentine thickness on the elastic
stretchability of the serpentine trace, showing thicker films are less stretchable due
to a change in the primary deformation mode from buckling to in-plane. Through
FEA, fatigue testing, and scanning electron microscopy (SEM) imaging, Kim et. al
demonstrated that a serpentines stretchability is directly proportional to substrate
thickness, with thinner substrates mechanically behaving the best (21; 38; 39).
Additionally, FEA has been used to investigate the electrical performance of
serpentine metallic traces for stretchable interconnects, and stretchable devices. For
example, Lazarus et al. investigated the influence of wavelength and amplitude of
periodic geometries on the electrical performance of serpentine structures for use in
stretchable inductor coils (48). Their findings, in agreement with Balakrisnan et al.,
show that copper metal interconnects without sharp corners (Sine Wave, Horseshoe,
and Curved Corner) gave not only the best mechanical performance, but also the
best electrical performance; however, curved structures are pointed out to be more
difficult to micro-fabricate (58). Curved structures mitigate stress concentrations
over a large area and perform the best electrically due to current switching directions
more gradually. Overall, these findings support the idea that patterning metal into
these periodic stretchable geometries will allow the system to survive significant
amounts of strain without electrical or mechanical failure.
With the growing popularity of stretchable crystalline materials, a few research
groups have looked at modeling the mechanical properties of semiconductor mate-
rials such as Si and GaN (2; 16; 38). Widlund et al. performed a very complete and
systematic FEA and experimental study on the stretchable behavior of free standing
2D silicon serpentine ribbons, assumed to be confined to in-plane deformation only.
They generated a model which explains serpentine mechanical behavior in terms of
dimensionless parameters such as such as Stretchability (εcrapp) which is the global
critical applied strain before the serpentine ribbon ruptures, given by
21
cr εcrεapp = ε (3.1)max
εapp
where εcr is the intrinsic strain-to-rupture, εmax is the maximum tensile strain of
the material, and εapp is the applied strain.
εmax is the given as the ratio between
εapp
maximum strain and the applied strain. The stretchability parameter controls the
structure’s stiffness which is related to the maximum end-to-end displacement that
can be achieved by a free standing serpentine ribbon. Using the isotropic materials
properties of silicon (E = 130 GPa, ν = 0.27), they found that Si serpentine ribbons
with a small w/r, large length-to radius ratio (l/R), and large arc angle α became
compliant and could reach strains several orders of magnitude higher than straight
Si wires. There results indicate that even brittle Si with εcr = 1%, could reach
εcrappup to 1000% with extremely large l/R ratios (16); however they did not report
experimental verification of these results. Additionally, in this model they used the
isotropic material properties of Si which does not accurately reflect the mechanics
of Si along different crystal axis.
Tompkins et. al. performed the first anisotropic 2D FEA study of single
crystal Si and GaN in serpentine geometries as structural candidates for fabrication
of the first stretchable high electron mobility transistor devices (HEMTs) (2). With
COMSOL Multiphysics 3.3, they performed a linear elastic model to look at the
effect of serpentine geometry on the maximum von Mises peak stress of Si and
GaN serpentines, after applying a 30% global strain parallel to the trace. They
determine that serpentine geometries could offer a 30 - 98% reduction in peak stress
for GaN, 28 - 92% reduction for Si, and that the optimal serpentine geometries were
ones with a more gradual change in direction (i.e Sinusoid) behaved could displace
by larger amounts than geometries with sharp corners (i.e rectangle). They also
performed the first anisotropic dependence study on the serpentines mechanical
behavior, by applying in-plane rotations about (0001) GaN and (100) Si. They
found the GaN behaves isotropically within the (0001) growth plane and (100)
Silicon behaves anisotropically, with the minimum stress occurring at a 45 degree
angle from the [110] direction.
22
3.2 (2D) Stationary Linear Elastic Model
Due to computational restraints the meshing conditions and curve smoothness
reported in the Tompkins et al. study were relatively poor, and it was pointed out
that further discretization of the individual curves could help further advance this
study. To create a valid model for comparison, a more powerful computer running
the newest available software (COMSOL Multiphysics 5.2) was used to refine and
obtain more accurate values in this work. 2D and 3D linear elastic models un-
der the stationary mechanics module in COMSOL Multiphysics 5.2 were used to
evaluate the influence of serpentine geometry and mechanical anisotropy of (0001)
GaN and (100) Si on crystalline stretchable behavior. The physics, boundary condi-
tions, and material properties are selected to mirror the conditions in the previous
reported simulations (2; 47). The results presented in this work are expected to
be more accurate due to a better discretization of curved geometries, which lead to
finer meshing conditions, more accurate modeling results, and later finer anisotropic
etching profiles.
3.2.1 Numerical Model Input Parameters to Evaluate the von Mises
Peak Stress
The 2D simulation geometries, boundary conditions, anisotropic variables, and
meshing conditions are discussed below.
23
3.2.1.1 Serpentine Geometries and Materials
Figure 3.1: Serpentine geometries analyzed in this Thesis: Straight, Curved
Corner, Rectangle, Horseshoe, Trapezoid, and Triangle. The geometrical
parameters modeled in this work are the amplitude height (h = 1 mm), wavelength
or length (l = 1 mm), width (w = 25 µm, 50 µm, 100 µm, 150 µm), arc radius (r =
250 µm), and number of periods (p = 5, 10).
The mechanical performance of five serpentine geometries (Horseshoe, Rect-
angular, Curved Corner, Triangle, and Trapezoid) are analyzed in comparison to a
traditional straight geometry, as shown in Figure 3.1. The dimensions and model
input parameters are intended to replicate the conditions used in the Tompkins et
al. study (2). First a 10 period Si or GaN trace with geometrical dimensions of am-
plitude height (h = 1 mm), wave length (l = 1 mm), arc radius (r = 250 µm), trace
width (w = 25, 50, 100, 150 µm), and trace thickness (t = 7 µm), is constructed
into the respective serpentine geometries, is embedded within a rectangular (3 mm
x 10 mm x 15 µm) elastomer substrate. Sylgard 184 (Dow Corning) was chosen as
the stretchable substrate for this study because it’s a PDMS based polymer often
used as a substrate material which offers mechanical protection and is assumed to
have superior isotropic stretchable behavior, reaching intrinsic tensile strains of up
to 40% (34). The material properties used in the following mechanical simulations
are shown in Figure 3.2
24
Figure 3.2: Material properties used to model anisotropy in the linear elas-
tic model The geometrical parameters modeled in this study are the amplitude
height (h = 1 mm), wavelength or length (l = 1 mm), width (w = 25 µm, 50 µm,
100 µm, 150 µm) arc radius (r = 250 µm) and number of periods (p = 5, 10).
3.2.1.2 Boundary Conditions
Next the boundary conditions are defined as follows. A fixed constraint is
enacted on one boundary edge of the system, preventing movement in the XYZ
directions. The opposite boundary is prescribed a uniaxial displacement of 3 mm
in the X direction (parallel to the 10 mm long side of the serpentine trace), while
holding the YZ directions fixed. This displacement imposes a constant global strain
of 30% while allowing the long ends of the serpentine / elastomer to be free bound-
aries, not restricted in movement on any axis. As shown in Figure 3.3, after applying
uniaxial deformation the serpentine undergoes geometric reconfiguration to relieve
stress, and the elastomer deforms as expected due to Poisson’s ratio.
25
Figure 3.3: 2D COMSOL simulation of a 10 period Si or GaN serpentine
trace embedded within a Sylgard 184 elastomer substrate after an applied
30% global strain parallel to the trace The curved corner serpentine displayed
in this image has a width = 50 µm which corresponds to a w/r = 0.2
3.2.1.3 Anisotropic Dependence on the Von Mises Peak Stress
The von Mises peak stresses can then be evaluated after applying a known
strain, given the stiffness tensor of the material, which is related to the geometry
and Youngs modulus, as described in section 2.4.2. Stress is related to strain through
Hookes Law for a continuous media, Eq 3.1.
σij = Cijklεkl (3.2)
where σij is the stress, εkl is the applied strain, and Cijkl is the stiffness tensor,
derived for each rotation using the equations in 2.4.2. The stiffness tensor is used
to describe the anisotropic mechanical properties of a material at certain crystallo-
graphic orientations, Eq 3.2. The stiffness is effectively the Youngs Modulus of the
material at a specific crystallographic orientation, and it is directly proportional the
stress at a given strain.
The yield stress, also referred to as the intrinsic tensile stress, is the maximum
internal force a material can undergo prior to fracture. The yield stress (σ) for Si is
7 GPa and using the Young’s modulus (E110 = 169 GPa) and Hooke’s law (σ = Eε),
we can calculate the tensile strain (ε) of Si (i.e 7 GPa / 130 GPa = 0.04 = ε). This
value is expected to be slightly higher for GaN, due to a stiffer Young’s modulus,
however, there is currently not a universally accepted value for GaN. After applying
26
a strain of 30% parallel to the trace, we want to ensure we are operating in the
linear elastic regime, which occurs when the stress within the system is far below
the yield stress of the material. If the von Mises peak stresses reported in the system
are lower than the yield stress of the material, the system is considered reversibly
elastic, and is suited for use in stretchable electronics. To compare the mechanical
performance of each geometry in Figure 3.1, we analyzed the maximum Von Mises
peak stress distribution. This is a convenient average of the three principal stresses
of the material governed by Equation 3.3, which is a function of the stiffness tensor
at a certain crystallographic orientation.
√
2 (σ 21 − σ2) + (σ 22 − σ3) + (σ3 − σ 21)
σv = (3.3)
2
3.2.1.4 Meshing Conditions
After applying a 30% strain parallel to the trace on the Curved Corner struc-
ture, the von Mises peak stress was evaluated as a function of number of mesh
points. Like most FEM softwares, COMSOL Multiphysics offers a range of meshing
conditions (extremely coarse to extremely fine) which changes the number of mesh
points. Figure 3.4 shows the 2D mesh convergence plot results on the maximum
von Mises peak stress on the Curved Corner serpentine structure embedded within
Sylgard 184 after applying a 30% strain. As the number of mesh vertices increased
from 1,300 to 14,000 points the von Mises peak stress decreased by 3 percent.
27
Figure 3.4: 2D COMSOL Mesh Convergence Plot The von Mises peak stress
value is reported as a function of number of mesh points after applying a 30% strain
parallel to the trace.
After performing this mesh convergence test, the finest mesh element size was
elected which ranged between 12,376 and 28,322 mesh points, depending on the
simulated serpentine geometry. This is a 9-21 % increase in number of mesh points
per geometry than used in the study reported by Tompkins (11,320 - 22,401 points),
which is most likely due to improved discretization of the curves from importing ge-
ometries directly from CAD as opposed to building them in the COMSOL software.
Once all boundary conditions are properly defined, the geometry is discretized
into extremely fine triangular mesh points, with a zoomed in view of a single period
shown in Figure 3.5. This figure also shows the Curved Corner structure concen-
trates stress in the regions with the largest change in curvature which occurs at
the amplitudes maximum and minimum. This is the location where peak stress is
predicted to be the highest, and it is likely the failure location of the structure.
28
Figure 3.5: Meshing conditions and COMSOL Multiphysics stress output of Curved
Corner serpentine. (left) Image showing the triangle mesh used for FEM simulation. The
serpentine geometry under analysis is a Curved Corner with a 1000 µm peak-to-peak amplitude,
1000 µm wavelength, a 50 µm width and 7 µm thickness. (right) Typical von Mises peak stress
distribution output of a 1000 µm amplitude Curved Corner serpentine structure, after a 30% strain
applied parallel to the trace.
3.2.2 Effect of Serpentine Geometry on Stretchable Behavior of (100)
Silicon and (0001) Gallium Nitride
The output of the von Mises peak stress distribution on a 1000 µm amplitude
curved corner is shown in Figure 3.5. The stress distribution of the other tested
serpentine geometries (Rectangle, Horseshoe, Trapezoid, and Triangle) are shown
in Figure 3.6. In agreement with prior simulations (2; 48; 58) the maximum peak
stresses were found to concentrate in the regions with the largest change in curva-
ture. Thus, the highest peak stress occurs at the maximum and minimum of the
amplitudes in the Curved Corner geometry, and along the beams parallel to the
applied strain for the Rectangular geometry.
29
(A) (B)
(C) (D)
Figure 3.6: Von Mises peak stress distribution on four tested serpentine geometries
A.) Rectangle B.) Horseshoe C.) Trapezoid D.) Triangle after a 30% strain applied parallel to the
trace.
Due to minor variations in meshing and boundary conditions, the program
tends to concentrate the peak stresses on the periods closest to the boundary edges
which could cause the program to output higher peak stresses values than the true
peak stress. To account for this potential source of error in our data, we devel-
oped a MATLAB script that systematically removes data related to edge effects,
outputting the true value and location of the maximum peak stress on the struc-
tures. In these simulations, it was found that after applying a 30 percent strain,
the Si curved corner structure (Figure 3.5) had a peak stress of 2.1 GPa, and GaN
Curved Corner structures had peak stresses of 4.76 GPa. The stresses are much
lower in the Si structure than GaN because Si is a less rigid material, described by
its lower stiffness tensor and lower elastic modulus. Similarly, the von Mises peak
stresses on the rectangular structure (Figure 3.5) for Si and GaN were 1.44 GPa
and 3.64 GPa respectively. Figure 3.7 show the maximum von Mises peak stress
30
of each geometry after applying a 30% strain parallel to the trace, both with and
without silicone (Sylgard 184). The maximum stress values for the same serpen-
tine geometries calculated by Tompkins et al (2) are also included in this figure for
reference.
Figure 3.7: Effect of serpentine geometry on the reduction of peak stress after applying
a 30% strain parallel to the trace for single crystal Si and GaN. Calculated in this work
is shown in solid colors, while Tompkins(2) is shown hashed. Note Tompkins did not calculate the
Triangle and Trapezoid geometry.
Overall, these results suggest the optimal stretchable geometries are structures
with rounded edges such as the Horseshoe and Curved Corner rectangle. Addition-
ally, lowest amount of stress was in the Rectangular structure while the triangular
structure concentrated the most amount of stress at all orientations. As expected,
stress in GaN serpentine structures is 1.2 - 2X larger than Si, due to the stiffer
elastic modulus. While the Horseshoe geometry mechanically behaves the best, the
following studies will analyze only the Curved Corner and Rectangular serpentine
geometries to explore the effect of anisotropy on geometries with round and sharp
edges.
31
3.2.3 In-Plane Rotation Dependence of (0001) GaN and (100) Si
While the wurtzite and diamond cubic crystal structure of GaN and Si results
in overall anisotropic materials, the basal plane (0001) GaN, and (111) Si are known
to behave isotopically, while the (100) Si plane behave anisotropically. To verify
mechanical isotropic/ anisotropic behavior, in-plane rotations were applied in 10◦
increments from the [0001] direction the (0001) plane of GaN, and similarly rotations
in 10◦ increments from the [100] direction on (100) Si, as described in section 2.3.3.
3.2.3.1 Isotropic (0001) Gallium Nitride
After applying these rotations, it was found that the stiffness tensor of GaN
is rotationally invariant(i.e C ′11 = C11). After applying a 30% strain and monitor
the peak stresses for each in-plane rotations angle in (0001) GaN we see the trend
line is flat indicating there is no variation in the stress value. This implies that the
mechanical properties behave isotropically in the (0001) growth plane of GaN, due
to 6-fold crystal rotation symmetry, which is highly desired in stretchable systems.
32
Figure 3.8: Maximum von mises peak stress value for all serpentine ge-
ometries as a function of in-plane rotations on (0001) GaN serpentines
after applying a 30% strain. No variations in the maximum stress indicates GaN
serpentines behave isotropically in the (0001) plane.
3.2.3.2 Anisotropic (100) Si
To evaluate the influence of anisotropy within (100) Si, in-plane rotations
were also applied in 10◦ increments about the [110] direction. It was found that the
stiffness tensor had a strong anisotropic dependence, exhibiting 4-fold rotational
symmetry(i.e C ′11 = C11 only for 90
◦ rotations). As shown in Figure 3.9, for all Si
serpentine geometries, rotations 0◦ and 90◦ from [110] direction result in the highest
peak stress which indicates this crystallographic orientation would have the lowest
Stretchability (εcrapp).
33
Figure 3.9: Maximum von Mises peak stress as a function of in-plane
rotations on (100) Si serpentines after applying a 30 % strain. The large
variations in the maximum stress indicates the serpentines behave anisotropically
in the (100) plane with the <110> direction corresponding to the least amount of
stress.
The plot shows that the maximum stress occurs at the [110] direction, which
is the cleavable direction parallel(0◦) and perpendicular (90◦) to the wafer flat. As
we move in 10◦ degree rotations away from the [110] direction at 0◦), the peak
stresses gradually decrease until we reach the minimum at the 45◦ angle at the [100]
direction. As we continue to the increase the rotation angle from 45◦ 90◦ the peak
stresses begin to increase symmetric about the [100] direction back to the maximum
stress at [110].
These results indicate that if one were to fabricate identical stretchable ser-
pentines geometries on a (100) Si wafer along different crystallographic orientations
(i.e <110> and <100>), the mechanical performance would dramatically differ.
This is because the elastic modulus of silicon is dependent on its crystallographic
orientation, therefore the stiffness tensor also has a crystallographic orientation de-
34
pendence.
3.2.4 Stretchability of (100) Silicon in the <100> and <110> directions
The most important design parameter in a stretchable system is the maximum
percent elongation (εcrapp) it can withstand before the formation of cracks which can
subsequently lead to fatigue, fracture and device failure. For wearable electronic
applications, these materials must be elastically stretchable, which means they need
to maintain full electrical and mechanical performance after cycling tens of percent
strain, without fatigue or fracture in the system. Any deformation imposed on the
stretchable system must be able to stretch and compress reversibly, by a minimum
of 30% strain for most wearable electronics applications, but could require reversible
deformation of us to 100s% strain in some locations such as behind the knee. We are
interested in determining the maximum end-to-end displacement (global elongation)
of Si serpentines in the <100> and <110> directions as a function of the structures
width-to-radius (w/r) ratio, as shown in Figure 3.10.
Figure 3.10: Width-to-radius (w/r) ratios analyzed Increasing the width of
serpentine traces from 25 µm to, 50 µm, 100 µm, and 150 µm, increases the w/r
from 0.1 to, 0.2, 0.4, and 0.6
To evaluate the dependence of crystallographic orientation on the stretchability
(maximum tensile strain ) of the serpentines, I investigated two geometries, Curved
Corner and Rectangle, varying the geometrical parameter of the width-to-radius
ratio (w/r). When the width of the device is much thinner than its length (w
< < l) under deformation, the atomic planes slip in the transverse direction to
35
accommodate induced stress which promotes a geometrical reconfiguration. I varied
the width of the serpentine trace from 25 µm, 50 µm, 100 µm, and 150 µm, which
changed the (w/r) from 0.1, 0.2, 0.4, and 0.6. Figure 3.11 shows the effect of
anisotropy on the maximum tensile strain of a silicon Curved corner trace patterned
in both the <100> and <110> directions at various w/r ratios.
Figure 3.11: Effect of anisotropy and width-to-radius ratio in Si on stretch-
able behavior for the Curved Corner and Rectangular serpentines. Lower
(w/r) ratios are 10 - 26% more stretchable than large (w/r) ratios. Both plots demon-
strate the maximum tensile strain of the serpentine geometries are dependent on the
crystalline anisotropy and plane it is patterned on and on its width. A.) Demon-
strates the Curved Corner tensile strain can vary due to mechanical anisotropy by
12-25% while B.) demonstrates the Rectangle varies by 25-30%.
Under applied tensile strain, it’s been reported that free standing serpentines
with a small width-to-radius (w/r) ratio have more degrees of freedom which allows
ribbons to flex, buckle out of plane and twist to accommodate deformation under
applied strain, while serpentines with a large w/r tend to be restricted to in-plane
deformation (37). The results shown in Figure 3.11 indicate serpentine geometries
with smaller widths (w/r = 0.1) can reach global end-to-end displacements 2.75X
their original length. However, larger widths (w/r = 0.6) increase the stiffness of the
serpentine geometries which only allow for elongations 0.3X their original length.
Additionally, these results indicate the [100] direction is the most stretchable for
Si, where serpentines patterned in the [100] direction can be up to 12-30% more
stretchable than serpentines patterned in the [110] direction. This is primarily due
36
to the [100] being the closed packed direction for the (100) plane, giving additional
molecules to slip to accommodate stress in the system, so it can achieve higher strain
percentages. Herein, we will be working with Si and GaN serpentines of a 50 µm
width which corresponds to a w/r ratio of 0.2.
3.3 (3D) Stationary Linear Elastic Model
There were some assumptions made in the 2D model, which may not reflect
true experimental conditions such as the serpentine is confined only to in-plane (2D)
deformation, and that all periods of the serpentine will stretch uniformly. In order
to more accurately model the experimental conditions, a 3D linear elastic COMSOL
Multiphysics 5.2 model is employed to analyze any out-of plane (Z-axis) buckling
deformation mechanisms on a free standing 5 period curved corner serpentine with
h = 1 mm, l = 1 mm, w/r = 0.2, t = 7 µm. I repeat the same mesh convergence
test in the 3D model, testing mesh vertices’s ranging between 1200 - 120000 points.
This is a large improvement in the number of points from the 2D model. Shown
in Figure 3.13, there is a non-linear variation in the value of stress with increasing
number of mesh points, which is on average 33% higher than the values reported by
the 2D model. I will point out however, the 3D model is not fully converged.
37
Figure 3.12: 3D mesh convergence test. The von Mises peak stress value is
reported as a function of number of mesh points after applying a 30% strain parallel
to the trace. The 2D mesh convergence data is also plotted for reference.
Next, I evaluate the effect of mechanical anisotropy on the maximum global
tensile strain of the Curved Corner serpentine in the <100> and <110> directions.
The maximum global strain is the maximum end-to-end displacement Si reaches
before the internal stress exceeds 7 GPa, similar to the methods performed on the
2D model. The COMSOL result of the non-uniform straining profile on the Si
Curved Corner serpentine in the <100> is shown in Figure 3.13.
38
Figure 3.13: 3D COMSOL model of a free standing 5 period <100> Si
Curved Corner serpentine trace stretching to a maximum global strain of
84%. The left boundary edge of the rectangular post is held fixed while the other
end is displace by 4.2 mm which corresponds to an end to end displacement of 84%.
Repeating this for the <110> we find a slightly lower tensile strain at 70%.
Figure 3.14 shows the fracture location of the serpentine with respect to crystalline
anisotropy, with <110> Curved Corner serpentines breaking at the Amplitude for
both the 2D and 3D model, while the <100> Curved Corner serpentine fractures at
the Bend in the 3D model. The end-to-end displacement tensile strain percentage
and fracture location variations between the 2D and 3D model are summarized in
Figure 3.15.
39
Figure 3.14: 3D FEA modeling results demonstrating the fracture location of <110>
and <100> Si Curved Corner serpentines. The <110> direction is shown to break at the
amplitude location in the 3D model, while the <100> fractures at the arc bend. The 2D model
originally predicted fracture at the amplitude for both orientations.
Figure 3.15: 2D and 3D FEA modeling results comparison of the maximum end-to-end
displacement (tensile strain) of <110> and <100> Si serpentines. 2D and 3D tensile
strain (% = ∆LL ) and fracture location results are compared, showing the 3D model on average
out-puts tensile strain 17% higher than the 2D model.
3.4 Modeling Crystalline Stretchable Behavior Summary
and Conclusions
Major design insights on the mechanical behavior GaN and Si serpentines were
provided through the 2D and 3D COMSOL 5.2 simulations performed. All serpen-
tine geometries tested for both GaN and Si resulted in a peak stress reduction of
20 - 98%, from convention straight geometries, showing these structures are well
suitable for use in wearable electronics. Curved geometries (Horseshoe and Curved
Corner) experience more gradual change in peak stresses due to the gradual change
in curvature along the structure, thus displaying overall lower stresses than geome-
40
tries with sharp corners. Anisotropy in Si plays a signifiant role on the stretchable
mechanics, displaying four-fold symmetry in the (100) plane, with the [110] crys-
tallographic direction (0◦), containing the highest peak stresses, while [100] at the
45◦ rotations result in the lowest peak stresses. I demonstrate this anisotropic de-
pendence could result in tensile strain variations of 12 - 30% for the Curved Corner
and Rectangular geometries (w/r = 0.1 - 0.6). Additionally, I showed GaN displays
isotropic behavior in the (0001) plane, which indicates uniform stretchable behav-
ior regardless of crystal orientation. This isotropic property is highly desired when
fabricating stretchable devices which rely on contact photolithography where slight
misalignments are common.
There was a discrepancy on the maximum tensile strain of 17% between the
2D and 3D models. Since the mesh converged linearly for the 2D model, but did not
fully converge on the 3D model, it is assumed that the 2D model more accurately
represents the local surface stress concentration. The additional degree of freedom
provided by the 3D model most likely will portray the out-of-plane deformation ex-
pected on the trace while under applied deformation. Another potential source of
error that could be the reason for this discrepancy is the models assume the starting
material (Si or GaN) is a relaxed single crystal patterned into a perfect serpentine
geometry. In general, the crystalline materials will have inherent stress from the
substrate, for instance, Si will be released from a silicon-on-insulator (SOI) wafer,
which generally induces inherent compressive stress. Similarly, GaN will be released
from a sapphire wafer (induced compressive stress) or a silicon wafer (induced ten-
sile stress). While FEA is a powerful tool for stretchable design, one shortcoming of
relying solely on FEA data is these modeling results do not factor in initial residual
stresses present from material growth or device manufacturing. Thermal and me-
chanical stresses present in the material from micro-processing can lead to the nucle-
ation and propagation of dislocations, and formation of cracks and voids. Presence
of these stresses directly from fabrication can ultimately lead to premature failure
of the devices, which is generally not predicted by the model. Therefore; experi-
mental verification of these results is crucial to understanding crystalline stretchable
41
behavior.
42
Chapter 4: Microfabrication of Stretchable Crystalline Serpen-
tine Structures
Chapter 4 presents the novel experimental procedure details of the fabrication
process I developed which allows for the fabrication and release of stretchable Si ser-
pentine mechanical test structures. The freestanding Si serpentine test structures
were fabricated through a combination of standard micro-machining processes, such
as photolithography, backside alignment, and a two step inductively coupled plasma
(ICP) deep reactive ion etch (DRIE) process, in the Class 10 and 100 Nanofabrica-
tion Center at the U.S Army Research Laboratory. Si serpentine mechanical test
structures are fabricated in both the <100> and <110> crystallographic directions,
from a (100) silicon-on-insulator wafer, which will allow us to evaluate the influence
of crystalline anisotropy on stretchable behavior. While this fabrication process
is compatible with many geometrical parameter, height (h), length (l), width (w),
radius (r), thickness(t), Curved Corner and Rectangular serpentine structures are
fabricated to reflect the conditions imposed by the FEA model (h = 1 mm, l = 1
mm, r = 250 µm, w = 50 µm, and t = 7 µm) presented in Chapter 3. Additionally,
a fabrication and release process is proposed which would allow the development
of serpentine mechanical test structures from (0001) GaN. The processes described
here can be adapted to allow the fabrication and release of most III-V material into
a serpentine structure, if epitaxially grown onto a Si substrate. We also demon-
strate one sided metalization (2 µm NiTi) onto the Si serpentine post release, which
could be then undercut and removed to leave freestanding NiTi. We speculate
that researchers could adapted this process to release other thin-film materials that
have yet to be explored by the stretchable electronics community. The non-uniform
43
stress distribution along multiple locations of the fabricated and released Si Curved
Corner serpentine structures will be evaluated while applying external strain via
micro-Raman spectroscopy in Chapter 5.
4.1 State of the Art Fabrication Approaches to Enable Flex-
ible and Stretchable Si and GaN
Vast strides on the production of flexible and stretchable single crystal semi-
conductor devices has been made over the last 20+ years, allow functional inorganic
crystalline materials to be integrated into high-performance stretchable electron-
ics (41), (30). Through these methods, silicon has been incorporated into many
flexible/ stretchable applications including lateral pn junction diodes (18), a hemi-
spherical electronic eye camera (12), structural health monitoring (60), sensors for
prosthetic skin (61), and photovoltaics (41). Flexible gallium nitride has been in-
tegrated into applications such as flexible RF AlGaN / GaN high electron mobility
transistors (HEMT) on plastic substrates (62; 63; 64; 65), and flexible optoelec-
tronic devices (66). Additionally stretchable GaN LEDs were demonstrated using
an island-bridge layout (67). To the best of our knowledge, to date our group is
the first to develop stretchable GaN devices into serpentine configurations to enable
stretchability within the crystal (3).
4.1.1 Methods to Enable Flexible / Stretchable Si
Due to the high temperature requirement for inorganic semiconductors pro-
cessing, crystalline materials cannot be simply grown directly onto a pre-strained
stretchable substrate. Instead, one method developed by the John Rogers group in
2006 was to process thin Si and GaAs nanoribbons on the wafer and then use a
transfer stamp to bind them to a pre-strained substrate. Similar to the previously
reported methodologies used for metals, when tension is released from the elastomer
substrate, the crystalline ribbons periodically buckle out-of-plane, which could reach
tensile strains of up to 100%, and compressive strains of 25% (68). Another example
44
they developed to enable stretchable Si used standard photolithography techniques
to pattern thin silicon ribbons (20 to 320 nm) on a silicon-on-insulator (SOI) wafer,
and use etching techniques to release the ribbon from the underlying SiO2 layer.
Next, a pre-strained elastomeric support is bonded to the silicon ribbon, which can
now easily peel off of the SOI wafer. Once the strain is released on the elastomer, the
Si ribbons spontaneously buckle into highly ordered, periodic wavy structures which
can repeatedly cycle -11% compression to 11% tension (30). While these methods
successfully allowed for the fabrication of stretchable crystalline materials they are
restricted to very thin Si device layers (< 500 nm), and the out-of plane wavy
buckling presents challenges for any further device processing. At very low widths
and thicknesses, thin Si serpentine ribbons tend to undergo out-of-plane buckling
deformation which limits the available characterization techniques, and potential
device applications. Moreover, these methods requires device encapsulation into an
elastomer support for mechanical protection, as opposed to allowing a free-standing
released structure, which creates challenges during device performance testing.
The MEMS community has developed many fabrication procedures utilizing
isotropic and anisotropic etching processes which allow for suspended Si structures
(69). For example, auxetic geometries display a negative Poisson’s ratio under
tension, which makes them highly deformable under applied strain. Auxetic Si was
developed using an SOI wafer where the Si device layer was directionally etched into
the defined auextic structure using fluorine-based gas in deep reactive ion etching
(DRIE). Next, the buried oxide and underlying Si layers were isotropically etched to
undercut the structure, allowing for a released auexetic Si piece. To develop a free
standing Si serpentine, I will be adapt anisotropic dry plasma etching techniques.
4.1.2 Methods to Enable Flexible / Stretchable GaN
AlGaN/ GaN high electron mobility transistors (HEMT) are a promising solu-
tion to wearable wireless power management, however, the semiconductors inability
to stretch or bend significantly presents challenges. Since the most brittle component
of HEMT devices are the inorganic semiconductor, this becomes the limiting mate-
45
rial in an integrated stretchable system. Our group is interested in using serpentine
structures to fabricate stretchable AlGaN/GaN HEMT free standing structure as
opposed to encapsulated in an elastomer (3). In this chapter, I propose a fabrication
process that would allow for the release of free standing AlGaN / GaN serpentines.
GaN patterned on Si substrates is an advantageous for designing flexible and
stretchable GaN devices because of the etch selectivity, Si will etch in fluorine based
chemistries while GaN etched in chlorine based gases. Lv et al demonstrated a
process that allowed for suspension of a large area GaN micro-structures using a two-
step dry release process. First a Cl2- based ICP-DRIE etch is performed define the
AlGaN / GaN mesa structure. Next an anisotropic ICP etch is performed to create
vertical profile side walls within deep Si trenches based on SF6 / O2 / C4F8. The
trench was then exposed to an isotropic plasma etch which released and suspended
the large area GaN structure from the Si wafer (70). Similar methodologies to
release GaN from Si are also reported in (71; 72).
Lee and coworkers were the first to investigate ways to increase the flexibility of
GaN. They successfully fabricated and released a flexible AlGaN/ GaN HEMT from
its Si substrate. Taking advantage of the fact that AlGaN / GaN HEMT devices are
thin films, they can withstand flexing forces, if removed from their bulk substrate.
To achieve this, they developed a procedure which uses standard top-down processes
to fabricate the device, release it from a Si substrate, and then transferred it to a
flexible substrate (polyethylene terephthalate) (65). Defrance et al. were the first
to investigate the radio frequency (RF) performance of AlGaN/GaN HEMTs on
flexible substrates (63). They developed a method to successfully fabricate and
release a HEMT device from a Si substrate without roughening the surface. After
lithographically processing the HEMT device onto a Si wafer, the front side of the
HEMT is temporarily bonded to a handling wafer, and the silicon substrate was
removed by mechanical lapping followed by a selective Xeon difluoride etch (XeF2).
They measured the direct current characteristics of the device before and after
the transfer and found the current density decreases with the transfer which they
attribute to the poor thermal conductivity of the stretchable substrate. Another
46
interesting finding of this group was the 2DEG concentration actually increases
with bending due to the induced piezoelectric polarization in AlGaN and GaN (63).
These results lead us to believe stretchable serpentine structures will increase the
2DEG concentration under tensile stresses.
4.2 Fabrication Process of <100> and <110> Serpentines
from (100) Silicon
While there are modeling efforts investigating the mechanical performance of
free standing Si into 2D planar serpentine structures, fabrication and experimental
verification is limited (2; 16). This work produces 2D in-plane serpentines structures,
as opposed to buckled out-of-plane 3D serpentines; therefore, an elastomer substrate
is not required to support the serpentine trace during characterization. Single crystal
silicon (Si) mechanical test structures were fabricated using (100) silicon-on-insulator
(SOI) wafers. As shown in Figure 4.1, devices patterned on a (100) wafer along the
standard x and y axis (0◦ and 90◦) are along the <110> family of directions while
the <100> family of directions is rotated 45◦ from the <110>. Serpentine test
structures area orientated in both <100> and <110> directions were fabricated by
strategically designing a contact photolithography mask plate, using AutoCAD 2013
software, which physically oriented geometries in both the 0◦ and 45◦ orientations.
The dimensions of each period of the serpentine are: 1000 µm amplitude, 1000 µm
wavelength, 50 µm width, and 7 µm thickness.
47
Figure 4.1: Diagram labeling the angle and family of directions on a (100) Si
wafer Serpentine will be patterned in both the <100> and <110> through physical
geometrical tilt in the photolithography mask.
The serpentine structures of interest require a final thickness of 7 µm. While
wafers < 10 µm thick are commercially available, they are extremely difficult to
handle and transfer during processing, and the materials tend to be costly. There-
fore, an SOI wafer was advantageous to use because it separates a thin device layer
of Si (7 µm) from a thick handle layer of Si (350 µm) by a sacrificial 3 µm thick
oxide. Additionally, SOI wafers are advantageous because they allow one to select
the device thickness ranging from a few nanometers up to 200 µm. Each step in
a micro-fabrication sequence require careful development and optimization to make
the step reliable, repeatable, and cost efficient.
The intention is to eventually characterize the stress/ strain behavior of the
mechanical test structures; therefore it is important to take precautionary measures
to ensure no external stresses are induced onto the crystal during processing and
handling. To realize this, I designed a structure consisting of a thick mechanical
rectangular frame which acts as the support to suspend a 7 µm thick serpentine.
The long supports parallel to the trace are break away regions that only serve the
purpose to provide rigidity during processing. The frame region is a hollow rectan-
gular structure that is intentionally created to provide a mechanically rigid support
area to suspend the final serpentine device. The advantage of this support is it helps
48
prevent inducing stresses within the serpentine during general handling and process-
ing. Figure 4.2 shows the process flow I developed fabricate and release <100> and
<110> Si serpentine mechanical test structures. This chart presents a summary of
the required machinery, materials, and experimental details of each major processing
step, while below the chart includes a full description of the fabrication step.
49
Figure 4.2: Procedure developed to fabricate and release Si serpentines
from an SOI wafer. 50
1. The starting material is 1.5 cm x 1.5 cm chip from a diced (100) silicon-on-
insulator (SOI) wafer (University Wafers). The cross section of the (100) SOI wafer
from the manufacturer consists of the following four layers: *top side* silicon device
/ buried silicon dioxide / silicon handle / oxide *bottom side*. The dimensions of
the four layers are *top side* 7 µm Si / 2 µm buried silicon dioxide (SiO2) / 350 µm
Si substrate / 2 µm SiO2. The SOI wafer is advantageous because our fabrication
processes uses use deep-reactive ion etching (DRIE) techniques in later steps, and
the middle buried oxide layer (SiO2) serves as an etch stop to the SF6-O2/ CHF4-O2
plasma chemistry from the DRIE process, with a selectivity of 40:1 for Si:SiO2 (73).
This SOI wafer structure was strategically chosen for fabrication of a serpentine
and a rectangular frame because the built in etch stop layers allow us to fabricate
the rectangular structure through the entire thickness of (360 µm) of the SOI stack
while leaving a released serpentine suspended in between the rectangular frame (7
µm thick). An top-down view of the photolithography pattern transfered to the
entire chip is shown in the processing step image.
2. Since SiO2 has a good etch selectivity to SF6/ C4F8 chemistry, it was
chosen to serve as the etch resistant hard-mask material. First, photolithography
was performed to pattern photoresist to etch a SiO2 hard mask on the *bottom side*
(2 µm oxide / 350 µm handle) of the piece. The bottom side pattern consists of the
rectangular frame to and alignment marks that will be used for backside alignment
later in step 3, without the serpentine suspended. The photolithography and oxide
etching procedures are as follows.
Photolithography: First hexamethyldisilizane (HDMS ALDRICH reagent grade
> 99%) is spin coated onto the *bottom side* SiO2 at 3000 rpm for 60 s, and then
soft-baked on a hot-plate at 100 ◦C for 60 s. The advantage of using HDMS is it
acts as an adhesion layer by providing a hydrophobic coating the SiO2 which pro-
motes wetting on the surface from the photoresist. Next, image reversal photoresist
AZ5214E (positive process) is spin coated at 3000 rpm for 60 s, soft-baked on a
hot-plate at 100 ◦C for 60 s. Finally, the photoresist covered chip is exposed to UV
light under the serpentine mask plate at 9 mW/cm2 for 8.6 s (Karl Suss MA/BA6),
51
and is then developed in AZ400K for 20 s.
Oxide Etching: An oxide hard mask of the frame is created by submerging the
patterned piece in a solution of 6:1 Buffered Oxide Etch with Surfactant (J.T. Barker
UN2922) for 18 minutes. The thickness of SiO2 results in purple hue in color and is
inherently hydrophobic to water, meaning water will not stick to the chip. Etching
is complete once the rinse water begins to stick on the piece, becoming hydrophilic,
and it will undergo a color change from purple to a blue hue, indicating that the
silicon is exposed. At this point the oxide hard-mask etching step is complete and the
photoresist is stripped away through a series of acetone, methanol, and isopropanol
baths for 1 minute each. This process cleans the wafer, leaving the *top side* (7
µm Si) ready for photolithography patterning.
3. Next, the chip is flipped back over exposing the *top layer* of Si and plasma
enhanced chemical vapor deposition (PECVD, Plasma Therm 790+) is used to de-
posit a layer of 0.1 µm SiO2. The photolithography procedure is repeated from step
2, and the features on the top of the piece is aligned to the bottom features, using
the backside alignment feature on the mask aligner (Karl Suss MA6). The topside
features also contain the mechanical frame, alignment marks, and serpentine struc-
ture in the respective geometry patterned in between the rectangular frame. After
the photoresist is patterned and developed, the top oxide hard mask is patterned by
repeating the oxide etching process in step 3, by submerging the part in 6:1 Buffered
Oxide Solution, this time for 30 s due to the thinner oxide layer etching faster. The
photoresist strip and cleaning procedure is then repeated from step 2.
4. Next, the chip is bonded *top side* facing down into a 4 in Si handle wafer,
using a thick layer of photoresist (10 µm AZ9245) for adhesion between the chip
and the handle wafer. Inductively Coupled Plasma Deep Reactive Ion Etching with
SF6 and C4F8 gas chemistries (ICP DRIE, PM1 Plasma Therm Versalock 700), was
used to anisotropically etch through the 350 µm Si handle to define the hollowed
rectangular frame on the backside of the SOI chip. The parameters of the DRIE
etching include RF power of 850 W with C4F8 / SF6 / Argon (70/0.5/40 sccm) gas
on for 4 seconds to passivate and C4F8 / SF6 / Argon (0.5/100/40 sccm) gas on for
52
6 seconds to etch, cycled for 1.5 hours. The helium cooler pressure was kept at 4000
mTorr the entire time.
The first silicon etch is complete once the buried oxide layer was exposed,
indicated by a color change from dark blue to purple. The oxide layer was removed
using anisotropic dielectric plasma etching (PM3 Plasma Therm Versalock 700) with
gas chemistries. Once the top silicon layer is exposed, indicated again by a color
change to dark blue, the wafer is submerged into acetone for 10 hours to de-bond
the piece part from the handle wafer. The structure at this point is very fragile with
extra care taken to clean it with acetone, methanol, and isopropanol then allowed
to dry on a hot plate at 100 ◦C. Air drying with N2 is not advised, due to the
high pressure of the air. The image of the process at this step shows the deep etch
of both the frame and serpentine, however, the process only etches the rectangular
frame at this step.
5. Next the *bottom side* of the chip is bonded to the handle wafer using
photoresist (10 µm AZ9245). Again, using the ICP DRIE (Plasma Therm Versalock
700), the 7 µm of Si on the *top side* anisotropicly etched for 15 minutes to define
the desired serpentine geometry. Once the etch is complete the stretchable serpen-
tine traces is now suspended between the rectangular frames. At this point, the
individual structures are carefully removed from the handle wafer by slightly heat-
ing and loosening the photoresist on a hot plate at 95◦ ◦C. The charged white region
shown in the scanning electron microscopy (SEM) image is due to the presence of
oxide.
Additionally, shown in Figure 4.3, multiple serpentine etch profiles were tested
using the methods reported here. Many of the Bosch process anisotropic (ICP DRIE)
plasma steps were first tested on a standard 4 in (100) Si wafer, as opposed to on
the expensive SOI wafers. These etching profile results show this technique can
fabricate serpentine traces as thick as 300 µm
53
(A) (B)
(C)
Figure 4.3: Scanning electron microscopy (SEM) images of the other serpentine ge-
ometries tested though DRIE A.) Rectangle B.) Horseshoe C.) Trapezoid
6. Next, the entire structure is stripped of all oxide hard masking material
and residual photoresist using an anhydrous hydrofluoric acid (Primaxx HF Etcher)
for 30 minutes. Additionally, I have demonstrated that these serpentines can sur-
vive one-sided metal deposition (2 µm NiTi AJA ATC 2200 Co-sputter Deposition)
after release, shown in the processing image in step 6. However, all experiments
demonstrated will be the bare Si serpentine.
7. Finally, the sample is clean and ready for mounting into the 3D printed
sample holder, described in section 5.2.4. The holder is intended to apply external
strain to the serpentine during Raman characterization. For mounting, a M31 Epoxy
is used to mount the serpentine onto microscope slides, which are secured into the
holder. This is the last step before characterization, shown in Figure 4.4.
54
Figure 4.4: Fabricated Curved Corner Si serpentine released and mounted
into the 3D printed sample holder, ready for Raman Spectroscopy char-
acterization.
4.3 Fabrication Process of Serpentines from (0001) Gallium
Nitride
The release process of Si serpentines was easily achieved by using an initial
wafer stack that separates the desired Si device layer from the handle through di-
electric material (SiO2) which has a different etch selectivity than Si. This type of
heterostructure etch selectivity is similar to the case of GaN on Si when in h selec-
tivity of Si and GaN in Cl2 plasma gas chemistry. The fabrication process developed
in Section 4.2 can be modified, tuned, and adapted allow fabrication of III- V mate-
rials such as AlGaN, GaN, and InGaN, epitaxially grown on to a Si substrate. For
the anisotropic etch of the III - V material, a Unaxis Versaline ICP III-V etcher can
be used. I propose a process flow to allow for the fabrication and release of GaN
serpentines. This work is preliminary, so far I have successfully demonstrated steps
1 - 5.
55
Figure 4.5: Simplified process flow chart showing the major steps required
to fabricate and release a GaN serpentine.
56
4.4 Fabrication and Release Summary and Conclusions
In this chapter, I presented a detailed fabrication process to allow for the re-
lease of free standing 2D Si serpentine traces, not bonded to an elastomeric support.
I demonstrated this by fabricating a 5 period Curved Corner serpentine structure
with a amplitude height of 1 mm, wave length of 1 mm, radius of 250 µm, width
of 50 µm, and thickness of 7 µm, patterned in the <110> and <100> crystallo-
graphic directions on a (100) Si wafer. The procedure I report can be repeated by
the average user in a standard clean room. The methods reported in this thesis
are advantageous to develop free standing single crystal silicon from an SOI wafer
which gives us control over the serpentine’s geometrical dimensions such as thickness
(up to 200 µm), and width (up to 250 µm). Additionally, I proposed a fabrication
process that would allow for the release of free-standing GaN serpentine traces. The
GaN fabrication method I proposed will eventually be integrated with the current
stretchable high electron mobility transistor (HEMT) fabrication process (3) to al-
low characterization of free standing stretchable AlGaN / GaN HEMT devices. It
is desirable to characterize stretchable devices without the presence of a substrate
to gain better insight on the crystalline materials performance.
57
Chapter 5: In-Situ Stress Measurements on Stretchable
Crystalline Si using micro-Raman Spectroscopy
Raman spectroscopy is a powerful, non-destructive characterization technique
that can optically provide structural information such as crystalline quality and the
amount of stress/ strain in a crystal (74; 75). In this work, for the first time, I demon-
strate micro-Raman Spectroscopy as an in-situ stress characterization technique on
stretchable crystalline semiconductors, while applying external strain. First, a fab-
ricated free standing (100) Si Curved Corner serpentine mechanical test structures
patterned in the <110> crystallographic direction is mounted into a custom built 3D
printed sample holder, which allows one to apply global external strain to the ser-
pentine during micro-Raman Spectroscopy characterization. Next, to demonstrate
that stretchable Si can survive a minimum applied external strain of 30%, opti-
cal microscopy was showed a strain-to-rupture (maximum tensile strain) of 84%.
The tensile strain performance is compared to the FEM results reported in Chap-
ter 3. Afterwards, a (100) Si Curved Corner serpentine patterned in the <100>
direction was characterized while applying global external strains of 0-72% strain.
Micro-Raman spectra were then taken as a function of position across the trace,
analyzed and converted to stress measurements on three locations of the <100> Si
Curved Corner serpentine (Amplitude, Bend, and Straight, shown in Figure 5.1) to
analyze the non-uniform stress distributions. Lastly, I demonstrated micro-Raman
spectroscopy can be used to optically monitor the elastic behavior of crystalline ser-
pentines by performing low-cycle stress experiments, globally straining the <100>
trace from 0 - 30% for 15 cycles.
58
Figure 5.1: Location of the Amplitude, Bend, and Straight part of a Si
Curved Corner serpentine trace.
5.1 Raman Spectroscopy as a Stress Measurement Tech-
nique
Inherent and induced residual stresses are known to affect the yield, function-
ality and reliability of fabricated microelectromechanical systems (MEMS), which
can lead to premature device failure in the form of cracking, curling, buckling, or fa-
tigue (76; 77). Stresses within a material can arise from internal and external factors
which can occur during any step within a fabrication process. Internal stresses com-
monly originate from temperature dependent processes such as deposition of thin-
film metals from sputtering or evaporation or deposition of oxides through plasma
enhanced chemical vapor deposition (PECVD) (78). Another source of internal
stress is epitaxial misalignment between a substrate and an epitaxially grown crys-
talline semiconductor through techniques such as molecular beam epitaxy (MBE)
or metal-organic chemical vapor deposition (MOCVD) (78). External stresses arise
from various micro-machining processes such as wet chemical etching, photolithog-
raphy, inductively coupled plasma deep reactive ion etching (ICP DRIE), ion milling
or even simply from device handling. Stress and strain present within a stretchable
crystalline serpentine could lead to a degradation or a detrimental effect in the ma-
terial’s electrical and mechanical performance which could cause premature device
59
failure. Predication of the location, and characterization of the residual and ap-
plied mechanical stresses present within traditional and stretchable MEMS devices
is essential for prediction of the material’s performance and lifetime (79).
While several characterization techniques exist that allow for inherent crystal
stress analysis, challenges arise when locally evaluating stress at the micro-scale, or
while applying controlled external deformation. Examples of direct internal stress
measurements include wafer curvature (57), bending tests, tensile tests and incor-
poration of strain sensors, however, these techniques often require lengthy user tool
training, extensive data analysis, and model correlation for correct interpretation
(78). Cross sectional transmission electron microscopy (XTEM) can be used to
generate local stress measurements with high precision (nm), however, it requires
destructive sample preparation (78), and can only be taken on a stationary sam-
ple. X-ray diffraction (XRD) can be used to generate the strain tensor components,
which can be resolved into the stress components and intrinsic lattice constants of a
crystal; however, laboratory scale XRD has such a low spatial resolution that only
the mean value stress is typically obtained over a large area (57). This problem
could be circumvented if the XRD is equipped with a micro-diffractometer, or if it
is powered by a high energy source such as a synchrotron, however these powerful
XRD sources are not easily accessed by the average user. As a result, the aforemen-
tioned techniques are insufficient to measure the internal and external stress effects
within free-standing crystalline serpentine structures.
As an alternative, micro-Raman Spectroscopy (µRS) has proven to be a power-
ful characterization method for evaluating residual and applied mechanical stresses
within crystalline materials. The effect of residual mechanical stress and externally
applied loads on the Raman scattering spectrum has been well studied for single
crystal silicon (75; 80). One of the first reports of stress on the Raman modes of
Si was by Ganesan et al in 1970 (81), and their results showed there is a linear
relationship between applied stress and wave number shift. De Wolf et al. also
showed a linear relation between uniaxial and biaxial stress and the peak position
for the mode in single crystal Si (74). When the wafer is under intrinsic or extrinsic
60
stress, the lattice strain causes linear shifts in the wavenumber of the active phonon
modes. Since the discovery of this relationship, researchers have adapted Raman
spectroscopy to measure stress in Si MEMS devices such as on released micro-bridges
(77; 82) and map stress in Si micro-capsules (83).
5.2 General Theory of Raman Spectroscopy
Crystalline materials are comprised of periodically arrayed atoms vibrating at a
characteristic frequency. Raman Spectroscopy has the ability to detect variations in
the crystals lattice vibrational energy, based on the energetic shifts which arise from
in-elastic scattering interactions with the active phonon modes. Typically, when
a monochromic radiation source is incident on the surface of a crystal, the light
wave (photon) will interact with the lattice vibration (phonon) through a first-order
elastic Rayleigh scattering process. However, one out of 1012 of these interactions
will result in an in-elastic energy exchange through a second order Stokes-Raman
scattering process (74). In this case, the coupling between the phonon/ photon c
hanges the crystals electrical susceptibility and polarizability, subsequently causing
a shift in the lattice vibrational energy through Raman Scattering. Stokes-Raman
and Anti-Stokes Raman scattering require that energy and momentum between the
phonon/ photon interaction must be conserved: w=wi - ws and q = ki - ks, where
wi and ki are the respective frequency and wave vector of the incident photon, and
ws and ks are the respective frequency and wave vector of the scattered photon
(74). The change in vibrational energy states in Rayleigh Scattering and Raman
Scattering is explained through a Jablonski energy diagram, depicted in Figure 5.2.
61
Figure 5.2: Jablonksi energy diagram of quantum energy transitons between
Raman and Rayleigh scattering. This diagram shows the difference between
Rayleigh and Raman scattering when an incident photon excites a phonon from a
vibrational state to a virtual state. Adapted from ref (84)
5.2.0.1 micro-Raman Experimental Information
The experimental apparatus required to perform Raman measurements is a
monochromic light source, a spectrometer, and a charge coupled detector (CCD).
When a Raman instrument is paired with a confocal microscope, the monochromic
light source can be focused onto a spot size of < 1 µm, allowing for micro-Raman
spectroscopy (µRS). µRS is desired for our experiments because the precision of the
measurement allows us to study the local surface stress distribution on the small fea-
tures of the serpentine. Further, the high mechanical stability of the micro-Raman
system allows the recording of phonon properties over large area maps using a piezo-
electric xy stage (74).The experimental apparatus used in the following experiments
is shown in Figure 5.3.
62
Figure 5.3: Micro-Raman experimental apparatus The apparatus consists of a
monochromic laser radiation source (Nd:YAC 1064nm frequency doubled to 532nm),
reflection mirror, piezoelectric XY stage holding the sample holder and serpentine,
detector, CCD camera and spectrograph
The Raman experiments performed in this thesis were with a WITec Al-
pha300RA confocal Raman Microscope, with 300 nm spatial resolution. Prior
to collecting Raman spectra, the laser is stabilized at the desired power for a mini-
mum of 2 hours and then calibrated to the WITec standard procedure. An Nd:YAC
1064 µm frequency doubled excitation laser source (532 nm, 0.5 mW) was focused
on Si serpentine samples through a 100X long working distance (LWD) microscope
objective lens. Single Raman spectra are collected in the Z(XX)Z̄ backscattered ge-
ometry of Si (001), with 0.5 second time integrations and 60 accumulations through
a 1800 g/mm grating spectrometer, equipped with a charge coupled detector (CCD).
The resolution of the measurements are 0.1 Rcm−1. Our instrument is paired with
an automatic XY piezoelectric stage, allowing for high resolution Raman mapping
capabilities with step sizes of 200 nm, which was utilized in calibration measure-
ments.
63
5.2.1 Raman To Measure Stress in Silicon
Silicon has three active optical phonon modes, two transverse optical (TO),
and one longitudinal optical (LO) modes (74; 75). Based on crystal symmetry in the
diamond cubic structure of Si, all of the optical phonon modes are triple degenerate,
corresponding to a characteristic wave number of w0 = 520 - 521 Rcm
−1. Note here
Rcm−1 is used which means relative cm1 because the wavenumber of the scattered
light is relative to the incident light. When Raman units are reported as cm−1 this
refers to angular frequency. For the backscattering geometry of a (100) Si surface,
the LO mode is the primary mode that contributes to the Raman signal. Reported
values of the peak position of the LO phonon in unstrained (100) Si is reported to
vary from as low as 520 Rcm1 (74) to as high as 521 Rcm1 (75). The peak posi-
tion is sensitive to the the Raman instrument, wavelength of the excitation source,
thickness of the sample, doping type, and any defects that could be present, induc-
ing strain within the material. Because of this variability, when performing stress
measurements with µRS, it is important to calibrate all measurements to a known
unstrained silicon reference sample. The absolute position of the reference value
is not necessarily important for these measurements since it can vary from instru-
ment to instrument. What is important is the change in this value during Raman
measurements, which reveals information about the local surface stress distribution.
Raman spectroscopy can be used to determine the built-in stress within a Si
crystal with very high precision. When a Si crystal is under uniaxial or biaxial
strain, the triple degeneracy of the optical phonons are lifted, resulting in a peak
broadening and linear shift in Raman wavenumber. As a result, many researchers
have found a direct linear correlation between a Raman wavenumber shift, and the
magnitude of stress/ strain change in the material (74; 75; 82; 85). (100) Si exhibits
a single Raman peak at ws = wi - w0 = 520-521 Rcm
−1. Here ws is the frequency
of the scattered light, and wi is the frequency of incident light, and w0 corresponds
to the triple degenerate optical phonon of the center of the Brillouin Zone, which
occurs at a frequency of 520-521 Rcm−1 (80).
64
The relationship between frequency shift of the three optical phonons of Si
be found through solving the secular equations (74; 81; 86) It has been shown that
Raman frequency shifts linearly with stress/ strain; under tensile stress, the peak
shifts to lower wavenumbers, while compressive stress shifts the peak to higher
wavenumbers. This is related through the following equations for uniaxial stress in
silicon (74):
λ1 1
∆ω1 = = (pS11 + 2qS12)σ
2ω0 2ω0
λ (5.1)2 1
∆ω2 = = [pS12 + q(S11 + S12)]σ
2ω0 2ω0
λ3 1
∆ω3 = = [pS12 + q(S11 + S12)]σ
2ω0 2ω0
Where λ is the eigen value calculated from the secular equation, p, q, and r are the
phonon deformation potential material constants, and Sij are the elastic compliance
tensor components. For a (001) backscattered surface, only the third optical mode
is observed (∆ω3).
Since the elastic compliance tensor components are an anisotropic material
property, the relationship between strain and Raman frequency shift can be evalu-
ated along the <110> and <100> directions on a (100) Si wafer. For the <100>
direction, S11 = 7.68 x 10
−12 Pa−1, S −12 −1 −1212 = -2.14 x 10 Pa , S44 = 12.6 x 10
Pa−1, and p = -1.43ω20, q = -1.89ω
2
0, r = -0.59ω
2
0, we find:
∆ω<100>(cm−1) = −1.936 ∗ σ<100>3 10−9Pa (5.2)
σ<100>(MPa) = −516∆ω(cm−1)
Anastassakis et. al (87) reports there is a mean derivation of 25% in literature
values for the phonon deformation potential coefficients of Si, and determined the
average coefficients values to be p/ω20 = -1.85 ± 0.06, q/ω20 = -2.31 ± 0.06, r/ω20
= -0.71 ± 0.02, the Grüneisen parameter γG = 1.08 ± 0.06, and that hydrostatic
65
stress along the [100] direction for silicon is (1.88 ± 0.05 cm−1 / GPa) which is close
to the calculated value in Equation 5.2. For the <110> direction on the (100) Si
plane, S = 5.45 x 10−2 Pa−111 , S12 = -0.835 x 10
−12 Pa−1, S −12 −144 = 12.6 x 10 Pa ,
and p = -1.43ω2, q = -1.89ω2, r = -0.59ω20 0 0, we find:
∆ω<110> −13 (cm ) = −1.962 ∗ σ<110>10−9 ∗ [Pa] (5.3)
σ<110>(MPa) = −509∆ω(cm−1)
Biaxial stress is treated similar using the x and y stress tensor components (σxx and
σyy), with a slightly lower stress dependence than in the uniaxial cases:
biaxial λ3 1∆ω3 = = [pS12 + q(S11 + S12)](σxx + σyy)2ω0 2ω0 (5.4)
σbiaxial(MPa) = −435∆ω(cm−1)
DeWolf (74) reports that Si in the [100] direction under 500 MPa of tensile
or compressive stress will demonstrate a peak shift of 1 Rcm−1, as shown in the
above calculations. Our instrument can detect wave number shifts with a precision
of about 0.1 Rcm−1, which corresponds to a stress of 50 MPa, and an intrinsic strain
level of 2 x 10−4. The coefficients I calculated describe the effect of anisotropy on
the stress and Raman frequency dependence, however, the values are within the
experimental resolution of the WITec instrument; therefore, we cannot use Raman
to measure the anisotropic stress dependence. The relationship between frequency
shift and stress is graphically demonstrated in Figure 5.4. For a very detailed,
mathematical explanation of Raman Spectroscopy, and its applications to measure
stress on silicon integrated circuits, please see De Wolf (74), Anastakkakis et al.
(85; 87), and Srikar et al. (78).
5.2.1.1 Raman Calibration used for Si Stress Measurements
As previously mentioned, it is very important to calibrate the system to a
known ”unstrained” reference sample, because micro-Raman spectroscopy mea-
66
sures relative changes in the wavenumber and thus the strain. After calibrating
the WITEc Raman system using the manufacturer’s standard procedure, an un-
strained (100) Si sample provided by WITec is measured to serve as the reference
sample in the following studies. The typical Raman spectra of Si is shown in Figure
5.4A (left), with the laser line at 0 Rcm−1, the primary LO Si peak used for stress
measurements at w0 = 521.7 Rcm
−1, and a secondary Si peak 950 Rcm−1. Figure
5.4B (right) the Raman shift in wavenumber of the primary shows three measured
spectrum’s of (100) Si with varying amounts of stress. The black curve serves as
the unstrained bulk (100) Si reference, the red curve is shifted due to tensile stress,
and the blue curve is shifted due to compressive stress.
Figure 5.4: Raman Spectra and stress relation in unstrained bulk (100) Si. Figure
A.) demonstrates the measured standard Raman Spectra of Si (provided by WITec), used as
the calibration reference standard for the following experiments. Figure B.) demonstrates the
relationship between wavenumber shift and tensile/ compressive stress. The red curved shifted to
lower wavenumbers is Si in tensile stress while the blue curved shifted to a higher wavenumber is
compression stress.
The standard (100) bulk Si sample provided by WITec results in an w0 =
521.7 Rcm−1, slightly higher than the range reported in literature (w0 = 520 - 521
Rcm−1). To provide a more accurate initial reference value for the Si serpentines
that I fabricated in Chapter 4, I also generated a reference value on the silicon-on-
insulator (SOI) wafer serpentines were processed on. Since the initial SOI wafer chip
is unprocessed, I could use the piezoelectric XY stage to generate a 10 µm x 10 µm
67
map of the wavenumber of the LO phonon in Si. As shown in Figure 5.5, the initial
unstrained position varies between 521.8 - 522.1 Rcm−1. The average wavenumber
value corresponds to 521.95 Rcm−1.
Figure 5.5: Micro-Raman wavenumber position map of reference SOI wafer. The
wavenumber map shows the average position in a 10 µm x 10 µm region results in a variation
between 521.8 - 522.1 Rcm−1. The average wavenumber value in this sample corresponds to
521.95 Rcm−1.
If we use the wavenumber value from the bulk (100) Si WITec sample as w0 =
521.7 Rcm−1 and the wavenumber value from the unprocessed SOI wafer as ws =
521.95 Rcm−1, we find ∆ω3 = 521.95 - 521.7 = 0.25 Rcm
−1. We can then calculate
the amount of intrinsic stress in the SOI wafer using Equation 5.2, where we find
σ<110> (MPa) = -509 * 0.25 = -127.25 MPa of stress. This means initially the SOI
wafer is under -127.25 MPa of compressive stress. SOI wafers are known to have a
built-in compressive stress, compared to bulk Si due to mismatch in the coefficient
of thermal expansion between Si (2.6 X 10−6/K) and SiO2 (0.5 X 10
−6/K), and
the relationship between stress and strain in SOI films is well studied using Raman
spectroscopy in ref (88). It is also reported compressive strain in Si results in a
decrease of the Hall mobility while tensile strain increases the Hall mobility, which
shows there is a strong dependence between the electrical and mechanical properties
of Si devices.
68
5.3 Experimental Modification to Allow Application of Ex-
ternal Strain during µRS Measurements
To be suited for stretchable and wearable electronic applications, the stretch-
able Si serpentine traces must elastically survive global elastic deformation by a
minimum of 30% strain to meet the performance of human skin (8). The advantage
of using the serpentine geometries is the structure mitigates stress under strain, so
while the serpentine is under 10s of percent global strain, locally the strain is far
below the < < 1% intrinsic tensile strain limit of Si. To allow applied deformation
to the serpentine, I designed and built a custom 3D printed sample holder that
allowed application of externally applied strain in increments of 4-12%. Next, to
demonstrate that serpentines I fabricated meet the wearable electronics minimum
requirement, I mounted a <110> Si Curved Corner serpentine into the sample
holder. I then performed tensile tests using optical microscopy demonstrating the
serpentine survived global strains of up to -24% compression and 84% tension.
5.3.1 3D Printed Sample Holder Design
The overall goal of this work is to perform in-situ local stress measurement
with Raman spectroscopy on released Si serpentines while applying external strain.
The WiTec Raman System is equipped with a piezoelectric XY mapping stage,
however, it is not equipped to apply deformation to a sample during measurements.
To overcome this limitation, I used the program Solidworks to design a custom
mechanical testing fixture (shown in Figure 5.6) which I then 3D printed using a
3D printer (Stratasys FDM Titan 3D printer with polycarbonate material). This
sample holder was designed to mimic the conditions modeled in the finite element
analysis which suspends and strains the serpentine while securely screwed in to
the Raman microscope. Either end of the serpentine is first glued to two separate
microscope slides, which are mounted onto both sides of the holder. One end of
the serpentine is held fixed in the holder, while the other end is able displace by X
69
amount, parallel to the trace. The main components of the holder are the solid base
plate, movable part, and tops to secure the microscope slides. The final assembled
holder mounted into the Raman microscope is shown in Figure 5.7.
Figure 5.6: Solidworks engineering drawing of the designed assembled sample holder.
All dimensions are in mm.
After the sample was fixed into the 3D printed sample holder described in
section 5.3.1, it is mounted onto the XY stage and is ready for µRS characteriza-
tion. Turning the black micrometer allows the sample to strain while in the Raman
microscope in 4 - 12% strain increments. The reason for the large range in values is
due to the imperfections within the 3D printed part which only allowed movement
in 40 - 120 µm increments. The range could be reduced if a machine shop polished
metal holder was instead designed.
70
(A) (B)
(C)
Figure 5.7: Custom built sample holder for the Raman Microscope. A.) The assembled
holder closed B.) The holder open C.) Sample holder mounted in the Raman microscope
5.3.2 Optical Straining Images of Stretchable <110> Si
Optical microscopy was used to monitor the end-to-end displacement (global
strain) of a <110> Si Curved Corner serpentine, as well as the local displacement
within the individual period of the serpentine. A Keyence VHX 6000 Microscope
with a 200X objective lens, was used to optically measure the individual period and
the global end-to-end displacement of the entire serpentine trace, as a function of
71
strain. The global strain %s refer to the end-to-end displacement, while the local
strain %s refer to the individual period strain, reported using the Keyance micro-
scope. The values were later verified by using the computer program ImageJ. As
shown in Figure 5.8 the serpentine survived global compressive strains between 0%
of -24%. Shown in Figure 5.9, the serpentine reached a maximum global tensile
strain of 84% before fracture. This end-to-end displacement was in excellent agree-
ment with the 2D COMSOL model, which predicted a global tensile strain of 84%
for this geometry in the <110> direction.
Figure 5.8: Optical images of compressive strain testing of a <110> Curved Corner
Si serpentine surviving a global strain of -24% compression. Note -24% was not the
maximum compressive strain value of strain on this sample.
72
Figure 5.9: Optical images tensile straining a <110> Curved Corner Si serpentine to a
global maximum of 84%, and a local maximum of 101%.
73
5.4 Optical Tensile Testing and FEM Result Comparison
The 3D finite element model (FEM) described in Figure 3.14 predicted the
maximum stress in a <110> Si Curved Corner serpentine occurs at the Amplitude
and at a maximum applied global tensile strain of 70%. The 2D FEM model also
predicted the maximum stress to concentrate at the Amplitude, however, it predicted
a larger maximum tensile strain at 84%. The experimental tensile testing results on
the <110> Si Curved Corner serpentine are in good agreement with the modeling
trends, showing a maximum applied global tensile strain of 84%, with breakage at
the Amplitude. Figure 5.10 shows the Experiment and Model of the serpentine held
at 84% and a cross section demonstrating similar out-of-plane bending motions.
Figure 5.10: Experiment and model strain comparison of the <110> Si
Curved Corner serpentine stretching to 84%. The model and experiment
show similar straining distributions.
The 2D FEM model predicted in Chapter 3 and the experiment give similar
strain-to-rupture values of 84% for <110> Si Curved Corner serpentine. However,
the 3D FEM model more accurately predicted the out-of-plane buckling which re-
sults in a non-uniform stress distribution throughout the trace. The both models
also correctly predicted the maximum stress to be concentrated on the Amplitude,
74
while the minimum stress is concentrated on the Straight part of the trace for a
<110> serpentine. Micro-Raman spectroscopy will be used in the next section to
gain insight on the local surface stress distribution of the serpentine while applying
external strain on a Si Curved Corner serpentine now patterned in the <100> di-
rection. For reference, the 3D COMSOL model predicts the maximum stress on a
<100> trace to concentrate on the Bend, with a maximum applied tensile strain of
84%.
5.5 Stress Measurements on Released <100> Si Curved Cor-
ner Serpentines: Results and Analysis
In this section I describe the experimental methodology used to generate stress
measurements along the three locations of a <100> Curved Corner Si serpentine. I
then explain the experimental results and trends observed after converting Raman
wavenumber position to stress values to analyze the non-uniform stress distribution
on Amplitude, Bend, and Straight locations on the serpentine, as I apply external
strains from 0 - 72%.
5.5.1 Stress Measurement Collection Techniques Using Raman
Individual Raman spectra’s were collected on three major locations of the
fabricated and released <100> Si Curved Corner Si serpentine: Amplitude, Bend,
and Straight. As shown in Figure 5.9 the serpentine bends out-of-plane to relieve
stress under strain, which was not originally predicted by the 2D COMSOL model,
however it was predicted by the 3D model. While the WITec system has Raman
mapping capabilities, the out-of-plane bending of the serpentine lead to poor micro-
scope focus, thus a map could not be generated. For this reason, individual Raman
spectra’s were instead collected at each strain increment as a function of position
across the trace, allowing me to monitor the non-uniform stress distribution changes
within various locations of the serpentine as external strains were imposed.
To study the non-uniform stress distribution across the 50-55 µm wide trace,
75
5 single Raman spectra points were taken at every applied strain increment. The
reason for the variation of trace width is most likely due to imperfect photolithog-
raphy and plasma etching steps during the processing. The top and bottom of the
period, is the region I refer to as Amplitude, position (A) in Figure 5.11. The origin
(0 µm, 0 µm) was located precisely at the top centered edge of amplitude on the
3rd (middle) period in the 5 period serpentine trace, and served as the reference
position for the measurements. The origin was redefined back to (0 µm, 0 µm)
for each global strain increment. The Bend is labeled position (B) in Figure 5.11,
at a location approximately (50,-120) µm away from the Amplitude. The Straight
position is labeled (C) in Figure 5.11, and has a location of approximately (500 µm,
-500 µm).
In Figure 5.11, 0 µm was defined at the origin (0 µm, 0µm) on the third
period’s Amplitude, where compression is expected to be found in the trace. As we
move down (y-axis) in 10 15 µm step sizes, we can monitor the local stress change
from compression to tension. The difference in the Z-height focus between 0 µm
and 50 µm was never more than 20 µm on the amplitude. Similar to the methods
used for the Amplitude, single spectra’s across the trace on the Bend and Straight
locations of the beam were also generated with 10-15 µm spacing.
76
Figure 5.11: Images demonstrating the locations on the serpentine measured with Ra-
man. Stress measurements were collected on the A.) Amplitude B.) Bend and C.) Straight parts
as a function of position across the trace. The COMSOL images of these locations are also included
for reference.
77
5.5.2 Raman Stress Characterization on Stretchable Si Curved Corner
Serpentines
Single Raman spectra were taken as a function of position across the trace on
the Amplitude, Bend, and Straight part of a <100> Curved Corner Si serpentine.
A minimum of 4 points were generated at each position as I applied global external
strains between of 0% and 72%. Optical microscopy demonstrated in the previous
section a strain-to-rupture (tensile strain) of 84% for a <110> Curved Corner Si ser-
pentine; therefore, a maximum strain of 72% was selected to prevent inducing plastic
deformation. The selection of a lower strain value will allow low-cycle stress fatigue
evaluation of the serpentines elastic behavior in Section 5.6. The non-uniform stress
distribution, and out-of-plane buckling across the Amplitude, Bend, and Straight
part of the trace after a 30% applied global strain are shown in Figure 5.12.
(A) (B)
Figure 5.12: A.) Raman measured stress distribution for all positions after applying a
30% global strain parallel to the trace. B.) Cross section of curved corner serpentine
buckling out-of-plane at the Bend and Amplitude under applied strain.
As shown in Figure 5.12, the maximum stress was concentrated at the Bend,
followed by the Amplitude, and then the Straight. Figures 5.13 A,C, and E shows
how the non-stress distribution changes while applying external strain from 0 - 72%
at each position (A) Amplitude, (C) Bend, and (E) Straight. Figures B, D, and
F show the color coordinated Raman position and intensity plot of the Amplitude,
Bend, and Straight location at its respective applied strain value.
78
Figure 5.13: Raman measured stress distribution across the Amplitude, Bend, and
Straight part of the serpentine trace as a function of applied strain. The measured
stress distribution and variation in Raman peak position and intensity shown for both locations.
Figures A-B show the distribution and Raman intensity plot for the Amplitude, C-D show the
Bend, and E-F show the Straight part of the serpentine.
These results indicate that the maximum tensile and compressive stress is
79
located in the Bend at each applied stain increments, while the minimum stress is
located on the Straight part of the serpentine. The maximum stress at the Bend
predicted by the 3D FEM for a <100> Curved Corner Si serpentine, due to the
out-of-plane buckling induced on the Bend under applied deformation. The Straight
part of the serpentine undergoes little buckling deformation, results in minimal stress
changes with applied strain. Additionally, all Raman intensity plots demonstrate
a decrease in intensity with applied external strain. This is most likely due to the
out-of-plane bending and twisting causing a loss in focus on the microscope, and
thus a loss in CCD counts on the spectrometer.
5.6 Low-Cycle Fatigue Evaluation on Stretchable <100> Si
using Raman Spectroscopy
Figure 5.14: Low-cycle fatigue testing of a <100> Curved Corner serpentine
from 0% to 30% applied global strain for 15 cycles. Raman spectra was
collected on each location after applying 0, 5, 10, and 15 cycles. Note that the period
is not straining uniformly, meaning a 30% global strain (end-to-end displacement)
corresponds to a local strain of 40% in the 3rd period.
In order to study the reversible (elastic) mechanical performance of the ser-
pentines, low cycle fatigue tests were performed to examine the strains required to
promote of crack propagation. After the final stress measurement was taken at 72%,
the serpentine was reset back to its 0% strain position. The trace was then cycled 15
times between 0 - 30% (end-to-end), which corresponded to a local strain within the
individual period of 40%, shown in Figure 5.14. After the 5th, 10th, and 15th cycle,
the Raman experimental protocol from above was repeated to collect 5 individual
spectra on the Amplitude, Bend, and Straight, shown in Figure 5.15.
80
(A)
(B)
(C)
Figure 5.15: Low-cycle stress and fatigue evaluation on the Amplitude, Bend, and
Straight of the <100> Si Curved Corner serpentine after applying a global strain of
30% for 0-15 cycles. Figure A.) Shows the maximum stress on the Bend, B.) Shows the stress
distribution across the Amplitude, and C.) Show81s the minimum stress on the Straight part.
These measurements fall within the uncertainty of the instrument (+/- 50
MPa) which indicates there is very little to no plastic deformation in this devices
after undergoing a low number of cycles. Since the measurements recorded here
follow a systematic baseline shift and the error bars of the measurements fall within
the uncertainty of each other, there is no appreciable change in the magnitude of
stress that would indicate fatigue in this serpentine trace after 15 cycles. During
continuous cycling, it is expected that residual stress gradually accumulates which
can lead to micro-cracking, which is problematic for wearable devices intended to
have long-term applications. For this reason, I would recommend high cycle fatigue
testing (< 1000 cycles) experiments, which I expect to complete on these serpentine
traces in the future.
5.7 Raman Spectroscopy to Measure Stress in Stretchable
Si Summary and Conclusions
The methods presented in this chapter show micro-Raman spectroscopy is a
powerful tool for measuring mechanical performance (stress and strain) in stretch-
able crystalline semiconductors. Through optical microscopy, I demonstrate a non-
uniform straining profile that resulted in a maximum end-to-end displacement of
84% on a <110> Curved Corner Si serpentine, which is in very good agreement with
the prior solved FEM models. I then shown I can measure the non-uniform stress
distribution across the Amplitude, Bend, and Straight part of a <100> Curved Cor-
ner Si serpentine, while applying external global strains of 0 - 72%. The maximum
stress was shown to concentrate in the Bend of this trace due to out-of-plane buck-
ling, while the minimum stress concentrated in the Straight part of the trace, also
predicted by the prior FEM model. Additionally, I demonstrate low-cycle fatigue
stress/ strain monitoring, using micro-Raman spectroscopy, by cycling an applied
0 - 30% end-to-end displacement 15 times, and then taking a set of Raman mea-
surements at each position every 5 cycles. The results demonstrate a baseline shift
in the stress measurements, within the experimental resolution of the instrument,
82
indicating this cycling resulted in elastic behavior. Overall, the results presented
in this chapter demonstrate micro-Raman spectroscopy is viable tool in-situ stress
characterization technique for stretchable crystalline materials while on the wafer,
free standing, and while applying external strain.
83
Chapter 6: Ex Situ Stress Measurements of Stretchable
AlGaN/ GaN HEMT Devices
Aluminum gallium nitride / gallium nitride high electron mobility transis-
tors (AlGaN/ GaN HEMTs) are high performance devices which could enable high
power and ultrafast switching wearable devices, if made stretchable. With most
crystalline materials, the challenge with GaN and AlGaN is the high strength and
low tensile strain makes the material inherently brittle to any applied deformation.
While device fabrication into serpentine structures can relieve stress under applied
strain, there are additional strain considerations inherent to the crystal such as
strain present at the interface between the AlGaN/ GaN heterostructure, and the
interphase of GaN/ substrate due to lattice constant mismatch. Additionally, depo-
sition of other materials such as metal contacts and passivation layers induces local
strain fields within the surface of the device. The presences of non-uniform stress
throughout the hetero-structure stack presents additional challenges during the fab-
rication, release, and encapsulation of stretchable AlGaN/ GaN HEMT devices. In
this chapter, I describe methodology and applications of Raman Spectroscopy as a
stress monitoring technique of multiple processing steps in the fabrication of stretch-
able AlGaN/ GaN HEMTs through two separate fabrication approaches: bottom-up
and top-down. This includes evaluation of the inherent stress present due to epitax-
ial mismatch from the as-grown heterostructure, stress within the device fabricated
into the serpentine geometry on the wafer, and finally stress within the AlGaN/
GaN HEMT once released from the wafer.
84
Figure 6.1: Scanning electron microscopy (SEM) images of a stretchable
AlGaN/ GaN HEMT devices grown through the bottom-up and top-down
approaches. (A.) Stretchable HEMT fabricated using the bottom-up approach by
Ms. Isra Mahaboob, SEM taken by Ms. Kasey Hogan. (B.) Stretchable HEMT
fabricated using the top-down approach by Dr. Randy Tompkins, SEM taken by Dr.
Milena Graziano.
In this study, I use Raman Spectroscopy as a stress monitoring technique to
evaluate the built-in and induced crystal stress during the fabrication and produc-
tion of stretchable AlGaN/GaN HEMTs through both the bottom-up and top-down
approach. The bottom-up approach refers to using selective area growth (SAG)
methods through metal organic chemical vapor deposition (MOCVD) to grow single
crystal AlGaN / GaN directly into serpentine structures onto a sapphire substrate.
The top-down approach refers to using standard photolithography and microma-
chining techniques to etch AlGaN / GaN in to the serpentine geometries and then
release the structure from its Si wafer. The scanning electron microscopy (SEM)
images of the top-down and bottom-up stretchable AlGaN/ GaN HEMT devices
that will be characterized are shown in Figure 6.1. The goal of this study is to eval-
uate how the various fabrication approaches and steps effect the amount of induced
stress in the AlGaN / GaN crystal.
First micro-Raman spectroscopy is used to evaluate the stress on the as grown
materials to serve as the references, 3.5 µm unintentionally doped GaN on bulk sap-
phire substrate (bottom-up study reference) and 1.5 µm AlGaN/ GaN stress on bulk
silicon substrate (top-down study reference). I then measure a traditional planar
HEMT (AlGaN/ GaN on bulk sapphire substrate) as a reference sample to generate
a baseline measurement for standard stress in a HEMT device. Next, I map the sur-
85
face stress on bottom-up stretchable AlGaN/ GaN HEMT devices (on a sapphire
substrate) grown on the wafer using two two different masking materials: silicon
dioxide (SiO2) and tungsten (W ). Afterwards, I map the surface stress on a top-
down stretchable AlGaN/ GaN HEMT (on a silicon substrate) while on the wafer.
I then finally map the surface stresses of the top-down stretchable HEMT released
(removed) from the Si wafer, and encapsulated within an soft silicone elastomer.
Overall, this is the first ex-situ mapping of the surface stresses within stretchable
AlGaN/ GaN HEMT devices, using micro-Raman spectroscopy.
6.1 AlGaN/ GaN HEMT Overview
6.1.1 Stretchable AlGaN/ GaN HEMT Motivation
A high electron mobility transistor (HEMT) is a type of hetero-structure field
effect transistor, which can operate at frequencies as high as 230 GHz with a power
of 250 W (89). The wide band gap semiconductor GaN is commonly used in HEMT
devices because it forms solid solutions with its III-Nitride counterparts (AlGaN, In-
GaN, AlInGaN), which demonstrates interesting electrical properties, such as high
electron mobility, and a high break down field, when joined together into a het-
ero junction. Extensive research has been conducted to understand the electrical
and mechanical material properties for traditional HEMT devices, demonstrating a
direct correlation between charge (free electron carriers) and the amount of stress
within the material, due to spontaneous and piezoelectric polarization (89; 90). The
Army Research Lab has partnered with the College of Nanoscale Science at SUNY
Polytechnic Institute to develop the first stretchable AlGaN/ GaN HEMT device for
wearable power management. Currently the relationship between HEMT device per-
formance, failure mechanisms, and initial material quality is limitedly understood
(89). My research contribution to this collaboration is the first ex-situ mapping
of the surface stresses within stretchable AlGaN/GaN HEMT devices with micro-
Raman spectroscopy on devices fabricated through the bottom-up and top-down
approaches. These results will eventually reveal how processing effects stretchable
86
crystalline GaN device electrical and mechanical performance.
6.1.2 AlGaN / GaN HEMT Hetero-Structure
A heterojunction is formed when an AlGaN layer is epitaxially grown onto
GaN, forcing the Fermi energies of two the material to reach an equilibrium which
induces a net positive polarization within the AlGaN at the AlGaN / GaN interface
and a negative polarization within the GaN at this interface (10; 51; 91). There is
a negative polarization that forms at the top of the AlGaN layer and the bottom
of the GaN layer. Due to this net polarization, there is an intrinsic electric field
present within the GaN and AlGaN materials themselves (EGaN and EAlGaN), and
additionally the net polarization due to the AlGaN/ GaN hetero-structure results
in the formation of a built in electric field at the interphase between the materials
AlGaN/GaN
EInterface ). At this interface, free electrons generated from the surface donor states
in AlGaN and electrons from the GaN will accumulate at an energy above the fermi
energy, resulting in an extremely conductive region known as the two-dimensional
electron gas (2DEG) (10; 51; 92).
The electrons from the surface donor states are thought to come from oxygen
impurities and nitrogen vacancies (10; 51; 91; 92). Additionally, since AlGaN and
GaN are piezoelectric materials, under an applied electric field or external tensile
strain, they will spontaneously generate free carriers (PGaN AlNspontaneous and (Pspontaneous)
which will also accumulate and contribute to the conduction in the 2DEG. The
2DEG formation is attributed to the piezoelectric response of GaN and AlGaN,
composition, polarization and strain which generate the various electric field lines
(72).The 2DEG is responsible for the fast switching performance, which is why
they are highly researched for high power and high frequency devices. Figure 6.2
demonstrates a cross section of a planar AlGaN/ GaN HEMT demonstrating the
polarization and electric field lines which lead to the formation of a 2DEG. Equa-
tion 6.1 shows the net polarization in the 2DEG that is from the combination of
the piezoelectric polarization and spontaneous polarization of AlN and GaN. The
piezoelectric contribution of AlN (AlGaN) is thought to be much greater than that
87
of GaN.
Figure 6.2: Cross section of a AlGAN/ GaN HEMT device showing the elec-
tric field lines that form the 2DEG Electric field lines of both AlGaN (EAlGaN )
and GaN (EGaN )point in the opposite direction of spontaneous and piezoelectric po-
larization. The 2DEG arises from the charge balance at the AlGaN/ GaN interface,
AlGaN/GaN
(EInterface ).
P GaN AlN AlN2DEG = Pspontaneous(1 − x) − (Pspontaneousx+ Ppiezoelectric) (6.1)
6.1.3 Built-In Stress within HEMT Structure
Due to the cost of production of GaN, hetero-epitaxial growth is used through
molecular beam epitaxy (MBE) or metal organic chemical vapor deposition (MOCVD)
onto a substrate of a different material such as silicon (Si), silicon carbide (6H-SiC),
or sapphire (Alpha-Al2O3). Epitaxial growth of high quality GaN onto a Si or
Al2O3 hetero-substrate is very challenging due to misalignment of the lattice con-
stants which leads to a mismatch in the coefficient of thermal expansion (CTE)
(66). This severe misalignment between the deposited GaN film and its substrate
leads to a built-in strain and intrinsic stress within the as-grown material, due to
the promotion of dislocations. GaN grown on Si is in tensile stress (56%) while GaN
grown on sapphire is in compressive stress (16%). The large difference in the CTE
and lattice mismatch induces a high defect density within AlGaN / GaN which can
be on the order of 1010 cm−2 (89).
AlGaN has a smaller lattice constant than GaN; growth of AlGaN material
on GaN results in lattice mismatch between the two materials causing the AlGaN
layer to be grown under tensile strain at the AlGaN/ GaN interphase. For electronics
88
applications, the AlGaN layer grown on top of GaN is typically limited to a thickness
of 30 nm, and critical composition of 30% to prevent crystal cracking. GaN is grown
in tension on a Si substrate, and often times an AlN buffer layer is used on the top
or bottom of the GaN to compensate for the induced strain (57; 89). µRS has been
used to study strain effects on Al0.5Ga0.5N/GaN on crack and dislocation density
(93). In Situ wafer curvature measurements, later verified by X-Ray Diffraction
(XRD) reveal GaN grown on sapphire induces a compressive stress of -0.66 GPa
µm at room temperature, and with increasing concentration of Si dopant, GaN can
experience an induced tensile stress of up to 0.15 GPa (57). The lattice constant
mismatch and coefficient of thermal expansion mismatch between GaN, AlN, and
common substrate materials is summarized in Figure 6.3.
Figure 6.3: Table showing GaN, AlN, Si, SiC, and Sapphire lattice constant
and coefficient of thermal expansion (CTE) mismatch, and dislocation
density values.
The problem of strong residual stress throughout the HEMT stack can be cir-
cumvented by releasing the hetero structure from the substrate, which allows the
AlGaN/ GaN hetero structure to strain relax to its lowest energy configuration.
Some methods to release GaN include laser ablation, mechanical polishing and re-
leasing, and chemical etch releasing; however, these techniques roughen the surface
which inhibits the amount of carriers which could contribute to the 2DEG. These
89
processes are known to increase the defects and dislocation density of the GaN ma-
terial, which is ideal for stretchable and flexible electronic applications (62). To
determine an optimal process to fabricate and release which induces minimal stress
into the GaN crystal during stretchable HEMT fabrication, we are exploring two
separate approaches with our collaborators: top-down and bottom-up. Both pro-
cesses are designed to be compatible with plasma dry etching to remove the substrate
which is less harsh on the crystal during release from the substrate.
Understanding the origin of stress in AlGaN/ GaN HEMT devices is important
because this type of heterostructure is known to have a direct correlation between
the number of free carriers in the 2DEG, and the amount of strain in the crystal.
Kuball demonstrated that micro-Raman Spectroscopy (µRS) could be used to in-
dependently measure both of these material properties: free carrier concentration
through the polar A1(LO) peak, and strain through the non-polar E2 (high) peak
(90). Many researchers have since then used µRS to monitor the relationship be-
tween both of these properties in GaN devices. For example µRS has been used
to study the free carrier concentration as a function of the as grown stress in the
fabrication of core-shell nanowire InN-GaN on devices (94) and in heavily-doped
GaN:Si micro-rods (95). µRS, correlated with FEM results, has also been used to
study the stress in GaN micro-beams before and after release (71).
6.2 Raman to Measure Stress in GaN
Raman Spectroscopy has extensively been used to non-invasively locally mon-
itor crystalline quality, such as stress, free carrier concentration, composition, thick-
ness, growth and operating temperature within semiconductor materials (90) through
changes in the Raman peak position and bandwidth. The III - V semiconductor
compounds GaN, AlGaN, and AlN all crystallize into hexagonal (wurtzite) crystal
structures, with four atoms in the primitive unit cell. For these materials, group
theory predicts eight sets of phonon modes: 2E2, 2A1, 2E1, and 2B1 within the
first Brillion Zone (q=0), however, the 2B1 mode is not active. The crystal orienta-
90
tion and polarization configuration of the material determines which phonon modes
are observed. All samples evaluated in this thesis are assumed to be in the (0001)
c-plane of GaN, which corresponds to a back scattered geometry of Z(XX)Z̄. For
a full description of the GaN group velocity derivation which explains where the
various phonon modes arise from, please see reference (96).
An individual Raman spectrum of single crystal GaN in the Z(XX)Z̄ backscat-
tered geometry has three characteristic Raman peaks: E2(low) 144 cm
−1, E2(high)
568 cm−1, and A1(LO) 733 cm
−1 (90; 96). Variations peak frequency position of the
E2(high) is indicative of changes within the stress in the GaN crystal stack, while
variations in the peak’s full-width half max (FWHM) reveal crystalline quality (90).
Additionally, in polar crystals, Raman has been demonstrated as a technique to
measure the free carrier concentration and determine the doping-type (n or p type)
based on interactions between plasmons and phonons, which is useful information to
evaluate HEMT performance; however, this is beyond the scope of discussion in this
thesis (90; 95; 96; 97; 98; 99). Figure 6.4 shows the Raman Spectra of A.) (solid) 3.5
µm unintentionally doped GaN, grown on bulk sapphire substrate and B.)(dashed)
1.5 µm intentionally doped AlGaN/GaN, grown on bulk silicon substrate, used as
the reference samples in the following studies presented in this thesis.
91
Figure 6.4: Raman Spectra of µm GaN in the (0001) back scattered geom-
etry on a bulk sapphire substrate. The image on the right demonstrates the
linear relationship between the shift in the E2(high) Raman wavenumber and tensile/
compressive stress.
6.2.1 Stress Measurement Methodology
Strain can lead to the formation of defects, which can increase the crack and
dislocation density of the material, and is observed through a linear shift in the
vibrational frequency position of E2 (high) mode in the Raman spectra of GaN.
Using the phonon deformation potential (DP), Raman peak shift can be resolved
into the magnitude of stress and strain present within the crystalline materials, with
compressive and tensile stress shifting the frequency to higher and lower values,
respectively (90; 100). This can provide extremely useful insight on strain effects
induced during growth and during each processing step of a stretchable AlGaN/ GaN
HEMT device. Using Equation 6.2, we can determine the stress-induced frequency
shift of the non-polar E2 (high) peak in GaN (101).
∆ω = ω − ω = Kσ cm−1s 0 xx (6.2)
Here K is the pressure coefficient for GaN (K = 4.3), ωs is the frequency of the
scattered light and ω0 is the frequency of the unstrained E2 (high) position. Kuball
suggests biaxial stress shifts linearly with 2.9 GPa Rcm−1. A thick (400 µm) bulk
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single crystal of unstrained GaN was reported to have a characteristic frequency of
567.5 Rcm−1 (90; 101).
6.2.1.1 AlGaN / GaN on Si and Sapphire Reference Samples
2D Raman maps of GaN samples can be generated since they are planar while
on the wafer. A 70 µm x 70 µm area with a 1 µm step size was scanned at each
location, generating a grid composed of 4,900 individual Raman spectra, which
creates a Raman map. Figure 6.5 show the Raman position map generated on the
1.5 µm AlGaN / GaN on 650 µm Si reference sample.
Figure 6.5: A 70 µm x 70 µm Raman position map of the as-grown AlGaN/
GaN on Si wafer This sample is used as the reference position for stress values
reported in the top-down maps. The average position w0 = 568.75 Rcm
−1
An unstrained bulk single GaN crystal was reported to have an E2 (high)
phonon mode corresponding to w = 567 Rcm−10 . If we take the average Raman
value for AlGaN / GaN grown on Si reported in Figure 6.5, as ws = 568.75 Rcm
−1,
then the built-in stress in this crystal can be calculated using δω = ws - w0 = 4.3σ.
Therefore the built-in stress of the GaN on Si reference sampl is σ = (568.75 -
567.5)/4.3 = +0.29 GPa . Note the sign of stress is positive which indicates this
sample is under tensile stress of GPa. The following measurements will report stress
changes with respect to the built in stress of the crystal (i.e w0 = 568.75 Rcm
−1
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is the 0 stress/ strain position). Following the same procedure above on the GaN
on sapphire reference sample used in the bottom-up study (spectra shown in Figure
6.4) we find an average position of which results in a built-in stress of -0.35 GPa
of compressive stress. All stress values reported are changes from the reference
as-grown materials.
6.3 Stress Measurements on Bottom-Up AlGaN/GaN HEMTs:
Results and Analysis
Figure 6.6: Diagram demonstrating the bottom-up fabrication approach
to build a stretchable AlGaN / GaN HEMT using selective area
growth (SAG). SAG was performed using metal organic chemical vapor deposi-
tion (MOCVD). Cross sections of the HEMT devices fabricated using the silicon
dioxide mask and tungsten mask are also included, with arrows pointing to the the
interfaces were stress is expected to be found.
6.3.1 Bottom-Up Approach Background
In this study, I use µRS to map the surfaces stresses within stretchable Al-
GaN/GaN HEMTs grown using the bottom-up, selective area growth (SAG) method,
with metal organic chemical vapor deposition (MOCVD). Two masking materials
were evaluated (silicon dioxide and tungsten) on the stress within the grown stretch-
able AlGaN/ GaN HEMT device, while still on its planar sapphire substrate. Since
94
these devices were still on the substrate, the WITec Raman Spectroscopy instrument
we have in house is equipped with a piezoelectric XY stage, is suited to generate
large area stress maps on these samples. For this study, I used a WITec Alpha300RA
confocal Raman Microscope, with 300 nm spatial resolution. An Nd:YAC 1064 nm
frequency doubled excitation laser source (532 nm) with 1 mW power was focused
on a sample through a 100 X microscope objective lens. A 70 µm x 70 µm large area
map with a step size of 1 µm was collected using a 1800 g/mm grating spectrometer
equipped with a charge coupled detector (CCD), with resolution of 0.1 Rcm−1 .
Measurements were carried out in the backscattered geometry of Z(XX)Z̄, with 0.5
second time integrations and 60 accumulations, to reduce the signal-to-noise ratio.
The position and intensity of the laser peak in the Raman spectra’s were used as
the calibration reference position between samples.
The bottom-up devices characterized in this study were grown, fabricated,
and graciously provided by Ms. Isra Mahaboob (Ph.D. student) in Prof. Shadi
Shahedipour-Sandvik’s group in the College of Nanoscale Science and Engineering
at SUNY Polytechnic Institute, Albany, NY. Information regarding the specifics in
the growth procedures from this group are reported elsewhere (101; 102; 103; 104).
6.3.2 Selective Area Growth with SiO2 Mask
The first device evaluated in this study was a SAG Stretchable AlGaN/ GaN
HEMT grown using a SiO2 mask. The device was already deposited with a Ti/Al/Ni/Au
(20/120/60/50 nm) metal contact along the Bend and Straight part of the sinusoid
serpentine device, leaving the Amplitude of the device exposed with crack free Al-
GaN/ GaN crystal. Figure 6.7 demonstrates an optical image, laser intensity plot
of the E2 peak used to evaluate stress, and the surface stress map on the Amplitude
and Bend of this device.
95
Figure 6.7: 2D Raman stress maps of bottom-up SAG AlGaN/ GaN
HEMTs with the SiO2 Mask. The left column (A) and (D) show the optical
images of the mapped regions along Amplitude and Bend, indicated by a red square.
The middle column (B) and (E) show the laser intensity plot of the GaN E2 peak,
used to extrapolate stress. Finally the right column (C) and (F) shows the 2D stress
maps calculated for the Amplitude and Bend of this stretchable AlGaN/ GaN HEMT.
As shown in Figure 6.7, there is an average stronger compressive stress in the
Amplitude than in the Bend (-1.5 GPa and -1.3 GPa respectively). The likely reason
for the reduction in stress within the Bend of the serpentine is due to the deposited
metal contact. The lattice constant of the metal contact is smaller than that of the
AlGaN/ GaN, which induces tension the surface of the crystal. As a result, the
magnitude of stress within the edge of the HEMT along the Bend is 300 MPa lower
than the magnitude of stress within the Amplitude.
6.3.3 Selective Area Growth with Tungsten (W) Mask
Repeating the same procedure from above, I evaluated the surface stress on
a SAG Stretchable AlGaN/ GaN HEMT grown using a tungsten (W) metal mask.
This serpentine had the same dimensions are the device characterized with the
silicon dioxide mask; however this device had no deposited metal contacts. The
region measured was a crack free region of exposed AlGaN / GaN crystal in the
96
stretchable serpentine geometry. The optical image, Raman intensity, and 2D stress
map of this device is shown in Figure 6.8.
Figure 6.8: 2D Raman stress map of bottom-up SAG AlGaN/ GaN HEMT
fabricated with the tungsten metal mask. (A) shows the optical image of the
mapped region, indicated by the red square. (B) shows the laser intensity plot of the
GaN E2 peak, used to extrapolate stress. (C) shows the calculated 2D stress map.
The stress map on this device reveals a uniform stress distribution along the
SAG AlGaN/ GaN crystal. The magnitude of stress is slighly higher in the sample
grown with the tungsten mask than with the silicon dioxide mask (-1.7 GPa vs -1.5
GPa respectively). This could be due to a lack of top metal contact. Additionally,
upon evaluation of the FWHM in the spectra of tungsten and silicon dioxide masked
samples, the FWHM was narrower in the tungsten mask sample which indicated
a lower dislocation density and a purer crystal. In the future we will look into
comparing stress in serpentines with similar cross sections grown using the two
different masking materials.
97
6.4 Stress Measurements on Top-Down AlGaN/GaN HEMTs:
Results and Analysis
Figure 6.9: Top-down fabrication approach for stretchable AlGaN/GaN
HEMTs. Simplified fabrication approach of the top-down devices tested, devel-
oped by Dr. Randy Tompkins and Dr. Nathan Lazarus. Step (a) uses standard
photolithography and micro-machining processes to develop a HEMT device into a
stretchable geometry. Step (b) performs an isotropic plasma etch to undercut the
HEMT from the Si wafer. Step (c) pours liquid silicone onto the front side of the
device to encapsulate and protect the structure. Step (d) is a backside removal of
the Si substrate using plasma etching (3).
6.4.1 Top-Down Approach Background
The second fabrication method explored is referred to as the top-down ap-
proach. The top-down method initially starts with a wafer of crystalline material,
and then one performs traditional photolithography and micro-machining processes
to etch a device into a desired geometry. The top-down stretchable AlGaN/GaN
HEMT devices explored in this study were fabricated by my collaborators and men-
tors Dr. Randy Tompkins and Dr. Nathan Lazarus at the Army Research Lab.
The general fabrication procedure they developed is shown in Figure 6.9. First the
HEMT structure is fabricated into a stretchable geometry on a 1 cm x 1 cm piece
part from an AlGaN/GaN/Si (30 nm / 1.47 µm / 650 µm) wafer using a traditional
fabrication approach (89). Next, XeF2 is used to isotropically undercut the struc-
98
ture, followed by device encapsulation in an elastomer (Sylgard 184). Sylgard 184 is
the same silicone rubber modeled in chapter 3. Finally, the Si substrate is removed
from the backside of the device using Xenon Diflouride (XeF2) gas chemistry to
fully release the device into the elastomer substrate (2; 3).
6.4.2 Stress in AlGaN/ GaN HEMT on the wafer
Here I use micro-Raman spectroscopy as a stress monitoring technique during
the fabrication of a stretchable AlGaN/ GaN HEMT using the top-down approach.
The stress was previously evaluated on the wafer from the original as-grown crystal.
Next, I generate a stress map of the stretchable AlGaN/ GaN HEMT while on
the wafer, as shown in Figure 6.10. The zero stress reference state was selected as
the average value of w0 = 568.75 Rcm
−1 from the as-grown material. This device
went under many fabrication steps including photolitograpy, metal deposition, and
anisotropic-plasma etching to define the HEMT device into a serpentine geometry.
The map results shown in Figure 6.10 (D) show that these fabrication procedures
induce up to 0.5 GPa of tensile stress within the AlGaN/ GaN crystal layer along
the amplitude of this serpentine.
99
Figure 6.10: 2D Raman stress map of a top-down stretchable AlGaN/ GaN
HEMT on the Si wafer. The optical image of the device measured for the map
is shown with a 20X objective in (A) and with a 100X objective in (B). The laser
intensity of the E2 (high) phonon peak is shown in (C), and finally the stress map of
the device in (D).
6.4.3 Stress in AlGaN/GaN HEMT when Released and Embedded into
a Stretchable Substrate
Next, I evaluate the the surface stress within a released and encapsulated
Stretchable HEMT, step (d) in Figure 6.9. This device was encapsulated on the top
side of the device, leaving the back of the device exposed for Raman measurements.
Since GaN is transparent, we can see the metal contact on the other side of the
device, also encapsulated in the silicone. Figure 6.11 show the optical image, Raman
map intensity, and stress map of the released device.
100
Figure 6.11: 2D Raman stress map of a top-down stretchable AlGaN/ GaN
HEMT released from the Si wafer and encapsulated in silicone. The optical
image of the device measured for the map (back side of GaN) is shown with a 20X
objective in (A) and with a 100X objective in (B). The laser intensity of the E2 (high)
phonon peak is shown in (C), and finally the stress map of the device in (D).
These results indicate that removal of the silicon substrate and encapsulation
within an elastomer increases the tensile stress of the device by 300 MPa. This
induced stress would be advantageous for a stretchable AlGaN/ GaN HEMT device
because this would induce additional free carriers within the 2DEG of the device.
6.5 Stress Measurements in AlGaN/GaN HEMTs Conclu-
sions
Micro-Raman spectroscopy was shown to be a viable optical stress monitoring
tool during the fabrication and processing of GaN crystals. In this chapter I used
micro-Raman spectroscopy to evaluate the surface stresses in stretchable AlGaN/
101
GaN HEMT samples fabricated through two separate approaches: bottom-up (sili-
con dioxide and tungsten mask) on sapphire substrates and top-down (on a Si sub-
strate and encapsulated in silicone after substrate removal). Through measurement
of the E2(high) phonon peak, it was revealed epitaxial growth of AlGaN/GaN on
a sapphire substrate induces intrinsic compressive stress while AlGaN/GaN growth
on a silicon substrate induces tensile stress due to differences in lattice constants and
coefficient of thermal mismatch. Next, I evaluated the stress in two stretchable ser-
pentine HEMT devices grown through the selective area method (bottom-up) with
two different masking materials (silicon dioxide and tungsten) onto sapphire sub-
strates. Both samples were shown to have an induced compressive stress, however,
the sample grown with the tungsten mask was under a higher order of magnitude of
compressive stress. A possible explanation for this is the tungsten masked sample
had no metal contact on the top surface which could induce a counter tensile stress,
as in the case with silicon dioxide sample.
Next, I evaluated induced tensile stress during the fabrication of stretchable
AlGaN / GaN HEMTs on silicon substrates through the top-down fabrication ap-
proach. Measurements were taken on the as grown material, stretchable HEMT
device fabricated on the wafer, and substrate removed (device encapsulated in sil-
icone). The HEMT device fabricated on the Si wafer was under up to +0.60 GPa
of tensile stress. It was shown that as the silicon substrate is removed after it is
encapsulated within silicone rubber, the tensile surface stress of the HEMT device
increased by +0.3 GPa of stress. Since GaN and AlGaN are piezoelectric materials,
an increase in tensile stress would indicate an increase in the number of free carriers
in the device. Micro-Raman spectroscopy can independently measure both of these
phenomena, and future studies by our group will explore the piezoelectric coupling
effects between induced tensile stress and generated electric charge in stretchable
AlGaN / GaN HEMT devices. These findings further support GaN-on-Si technology
will becoming exciting for wearable electronics in the future.
102
103
Chapter 7: Outlook for Stretchable Crystalline Materials
7.1 Conclusions and Summary of Contributions
Throughout my Masters thesis, I showed modeling, fabrication, and characterization
results on the mechanical performance of the stretchable crystalline semiconductors
silicon and gallium nitride. The research presented has yielded the following contri-
butions and main conclusions:
(i.) Stretchable anisotropic modeling of crystalline semiconductors.
I used finite element analysis, through COMSOL Multiphysics 5.2 to evaluate the
effect of mechanical anisotropy on stretchable behavior of (0001) GaN and (100)
Si. It was determined that serpentine geometries can offer a reduction in the von
Mises peak stress by 20 to 90%, with geometries displaying strong curvature, such
as Curved Corner or Horseshoe, demonstrated improved stretchable behavior over
geometries with sharp corners. I showed (0001) GaN displays isotropic stretchable
behavior which means there is no crystallographic orientation dependence on me-
chanical behavior for GaN devices fabricated in this plane; however, (100) Si displays
strong stretchable anisotropic behavior, with the <100> orientation performing the
best. I showed this anisotropic dependence as a function of serpentine stiffness
through varying the width-to-radius ratio (0 to 0.6) can results in a 12% variation
in the tensile strain results of Rectangular serpentine structures and a 36% variation
for Curved Corner serpentine structures. At small w/r ratios both the Curved Cor-
ner and Rectangular structure could reach large strain-to-ruptures of > 100% which
is attributed to an out-of-plane buckling mode to relieve stress under strain, which
far exceeds the expected intrinsic tensile strain of Si (< 1%). At high w/r ratios it
was found these structures were confined to in-plane deformations to relieve stress
104
under strain and thus achieved lower strain-to-ruptures, however; they could still
the minimum 30% tensile strain requirement for wearable electronics. These results
then indicate that more square-like serpentine geometries display less variation in
their mechanical properties due to crystalline anisotropy than geometries with cur-
vature. Overall, mechanical anisotropy presents many challenges when fabricating
stretchable devices in (100) Si, therefore, I recommend fabrication on a (111) Si
wafer for processes requiring uniform devices, which would result in Si devices with
isotropic stretchable behavior.
(ii.) Stretchable fabrication and release process of crystalline mate-
rials. I demonstrate a micro-fabrication process which allows for the release of free
standing 2D in-plane Si serpentines, with freedom to tune many geometrical param-
eters such as serpentine amplitude, wavelength, width, and thickness. This process
is compatible with other fabrication procedures such as metal and dielectric depo-
sition, which are essential components in most device fabrication processes. With
careful optimization my process can be adapted to develop released free standing
stretchable Si device such as sensors, actuators, and solar cells, without requiring
the presence of an elastomer support. I have also proposed a modified process flow
which will allow for the release of stretchable single crystal GaN (and most III-V
materials), which will eventually be employed to fabricate free-standing stretchable
AlGaN/ GaN HEMT devices.
(iii.) In-situ stress characterization and fatigue evaluation of stretch-
able Si with micro-Raman spectroscopy. Measuring local stress/strain within
silicon micro-electronics is well known using micro-Raman spectroscopy. For the first
time, I demonstrated an application of micro-Raman spectroscopy to measure stress
within a stretchable Si Curved Corner serpentine, while applying external strain of 0
72%. With this technique, I could resolve the local non-uniform stress distribution,
with a resolution of 50 MPa, along three different locations of the Si serpentine (Am-
plitude, Bend, and Straight). For the case of a <100> Si Curved Corner serpentine
the in-situ stress measurements revealed the largest peak stress distribution were
found to concentrate in the Bend (-0.6 GPa to 1.2 GPa) which is the region which
105
undergoes the most out-of-plane buckling deformation after applying a 72% uniaxial
external strain. The minimum stress was found to concentrate along the Straight
part of the trace (-0.1 GPa to +0.25 GPa), and the amplitude ranged from (-0.15
GPa to + 0.25 GPa) after applying a 72% uniaxial external strain. I also performed
preliminary low-cycle fatigue tests showing after 0 - 15 cycles, from 0 40% the stress
varied in the Amplitude by (0.015 GPa to -0.175 GPa), in the by (0.7 GPa to 0.5
GPa (-28%), and Straight by (0.05 GPa to -0.04 GPa, -180%). These results would
need further exploration with other experiments such as X-Ray Diffraction or high-
cycle fatigue testing to draw conclusive results regarding the elastic/plastic behavior
of stretchable crystalline Si. Additionally, I demonstrated a strain-to-fracture on a
<110> Si Curved Corner serpentine at 84% which is in excellent agreement with
the FEA modeling results. While I demonstrated micro-Raman Spectroscopy stress
measurements with only Si, the methods I described could be adapted to measure
stress and evaluate fatigue with many crystalline materials which have well-defined
phonon deformation potentials, which relate stress to Raman frequency shifts.
(iv.) Stress monitoring during fabrication of stretchable AlGaN /
GaN HEMT devices using micro-Raman spectroscopy. Gallium nitride is
another material with a well-known relationship between stress and Raman fre-
quency shift of the E2(high) phonon peak. During the fabrication of Stretchable
AlGaN/ GaN high electron mobility transistors (HEMT), I applied micro-Raman
Spectroscopy as a stress monitoring technique to spatially map and resolving the sur-
face stresses of GaN devices fabricated through two different approaches: bottom-up
and top-down. First, the stress was resolved in the reference samples (as-grown ma-
terials) where 3 µm GaN on bulk sapphire had an intrinsic stress of (-1.0 GPa) while
1.5 µm AlGaN/GaN on bulk Si had an intrinsic tensile stress of (+0.29 GPa), with
respect to the literature value of unstrained bulk GaN. The first method, bottom-up
approach, creates a stretchable AlGaN/ GaN HEMT devices on a sapphire substrate
through selective area hetero-epitaxial growth. Using two-different masking mate-
rials, it was found selective area growth induced further compressive stress in the
crystal, averaging (-1.3 to -1.5 GPa) with a SiO2 mask and (-1.7 GPa) with a W
106
mask. The area measured with an W mask had no metal contact while the area
measured with the SiO2 mask contained a deposited front metal contact. I specu-
late the stress is lower in the SiO2 mask due to the metal contact inducing tensile
stress within the surface of AlGaN/ GaN crystal, resulting in an average lower mag-
nitude in stress. Lastly, I evaluated effect of removing the silicon substrate and
embedding a stretchable AlGaN/ GaN HEMT device into a stretchable substrate,
through the top-down approach. It was shown that traditional processing of the
HEMT structure onto the wafer induced (+0.5 GPa) of tensile stress within the
HEMT device while on the wafer. Further processing to undercut the structure,
encapsulate the device in silicone, and remove the Si substrate was shown to induce
an additional stress of 300 MPa average the total stress to (+0.8 GPa). Overall,
these results show micro-Raman spectroscopy is an extremely useful tool for fab-
rication processes monitoring, and characterization of stretchable GaN devices. In
the future we will explore similar measurements while straining the GaN devices,
using similar methods reported in the Si case.
107
7.2 Future Work
Future research opportunities on stretchable crystalline materials is quite fruit-
ful and expected to explode in the years to come. Raman spectroscopy is well known
as a fast, non-destructive characterization technique to measure residual and applied
stress, and monitor the local strain within crystalline semiconductors and other
materials. The work presented in this thesis demonstrated a micro-Raman Spec-
troscopy as a direct stress measurement technique while applying external strain
to stretchable single crystalline Si serpentines and as stress monitoring technique
during various stages of the production of and stretchable single crystal GaN de-
vices. While only two stretchable single crystal materials were explored in my stud-
ies, the techniques developed in this thesis can be adapted to use micro-Raman
Spectroscopy measure stress within other stretchable crystalline materials where
the phonon-deformation potential is well-known for example possible candidates in-
clude diamond and zinc-blend type semiconductors include Ge, GaAs, GaSb, InAs,
and ZnS (105). Raman can also be used to determine induced crystal stress within
polycrystalline thin films (i.e synthetic diamond films) due to growth on multiple
substrate materials (i.e alumina, tungsten carbide, SiAlON, and SiO2 glass) (106)
and can even resolve the stress dependence on the exact microcrystal shapes within
polycrystalline films (107). Additionally, Raman has been shown to measure stress
in dielectric films deposited onto crystalline semiconductor materials such as Si3N4
(74), SiO2 (86), and anatase TiO2 (108), which are thin-film materials integrated
as absorption layers in crystalline solar cells (Si and GaAs), and AlGaN/ GaN
HEMT devices. With all of the exciting material classes readily available for stress
characterization using micro-Raman Spectroscopy, the doors are wide open to use
implement this as a standard crystalline stretchable electronic technique.
The next steps to continue the studies I presented in this thesis would be
to integrate the fabrication and characterization techniques I developed to build
stretchable crystalline power and energy devices. One such device I briefly explored
with my undergrad capstone senior design team during the 2016 - 2017 school year
108
is stretchable Si photovoltaic devices. Since Si is the most brittle component in a
solar cell, this is the limiting material to produce a stretchable solar cell. We devel-
oped two fabrication approaches that allowed us to develop a Si solar cell, etched
into a stretchable serpentine geometry, with both a lateral and a vertical PN junc-
tion, as shown in Figure 7.1. While the preliminary devices we demonstrated were
stretchable solar cells patterned into single serpentine traces on the wafer, this pro-
cess could be combined with my previously described fabrication process to release
stretchable solar cells from the wafer. I would suggest characterization on a solar cell
fabricated into a traditional geometry, released from the wafer, and while stretched
under tension to determine the change in the device’s mechanical and electrical
performance under applied external strain. In addition to performance monitoring
with micro-Raman Spectroscopy, complimentary measurements would include high
resolution X-Ray diffraction to determine the change in the lattice constant spacing,
and nanoscale functional imaging with photoluminescence spectroscopy to resolve
the changes in the band-gap behavior of the device as a function of applied external
strain(109).
(A) (B)
Figure 7.1: Fabricated stretchable silicon photovoltaic devices. (A) shows a
scanning electron microscopy image of a curved corner PV on the Si wafer (B) shows
an optical image of a rectangle PV with a top metal contact.
109
7.3 Products of this Research
7.3.1 Honors and Awards
[1] Recipient of the 2018 National Science Foundation (NSF) Graduate Research
Fellowship Program (GRFP) Fellowship (April 2018)
[2] Undergraduate Finalist: National Inventors Hall of Fame Collegiate Inventors
Competition (November 2017)
[3] First Place in the U.S Army Research Labs (ARL) Sensors and Electron Devices
Directorate Summer Student Oral Presentation: Branch, Division, and Directorate
Undergraduate Winner (July 2017)
[4] Second Place Poster Award Mid-Atlantic Micro-Nano Alliance (MAMNA) Spring
2017 Symposium (April 2017)
7.3.2 Oral Presentations
[1] Micro-Raman Spectroscopy for Stress Mapping of Crystalline Stretchable Semi-
conductors S.M. Curtis, R. Tompkins, B. Nichols, I. Kierzewski, and N. Lazarus
Invited Seminar Talk University of Kiel. Kiel, Germany. December 18, 2017
[2] Effect of Mechanical Anisotropy in Silicon and Gallium Nitridde for Stretchable
Electronics S.M. Curtis, R. Tompkins, and N. Lazarus Army Research Labs Sen-
sors and Electron Devices Directorate Summer Student Competition. Adelphi, MD.
July 16-27, 2017
7.3.3 Posters
[1] Design, Fabrication, and Characterization of Stretchable Silicon Photovoltaic
Devices S.M. Curtis, H. Wang, A. Randolph, G. Anfinrud, G. Vostal, and K.
Chang. Capstone Senior Design Day 2017. University of Maryland, College Park,
MD. May 2017.
[2] Effect of Mechanical Anisotropy in Gallium Nitride and Silicon for Stretchable
Electronics S.M Curtis, H. Wang, R. Tompkins, N. Lazarus. Poster: Mid Atlantic
110
Micro-Nano Alliance (MAMNA) Spring 2017 Symposium. Johns Hopkins Applied
Physics Laboratory, Laurel, MD. April 2017.
7.3.4 Publications
[1] Growth and Characteristics of Nanostructured IrOx Films M.B Graziano, B.
Hanrahan, B. Sanchez, T. Parker, S. Curtis, M. Rivas, and P. Sunal In preparation
April 2018
111
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