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Nano-engineered devices for optical application, biomedical detection and circuit accelerator

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Nano-engineered devices for optical application, biomedical detection and circuit accelerator

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Content NANO-ENGINEERED DEVICES FOR OPTICAL APPLICATION, BIOMEDICAL
DETECTION AND CIRCUIT ACCELERATOR

by

Deming Meng

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)

December 2022

Copyright 2022 Deming Meng
ii

Dedication

To my loving family and to my love.

iii

Acknowledgements
Firstly, I would like to give my sincerely thank to my advisor Professor Wei Wu. Seven years ago,
there was only one step for me to start pursuing the Ph.D study. However, I quit and escaped. I
was confused at that time. I did not know whether research field was still a suitable way to my
future. Thanks Professor Wu. It is his patience, mentoring and knowledge to guide me to the
research field again. His curiosity to knowledge inspired my passion and supported me to finish
my Ph.D study. In addition, when facing very tricky problems, he could always give me useful
opinions and we fixed lots of problems in these years. I could not imagine what a better advisor
would be like because I think he is already the best advisor.
In addition, I should thank the rest members of my dissertation committee and my
qualifying exam committee. They are Professor Stephen Burke Cronin, Professor Aiichiro Nakano,
Professor Yong Chen, Professor Eun Sok Kim, and Professor Michelle Povinelli. Thanks for their
support and kind advice.
Furthermore, I should give my sincere thanks to my collaborators. Thanks Professor
Michelle Povinelli and Max Lien for the collaboration with the Light Sail Project. Thanks
Professor Stephen Burke Cronin for the atomic layer deposition machine to prepare Al 2O3 and
TiO2 films. Thanks Professor Fanxin Liu and Junhan Wei for their data of Raman spectroscopy.
Thanks Huandong Chen for his help of deposition of TiO2 films by sputtering. Thanks Professor
Yong chen for the discussion about the feasibility of ultra-high resolution 3-D printing project.
These excellent researchers shared their professional experience with me and helped me a lot in
my Ph.D study. I broadened my vision and got the knowledge from you. Without your help, my
Ph.D study would be much more tough.
iv

I would like to thank my labmates during my Ph.D study. Thanks Yifei Wang for his
guidance on my experiments at the start point of the research study. Thanks Zerui Liu for the
collaborations on Light sail project, AMI fast warning project and circuit accelerator for Boolean
Satisfiability project. Thanks He Liu, Yuhan Yao, Yuanrui Li, Boxiang Song, Hao Yang, Buyun
Chen, Yunxiang Wang, Pan Hu, Tse-Hsien Ou and Sushmit Hossain for their support and help in
my Ph.D study and daily life. I am so lucky to be a friendly group in these years. All the
achievements I got during my Ph.D study include your collaboration and contributions.
Also, I would like to thank my friends in my daily life. They are but not limited to Boxiang
Song, Hongpeng Duan, Yihao Wang, Siteng Wang, Xubo Gu, Heng Wei, Qitao Cao and Yihao
Chen. They gave me their kind help in the study and the daily life. Thanks them to make me a have
a wonderful memory during my Ph.D life.
Finally, and the most important, I should thank my parents for their supporting and endless
love. They are the most important people to me in this world and I am so happy to be one of the
members in this family. Thank my parents to allow me to find which field I would like to pursue
in the future even though I have taken so many wrong turns. Thanks my wife Yichen Gong. It’s
your accompaniment and supporting to make me not alone here. Without your patience and love,
I would not get all the achievements today.

v

Abstract
This dissertation summarized four projects in my Ph.D study. The focus is nano-engineered
devices for optical application, biomedical detection and circuit accelerator.
The first part (chapter 1-6) is about Optical metrology of characterizing wetting states. The
unique properties of superhydrophobic surfaces have already been widely introduced into many
applications and play a more and more important role in our daily life. However, different wetting
states will lead to different properties and performances so that distinguishing the wetting states is
essential. Until now, as it lacks an accurate and nondestructive technology to test the wetting states
in real time, this prevents the study of superhydrophobic phenomena and their applications.
Although this has already caught the attention of the scientific community, there is still no
successful solution presented yet. Here, we develop a nondestructive in situ optical technology
based on characterizing the transmission spectrum of the superhydrophobic surfaces, which is
capable of distinguishing the different wetting states such as the Cassie–Baxter state, the mixed
wetting state, and the Wenzel state. By using the finite-difference time-domain method, field
distribution and transmission spectrum of the superhydrophobic surfaces can be simulated. The
experimental data fit well with simulation data. All the results prove the feasibility of the new
optical technology to characterize wetting states.
The second part (chapter 7-13) is about Experimental characterization of a silicon nitride
photonic crystal light sail. The Breakthrough Starshot Initiative, established in 2016, aims to propel
an ultralightweight spacecraft to Alpha Centauri using radiation pressure from a high-power,
ground-based laser. Nanopatterned silicon nitride has been proposed as a candidate material for
the laser sail. In this work, we design and fabricate a silicon nitride photonic crystal with high
vi

reflectivity around a laser wavelength of 1064 nm. We demonstrate the ability to shift the resonant
features of the laser sail using titanium dioxide coatings and increase the longwave infrared
emissivity using polymer coatings. We also characterize the response of the sail to temperature
and optical power.
The third part (chapter 14-17) is about Ultrafast Early Warning of Heart Attacks through
Plasmon-Enhanced Raman Spectroscopy Using Collapsible Nanofingers and Machine Learning.
As the leading cause of death, heart attacks result in millions of deaths annually, with no end in
sight. Early intervention is the only strategy for rescuing lives threatened by heart disease.
However, the detection time of the fastest heart-attack detection system is >15 min, which is too
long considering the rapid passage of life. In this study, a machine learning (ML)-driven system
with a simple process, low-cost, short detection time (only 10 s), and high precision is developed.
By utilizing a functionalized nanofinger structure, even a trace amount of biomarker leaked before
a heart attack can be captured. Additionally, enhanced Raman profiles are constructed for
predictive analytics. Five ML models are developed to harness the useful characteristics of each
Raman spectrum and provide early warnings of heart attacks with >98% accuracy. Through the
strategic combination of nanofingers and ML algorithms, the proposed warning system accurately
provides alerts on silent heart-attack attempts seconds ahead of actual attacks.
The fourth part (chapter 18-21) is about circuit accelerator for Boolean Satisfiability.
Boolean Satisfiability (SAT), a most common NP-Complete problem, shows plenty of applications
in the research, industry, and daily life. Each category of NP-complete problem can be transferred
to another category of NP-complete problem in polynomial time. Accelerating the SAT problem
solving time means that accelerate the whole class of NP-complete problem solving time. However,
the exiting methods are still not power enough because when the size of SAT increases, the
vii

complexity grows exponentially. Here, our group proposed a hardware circuit accelerator for SAT
problem, which could transform the SAT equation to a circuit. Under this situation, solving the
SAT problem is equal to solving an optimization problem. In addition, our circuit is a dynamic
circuit, which means that it will forbid to get stuck in the local minima during the search, which
will greatly improve our circuit performance and accelerate the solving time. Our results show that
when variable increases, the solving time grows with polynomial but not exponential time, which
shows a great way to solve the large size SAT problem.

viii

Table of Contents
Dedication ...................................................................................................................................... ii
Acknowledgements ....................................................................................................................... iii
List of Tables ................................................................................................................................ xii
List of Figures .............................................................................................................................. xiii
Abstract ...................................................................................................................................... xxii

Topic 1: Optical Metrology of Characterizing Wetting States ....................................................... 1
Chapter1 Introduction ............................................................................................................... 2
1.1 Wetting States on the Superhydrophobic Surfaces........................................................ 2
1.2 Existing Methods to Characterize Wetting States on the Superhydrophobic Surfaces. 3
Chapter 2 Design of Optical Technology to Characterize the Wetting States........................... 6
2.1 Fundamental Principles of the Optical Technology ..................................................... 6
2.2 Numerical Calculations of the Optical Technology....................................................... 6
Chapter 3 Fabrication of the Superhydrophobic Surfaces........................................................ 10
Chapter 4 Experimentally Characterization the Wetting States............................................... 13
4.1 Experimental Setup and Realization of Different Wetting States ............................... 13
4.2 Optical measurements of Different Wetting States...................................................... 15
Chapter 5 Comparison with the Traditional Characterization Method and Wide Application
Scenario................................................................................................................................... 18

5.1 Comparison with Contact Angle Characterization....................................................... 18
5.2 Application Conditions of this Optical Technology..................................................... 19
5.3 Restriction of this Optical Technology........................................................................ 22
Chapter 6 Summary................................................................................................................. 24
ix

Topic 2: Experimental Characterization of a Silicon Nitride Photonic Crystal Light Sail............ 25
Chapter 7 Introduction ............................................................................................................ 26
7.1 Introduction to the Light Sail....................................................................................... 26
7.2 Introduction to the Breakthrough Starshot Initiative.................................................... 26
Chapter 8 Design of Light Sail................................................................................................ 28
8.1 Concept of the Light Sail.............................................................................................. 28
8.2 Parameter of the Light Sail........................................................................................... 29
Chapter 9 Fabrication of Light Sail.......................................................................................... 31
Chapter 10 Characterization of Light Sail................................................................................ 33
10.1 Reflection Characterization of Bare and Patterned silicon nitride Light Sail............ 33
10.2 Comparison of the Simulated Data and Experimental Data....................................... 35
10.3 Tuning Resonance by Coating Films......................................................................... 37
10.4 Thermal Properties of the Light Sail.......................................................................... 39
10.5 Increase Emissivity at Mid- and Long-Wave Infrared............................................... 40
10.6 Characterization of Input-Output Power Dependence............................................... 42
Chapter 11 Optical Setup of Characterization ......................................................................... 43
11.1 Optical Setup in the Reflectance and Transmittance Characterization...................... 43
11.2 Optical Setup in the Input-Output Power Relationship Characterization................... 44
Chapter 12 Calculation of Acceleration Distance.................................................................... 45
Chapter 13 Summary............................................................................................................... 46

Topic 3: Ultrafast Early Warning of Heart Attacks through Plasmon-Enhanced Raman
Spectroscopy Using Collapsible Nanofingers and Machine Learning........................................... 47
x

Chapter 14 Introduction .......................................................................................................... 48
14.1 Introduction to Acute Myocardial Infarction............................................................. 48
14.2 Prevailing Diagnosis Methods of Acute Myocardial Infarction................................. 48
14.3 Detect BNP Biomarker to Diagnose Acute Myocardial Infarction........................... 49
Chapter 15 Device Fabrication and Diagnosis Procedures...................................................... 52
15.1 Nanofinger Platform Fabrication............................................................................... 52
15.2 Human Serum Sampling............................................................................................ 55
15.3 Raman Data Collection.............................................................................................. 57
Chapter 16 Classification Results by Machine Learning......................................................... 58
16.1 Raman Spectra of the Serum...................................................................................... 58
16.2 Decision Tree Model and Random Forest Model...................................................... 59
16.3 K-nearest Neighbor Model........................................................................................ 61
16.4 Support Vector Machine............................................................................................ 63
16.5 Voting Classifier........................................................................................................ 65
16.6 Performance Evaluation............................................................................................ 66
Chapter 17 Summary............................................................................................................... 70

Topic 4: Circuit Accelerator for Boolean Satisfiability Problem.................................................. 71
Chapter 18 Introduction .......................................................................................................... 72
18.1 Boolean Satisfiability Problem.................................................................................. 72
18.2 Hardware Accelerator................................................................................................ 73
Chapter 19 Architecture and Fundamental Principles of the SAT Problem Accelerator......... 77
19.1 Architecture of the SAT Problem Accelerator........................................................... 77
xi

19.2 Fundamental Principles of the SAT Problem Accelerator......................................... 79
19.3 Algorithm of the Random Switch Function............................................................... 79
Chapter 20 Performance and Optimization of the Circuit Accelerator.................................... 86
20.1 Simulation Results by LTspice.................................................................................. 86
20.2 Simulation Results by Cadence.................................................................................. 91
20.3 Optimization of the Circuit Accelerator..................................................................... 94
20.4 Pseudorandom Random and Solving Rate................................................................. 98
20.5 Average Time Versus Variable Size Fitting............................................................. 100
Chapter 21 Summary............................................................................................................. 107
References .................................................................................................................................. 108
Appendix A: Publications & Patents ........................................................................................... 127
Appendix B: Code of Auto Generation Circuit by Cadence......................................................... 129

xii

List of Tables
Table 12.1: Total Mass mT and Acceleration Distance D for Four Light Sail Designs................. 45
Table 20.1: SPICE simulation results under different initial states................................................ 87
Table 20.2: Solved cases and average calculation time under different sampling rates................. 97
Table 20.3: Solving time for different equations with 100 variables............................................. 99
Table 20.4: Fitting performance of Linear fit, Polynomial Fit and Exponential Fit..................... 104

xiii

List of Figures
Figure 1.1: Schematics of three different wetting states. (a) Cassie–Baxter state. (b) Mixed
wetting state. (c) Wenzel state......................................................................................................... 3
Figure 2.1: Electric field distribution (cross-sectional view) of three different wetting states at
340 nm........................................................................................................................................ 7
Figure 2.2: Liquid-gas boundary on top of 2D-gratings of different wetting states........................ 8
Figure 2.3: Transmission spectra of the Cassie–Baxter state, the mixed wetting state, and the
Wenzel state.................................................................................................................................... 9
Figure 3.1: Flow chart of the fabrication process........................................................................... 10
Figure 3.2: Structure of two-dimensional gratings. ....................................................................... 11
Figure 3.3: SEM images of fabricated two-dimensional gratings.................................................. 12
Figure 4.1: Surface tension coefficient vs ethanol concentration in ethanol water solution.......... 14
Figure 4.2: The experimental setup used for the transmission spectrum measurements................ 15
Figure 4.3: Transmission spectra of superhydrophobic surfaces covered by different surface
tension coefficient liquid............................................................................................................... 16
Figure 4.4: Wetting states relationship with transmittance............................................................ 17
Figure 5.1: (a) Optical image of ethanol water solution on the superhydrophobic surfaces in
the Cassie–Baxter state. (b) Optical image of ethanol water solution on the superhydrophobic
surfaces in the mixed wetting state................................................................................................ 19
Figure 5.2: Electric field distribution of the Cassie–Baxter state, the mixed wetting state, and
The Wenzel state, transmission/reflection spectra and nanostructures.......................................... 22
Figure 8.1: Depiction of the Starshot sail being accelerated by an Earth-based laser array........... 29
Figure 8.2: Silicon nitride photonic crystal laser sail design.......................................................... 30
xiv

Figure 9.1: SEM image of the fabricated Si3N4 photonic crystal................................................... 32
Figure 10.1: Measured transmittance T and calculated reflectance R= 1 – T of a bare Si3N4
membrane...................................................................................................................................... 34
Figure 10.2: Measured transmittance and calculated reflectance of Si3N4 light sail and bare
Si3N4 membranes........................................................................................................................... 35
Figure 10.3: Simulated reflectance of the Si3N4 light sail from FDTD calculations compared to
measured values............................................................................................................................ 36
Figure 10.4: Simulated and measured transmittance of the Si3N4 light sail.................................. 37
Figure 10.5: (a) Measured transmittance of the Si3N4 light sail before and after applying a 10 nm
thick layer of TiO2. (b) Reflectance (R = 1 - T) of the Si3N4 light sail before and after applying a
10 nm thick layer of TiO2. Simulated transmittance (c) and reflectance (d, R = 1- T) of the Si3N4
light sail before and after applying a 10 nm thick layer of TiO2.................................................... 38
Figure 10.6: Transmittance spectra of the (a) uncoated and (b) coated Si3N4 light sails at
23.5° C and 80° C............................................................................................................................ 39
Figure 10.7: (a) NIR Transmittance of the Si3N4 light sail and (b) Mid- and long-wave infrared
emissivity (E = 1 - T - R) of the Si3N4 photonic crystal after spin-coating on different thickness
of PDMS layers............................................................................................................................. 41
Figure 10.8: (a) Transmittance spectrum of the uncoated Si3N4 light sail’s resonance at 1306 nm.
(b) Measured input-output power dependence of the light sail at 1306 nm with a fitted linear
curve.............................................................................................................................................. 42
Figure 11.1: Optical setup for NIR transmittance and reflectance measurements......................... 43
Figure 11.2: Optical setup for measuring the input-output power dependence of the light sail at
1306 nm......................................................................................................................................... 44
xv

Figure 14.1: Schematic of the SERS-based platform using collapsed nanofingers to acquire
Raman spectra for ML-driven identification and early intervention of heart attacks..................... 51
Figure 15.1: (a) Numerical simulation of the electric-field enhancement of collapsed
nanofingers. (b) TEM image of the nanogap between the nanofingers and energy-dispersive
X-ray spectroscopy (EDS) mapping of Au in the TEM image. (c) SEM image of nanofingers
after collapse.................................................................................................................................. 53
Figure 15.2: Fabrication process for functionalizing nanofingers.................................................. 55
Figure 16.1: (a, b) Raman signals of serum from healthy individuals collected by the nanofinger
platform. (c, d) Raman signals of the serum collected before the onset of a heart attack.............. 59
Figure 16.2: Normalized confusion matrices of (a) well-trained personnel, (b) the DT, (c) the
SVM, (d) the KNN classifier, (e) the random forest classifier, and (f) the voting classifier.......... 67
Figure 16.3: 10-fold cross-validation of five classifiers: (a) DT; (b) random forest; (c) SVM;
(d) KNN classifier; (e) voting classifier. (f) Average accuracies of 10-fold cross-validation for
the five models............................................................................................................................... 69
Figure 19.1: Schematic of the circuit accelerator........................................................................... 78
Figure 19.2: Original schematic of the circuit accelerator............................................................. 80
Figure 19.3: The circuit implement a simple 2-SAT problem of (X1 ⋁ X2) ⋀ (X1 ⋁ ¬X2) ⋀ (¬X1
⋁ X2) = True................................................................................................................................... 81
Figure 19.4: (a) Karnaugh map of the X1, X2, X3 and X4. (b) Flow charts of flipping all the
literals in only one unsatisfied clause. (c) Flow charts of flipping all the literals in all the
unsatisfied clauses......................................................................................................................... 83
Figure 19.5: (a) Flow charts of flipping only one of the literals in only one unsatisfied clause.
(b) Flow charts of flipping only one of the literals in all the unsatisfied clauses........................... 84
xvi

Figure 19.6: Circuit of clause-logic block using SPICE simulation.............................................. 85
Figure 20.1: SPICE simulation of circuit accelerator for solving Equation 20.1........................... 86
Figure 20.2: SPICE simulation results of Equation 20.1................................................................ 87
Figure 20.3: SPICE simulation results of Equation 20.2................................................................ 88
Figure 20.4: SPICE simulation of circuit accelerator for solving Equation 20.3........................... 90
Figure 20.5: SPICE simulation results of Equation 20.3................................................................ 91
Figure 20.6: Schematic of the random switch function in Cadence.............................................. 92
Figure 20.7: Cadence simulation of circuit accelerator for solving Equation 20.3....................... 93
Figure 20.8: Cadence simulation results of Equation 20.3............................................................. 94
Figure 20.9: Cadence results with 0.1ns sampling rate.................................................................. 95
Figure 20.10: (a) Cadence results with 0.5ns sampling rate. (b) Cadence results with 1ns
sampling rate................................................................................................................................. 96
Figure 20.11: (a) - (i) show the Cadence simulation results from 20 variables to 250 variables....103
Figure 20.12: (a) - (i) show the histograms of the simulation results from 20 variables to
250 variables................................................................................................................................ 104
Figure 21.13: Average calculation time versus variable size relationship. (a) Linear Fit. (b)
Polynomial Fit. (c) Exponential Fit.............................................................................................. 105

1

Topic 1
Optical Metrology of Characterizing Wetting States

2

Chapter 1 Introduction
1.1 Wetting States on the Superhydrophobic Surfaces
It has been widely reported that superhydrophobic surfaces can be produced by introducing
roughness onto the hydrophobic surfaces
1-7
. Superhydrophobic surfaces have been widely used in
many applications due to the unique properties such as water repellency, scratch resistance, and
self-cleaning and play a more and more important role in our daily life. There are several states of
the liquid on the superhydrophobic surfaces. Besides the Cassie–Baxter state
8
and the Wenzel
state
9
, the mixed wetting state
10-13
still exists between the Cassie–Baxter state and the Wenzel state
(as shown in Fig. 1.1). The fundamental difference among the different wetting states is that the
liquid will penetrate into different regions of the superhydrophobic surfaces. The liquid will stand
on top of the surface without penetration in the Cassie–Baxter state (Figure 1.1(a)). The liquid will
penetrate into half of the superhydrophobic surfaces in the mixed wetting state (Figure 1.1(b)).
The liquid will cover all the superhydrophobic surfaces in the Wenzel state (Figure 1.1(c)).
3

Figure 1.1: Schematics of three different wetting states. (a) Cassie–Baxter state. Liquid stands on
the superhydrophobic surface. (b) Mixed wetting state is between the Cassie–Baxter state and the
Wenzel state. (c) Wenzel state. No air is trapped between the liquid and superhydrophobic surface.

1.2 Existing Methods to Characterize Wetting States on the Superhydrophobic
Surfaces
Different states will lead to totally different properties so that distinguishing the state is essential.
For example, electrowetting has already been a widely used tool for our daily life such as
electrowetting display
14-17
, lab-on-chip liquid modulation
18, 19
, and adaptive focus lens
20-24
.
Meanwhile, electrowetting is hardly fully reversible on superhydrophobic surfaces
25
. For instance,
a study by Barberoglou et al.
26
used electrowetting to tune the droplet on superhydrophobic
surfaces. The contact angle could change from 151° to 108° then back to 140° . Under this situation,
they reached the conclusion that the droplet changed from the Cassie–Baxter state to the mixed
4

wetting state then came back to the Cassie–Baxter state. However, they could not explain why the
contact angle of the droplet has an 11° difference between the initial Cassie–Baxter state and the
final Cassie–Baxter state. In addition, testing the contact angle of the droplet is the most popular
method to judge the wetting states in the scientific community, which is not accurate enough and
may even be misleading. For example, a study by Lafuma and Qué ré
7
reported that the contact
angle itself cannot indicate the wetting states accurately. When the contact angle θ on the flat
surface is 90° < θ < θc, the droplet is often in the Wenzel state and when the contact angle θ on the
flat surface is θ > θc, the droplet is often in the Cassie–Baxter state [θc is defined by cos θc = (ws −
1)/(r − ws), where r is defined as the ratio of the actual over the apparent surface area of the
substrate and ws is defined as the fraction of solid in contact with the liquid]. However, they also
reported that sometimes even though the contact angle on flat surface θ is 90° < θ < θc, the droplet
is still on the Cassie–Baxter state.
Recently, more methods were invented to characterize the wetting states based on the
advanced technologies; however, some deficiencies in them still exist. Jones et al.
27
combined
cryogenic focus ion beam milling and SEM imaging to characterize the wetting states. However,
this process is not nondisruptive, which limits the applications of this technology. Ahmmed and
Kietzig
28
reported using the confocal laser scanning microscope with immersion lens to acquire
the air-water interface on the pattern surfaces. However, this technology is limited by the optical
resolution. When the patterns substrate roughness is smaller than several hundred nanometers,
wetting states can no longer be distinguished based on this technology.
Until now, no technology with properties such as in situ, nondestructive, accurate, and high
resolution has been invented, which introduces huge difficulties in the superhydrophobic surfaces
research and applications. Many researchers such as Jeevahan et al.
29
and Voronov et al.
30
pointed
5

out that better methods to gauge the wetting states on the superhydrophobic surfaces are essential.
Here, we developed an optical technology to characterize the state of superhydrophobic surfaces.

6

Chapter 2 Design of Optical Technology to Characterize the Wetting
States
2.1 Fundamental Principles of the Optical Technology
The nondestructive and accurate optical technology was invented based on the different wetting
states that could have different optical responses with the superhydrophobic surfaces. The
fundamental difference among the different wetting states is that the liquid will penetrate into
different regions of the superhydrophobic surfaces. The liquid will stand on top of the surface
without penetration in the Cassie–Baxter state (Figure 1.1(a)). The liquid will penetrate into half
of the superhydrophobic surfaces in the mixed wetting state (Figure 1.1(b)). The liquid will cover
all the superhydrophobic surfaces in the Wenzel state (Figure 1.1(c)). To realize nondestructive
and in situ characterization, the optical approach will be the perfect choice. However, the
differences among the various wetting states are very subtle, which means that only the liquid-gas
boundary will have a subtle difference. Even the difference is very small, if an optical mode
sensitive to the liquid-gas boundary exists, this small difference will produce obvious optical
effects.
2.2 Numerical Calculations of the Optical Technology
Here, the two-dimensional gratings will be used as examples. The wavelength range of
spectrum will be chosen based on the optical mode to make the optical properties very sensitive to
the environment refractive index changing in gaps, and hence a great tool to detect those states.
The two-dimensional gratings are made of silicon nitride. The pitch of the two-dimensional
gratings is set to be 390 nm. Both the length and the width of the two-dimensional gratings are 140
7

nm. The height is 500 nm. Beneath the two-dimensional gratings is a 500 nm thick silicon nitride
layer. All the structures are on top of a glass substrate. As the state changes, the optical response
will change because the change in the refractive index in gaps affects the optical mode. By using
the finite-difference time-domain (FDTD) method, field distribution and transmission spectrum of
the superhydrophobic surfaces can be simulated. Figure 2.1 shows the electric field distribution of
the Cassie–Baxter state, the mixed wetting state, and the Wenzel state at 340 nm. A great difference
in the optical mode can be observed.

Figure 2.1: Electric field distribution (cross-sectional view) of three different wetting states at
340 nm. White line shows the boundary of liquid and gas. From left to right: Cassie–Baxter state,
mixed wetting state, and Wenzel state.

As the liquid penetrates deeper into the gap of the two-dimensional gratings, the refractive
index surrounding the two-dimensional gratings will increase. The region of liquid-gas boundary
(Figure 2.2) will influence the optical modes in the two-dimensional gratings. In the Cassie–Baxter
state, field distribution will be more concentrated in the two-dimensional gratings due to the high
8

refractive index contrast inside and outside of the two-dimensional gratings. In the Wenzel state,
as the liquid will cover the two-dimensional gratings and no air will be trapped between the gap
of the two-dimensional gratings, the refractive contrast of the gratings and the gap will be much
smaller than the Cassie–Baxter state. Under this situation, the electrical field will span much wider
over the two-dimensional gratings compared with the Cassie–Baxter state. The electrical field
distribution of the mixed wetting state will be between the Cassie–Baxter state and the Wenzel
state.

Figure 2.2: Liquid-gas boundary on top of two-dimensional gratings of different wetting states.

9

To realize the nondestructive and real-time monitoring function, testing the transmission
spectrum is the most convenient method. As the optical modes are different when the states change,
the transmittance will have significant differences among the three wetting states. The target
wavelength range is set near the optical mode that we are interested in, which amplifies the optical
response. Here, we consider only the 0th order diffraction because only 0
th
of order diffraction is
collected by our detector. Figure 2.3 shows the simulation results of 0
th
order diffraction
transmission spectrum of the Cassie–Baxter state, the mixed wetting state, and the Wenzel state.
The simulation results of the Cassie–Baxter state, the Wenzel state, and the mixed wetting state
show that the design goal has been successfully achieved: optical responses at 340 nm wavelength
are very sensitive to the different wetting states, producing a huge difference in optical
characteristics.

Figure 2.3: Transmission spectra of the Cassie–Baxter state, the mixed wetting state, and the
Wenzel state.

10

Chapter 3 Fabrication of the Superhydrophobic Surfaces
The two-dimensional nano grating fabrication process is aggregated in Figure 3.1. The mother-
molds were fabricated by interference lithography
17
. After the mother-molds were fabricated, the
two-dimensional polydimethylsiloxane (PDMS)-based soft molds
31
were duplicated from the
mother-molds. 1 μm silicon nitride was grown on top of the glass substrate by the plasma etching
chemical vapor deposition process. A layer of lift-off underlayer (I-ULP, EZImprinting Inc.) was
spin-coated on top of the silicon nitride, then baked as a lift-off layer. The patterns on the mold
were transferred onto the UV-NIL resist (I-UVP, EZImprinting Inc.) layer spin-coated on top of
the lift-off underlayer by nanoimprint using the two-dimensional PDMS soft molds. After the
reactive ion etching process, metal deposition, and lift-off process, the two-dimensional metal
mask was formed.

Figure 3.1: Flow chart of the fabrication process.

11

After etching 500 nm silicon nitride and removing the metal mask, the final two-
dimensional gratings were fabricated, as shown in Figure 3.2.

Figure 3.2: Structure of two-dimensional gratings. [Pitch: 390 nm. Width:140 nm. Height of
silicon nitride (green rectangular pillar) gratings: 500 nm. Substrate: 500 nm silicon nitride on
top of silicon dioxide.]

A self-assembled monolayer (tridecafluoro-1,1,2,2-tetrahydrooctyl) was coated on the
surface of the two-dimensional gratings as the hydrophobic treatment. An SEM image of
fabricated two-dimensional gratings is shown in Figure 3.3.
12

Figure 3.3: SEM images of fabricated two-dimensional gratings. The Inset image is the zoom-in
view. Scale bars of the zoom-out and zoom-in images are 1 μm and 250 nm.

13

Chapter 4 Experimentally Characterization the Wetting States
4.1 Experimental Setup and Realization of Different Wetting States
We experimentally verified the optical method by putting various liquids with different surface
tension coefficients and same refractive index coefficients onto the superhydrophobic surfaces,
then observe the optical responses. Liquid with different surface tension coefficients may lead to
different states on the superhydrophobic surfaces. After getting the different wetting states on the
superhydrophobic surfaces, transmission spectra are used to characterize the optical responses.
Different states were achieved by controlling the surface tension of the liquid. By tuning
the concentration of ethanol in water solution, we can tune surface tension (Figure 4.1) without a
significant change in the refractive index
32
, and hence realize different states on superhydrophobic
surfaces.
14

Figure 4.1: Surface tension coefficient vs ethanol concentration in ethanol water solution.

The optical setup is shown in Figure 4.2. The transmission spectra were measured with an
Ocean Optics USB4000 spectrometer.
15

Figure 4.2: The experimental setup used for the transmission spectrum measurements.

Chapter 4.2 Optical measurements of Different Wetting States
Figure 4.3 shows the transmission spectra of superhydrophobic surfaces covered by different
surface tension coefficient liquid. As compared with Figure 2.3, solution with a surface tension
coefficient larger than 48.14 mNm
−1
fits well with the Cassie–Baxter state simulation curve;
solution with surface tension coefficient smaller than 38.56 mNm
−1
has the same trend as the
Wenzel state simulation curve; solution with surface tension coefficient between 38.56 and 48.14
mNm
−1
is similar to the mixed wetting state simulation curve (as shown in Figure 4.4). The
difference between the simulation results and the experimental results may come from the
fabrication defects and the surface roughness of the sample. If a more quantitative result is needed,
the surface roughness should be considered in the simulation
33
. The consistency between the
16

experimental transmission spectra and the theoretical results proves the feasibility of
characterizing different wetting states on the superhydrophobic surfaces.

Figure 4.3: Transmission spectra of superhydrophobic surfaces covered by different surface
tension coefficient liquid.
17

Figure 4.4: Wetting states relationship with transmittance.

18

Chapter 5 Comparison with the Traditional Characterization
Method and Wide Application Scenario
5.1 Comparison with Contact Angle Characterization
Figures 5.1 (a) and (b) show the different concentrations of ethanol in water solution on the
superhydrophobic surfaces. To be noted, the surface tension coefficient of the ethanol in water
solution is smaller than pure water, as shown in Figure 4.1. As the liquid is ethanol in water
solution but not water, the contact angle can be much smaller than 150° when the wetting state
still keeps in the Cassie–Baxter state
34
. The contact angle of Figure 5.1(a) was measured as 111°
and it was in the Cassie–Baxter state. The contact angle of Figure 5.1(b) was measured as 108°
and it was in the mixed wetting state. The contact angle was measured with a sessile droplet of
15μl dispersed on the test surface, and the captured image was further measured using IMAGEJ
software
35
to obtain an accurate value of the stationary contact angle. First, if the contact angle is
only 111° , it is easy to be misunderstood to be the Wenzel state rather than the Cassie–Baxter state
by traditional contact angle characterization. In addition, the difference in the contact angle
between the Cassie–Baxter state and the mixed wetting state is only 3° as shown in Figure 5.1(a)
and Figure 5.1(b). Considering the inaccuracy of image capture, boundary selection, and software
fitting, only using contact angle to detect wetting states is very hard and challenging under a small
contact angle difference. However, using our novel optical technology can easily distinguish the
different wetting states.

19

Figure 5.1: (a) Optical image of ethanol water solution on the superhydrophobic surfaces in the
Cassie–Baxter state. (b) Optical image of ethanol water solution on the superhydrophobic surfaces
in the mixed wetting state.

Although using the contact angle to judge wetting states is not accurate, most researchers
26,
31, 36-45
used it to determine whether the droplet is reversible or irreversible in electrowetting on
superhydrophobic surface experiments because it is the only nondestructive and in situ method
before this paper. In addition, many reasons could lead to droplet irreversible in the electrowetting
on superhydrophobic surfaces such as droplet remaining in the Wenzel state, electrical charge
trapped in the hydrophobic treatment layer, and dielectric layer breaking down by voltage. If this
new optical technology can be applied into electrowetting on superhydrophobic surfaces
experiment, it will be a better choice to real-time monitor the droplet state without any disturbances
on the system when applying the voltage, which help the scientific community understand the
process more clearly and get the state more precisely.

5.2 Application Conditions of this Optical Technology
Although two-dimensional gratings were chosen as the example to illustrate this new optical
technology, this optical technology can be applied to a wide range of periodical structures with
varied materials, dimensional parameters, and spatial structures as long as suitable optical modes
20

can be chosen. The optical modes can be influenced when the refractive index of the environment
changes. The more sensitive the optical modes are to the environment between structures, the more
obvious optical responses we can detect in the experiments. To illustrate the process, the following
four examples with four different structures are shown. Figure 5.2(a) shows a type of metasurfaces
designed for an electrowettting-based full-color reflective display
17, 33, 46
. The metasurfaces were
fabricated using silicon dioxide and titanium dioxide. Figure 5.2(b) shows conical gratings
47, 48

made by silicon nitride on top of the silicon dioxide substrate. Figure 5.2(c) shows cylindrical
gratings which the scientific community
49, 50
usually uses to build superhydrophobic surfaces.
Figure 5.2(d) shows a mushroom structure that is popular in a recent superhydrophobic study
51-53
.
Although the structures are totally different among the four examples, optical modes sensitive to
the environment of the structure can be found, respectively, at various wavelengths. As shown in
Figure 5.2(a)-(d), the transmittance of different wetting states will have huge differences at 514,
524, 432, and 550 nm, respectively. The more the optical mode is sensitive to the refractive index
of the environment, the more obvious responses can be achieved in characterization. High-contrast
gratings are very sensitive to the refractive index of the environment. The electrical field (Figure
5.2(a)) will mainly be concentrated in the titanium dioxide region because of the high refractive
index contrast between titanium dioxide and the air under the Cassie–Baxter state. When the liquid
penetrates into the gap, the optical modes will dramatically change because the refractive index
contrast decreases. The optical modes changing will result in a big transmittance spectra difference
among the Cassie–Baxter state, the mixed wetting state, and the Wenzel state. In contrast, the
electrical field of silicon nitride conical structures (Figure 5.2(b)) will mainly be concentrated in
the base silicon nitride region under the Cassie–Baxter state and the mixed wetting state. The
electrical field distribution will make the optical modes change drastically when the liquid contacts
21

the base silicon nitride region. The optical responses will be more sensitive between the Wenzel
state and the mixed wetting state rather than the Cassie–Baxter state and the mixed wetting state
under this optical mode. Previous results show that transmission spectra can be a perfect tool to
characterize the wetting states on the transparent substrate. When the substrate is not transparent,
using reflection spectra can also characterize the wetting states. Figure 5.2(e) shows silicon
cylindrical gratings on top of the silicon substrate. The reflectance of different wetting states shows
a huge difference at 540 nm, which proves the feasibility of this optical technology applied to
opaque substrates.

22

Figure 5.2: (a) Electric field distribution of the Cassie–Baxter state, the mixed wetting state, and
the Wenzel state (from left to right) at 514 nm spectra and structure of high-contrast gratings.
[Pitch: 460 nm. Width:230 nm. Height of titanium dioxide gratings (purple rectangular pillar): 200
nm. Height of silicon dioxide gratings (gray rectangular pillar under titanium dioxide pillar): 300
nm. Substrate: silicon dioxide.] (b) Electric field distribution of the Cassie–Baxter state, the mixed
wetting state, and the Wenzel state (from left to right) at 524 nm, transmission spectra and structure
of conical gratings. [Pitch: 460 nm. Height of silicon nitride cone (green cone): 500 nm. Radius of
cone: 125 nm. Substrate: 500 nm silicon nitride on top of silicon dioxide.] (c) Electric field
distribution of the Cassie–Baxter state, the mixed wetting state, and the Wenzel state (from left to
right) at 432 nm, transmission spectra and structure of cylindrical gratings. [Pitch: 500 nm. Height
of titanium dioxide cylinder (purple cylinder): 500 nm. Radius of titanium dioxide cylinder (purple
cylinder): 125 nm. Substrate: silicon dioxide.] (d) Electric field distribution of the Cassie–Baxter
state, the mixed wetting state, and the Wenzel state (from left to right) at 550 nm, transmission
spectra and structure of mushroom-like gratings. [Pitch: 500 nm. Radius of titanium dioxide
(purple hemisphere): 150 nm. Radius of silicon dioxide cylinder (gray cylinder): 100 nm. Height
of silicon dioxide cylinder (gray cylinder): 350 nm. Substrate: silicon dioxide.] (e) Electric field
distribution of the Cassie–Baxter state, the mixed wetting state, and the Wenzel state (from left to
right) at 540 nm, reflection spectra and structure of cylindrical gratings. [Pitch: 500 nm. Height of
silicon cylinder (lavender cylinder): 500 nm. Radius of silicon cylinder: 125 nm (lavender
cylinder). Substrate: silicon.]

5.3 Restriction of this Optical Technology
However, there are still some restrictions when applying this optical technology. The optical
technology can only be applied on the periodical structures, and the wavelength has to be in the
23

visible light range. If the structure is not periodical, different regions of the structure will have
different optical modes at different wavelengths, the peaks will be averaged out during optical
characterization. If the wavelength range goes out of the visible light range, the water will become
a highly light-absorbing material and the optical responses will be much more weaken under these
wavelengths.

24

Chapter 6 Summary
We developed a novel in situ, nondestructive optical technology to characterize the different states
of superhydrophobic surfaces and proved the feasibility of this technology. By choosing the
optimized optical modes and characterizing the transmission spectra, the Cassie–Baxter state, the
mixed wetting state, and the Wenzel state can be easily distinguished. This new optical technology
will open a door to deepen understanding of the wetting states in research and pave the way for
making superhydrophobic-based applications more easily.

25

Topic 2
Experimental Characterization of a Silicon Nitride Photonic Crystal
Light Sail

26

Chapter 7 Introduction
7.1 Introduction to the Light Sail
Analogous to a sailboat being accelerated by the momentum of wind, a light sail is accelerated by
the momentum of photons. The concept of light sailing is not new: spaceflight pioneers Konstantin
Tsiolkovsky and Friedrich Zander hypothesized using radiation pressure from photons to propel a
spacecraft in 1924
54
. In the last half-century, efforts to experimentally demonstrate the concept of
light sailing have been focused on using the Sun as the source of radiation pressure. In 2010, the
Japan Aerospace Exploration Agency successfully demonstrated the IKAROS spacecraft, which
used a broadband reflective coating to harness radiation pressure from the Sun
55
. Since then, other
solar sails have been demonstrated, such as the NanoSail-D (NASA, 2010) and the LightSail-1
and-2 (The Planetary Society, 2015 and 2019)
56, 57
. More recent work has explored the use of laser
light sources for propulsion.
7.2 Introduction to the Breakthrough Starshot Initiative
In 2016, the Breakthrough Starshot Initiative has proposed the use of an Earth-based laser array to
accelerate an ultra-lightweight spacecraft to relativistic speeds
58
. Specifically, a phased laser array,
emitting power on the order of gigawatts per square meter, would propel a light sail to a velocity
that is approximately 20% of the speed of light
59
. To achieve this goal, one key engineering
challenge is the design of the laser sail. An emerging body of literature has examined key principles
of sail design. Multiple materials, such as silicon and silicon nitride, have been examined for their
ability to enable an efficient exchange of momentum between photons and the sail
59-61
.
27

Additionally, studies have explored the theoretical feasibility, and stability of, a rigid mass being
propelled to relativistic speeds, at which the Doppler effect broadens the accelerating laser’s
bandwidth
54, 62-64
. Methods to leverage nonlinear effects, recent advances in metasurface
technology, and spherical sail designs have been proposed to ensure the stability of the spacecraft
in the laser’s beam
54, 65-71
. Stability considerations must carefully consider both the impact of any
beam fluctuations and tip/tilt perturbations to the sail. Moreover, the maximum impinging beam
intensity will be a critical parameter to ensure thermal stability of the sail
72
. In light of these
theoretical analyses, a major focus of ongoing research will be to fabricate, characterize, and test
the stability of experimental laser sail prototypes
69, 70, 73, 74
.
In this work, we designed, fabricated, and characterized a silicon nitride photonic crystal
for use as a light sail. The photonic crystal was designed to both reduce mass and increase
reflectance at near infrared (NIR) wavelengths, two desirable properties for light sails. First, we
fabricated a small-area sample using electron-beam lithography and reactive ion etching. We
measured the sample’s basic optical properties, including the reflectance and transmittance spectra
in the near infrared. We next demonstrated the ability to controllably shift the spectral features of
the sample via thin film deposition of titanium dioxide. We characterized its response to a
temperature increase to 80° C and did not observe a measurable shift in the spectral features. We
then measured the emissivity of the sample at longer wavelengths (4 - 16 μm) and showed that the
emissivity can be increased by adding a layer of polydimethylsiloxane (PDMS) polymer. Last, we
studied the transmitted optical power as a function of the input power at a laser wavelength tuned
to a photonic resonance mode of the sail. Our results provide valuable information for the further
design and characterization of silicon nitride light sails.

28

Chapter 8 Design of Light Sail
8.1 Concept of the Light Sail
Figure 8.1 depicts the concept of the Breakthrough Starshot Initiative. A phased-array of Earth-
based lasers accelerates a light sail towards the Alpha Centauri system, via radiation pressure. We
investigate the use of a Si3N4 photonic crystal to address the laser propulsion requirements for the
light sail. Si3N4 is a strong candidate for the laser-propelled spacecraft due to its low absorption
and high refractive index at near IR wavelengths
59
. By patterning holes in the Si3N4 membrane,
the mass can be reduced, which is desirable for creating a lightweight laser sail
59, 60
. Moreover, the
hole pattern can be chosen to create photonic resonances within the near IR, which can be used to
boost reflectivity at specific wavelengths
75-77
and/or magnify nonlinear effects that may help to
stabilize the sail against beam fluctuations
68
. While Si3N4 photonic crystals have previously been
studied for other applications, such as optical sensing
77
, experimental characterization of several
properties relevant to laser propulsion has not been carried out. For this study, we fabricated a
prototype Si3N4 light sail (SLS) and measured its spectral and thermal properties in the NIR,
emissivity in the mid- and long-wave infrared (M/LWIR), and its power dependence at a resonance
in order to understand the potential use of silicon nitride photonic crystals for the Breakthrough
Starshot application.
29

Figure 8.1: Depiction of the Starshot sail being accelerated by an Earth-based laser array.

8.2 Parameter of the Light Sail
For our prototype SLS, we selected and fabricated a 2D square lattice photonic crystal consisting
of etched holes. A schematic is shown in Figure 8.2, and has period a, hole diameter d, and
thickness t. Our prototype consists of structural parameters a = 1064 nm, d = 415 nm, and t = 690
nm, and we discuss these choices later in the text.
30

Figure 8.2: Silicon nitride photonic crystal laser sail design: a = period, d = diameter, t = thickness.

31

Chapter 9 Fabrication of Light Sail
Si3N4 membranes were fabricated onto Si wafers to create our SLS samples. First, a Si 3N4 film
(690 nm) was grown on a Si wafer with low-pressure chemical vapor deposition (Tystar Mini-
Tytan). Then, a photoresist layer (AZ 5214E) was spin-coated onto the back side of the wafer and
photolithography (SUSS MA/BA6 Gen4 mask and bond aligner) was performed with a custom
photomask. The photoresist etch mask was transferred onto the back side of the wafer after
exposure (85 mJ/cm2) and development (AZ 400K). By using reactive-ion etching (Oxford
PlasmaPro 100), regions of Si3N4 were created through the back side of the wafer. After removing
the residual photoresist with acetone, a Si3N4 mask remained on back side of the silicon wafer.
Finally, we used potassium hydroxide wet etching to create the Si3N4 membranes (20% solution
for 3.5 hours at 85° C).
To fabricate photonic crystals on the Si3N4 membranes, we used electron beam lithography,
off-normal electron beam metal evaporation, and reactive-ion etching. 150 nm of polymethyl
methacrylate (PMMA) was spin-coated onto the Si3N4 membranes, and e-beam lithography (Raith
EBPG 5150) was used to expose the circular regions. We expose 200 × 200 unit cells (circles) for
our experiments. After development (Methyl isobutyl ketone : isopropyl alcohol, 1:3), the PMMA
in the exposed regions was removed. Then, four repetitions of off-normal (75° ) metal evaporation
(Temescal BJD 1800) were used to create a chromium etch mask that covered the unexposed
regions. We used off-normal metal evaporation to avoid a lift-off process, protect the Si3N4
membranes, and reduce e-beam lithography time. Next, reactive-ion etching was used to etch
through the uncovered Si3N4 regions. After soaking the sample in chromium etchant (Sigma-
Aldrich) for 15 minutes, and then acetone for 3 hours, the photonic crystal samples were completed.
32

An SEM image of the fabricated Si3N4 sail is shown in Figure 9.1.

Figure 9.1: SEM image of the fabricated Si3N4 photonic crystal.

33

Chapter 10 Characterization of Light Sail
10.1 Reflection Characterization of Bare and Patterned Silicon Nitride Light
Sail
The optical response of a 2D photonic crystal at normal incidence is characterized by several
general features
75
. For a non-absorptive material, the transmission spectrum has an overall Fabry-
Perot background resulting from reflections off the top and bottom sides of the crystal. In addition,
the spectrum exhibits narrower, Lorentzian lineshapes, corresponding to guided-resonance modes.
At the extremely high incident intensities anticipated in the Breakthrough project (in excess of 10
GW/m2), the nonlinear properties of such guided-resonance modes may be useful for providing
stability against spatial beam fluctuations
68
.
We began by choosing the thickness of the slab to maximize broadband reflectivity in the
near infrared. For an unpatterned dielectric slab, its thickness and refractive index will determine
the location and width of reflective Fabry-Perot fringes, and maximizing the reflectance in the
range of the ground-based laser is desirable for efficient transfer of momentum to the light sail. As
the light sail accelerates, the laser wavelength will experience a Doppler shift Δλ/λ0 = v/c where
Δλ is the is the Doppler shift in wavelengths, λ0 is the laser wavelength, and v is the velocity of
the moving body
78
. The Doppler-broadened wavelength range for a light sail travelling at 0.2*c
and illuminated by a laser at λ0 is approximately λ0 to 1.2*λ0
59, 60, 66
. Thus, if the Earth-based laser
operates at λ0 = 1064 nm, the incident laser radiation will redshift to 1.2*λ0 = 1277 nm as the light
sail accelerates to its final velocity. We selected a thickness of t = 690 nm to produce a broadband
Fabry-Perot fringe around these wavelengths. The measured reflectance and transmittance of the
unpatterned slab are shown in Figure 10.1. We assume that the Si3N4 is lossless; Reflectance is
34

calculated as R= 1 – T, and the transmittance T is measured directly. The spectra exhibit clear
Fabry-Perot fringes, and the reflectance peaks are close to 40% near 1.2 μm.

Figure 10.1: Measured transmittance T and calculated reflectance R= 1 – T of a bare Si3N4
membrane.

The transmittance of the photonic crystal slab is shown as a thicker, black line in Figure
10.2, and the transmittance of the unpatterned slab in Figure 10.1 is shown again in Figure 10.2 as
a thinner line. The corresponding reflectance spectra are plotted assuming R = 1 - T and shown in
red. The measured spectra show overall Fabry-Perot behavior with superimposed resonant
features
75, 79
. The Fabry-Perot features are shifted to lower wavelengths relative to the unpatterned
slab, as expected from dielectric perturbation theory
79, 80
. Resonances are created in the slab by
patterning holes with a period of a = 1064 nm and diameter d = 415 nm. Resonant peaks are
35

apparent and result from Fano interferences in the photonic crystal
81
. The exact location of the
resonant peaks can be tuned by adjusting period and diameter, if desired
75
.

Figure 10.2: Measured transmittance and calculated reflectance of Si3N4 light sail and bare Si3N4
membranes. The bare (patterned) membrane’s transmittance and reflectance are the thinner
(thicker) curves.

10.2 Comparison of the Simulated Data and Experimental Data
We compared the measured transmittance spectra of our SLS to its simulated transmittance spectra
(Finite-Difference Time Domain, FDTD). The measured and simulated reflectance and
transmittance spectra are shown in Figure 10.3 and Figure 10.4, respectively. The resonances’
spectral locations are in good agreement. There is a significant decrease in the quality factor Q
from the simulation to measurement, as is typical in experiment
82
. Q can be quantified as Q= f/Δf,
where Q is the quality factor, f is the resonant frequency, and Δf is the full width at half maximum
36

(FWHM) of the resonance. For the simulated and measured resonances around 1460 nm in Figure
10.3, the simulated and measured Q are 155 and 85 respectively, which corresponds to decrease
by a factor of approximately 1.8 from simulation to measurement. The decrease in Q can be
attributed to imperfections in the fabrication process
83, 84
and/or beam divergence in our
measurement setup.

Figure 10.3: Simulated reflectance of the Si3N4 light sail from FDTD calculations compared to
measured values.

37

Figure 10.4: Simulated and measured transmittance of the Si3N4 light sail.

Chapter 10.3 Tuning Resonance by Coating Films
The spectral response of the light sail can be tuned by coating the photonic crystal with a thin
dielectric film. We deposited TiO2 onto the surface of the SLS with atomic layer deposition and
then recharacterized its spectra in the NIR. The 10-nm-thick TiO2 coating uniformly coats the
surface of the SLS.
Respectively, Figure 10.5(a) and Figure 10.5(b) show the measured transmittance and
reflectance of the SLS before and after depositing a 10-nm-thick layer of TiO2 on its surface;
reflectance was obtained from transmittance as R = 1 - T. The TiO2 coating red-shifted the spectra
of the uncoated sample. Figure 10.5(c) and Figure 10.5(d) show the simulated transmittance and
reflectance of the SLS after before and after depositing the same TiO2 film. Here, T and R were
38

separately calculated in the FDTD simulation. It is apparent that the measured red-shift seen in
Figure 10.5(a) and Figure 10.5(b) is consistent with the corresponding simulations. Additionally,
the coated SLS retained the shapes of and distances between the resonant peaks of the uncoated
SLS. Shifting the SLS’s resonant peak locations in a simple and controllable manner will enable
finer control over the final light sail design.

Figure 10.5: (a) Measured transmittance of the Si3N4 light sail before and after applying a 10 nm
thick layer of TiO2. (b) Reflectance (R = 1 - T) of the Si3N4 light sail before and after applying a
10 nm thick layer of TiO2. Simulated transmittance (c) and reflectance (d, R = 1- T) of the Si3N4
light sail before and after applying a 10 nm thick layer of TiO2. The resonances red-shift after the
deposition of TiO2.

39

Chapter 10.4 Thermal Properties of the Light Sail
In addition to its spectral properties, the thermal properties of the light sail play an important role
in performance. As a light sail is propelled by incident radiation pressure, any consequent increase
in temperature could create thermo-optic or expansion effects that change the SLS’s spectral
response. To study this effect, we measured the transmittance spectra of our prototype SLS at low
and high temperatures. The temperature of the SLS was controlled and maintained by a heated
lens tube that has a maximum range of 23.5 to 80° C. Additional details of this measurement are
available in the Methods section. The transmittance spectra of the uncoated and coated SLS at
23.5° C and 80° C are presented in Figure 10.6(a) and Figure 10.6(b), respectively. From both
Figure 10.6(a) and Figure 10.6(b), we observe little to no spectral shift for a temperature increase
of ∼56.5° C relative to room temperature.

Figure 10.6: Transmittance spectra of the (a) uncoated and (b) coated Si3N4 light sails at 23.5° C
(below) and 80° C (above). A spectral shift was not observable in this temperature range, which is
emphasized by the dashed lines.

40

The observed lack of significant spectral shifts in this temperature range is consistent with
previously reported temperature-dependent coefficients for CVD-grown Si3N4 films. The thermal
expansion and thermo-optic coefficients are 3.27 × 10−6 °C
−1
and 2.45 ± 0.09 × 10
−5
(RIU/° C)
respectively
85, 86
. Using these values and assuming a temperature increase of ∼56.5° C, we can
conclude that any temperature-dependent changes in the geometrical parameters (slab thickness,
hole size, etc.) or refractive index are negligible over the range measured.

Chapter 10.5 Increase Emissivity at Mid- and Long-Wave Infrared
Thermal management of the spacecraft could be required to maintain the sail within a
specified temperature range. For example, any on-board electronic components will have
temperature specifications for their use
87
, and improper thermal management can result in thermal
runaway and structural damage
61, 72
. Because the vacuum environment of space and lightweight
design requirements make active thermal control of the spacecraft difficult, a passive, emission-
based thermal management scheme is ideal for the Breakthrough mission
88
. The design of such a
scheme requires detailed knowledge of the mid-wave and long-wave infrared emissive properties
of the light sail. Moreover, techniques for increasing the emissivity in this range, while maintaining
the optical properties of the sail at the operating wavelength of the laser, will lead to improved
thermal management.
We have characterized the infrared emissivity of our sail both as fabricated, and with the
addition of a PDMS coating layer. We chose PDMS because Si-O and Si-C bonds facilitate high
emissivity in the M/LWIR, which can reach near unity for film thicknesses greater than 100um
89
.
To increase the emissivity in the M/LWIR, we spin-coated PDMS layers of different thickness
41

onto the uncoated SLS (8 and 16 μm). Afterwards, we recharacterized NIR spectra and measured
M/LWIR emissivity with FTIR spectroscopy. The NIR transmittance/reflectance and M/LWIR
emissivity spectra of the PDMS-coated and SLS are respectively shown in Figure 10.7(a) and
Figure 10.7(b).

Figure 10.7: (a) NIR Transmittance of the Si 3N4 light sail and (b) Mid- and long-wave infrared
emissivity (E = 1 - T - R) of the Si3N4 photonic crystal after spin-coating on different thicknesses
of PDMS layers. The PDMS increases emissivity at longer wavelengths; some resonances are
retained at shorter wavelengths.

Figure 10.7(a) reveals that spin-coating PDMS onto the SLS degrades and redshifts many
of the resonances, although some are retained. However, Figure 10.7(b) reveals that the PDMS
films significantly increase emissivity at longer wavelengths, and that thicker films result in greater
emissivity. These findings imply that the PDMS film thickness could be optimized to enhance
emissivity while still retaining resonances, and that thicker films result in greater emissivity at the
cost of adding mass to the sail.

42

Chapter 10.6 Characterization of Input-Output Power Dependence
Finally, we characterized the SLS by measuring its input-output power dependence at the
resonance near 1306 nm. The details of this measurement are described in the Methods section.
From Figure 10.1, the SLS has a resonance at 1306 nm. Transmittance from 1290 to 1320 nm,
given by a photodetector readout, is shown in Figure 10.8(a).
Next, we measured the input-output power dependence at 1306 nm. The laser was fixed to
radiate at 1306 nm, and the input power was controlled with a fiber attenuator. Figure 10.8(b)
shows a linear relationship between incident and transmitted power at 1306 nm. The linear
relationship implies that our laboratory laser power is not sufficient to induce nonlinear effects.

Figure 10.8: (a) Transmittance spectrum of the uncoated Si3N4 light sail’s resonance at 1306 nm,
measured by sweeping a tunable laser diode between 1290-1320 nm. The dashed red line is at
1306 nm. (b) Measured input-output power dependence of the light sail at 1306 nm with a fitted
linear curve.

43

Chapter 11 Optical Setup of Characterization
11.1 Optical Setup in the Reflectance and Transmittance Characterization
Reflectance and transmittance in the NIR were measured with a free-space optical bench
setup. The setup is shown below in Figure 11.1. First, light from a broadband white light source
(‘Lamp’, 360 - 2400 nm, Ocean Optics HL2000) was launched into free space from an optical
fiber, collimated by L1, and then focused onto the SLS with an NIR objective lens (L2).
Transmitted light is collected with an objective lens on other side of the sample (L3). Transmitted
light then couples into an optical fiber via L4 so that the transmittance spectra could be measured
with an NIR spectrometer (‘Spec.’, 900 -1700 nm and 1.6 nm per spectral band, Ocean Optics
NIRQuest 512). The beamsplitter BS1 is used to guide the Lamp’s illumination path to a visible
wavelength CCD camera, which is used for free-space alignment only. The temperature dependent
transmittance measurements in Figure 10.6 were conducted in the same manner, except that the
sample was mounted to a temperature-controlled lens tube (ThorLabs SM1L10HR). The stage’s
temperature is maintained with a with a thermistor and PID controller. The sample and stage were
maintained at each target temperature for 15 minutes before extracting spectra.

Figure 11.1: Optical setup for NIR transmittance and reflectance measurements.
44

11.2 Optical Setup in the Input-Output Power Relationship Characterization
The measurement setup to study the input-output power relationship of the SLS is shown
in Figure 11.2. To characterize the resonance shown in Figure 10.7, we illuminated the SLS with
a continuous wave tunable laser diode and measured the transmitted power with a calibrated
photodetector (ThorLabs PM100D Laser Diode, PDA10CS InGaAs Amplified Detector). We
swept the tunable laser diode from 1290 nm to 1320 nm to locate the resonance wavelength with
high accuracy. Once the resonance was located at 1306 nm, we fixed the laser diode to radiate at
this wavelength and controlled its incident power on the sample with a fiber attenuator. The
radiation from the laser was split with a 50:50 fiber splitter after the attenuator so that half of the
power was sent to the sample and the other half was measured by an optical power meter (OPM,
ThorLabs PM100D), which we used to extract the input power.

Figure 11.2: Optical setup for measuring the input-output power dependence of the light sail at
1306 nm.

The emissivity measurements for Figure 10.6 were performed with a Bruker Hyperion
FTIR spectrometer.

45

Chapter 12 Calculation of Acceleration Distance
We characterize our light sail by evaluating its acceleration distance, or the distance travelled
before reaching the final velocity. Following
59
, we calculate
Eq 12.1
where vf is the final velocity, I is the laser intensity, A is the area of the sail, R(v) is the reflectance
for the Doppler-shifted beam, γ(v) = (1 - v
2
/c
2
)
-1/2
is the Lorentz factor, and mT is the total mass
(msail + mpayload). Also following
59
, we assume I = 10 GW/m
2
, A = 10 m
2
, vf = 0.2*c, and mpayload =
0.1 g. Using the spectral data from Figure 10.1 to Figure 10.7 for R(v), we calculated acceleration
distances for the unpatterned Si3N4 slab, patterned Si3N4, patterned Si3N4 with a 10 nm TiO2
coating, and patterned Si3N4 with 8 µ m PDMS coating. Each structure’s acceleration distance D
is listed in Table 12.1. We note that the patterned Si3N4 sail has a slightly lower mass and shorter
acceleration distance than the unpatterned Si3N4 sail. While adding the thin TiO2 coating has a
slight impact on mass and acceleration distance, the thicker PDMS coating increases the
acceleration distance by more than a factor of 4. We may conclude that the PDMS coating should
only be used if thermal management strategies prove necessary for sail operation.

Table 12.1: Total Mass mT and Acceleration Distance D for Four Light Sail Designs. Acceleration
Distance D is calculated from Eq. 12.1.
46

Chapter 13 Summary
In this study, we have designed, fabricated, and charactered a prototype Si 3N4 light sail that could
be leveraged for the Breakthrough Starshot Initiative. We designed the light sail to create
resonances and broadband reflectance in the NIR, and measured the resulting reflectance and
transmittance spectra under different thin film and thermal conditions. We also demonstrated that
the resonances can be easily shifted with thin film dielectric coatings. Additionally, we showed
that the M/LWIR emissivity of our prototype light sail can be increased with PDMS films. Lastly,
the input-output power dependence of a resonance at 1306 nm was observed to be linear. In
conclusion, our work demonstrates the significant potential for silicon nitride as a light sail
material for the Breakthrough Starshot Initiative.

47

Topic 3
Ultrafast Early Warning of Heart Attacks through Plasmon-Enhanced
Raman Spectroscopy Using Collapsible Nanofingers and Machine Learning

48

Chapter 14 Introduction
14.1 Introduction to Acute Myocardial Infarction
The incidence of heart attacks, which are represented by acute myocardial infarction (AMI), is
increasing annually. The sudden onset and rapid progression of heart attacks are responsible for
their high lethality. Over 30.3 million U.S. adults are threatened by AMI, and 1 in 4 deaths in the
U.S. is due to a heart attack
90
. Although considerable effort and resources, i.e., $351 billion per
year from 2016 to 2017
91
, have been directed toward AMI prevention, rescue, and treatment,
approximately 659000 people in the U.S. die from AMI each year
91, 92
. Moreover, according to the
World Health Organization, AMI is the leading cause of death globally, taking approximately 17.9
million lives annually
93
. Because AMI causes the heart to stop suddenly without warning, early
intervention is the only way to prevent mortality and morbidity associated with the condition
93, 94
.
Thus, an ultrafast, low-cost, high-sensitivity, and widely deployable early warning platform with
high accuracy is urgently needed to perform the life-saving treatments that patients require.

14.2 Prevailing Diagnosis Methods of Acute Myocardial Infarction
The prevailing diagnosis methods include the electrocardiogram (ECG), blood tests, and the
echocardiogram. An ECG records electrical signals as they travel through the human heart via
electrodes attached to the chest. Because only an unhealthy heart produces abnormal signals, an
ECG only works when a heart attack has occurred or is in progress, which is too late to rescue
lives. Moreover, the specificity of the ECG is limited by large individual variations in the anatomy
of the heart as well as by preexisting heart diseases, injuries, or operations, such as coronary artery
49

bypass surgery, myocardial infarction, and collateral circulation
95
. The echocardiogram creates
images of a beating heart using sound waves (ultrasound) for identifying whether an area of the
heart has been damaged. It has the same drawbacks as the ECG, preventing it from being an early
diagnostic method
96
. These techniques are time-consuming and labor-intensive, and the accuracy
of identifying AMI depends entirely on the experience of the doctors.

14.3 Detect BNP Biomarker to Diagnose Acute Myocardial Infarction
Comparatively, the detection of AMI biomarkers in the blood is less expensive, faster, and more
objective. Before AMI, certain proteins and enzymes slowly leak into the blood, such as troponin
myoglobin, creatine kinase isoenzymes, and brain natriuretic peptide (BNP)
97-105
, which can be
discovered via blood tests. However, the current blood tests require at least 15 min to isolate the
serum from the blood, identify the target proteins, and collect data for the laboratory technician to
obtain a result. Additionally, blood tests suffer from low sensitivity, which makes them auxiliary
tests only
106, 107
. Furthermore, they are not fast enough to save lives from heart attacks, because
they are time-consuming and labor-intensive and lack sensitivity. Ultrafast detection and
identification of biomarkers in blood is a promising way to solve the aforementioned problems.
Currently, the natriuretic peptides, such as BNP and NT-proBNP, are the most commonly
referenced biomarkers for heart attacks
104, 108-111
. BNP has proven clinical utility in the diagnosis
of heart failure and heart-failure exacerbation
112
. According to the American College of
Cardiology Foundation, BNPs are the most valuable and reliable biomarkers for warnings of heart
attacks
98, 105, 113-116
. Thus, BNP was used as the biomarker of AMI in this experiment. The
50

corresponding receptors were attached to nanofingers to form the targeted capture platform for
BNP molecules.
Raman spectroscopy, which relies on the inelastic scattering of photons, allows the label-
free detection of molecules
117, 118
. However, spontaneous Raman scattering is too weak to be
detected. Surface-enhanced Raman spectroscopy (SERS) can increase the intensities of Raman
signals using metal nanostructures and provides intrinsic fingerprint information of molecules
attached to the surfaces of nanostructures with high sensitivity
119-122
. Considerable research has
been performed in this field, and SERS has become the most suitable method for the detection of
biomarkers. It has been demonstrated that ultra-strong electromagnetic (EM) fields can be
achieved between pairs of plasmonic nanostructures that are formed by sub-nanometer metal
nanoparticles. The critical goal is to precisely control the size of the gap between adjacent metal
structures
101, 103, 123-126
. Unfortunately, owing to the limitation of lithographic technologies, for
most conventional structures, the gap size cannot be controlled reliably and precisely resulting in
the inability to achieve single-molecule detection. Owing to the wide applications of emerging
nanofabrication techniques, a high-aspect ratio nanofinger structure ensuring ultra-high SERS
enhancement for sensitive molecular detection has been invented.
127-136
The nanofinger—a unique
nanostructure created through nanoimprint lithography (NIL)—achieves over 10
11
-fold SERS
enhancement resulting from the precise engineering of the gap size
137, 138
. The resultant gap
plasmon structures realize chemical detection of single molecules which is currently difficult to
achieve using other detection platforms.
In this study, we invented a SERS-based ultrafast early warning platform for heart attacks
using collapsed nanofingers, as shown in Figure 14.1, and machine learning (ML). The biomarkers
of heart attacks are captured by collapsed nanofingers for constructing the Raman signals, i.e., the
51

fingerprints of the biomarkers. Even trace amounts of metabolites of heart attacks are easily
detected by collapsed nanofingers, allowing the early warning of heart attacks. Because of the
complex components in the serum, there is too much noise in the Raman signal, making it difficult
to distinguish between the healthy individuals and patients by the existing systems or well-trained
personnel. We employed ML algorithms to analyze the mixed Raman signals. The analysis of
mixed Raman signals using ML-driven models significantly increases the accuracy of heart-attack
identification. We analyzed mixed Raman signals using the decision tree (DT) model, random
forest classifier, k-nearest neighbors (KNN) model, support vector machine (SVM) model, and
voting classifier. The prediction accuracies of all five models for heart attacks were >93%. The
prediction accuracy of the KNN model for heart attacks was 100%, indicating that all heart attacks
were identified ahead of time. This heart attack early warning system can significantly reduce the
rescue time for saving patient lives.

Figure 14.1: Schematic of the SERS-based platform using collapsed nanofingers to acquire Raman
spectra for ML-driven identification and early intervention of heart attacks.
52

Chapter 15 Device Fabrication and Diagnosis Procedures
15.1 Nanofinger Platform Fabrication
The high-aspect ratio nanofingers were composed of flexible polymer pillars with a height of 300
nm and metal particles covered with a dielectric layer. Using interference lithography (NIL), two-
dimensional cap array mother molds were fabricated using 4% ultraviolet (UV) resist (I-UVP,
EZImprinting Inc.). Using NIL, the cap array pattern was transferred onto the top surface of a
triple-layer resistor consisting of 15% UV resist, 3.5% PMMA, poly (methyl methacrylate), (I-
ULP, EZImprinting Inc.), and 4% UV resist. Then, the samples were etched via RIE (Oxford
PlasmaPro 100) to remove the residual resistor resulting from the NIL. Following 2 nm Ti/50 nm
Au deposition (Temescal BJD-1800 E-Beam Evaporator) and liftoff processes, the metallic cap
array was created uniformly. The heights of the nanofingers were defined by the deep RIE process.
NIL allows nanofingers to be fabricated with a high throughput and high reliability at a low cost.
The gap size between metallic particles was defined accurately by ALD with atomic precision
139,
140
. With atomic precision for the gap thickness, a large enhancement factor of ~10
11
is realized,
which is sufficient for detecting single molecules
137
. The enhancement factor is affected by
parameters such as the gap materials, gap distance, and background refractive index. Because
proteins were used as the gap materials in this study, the gap size was enlarged by the thick
proteins. Therefore, the enhancement factor was ~2× 10
8
, which is slightly smaller than that in the
previous study due to the large gap size
137
. The numerical simulation of the electric-field
enhancement of a collapsed nanofinger is shown in Figure 15.1(a). Figure 15.1(b) shows a
transmission electron microscopy (TEM) image of the nanogap after the nanofingers collapsed. A
53

scanning electron microscopy (SEM) image of the nanofingers after collapse is shown in Figure
15.1(c).

Figure 15.1: (a) Numerical simulation of the electric-field enhancement of collapsed nanofingers.
(b) TEM image of the nanogap between the nanofingers and energy-dispersive X-ray spectroscopy
(EDS) mapping of Au in the TEM image. (c) SEM image of nanofingers after collapse.

In addition to the high sensitivity, ultrahigh selectivity was achieved by attaching
antibodies corresponding to heart-attack biomarkers to the surfaces of metal particles on top of the
fingers. First, the nanofinger platform shown in Figure 15.2(a) was prepared using a method
previously reported by our group
131
. Then, the adjacent fingers collapsed together, forming a
54

sandwich structure (finger/antibody/finger), driven by the capillary force after soaking in an
antibody solution followed by air drying, as shown in Figures 15.2(b)–(d)
141-144
. Using the standard
methods, the antibody is connected to the surface of gold nanoparticle via covalent bond provided
by thiols
145-150
. The receptors attached to the fingers could detect the target biomarker among
thousands of complex components in the blood, as shown in Figures 15.2(e) and (f). Moreover,
the target biomarkers were fixed in the gap between fingers, which was the location with the
maximum enhanced EM field due to gap–plasmon resonance created by closed nanofingers. The
high selectivity was realized via a simple surface treatment. Then, the enhanced Raman signals
were collected from the captured BNP, as shown in Figures 15.2(g) and (h). The BNP was not
guaranteed to be trapped by every hotspot. The spot size of our 785-nm laser was ~1.9 µ m. This
spot covered 25 nanofinger clusters each consisting of four nanofingers. Four nanofingers
collapsed together produced 100 hotspots. The signals were the averages of 100 hotspots.
Statistically, there was a sufficient probability for BNP to be captured in one or more hotspots.
Therefore, the enhanced Raman signals were easily collected. Moreover, the BNP antigen was
easily combined with the BNP antibody attached to metallic particles. These areas were either
hotspots or covered by hotspots. Therefore, the Raman signals were enhanced by the hotspots.
55

Figure 15.2: Fabrication process for functionalizing nanofingers. (a) Nanofinger sample is
fabricated via NIL. (b) Nanofingers are soaked in an antibody solution. (c) Air drying to induce
the collapse of nanofingers. (d) Forming a metallic nanoparticle/antibody layer/metallic
nanoparticle sandwich structure. (e) Soaking in human serum. (f) Capturing and fixing the
biomarker using antibodies attached to the nanofingers. (g) Collecting Raman signals. (h)
Schematic of a hotspot with the captured biomarker from human serum.

15.2 Human Serum Sampling
Samples of human serum were obtained from healthy individuals and patients who were threatened
by heart-attack attempts or suffered from pre-heart attack symptoms. Many volunteers participated
in our research. The serum was collected from patients on different days and at different times.
When a patient felt discomfort, the serum was immediately collected. The heart rhythms of patients
were monitored using ECGs, and blood tests were performed simultaneously as a reference for a
doctor to check whether a heart attack would occur. If a heart attack occurred, the doctor started
56

to rescue the patient, and the serum just collected was labeled as “Patient No. XX before the onset
of heart attack.”
Not every AMI patient was qualified for our research. First, only hospitalized patients were
selected as volunteers, as they could be kept under observation and their serum could be collected
once they felt uncomfortable. Second, the selected hospitalized patients were willing to participate
in this research, and their decisions had to be approved by the ethical and clinical committees.
Third, the participants had to represent different age groups, with each age group including
balanced numbers of males and females. More importantly, only the serum from the patients with
a confirmed heart attack after collection of the serum was labeled as “Patient No. XX before the
onset of heart attack,” and this serum was employed for subsequent analysis using ML.
Although many volunteers participated in our research, the serum from nine patients was
qualified after our strict screening process. These nine patients’ serum was successfully collected
before the onset of a heart attack. Four of the patients were female, and the remaining patients
were male. There were three age groups: 18–35 years (one male and one female), 36–55 years
(two males and two females), and 56–80 years (two males and one female). Because we collected
serum from these patients on different days and at different times, we obtained many serum
samples. Additionally, serum was obtained from nine healthy individuals following the same
procedure, rules, and requirements.
Then, human serum was dropped on the functionalized nanofingers directly without
preprocessing, as shown in Figure 15.2(e). The BNP antibodies captured the BNP antigens and
then fixed them onto collapsed nanofingers. The Raman signals of the human serum were collected
for predictive analysis using ML models.
57

15.3 Raman Data Collection
Raman measurements were performed using a Renishaw inVia Raman microscope. They were
conducted with 785-nm laser excitation, and a 50× standard objective was used in the spot focus
mode. Each Raman signal ranged from 500 to 2500 cm
-1
, with 1800 data points. Because serum is
a complex mixture of numerous and various components, the spectral variations between
measurements of each sample were large. Therefore, each sample was measured multiple times to
obtain more comprehensive information for further analysis.
530 Raman spectra were collected from the serum samples: 144 from healthy individuals
and 386 from patients. 80% of the spectra of each group (healthy and patients) were randomly
selected as a training set for building ML models. The remaining 20% were kept as the test data to
evaluate the performance of each ML model.

58

Chapter 16 Classification Results by Machine Learning
16.1 Raman Spectra of the Serum
Four examples from the 530 Raman spectra are shown in Figure 16.1. Because of the complex
components in the serum, there was too much noise in the Raman signals. Therefore, it was
difficult to recognize heart attacks via specific peaks in the Raman spectra with the naked eye. We
invited one student to identify the Raman signals. After a long training period, he recognized the
Raman signals corresponding to heart attacks with only 73.85% accuracy.
Because the subtle changes in the Raman signals were difficult to recognize through visual
inspection, ML algorithms are used to unveil intricate data structures, enabling precise analysis of
the Raman signals
151-156
. More importantly, an ML algorithm built on statistical models objectively
eliminates subjective judgment, which significantly reduces the probability of misdiagnosis
157-159
.
In this study the analysis of mixed Raman signals using ML-driven models was performed,
significantly increasing the heart-attack identification accuracy. However, there were three main
challenges. First, the signals were too noisy, which made it difficult to extract the useful features
for training ML models. Second, only several hundred signals were collected. The ML models had
to be built such that they did not rely heavily on the amount of the data. Third, the dimension of
each signal was high. High-dimensional data result in a large computational burden and limit the
prediction performance. After evaluating various ML algorithms, we decide to build the models
using five supervised algorithms to analyze the mixed Raman signals: the DT model, random forest
classifier, KNN model, and SVM model, and voting classifier.
59

Figure 16.1: (a, b) Raman signals of serum from healthy individuals collected using the nanofinger
platform. This serum did not contain the biomarker BNP. (c, d) Raman signals of the serum
collected before the onset of a heart attack. This serum contained the biomarker BNP.

16.2 Decision Tree Model and Random Forest Model
The DT algorithm is a nonparametric supervised learning algorithm used for classification
problems that summarizes decision rules from a well-labeled dataset
160-163
. It employs a graph
structure whose decision rules are represented by a tree structure. Nodes and leaf nodes constitute
the tree-like structure, in which each internal node represents a judgment on one feature and each
leaf node represents a class label. Each node splits the dataset into two branch nodes based on one
feature, which tends to have as many samples in each group belonging to the same label as
60

possible. In general, if more samples in a branch node of a DT belong to the same class, the node
has a higher “purity.” Therefore, each node has a corresponding purity. Two methods are widely
used to calculate the purity: the information entropy and the Gini index
164, 165
. Assuming that the
proportion of samples labeled k in dataset D is 𝑝 𝑘
(𝑘 = 1,2, … , |𝑦 |), the information entropy and
Gini index of dataset D are defined as follows:
𝐸𝑛𝑡𝑟𝑜𝑝𝑦 (𝐷 ) = − ∑ 𝑝 𝑘 log
2
𝑝 𝑘 |𝑦 |
𝑘 =1

𝐺𝑖𝑛𝑖 (𝐷 ) = 1 − ∑ 𝑝 𝑘 2
|𝑦 |
𝑘 =1
.
The splitting rules significantly affect the accuracy of the DT. The top priority for building
a DT is to select the splitting function. Comparing the aforementioned mathematical expressions
reveals that the information entropy is more sensitive to the purity than the Gini coefficient and
therefore penalizes impurity more strongly. This leads to a more detailed DT that is prone to
overfitting. Using information entropy as an indicator of node purity results in weaker
generalization of the tree model. This drawback is more evident for higher-dimensional data
166-171
.
Thus, for high-dimensional data, the Gini index is more suitable. Because the Raman data were
high-dimensional data, the Gini index was selected as the criterion to form the tree model. After
optimization and branch reduction of the DT, the model achieved an accuracy of 94% for the test
set and an average accuracy of 89.81% for 10-fold cross-validation, indicating that the model has
a high accuracy and strong generalization performance.
Although the prediction accuracy of a single DT was high, the prediction accuracy can be
increased by combining multiple DTs. The random forest algorithm consists of multiple DT
61

models
172-174
. It constructs multiple independent DTs to predict the samples separately and then
averages or votes on these predictions to determine the final prediction result. Generally, the
number of DTs in a random forest significantly affects the prediction accuracy. Therefore, we
focused on optimizing the number of DTs in the random forest model. After optimization, the
random forest achieved an accuracy of 95% for the test set. Moreover, the average 10-fold cross-
validation accuracy was 93.58%, which was 3.77% higher than that for the single DT. This
indicates that the random forest model has not only a higher accuracy but also the generalization
ability.

16.3 K-nearest Neighbor Model
The KNN model is one of the most widely used supervised ML algorithms. The key principle of
this algorithm is to classify the data according to their similarity to previously labeled data
175, 176
.
By using the labeled data points as the training set, the KNN algorithm calculates the distances
between the test object, such as new patient data, and all each objects in the training set. Then, the
k-nearest objects are determined as the neighbors of the test object. The labels of most frequently
occurring objects among the k data points are identified, and new data points are assigned the same
label
177
. The KNN model is easy to implement owing to the single hyperparameter, i.e., k, which
makes hyperparameter tuning easy. More importantly, it constantly evolves as new data are added
to the training set, and the predictive results are generated without building a new KNN model.
Various distance metrics are available, e.g., Euclidean, Manhattan, and Minkowski. We calculated
the Euclidean distances between data points using the following formula:
62

𝑑 (𝑥 𝑖 , 𝑦 𝑖 ) = √(𝑥 1
− 𝑦 1
)
2
+ (𝑥 2
− 𝑦 2
)
2
+ (𝑥 3
− 𝑦 3
)
2
+ ⋯ + (𝑥 𝑖 − 𝑦 𝑖 )
2
= √∑(𝑥 𝑖 − 𝑦 𝑖 )
2
𝑛 𝑖 =1
.
The well-labeled Raman signals were fed to the KNN model as a training set. The KNN
model creates an N-dimensional space, and each Raman signal in the training set is converted into
a point in this high-dimensional space with a clear label. After receiving unclassified data, the
KNN model transforms the new data into a point in the same space. Then, it calculates the distance
from the new point to each existing point and sorts all the points from nearest to farthest according
to the calculated distances, forming a list. The category of top k points from the list are counted.
Finally, the category of the new point is assigned by the most common label among the k closest
points.
In our study, first, the dataset was randomly split into a test set and a training set. 20% of
the dataset was kept as the test set to evaluate the performance of our model. The remaining data
were used as the training data and were loaded into the KNN model directly. We performed the
predictions using the whole Raman signals rather than a few sharp peaks because the predictions
were sensitive to noise; thus, predictions obtained by simply identifying the peaks were inaccurate.
More importantly, focusing on peaks ignores the underlying structure of the signals, which is easily
identified using the KNN model.
Each Raman spectrum collected from human serum comprised 1800 Raman intensity
signals under 1800 different wavenumbers. The whole spectrum was viewed as a point in 1800-
dimensional space by the KNN model. As discussed previously, the KNN model calculated the
Euclidean distances between the existing well-labeled points and new points. Next, the previously
known training points were listed in increasing order of distance. The value of k was set as 22.
63

When the k value was smaller than 22, the prediction became causal, and overfitting occurred.
With an increase in k, the prediction tended to underfit, and eventually, every prediction belonged
to one class, which was the majority class in the training set. Finally, the prediction of each new
point was determined by the most frequently occurring category of 22 data points. We achieved
100% accuracy in predicting AMI using our well-trained KNN model: i.e., every patient was
recognized accurately and quickly. However, the KNN model—the most famous nonparametric
model—has a major drawback. It cannot classify data if it does not carry all the training data. Thus,
a parametric model, i.e., an SVM, was built to eliminate the training data.

16.4 Support Vector Machine
In ML, SVMs are powerful yet flexible supervised algorithms and are among the most efficient
algorithms. The aim of the SVM algorithm is to create a hyperplane separating the data points in
an N-dimensional space. The dimensionality of the space is determined by the number of features
of the input data. One useful feature of SVMs is that their performance does not deteriorate
significantly as the dimensionality of the data increases, which breaks the curse of dimensionality.
In addition to their effectiveness for high-dimensional data, they are memory-efficient, as only part
of the training data are used for determining the decision function, i.e., the boundary to separate
the data in the N-dimensional space. More importantly, SVMs can classify nonlinear data, such as
Raman spectra
178
. These features make SVMs useful for the classification of high-dimensional
data. Owing to their unique advantages, SVMs have emerged as the most popular method for
identifying Raman signals with high-dimensional features
99, 179-181
.
64

As mentioned previously, the SVM creates a boundary defined by the decision function to
separate the linearly separable or non-separable data. To precisely create the boundary for non-
separable data, the SVM uses mathematical functions called kernels to transform the data to a high-
dimensional space where the data become separable. The popular kernels are as follows: linear,
nonlinear, polynomial, radial basis function (RBF), and sigmoid. Their mathematical equations are
presented below.
Linear kernel: 𝐾 (𝑥 𝑖 , 𝑥 𝑗 ) = 𝑥 𝑖 𝑇 𝑥 𝑗
Polynomial kernel: 𝐾 (𝑥 𝑖 , 𝑥 𝑗 ) = (𝛾𝑥
𝑖 𝑇 𝑥 𝑗 + 𝑟 )
𝑑 , 𝑑 > 1
RBF kernel: 𝐾 (𝑥 𝑖 , 𝑥 𝑗 ) = 𝑒𝑥𝑝 (−𝛾 ‖𝑥 𝑖 − 𝑥 𝑗 ‖
2
), 𝛾 > 0
Sigmoid kernel: 𝐾 (𝑥 𝑖 , 𝑥 𝑗 ) = 𝑡𝑎𝑛 ℎ(𝛾𝑥
𝑖 𝑇 𝑥 𝑗 + 𝑟 ), 𝛾 > 0, 𝑟 < 1
After the data are transformed to a higher-dimensional space, the SVM searches for
hyperplanes that can divide the data into corresponding categories. However, there are many such
hyperplanes. The best hyperplane is the one that has the farthest distance to the nearest data point
belonging to any class. The distance between hyperplanes and the nearest data point is called the
margin. A larger margin corresponds to a better generalization ability of the SVM
182
. Another
scenario is that transforming the data to a higher-dimensional space results in an infinite number
of hyperplanes that can classify the data, which causes overfitting. Therefore, penalty factors are
added to relax the restrictions and allow the model to misclassify some of the training data during
the learning process to avoid the overfitting problem. By transforming data to a high-dimensional
space and finding the hyperplane with the maximum margin, the SVM achieves accurate
classification of linearly inseparable data.
65

An SVM model using the RBF kernel was applied to our Raman spectra. Intuitively, the
linear kernel is only applicable to linearly separable datasets, limiting its use. The polynomial
kernel suffers from numerical instability resulting from 𝑥 𝑖 𝑇 𝑥 𝑗 while dealing with least squares
183-
185
. In addition, it requires many parameters to be adjusted, which makes model optimization
difficult. The sigmoid kernel faces the same issue. As the most widely preferred kernel function
for SVMs, the RBF kernel can handle linearly non-separable data, avoids numerical instability,
and generally requires only one parameter (penalty factor C) to be adjusted, which makes the SVM
model easy to optimize
186
. After optimization, our model achieved a diagnostic accuracy of 96.3%
for heart attacks.

16.5 Voting Classifier
Although four models were built and achieved high prediction accuracies, their performance is
limited by their characteristics. The voting classifier created by aggregating numerous models is a
strong classifier that balanced out the models’ weaknesses
187-190
. The final prediction is determined
by the average predicted probabilities of all weak classifiers. By combining the SVM, DT, random
forest classifier, and KNN classifier, the voting classifier achieved 98.11% accuracy and an
average accuracy of 94.70% for 10-fold cross-validation. Its performance was better than that of
the SVM and tree-based classifiers and comparable to that of the KNN classifier. As parametric
and nonparametric models are exploited to build the voting classifier, it can maintain high
performance when faced with complex situations and large datasets.

66

16.6 Performance Evaluation
To quantitatively evaluate the performance of our five ML models, confusion matrices were
created. The confusion matrix overcomes the accuracy limitation, which is misleading when there
is a large imbalance between two classes, as the model tends to simply predict the majority class
for all new cases for achieving a high accuracy. To unveil the actual performance of each model
hidden behind the accuracy metrics, the confusion matrix presents a table visualizing all outcomes
from each model. It consists of true positive (TP), false positive (FP), false negative (FN), and true
negative (TN). TP and TN correspond to the number of correct predictions achieved by the model
for each class. FP and FN correspond to the number of incorrection predictions for each class.
Figure 16.2 shows the confusion matrices of the three models after normalization.
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Figure 16.2: Normalized confusion matrices of (a) well-trained personnel, (b) the DT, (c) the SVM,
(d) the KNN classifier, (e) the random forest classifier, and (f) the voting classifier.

Cross-validation is a technique for testing the performance of ML models in which models
are trained using a subset of the dataset and evaluated using the complementary subset of the
dataset
191-193
. This method can highlight issues such as model overfitting or underfitting from a
training dataset. The results can indicate the performance of the model performs for unseen
datasets
194-197
. The most widely used cross-validation method is K-fold cross-validation, which
involves dividing the dataset randomly into K subsets, one of which is the holdout test set. K–1
folds of the dataset are used for training the models, and the K
th
fold serves as the performance
metric for calculating the accuracies of the models. These steps are repeated until every fold has
68

become the test set. The average accuracy calculated from K subset is the result of cross-validation.
This approach guarantees that the prediction accuracy does not depend on how the dataset is split
between training and test sets, as it ensures that all the data from the original dataset can be the
training data or testing data
198-202
. We used 10-fold cross-validation in this study. The dataset was
randomly divided into 10 parts, one of which was reserved to evaluate the model by calculating
the prediction accuracy. As shown in Figure 16.3, the average 10-fold cross-validation accuracies
for the DT, SVM, random forest classifier, voting classifier, and KNN classifier were 89.81%,
93.20%, 93.58%, 94.70%, and 95.09%, respectively, indicating that our models are stable and not
only performed well for the test dataset but also would achieve high performance for an unseen
dataset. Because the ML models were trained and tested using Raman spectra collected from
individuals of different age groups and genders, they can identify heart attacks regardless of age
and gender.
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Figure 16.3: 10-fold cross-validation of five classifiers: (a) DT; (b) random forest; (c) SVM; (d)
KNN classifier; (e) voting classifier. (f) Average accuracies of 10-fold cross-validation for the five
models: 89.81%, 93.20%, 93.58%, 94.70%, and 95.09%, respectively.

70

Chapter 17 Summary
We combined ML with a SERS-based platform using collapsed nanofingers to achieve a high
prediction accuracy for heart attacks. First, the functionalized nanofingers accurately detect the
biomarkers of heart attacks from human serum. Then, the Raman signals are significantly
enhanced by the hotspot, which is crucial for the construction of the Raman profile of the human
serum. Next, five ML models identify heart attacks using noisy Raman signals rapidly and
precisely. Importantly, we demonstrated the ability of our models to predict heart attacks using an
unseen dataset through 10-fold cross-validation. This SERS-based and ML-driven heart-attack
warning system overcomes the challenges of rescuing patients suffering from heart disease. For
now, the number of patients participating in this project was relatively small. We still have not
stopped collecting data on patients threatened by heart attacks. As more data are collected, this
prediction system will be improved. Millions of lives can be saved by applying it on a large scale
in the future.

71

Topic 4
Circuit Accelerator for Boolean Satisfiability Problem

72

Chapter 18 Introduction
18.1 Boolean Satisfiability Problem
The P-problem means that this kind of problem can be solved in "polynomial time" easily.
Therefore, P-problems are considered to be tractable or easy. The name "NP-complete" is short
for "nondeterministic polynomial-time complete". Effective solving NP-complete problems would
greatly benefit to the computer science and engineering
203
. However, these problems are not easily
to solve on digital computers based on von Neumann structures. Therefore, both the industry and
the science are seeking to the alternative solutions to the NP-complete problem. Among all NP-
complete problems, Boolean satisfiability problem (SAT) is the most well-known problem. In the
field of computer science and logic, SAT problem is the problem of finding out whether there is
an answer that satisfies a given Boolean equation
204-206
. In other words, SAT problem questions
whether after assigning true or false to the variables in the Boolean equations, the equation can
still be satisfied as true. If such variables assignment exists, this equation is claimed as satisfiable.
Otherwise, if such variables assignment does not exist, this equation is claimed as unsatisfiable.
For example, the Boolean equation is “X1 AND X2”. This equation is satisfiable because if both X1
and X2 are set to True, the equation X1 and X2 is True under such conditions. However, not every
Boolean equation is satisfiable. For example, the Boolean equation is “X1 AND NOT X1”. No
matter which value is assigned to X1, the equation cannot get the True value, so this equation is
unsatisfiable.
Solving SAT is extremely important because it has widely applications in industry, science
and daily life. In addition, SAT belongs to a large class problem called NP-complete problem
204
.
Each category of NP-complete problem can be transferred to another category of NP-complete
73

problem in polynomial time. Accelerating the SAT problem solving time means that accelerate the
whole class of NP-complete problem solving time. Lots of the researchers study how to accelerate
the SAT problems because SAT can be implemented into huge practical problems. For example,
the 2021 “Decadal Plan in Semiconductors” by the Semiconductor Research Corporation
207

mentions satisfiability (SAT) problems as “… specific to applications such as crosstalk noise
prediction in integrated circuits, model checking, testing of finite-state systems, technology-
mapping in logic synthesis, and AI planning and automated reasoning.” However, the exiting
methods are still not power enough because when the size of SAT increases, the complexity grows
exponentially. It is generally thought that due to the exponential complexity, no such powerful
algorithm exists based on using digital computer to solve this problem, although this statement has
not been proved theoretically.

18.2 Hardware Accelerator
A substantial part of the economic and societal benefits of future semiconductors will be realized
by the development of systems that include task automation such as planning, learning, and
reasoning. Due to their inherent complexity and the high volumes of input data, such tasks cannot
be automated today for many applications, while also satisfying their requirements on
effectiveness, speed, power, and reliability. Hence, such tasks are ideal candidates for developing
hardware accelerators.
Our research direction was determined by the following question: Is it possible to develop
a single accelerator for a wide class of problems or do we need to develop a separate application-
specific accelerator for each problem? Computer science researchers have created a rich set of
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efficient algorithms, each solving a wide range of problems. Further, they have created large
classes of problems, e.g., the NP-Complete class, by creating polynomial-time methods that
transform any problem in the class to any other problem still in the class. In particular, Boolean
Satisfiability (SAT) is used as a computational workhorse by a wide range of fields. Hence, a
hardware accelerator for SAT (HW SAT) will enable development of impactful systems for
planning, learning, and reasoning under stringent requirements. Further, via the theory of NP-
completeness, a hardware accelerator for SAT will also accelerate a very wide range of other
fundamental algorithms, many of which are also widely used, e.g., integer programming, just to
name one of the other workhorses in the NP-Complete class.
We then faced the next question as follows: SAT is an active area of research, so will a
hardware accelerator be useful? Over recent decades, intensive research in SAT algorithms and
software innovations (spurred by SAT competitions
208
) has indeed dramatically accelerated
software SAT solvers (SW SAT). For example
209
, it shows the dramatic reduction in run-times
for SW SAT between 2000 and 2007. Despite this, the need for SAT hardware accelerators remains
strong. For example, SAT-based model checking is extensively used in the verification of
hardware
210
, software
211
, and cyber-physical systems
212
. Verification can amount to 70% of a
product’s development cycle and is arguably its most time-consuming part
213, 214
. Hence, if a
hardware accelerator for SAT (HW SAT) accelerates SAT by even 10x over state of-the-art SW
SAT, the time-to-market for such systems will decrease by near 3x, a major economic benefit for
the semiconductor sector. SAT solving is also widely used to perform path planning tasks in
robotics. However, there is an inherent trade-off between the quality of the solution and the time
to find it
215
. In scenarios where decision must be made in real-time, the runtime of SW SAT solvers
limits the quality of the decision and hence limits the safety and dependability of the planner. It
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follows that HW SAT will make possible many types of autonomous robotic systems that are
currently unable to provide necessary safety and performance. SAT solving is also increasingly
used to execute core tasks in computational biology
216, 217
and HW SAT will improve the rate of
research and discoveries in this domain. In these and many other applications, HW SAT will
directly provide dramatic benefits for a very large user base.
Prior research efforts for hardware acceleration
218-220
have had limited impact as most of
these used field-programmable gate arrays (FPGAs). The most successful of these
218
approaches
used the embedded processors and block RAM modules (BRAMs) within FPGA chips to
accelerate a major task, namely Boolean Constraint Propagation (BCP), which accounts for around
80% of SW SAT run time for large problems. However, the impact of the total runtime of SAT
was limited to much smaller than 5x, since the remaining tasks of SW SAT become a performance
bottleneck.
Recent research
221
has shown that SAT is especially suited for a transistor-level
implementation as most data and operations are Boolean, hence directly implementable using
simple digital primitives, e.g., logic gates, static random-access memory (SRAM) cells, content
addressable memory (CAM) cells, and so on.
Our custom transistors-to-algorithm designs to date have demonstrated that >1000x
speedup, and much higher performance-power-area (PPA) improvements, can be achieved at
reasonable power consumption, in a 65-nm technology. Estimates show that, in a 7-nm technology,
our approach can provide single-chip SAT accelerators that can tackle the largest benchmark
problems used in annual SAT competitions
208
, under reasonable power budgets. Finally, we
contend that dramatically higher improvements to the runtimes and PPA for SAT can be achieved
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via joint research that spans devices, VLSI circuits and architectures, algorithms, and applications.
This will enable us to create new devices with unique specifications, tailored to the needs of our
accelerator; new VLSI circuits and architecture designs that maximally utilize new devices; and
new versions of algorithms reshaped to maximally harness the capabilities that devices and VLSI
can provide.
Here, our group proposed a hardware circuit accelerator for SAT problem, which could
transform the SAT equation to a circuit. Under this situation, solving the SAT problem is equal to
solving an optimization problem. In addition, our circuit is a dynamic circuit, which means that it
will forbid to get stuck in the local minima during the search, which will greatly improve our
circuit performance and accelerate the solving time.

77

Chapter 19 Architecture and Fundamental Principles of the SAT
Problem Accelerator
19.1 Architecture of the SAT Problem Accelerator
Figure 19.1 shows the principal schematic of the circuit accelerator designed to solve SAT
problems, provided as 3-CNF expressions with less than Nv variables and less than Nc clauses. The
circuit has the following key components.
1) An input plane consisting of Nv pairs of vertical wires, i.e., a total of 2Nv vertical
wires. Each input variable is associated with one pair of wires, where one wire in each pair is
associated with the literal Xi and the other is associated with 𝑋 ̅
i.
2) Each pair of wires has two input inverters, one with input Xi and output 𝑋 ̅
i and the
other with input 𝑋 ̅
i and output Xi.
3) An output plane consisting of three horizontal wires for each clause, i.e., a total of
Nc horizontal wires.
4) The three wires for each clause are connected to the three bi-directional ports of a
clause-logic block, i.e., we have Nc copies of the clause logic block. Each clause-logic block
contains three bi-directional ports. Each port contains three P-type metal-oxide-semiconductor
field-effect transistors (PMOS) plus a switch component and it is also connected to Vdd. Only
one of the switches is turned on in the three ports at the same time, which can be realized by
the random number generator or the clock function.
5) A crosspoint array with a total of 6NvNc programmable crosspoints. Each
crosspoint is placed at the intersection of a vertical wire in the input plane and a horizontal
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wire in the output plane and consists of an N-type metal-oxide-semiconductor field-effect
transistor (NMOS) whose source and drain are connected to these two wires. The gate of each
crosspoint transistor is controlled by the value in an SRAM cell.
6) The 6NvNc SRAM cells are organized as a standard 2Nv * 3Nc SRAM array (or
emerging devices such as ReRAM or memristor) with row and column decoders and read and
write circuitry. The bi-directional circuit can be configured for any given 3-CNF by loading 0
or 1 into the cells in the SRAM array.
7) A completion monitor which checks whether the values at the input lines (Xi and
𝑋 ̅
i, ∀i) have ceased oscillations and stabilize at meaningful logic values.

Figure 19.1: Schematic of the circuit accelerator.
79

19.2 Fundamental Principles of the SAT Problem Accelerator
The basic idea of this circuit is that the SAT problem is transformed into a circuit and the circuit
can find out whether this SAT equation is satisfiable. The crossbar circuit is a configurable switch
matrix that allows the circuit to be configured according to the desired problem. Each constraint
circuit will be transformed from each clause in the SAT problem. As shown in Figure 19.1, the
circuit is designed by the constraint: If the values of the variables cannot satisfy the equation, the
value of the variables will be flipped by the constraint circuit. For example, if the statement is (X1
∨ X2 ∨ X3), then X1, X2, and X3 will be connected to the constraint circuit. From Figure 19.1, it
can be well known that if all the variables become 0 voltage, then the PMOS in the constraint
circuit will be turned on. Thus, the drain power voltage will drive the input of the memory cell
from low to high. Under this situation, the variables in one clause cannot be 0 voltage at the same
time. Thus, the voltage output of the variables that does not satisfy the SAT problem cannot exist
in this circuit. Therefore, if the circuit can find the answer, the SAT problem is satisfiable.
Otherwise, if the SAT problem is not satisfied, the circuit will not be stable, and the voltage of the
different variables will bounce back and force forever.

Chapter 19.3 Algorithm of the Random Switch Function
Originally, the circuit accelerator does not contain the random switch function claimed in Chapter
19.4 Part 4). The original schematic of the circuit accelerator is shown in Figure 19.2. If the SAT
equation contains very few variables, the circuit will be very simple. As shown in the Figure 19.3,
the SAT equation: (X1 ⋁ X2) ⋀ (X1 ⋁ ¬X2) ⋀ (¬X1 ⋁ X2) is transferred into the circuit. This SAT
80

equation is satisfiable with the solution: X1=1 and X2=1. From the simulation results by LTSPICE,
our circuit accelerator could solve this problem perfectly, the theoretical result matches with the
simulation result. However, the simulation only shows the feasibility of small-scale problems (2-
SAT problems). In the next section a more serious mathematical proof of the stability of this circuit
would be shown over a large range.

Figure 19.2: Original schematic of the circuit accelerator.
81

Figure 19.3: The circuit implement a simple 2-SAT problem of (X1 ⋁ X2) ⋀ (X1 ⋁ ¬X2) ⋀ (¬X1 ⋁
X2) = True.

When the size of the problem grows bigger (3-SAT problem with more clauses), more
strategies should be implemented into the original design of the circuit. From the circuit shown
above in Figure 19.2, if a clause such as (X1 ∨ X2 ∨ X3) is not satisfied, which means all the variables:
X1, X2 and X3 are 0 voltage, then the PMOS in the constraint circuit will flip all the variables at the
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same time. However, this algorithm is not good enough, which will be proved in the following
part.
It exists two main drawbacks when flipping all the literals in one clause simultaneously.
Firstly, this algorithm cannot fully retrieve all the states and it exists infinite loops during the
flipping process. Equation 19.1 and Figure 19.4 are used as an example to illustrate the reason.
Equation 19.1 contains 4 variables and 5 clauses. It is satisfiable and the solutions are 0100 and
0110 for X1~ X4. The Karnaugh map of X1~ X4 is shown in Figure 19.4 (a). Figure 19.4 (b) and
Figure 19.4 (c) show the state changing flow charts on the Karnaugh maps. In Figure 19.4 (b), the
literals flip the states in only one clause due to the unsatisfaction. In Figure 19.4 (c), the literals
flip all the states in all the unsatisfied clauses. As we can see, in both algorithms, some of the
solutions cannot be achieved forever. In addition, it exists some infinite loops such as 0 → 5 →
12 → 0 and 2 → 7 → 14 → 2 in both algorithms. These infinite loops could make the literals
bounce back and force, leading to infinite retrieving time. In addition, flipping all the literals
increases the possibility of the circuit stuck, which is a huge problem we met in the simulation
process. Considering that it exists a cost function for the circuit system, the global minima means
that the entropy of the whole system is on the lowest points, which means that the values of the
different variables represent the solutions of the equation. The stuck makes the values of the
variables stop in the local minima but not the global minima, which prevent the system to find out
the final solution. Based on these reasons, flipping all the literals is not a good enough algorithm
and a better solution needs to be raised.
(¬X1 ∨ ¬X2) ∧ (¬X1 ∨ X2 ∨ ¬X3) ∧ (¬X1 ∨ X3 ∨ ¬X4) ∧ (X1 ∨ ¬X4) ∧ (X2 ∨ X4) Equation 19.1
83

Figure 19.4: (a) Karnaugh map of the X1, X2, X3 and X4. (b) Flow charts of flipping all the literals
in only one unsatisfied clause. Different colors of the arrows represent the operation by different
unsatisfied clauses. Yellow marked 0100 and 0110 are the solutions to this equation. (c) Flow
charts of flipping all the literals in all the unsatisfied clauses. Different colors of the arrows
represent the operation by different unsatisfied clauses. Yellow marked 0100 and 0110 are the
solutions to this equation.

An updated algorithm is that only one random literal is flipped per clause. There are many
advantages to this algorithm. Firstly, only flipping one literal will not jump any solutions compared
with flipping all literals which will lead some solutions cannot be achieved forever. Secondly,
flipping only one literal will get rid of the infinite loop problem due to the multiple choices. Both
advantages are shown in Figure 19.5. Furthermore, only flipping one literal will improve the
stability of the circuit and totally resolve the stuck issues in the circuit. The results will be shown
in the following part. Finally, this algorithm could make the searching process increase
dramatically, which will be discussed in the next section.
84

Figure 19.5: (a) Flow charts of flipping only one of the literals in only one unsatisfied clause.
Different colors of the arrows represent the operation by different unsatisfied clauses. Yellow
marked 0100 and 0110 are the solutions to this equation. (b) Flow charts of flipping only one of
the literals in all the unsatisfied clauses. Different colors of the arrows represent the operation by
different unsatisfied clauses. Yellow marked 0100 and 0110 are the solutions to this equation.

LTspice is used as the simulation software for some equations with variable numbers
smaller than 20. In Figure 19.6, random voltage sources are used in the clause-logic block to realize
the function of only turning on one port at the same time. There are lots of similar functions which
can accomplish this goal, too. Such as clock function, random number generator, single pole
multiple throw switch/relay, etc.
85

Figure 19.6: Circuit of clause-logic block using LTspice simulation. AO6407: PMOS Part No.
using in the circuit. SW2: switch with 2V threshold voltage. SW3: switch with 3V threshold
voltage. Vdd: 5V.

86

Chapter 20 Performance and Optimization of the Circuit Accelerator
20.1 Simulation Results by LTSPICE
LTspice is used at the start to simulate some problems with few variables. Figure 20.1 shows a
simulation of circuit accelerator for solving Equation 20.1. Equation 20.1 is satisfiable and 001110
is one of the solutions. Figure 20.2 shows the simulation results of the SPICE. From the result we
can see the initial state of X1~ X6 is 100001. After less than 0.2us tuning time, the circuit finally
stabilizes at the solution 001110.

Figure 20.1: SPICE simulation of circuit accelerator for solving Equation 20.1.

(¬X1 ∨ X5) ∧ (¬X2 ∨ X3 ∨ ¬X6) ∧ (¬X1 ∨ ¬X3 ∨ ¬X5) ∧ (X2 ∨ ¬X6) ∧ (X1 ∨ X4) ∧ (X3 ∨ ¬X5∨ X6)
∧ (¬X1 ∨ ¬X2 ∨ X4) Equation 20.1
87

Figure 20.2: SPICE simulation results of Equation 20.1.

Table 20.1 shows the completeness test results of Equation 20.1. From the table we can
conclude that no matter the initial state changes, the analog circuit could always find the solutions.

Table 20.1: SPICE simulation results of the Equation 20.1 under different initial states.
88

Another important feature is what the performance of the unsatisfiable equation will show.
Figure 20.3 shows the SPICE simulation results of Equation 20.2. Equation 20.2 is an unsatisfiable
SAT equation. From the results, the literals always bounce back and force because no solution can
satisfy all the constraint circuit simultaneously. The performance of the unsatisfiable formula is
totally different from a satisfiable formula and distinguishable.
(¬X1 ∨ ¬X2) ∧ (¬X1 ∨ X2 ∨ ¬X3) ∧ (¬X1 ∨ X3 ∨ ¬X4) ∧ (X1 ∨ ¬ X4) ∧ (X2 ∨ X4) ∧ (X1 ∨ ¬ X2 ∨ X4)
Equation 20.2

Figure 20.3: SPICE simulation results of Equation 20.2.

The above results show some easy problems with few variables and small clause variable
ratio α. When the α is larger than 4, the problem becomes a hard problem and the difficulty to
solve the problem dramatically increases
222
. Equation 20.3 is a problem from benchmark SAT
problems
222
. It contains 20 variables and 91 clauses. 29 solutions exist from the 1048576
possibilities. Figure 20.4 shows the SPICE simulation of circuit accelerator for solving Equation.
Figure 20.5 shows the SPICE simulation results of the Equation 20.3. Depending on the initial
condition, it takes from 60 ns to 3.15 us to stabilize. The average calculation time is around 520ns.
Considering that the flipping time is 26ns based on the PMOS and inverter component in the circuit,
89

the circuit only takes tens of cycles to find the solution. Compared with lower than 0.003%
satisfaction rate for this equation, the calculation time is extremely fast.
(¬X10 ∨ ¬X16 ∨ X5) ∧ (X16 ∨ ¬X6 ∨ X5) ∧ (¬X17 ∨ ¬X14 ∨ ¬X18) ∧ (¬X10 ∨ ¬X15 ∨ X19)
∧ (¬X1 ∨ ¬X9 ∨ ¬X18) ∧ ( X3 ∨ X7 ∨ ¬X6 ) ∧ ( ¬X13 ∨ X1 ∨ X6 ) ∧ (¬X2 ∨ ¬X16 ∨ ¬X20)
∧ (X7 ∨ X8 ∨ X18) ∧ (¬X7 ∨ X10 ∨ ¬X20 ) ∧ (X2 ∨ ¬X14 ∨ ¬X17) ∧ (X2 ∨ X1 ∨ X19) ∧ (X7
∨ ¬X20 ∨ ¬X1) ∧ (¬X11 ∨ X1 ∨ ¬X17) ∧ (X3 ∨ ¬X12 ∨ X19) ∧ (¬X3 ∨ ¬X13 ∨ X6) ∧ (¬X13
∨ X3 ∨ ¬X12) ∧ (X5 ∨ ¬X7 ∨ ¬X12) ∧ (X20 ∨ X8 ∨ ¬X16) ∧ (¬X13 ∨ ¬X6 ∨ X19 ) ∧ ( ¬X5
∨ X1 ∨ X14 ) ∧ (X9 ∨ ¬X5 ∨ X18) ∧ (¬X12 ∨ ¬X17 ∨ ¬X1) ∧ (¬X20 ∨ ¬X16 ∨ X19 ) ∧ (X 12
∨ X10 ∨ ¬X11) ∧ (X6 ∨ ¬X7 ∨ ¬X2) ∧ (X13 ∨ ¬X10 ∨ X17) ∧ (¬X20 ∨ X8 ∨ ¬X16) ∧ (¬X10
∨ ¬X1 ∨ ¬X8) ∧ (¬X7 ∨ ¬X3 ∨ X19) ∧ (X19 ∨ ¬X1 ∨ ¬X6) ∧ (X19 ∨ ¬X2 ∨ X13) ∧ (¬X2
∨ X20 ∨ ¬X9) ∧ (¬X8 ∨ ¬X20 ∨ X16 ) ∧ (¬X13 ∨ ¬X1 ∨ X11) ∧ (X15 ∨ ¬X12 ∨ ¬X6) ∧
(¬X17 ∨ ¬X19 ∨ X9) ∧ (X19 ∨ ¬X18 ∨ X16) ∧ (X7 ∨ ¬X8 ∨ ¬X19) ∧ (¬X3 ∨ ¬X7 ∨ ¬X1) ∧
(X7 ∨ ¬X17 ∨ ¬X16) ∧ (¬X2 ∨ ¬X14 ∨ X1) ∧ (¬X18 ∨ ¬X10 ∨ ¬X8) ∧ (¬X16 ∨ X5 ∨ X8 )
∧ (X4 ∨ X8 ∨ X10 ) ∧ (¬X20 ∨ ¬X11 ∨ ¬X19) ∧ (X8 ∨ ¬X16 ∨ ¬X6) ∧ ( X18 ∨ X12 ∨ X8 )
∧ (¬X5 ∨ ¬X20 ∨ ¬X10) ∧ (X16 ∨ X17 ∨ X3) ∧ (X7 ∨ ¬X1 ∨ ¬X17) ∧ (X17 ∨ ¬X4 ∨ X7) ∧
(X20 ∨ ¬X9 ∨ ¬X13) ∧ ( X13 ∨ X18 ∨ X16 ) ∧ ( ¬X16 ∨ ¬X6 ∨ X5 ) ∧ (X5 ∨ X17 ∨ X7) ∧
(¬X12 ∨ ¬X17 ∨ ¬X6) ∧ (¬X20 ∨ X19 ∨ ¬X5 ) ∧ (X9 ∨ ¬X19 ∨ X16) ∧ (¬X13 ∨ ¬X16 ∨ X11)
∧ (¬X4 ∨ ¬X19 ∨ ¬X18) ∧ (¬X13 ∨ X10 ∨ ¬X15) ∧ (X16 ∨ ¬ X7 ∨ ¬ X14) ∧ (¬X19 ∨ ¬ X7
∨ ¬X18) ∧ (¬X20 ∨ X5 ∨ X13) ∧ (X12 ∨ ¬ X6 ∨ X4) ∧ (X7 ∨ X9 ∨ ¬ X13) ∧ ( X16 ∨ X3 ∨
X7 ) ∧ ( X9 ∨ ¬X1 ∨ X12 ) ∧ (¬ X3 ∨ X14 ∨ X7) ∧ (X1 ∨ X15 ∨ X14) ∧ (¬ X8 ∨ ¬X11 ∨ X18 )
∧ (X19 ∨ ¬ X9 ∨ X7) ∧ (¬ X10 ∨ X6 ∨ X2) ∧ (X14 ∨ X18 ∨ ¬ X11) ∧ (¬X9 ∨ ¬X16 ∨ X14) ∧
(X1 ∨ X11 ∨ ¬X20) ∧ (X11 ∨ X12 ∨ ¬X4) ∧ (X13 ∨ ¬ X11 ∨ ¬X14) ∧ (X17 ∨ ¬X12 ∨ X9) ∧
(X14 ∨ X9 ∨ X1) ∧ ( X8 ∨ X19 ∨ X4 ) ∧ (X6 ∨ ¬X13 ∨ ¬X20) ∧ (¬ X2 ∨ ¬ X13 ∨ X11) ∧ (X14
∨ ¬X13 ∨ X17) ∧ (X9 ∨ ¬X11 ∨ X18) ∧ (¬X13 ∨ ¬ X6 ∨ X5) ∧ (X5 ∨ X19 ∨ ¬X18) ∧ (¬X4
∨ X10 ∨ X11) ∧ (¬ X18 ∨ ¬ X19 ∨ ¬X20) ∧ (X3 ∨ ¬X9 ∨ X8) Equation 20.3

90

Figure 20.4: SPICE simulation of circuit accelerator for solving Equation 20.3
.
91

Figure 20.5: SPICE simulation results of Equation 20.3. It takes 350 ns to find out the solutions.

20.2 Simulation Results by Cadence
When the SAT problem’s size grows larger and larger, the LTspice cannot solve the problem
efficiently. Under this situation, Cadence is used as the simulation software to simulate SAT
problem with much larger size. In addition, the device using in Cadence matches modern
semiconductor fabrication process. In this paper, TSMC 65nm process is used to fabricate the
PMOS and NMOS inside the circuit accelerator. After using more advanced process, the response
time for the device becomes faster. The response time of Cadence device is 35ps and the response
time of LTspice device is 26ns. The response time is defined by the pulse width to make a clause-
logic block flip in a 20 variable size circuit accelerator. Compared with the device used in LTspice,
the response time is faster around 1000X. This update makes the whole system have a much shorter
calculation time.
Unlike a random voltage source is used to realize the random function in LTspice. Here,
four digital random generators and 6 PMOS are implemented to realize the random switch function.
The random number generator could generate high and low voltage randomly in the desired
sampling rate. By our design, the top and bottom random number generators generate the random
92

numbers oppositely, as shown in Figure 20.6. Based on the circuit, one of the four lines will be
turned on. Three of them will be connected to the constraint circuit and the fourth is floated.

Figure 20.6: Schematic of the random switch function in Cadence.

Figure 20.7 shows the schematic of the circuit accelerator to solve Equation 20.3 by
Cadence. From the results shown in Figure 20.8, it only costs 3.2ns to get the final solution.
93

Figure 20.7: Cadence simulation of circuit accelerator for solving Equation 20.3.

94

Figure 20.8: Cadence simulation results of Equation 20.3. It takes 3.2 ns to find out the solutions.

20.3 Optimization of the Circuit Accelerator
When the size of the circuit grows larger and larger, the circuit should be optimized to achieve
better performance. In the following part, different parameters such as internal resistance of the
PMOS/NMOS, Vdd voltage and sampling rate of the random number generator would be discussed.
There are four types of the transistors in the circuit. They are PMOS and NMOS in the
inverter part. PMOS in the constraint circuit and PMOS in the random switch part. The internal
resistance is defined by the resistance during turning on state. The internal resistance of NMOS is
proportional to the ratio of length and width. The internal resistance of PMOS is proportional to
the ratio of three times of length and width due the mobility difference between the electrons and
the holes. In the inverter, we set the internal resistance the same for the PMOS and the NMOS.
The resistance of the inverter part, constraint part and the random switch part are R inverter, Rclause
95

and Rswitch respectively. We set the Rinverter: Rclause: Rswitch = 20:4:1 by tuning the length and the
width of the transistors.
Considered the voltage drop by different part of the device. Vdd is chose as 1.2 V rather
than 1V in this circuit. It satisfies the requirements of the TSMC 65nm node. A larger Vdd would
also make the response time of the circuit faster.
The sampling rate influences the calculation time dramatically. It also influences the
solving rate under limited solving time. When the variable size increases, the RC delay and the
complexity of the circuit increase. If the sampling rate is too fast, the values of the literals cannot
follow the change of the constraint circuit. Under this situation, some strange phenomena would
happen. For example, as shown in Figure 20.9, it is a result to solve an equation containing 20
variables. The sampling rate is 0.1ns here. Only three of the literals bounce back and force over a
long time range.

Figure 20.9: Cadence results with 0.1ns sampling rate. The equation contains 20 variables.
96

The sampling rate is related to the circuit size. When the circuit contains 20 variables, 0.5ns
sampling rate can solve all the equations we have tested. However, when the circuit size increases
to 50 variables, 0.5ns is not sufficient. Figure 20.10 (a) shows a result with 0.5ns sampling rate.
Figure 20.10 (b) shows a result with 1ns sampling rate. The threshold simulation time is 1.5us/3us.
Each simulation contains 3000 cycles. In Figure 20.10 (a), only few literals bounce back and force.

97

Figure 20.10: (a) Cadence results with 0.5ns sampling rate. (b) Cadence results with 1ns sampling
rate. The equation contains 20 variables. The whole simulation time is 1.5us/3us.

As the size of the circuit grows, auto generating circuit by the code using OceanScript
function in Cadence is used. The code to generate Equation 20.3 is used as an example, as attached
in Appendix B.
When the size of the circuit grows even larger, the sampling rate shows a very large
influence on the solving rate and the average solving time. Here we do sampling rate test on 125
variables size. The Table 20.2 shows the results. As we can see, the solving rate increases at first.
Then it maintains a flat region from 0.75ns to 1.25ns. When the sampling rate becomes even larger,
the solving rate becomes smaller. This phenomenon shows that in the real circuit, the frequency
of the random number generator should be optimized. An overlarge or a too small number will
make the circuit performance worse. The larger sampling rate will not make the solving
performance better can be explained as the too long time would make the circuit fall into the local
minima. These local minima will get the circuit stuck and make the circuit harder to go the next
state. A suitable sampling rate means that the circuit always work in an efficient region. This
efficient region will save the average calculation time, prevent the circuit stuck and increase the
solving rate of the different problems within threshold time.

Table 20.2: Solved cases and average calculation time under different sampling rates. 41 Equations
are simulated based on different sampling rates. Each equation contains 125 variables.

Sampling rate (ns) 0.5 0.75 0.9 1 1.1 1.25 1.5 2 2.5 4
Solved Cases 24 29 29 32 27 29 25 13 8 10
Average time (ns) 3796.8 3724 2343.5 4214.3 3308.4 6357 7702.9 5605 15899.8 22589.2
98

20.4 Pseudorandom Random and Solving Rate
Random in Cadence simulation is pseudorandom. Pseudorandom means that the same results will
be got after different times of simulation. From the test, we find out some equations could be
solved within a very short time. However, some equations cannot be solved within the threshold
time. Some problems can be solved after elongating the threshold time. Some problems are even
harder. Even though after very long time, they cannot be solved. Table 20.3 shows a 35-case test.
Each equation contains 100 variables. As we can see 28 of 35 could be solve with 10us. 4 of 35
could be solved after elongating the threshold time to 40us. 1 of 35 could solve after elongating
the threshold time to 80us. 2 of 35 cannot be solved.
99

Table 20.3: Solving time for different equations with 100 variables. Black label: solved within
10us. Blue label: Solved within 40us but larger than 10us. Red label: Unsolved within 40us.

However, all the 35 cases are satisfiable equations. The equations which cannot be solved
within the threshold time will perform the same results as the unsatisfiable equations. Under this
No. 1ns pulse 10000ns max 1ns pulse 40000ns max 1ns pulse 80000ns max
1 262
2 Over limit time Over limit time Over limit time
3 4638
4 2032
5 Over limit time 13954
6 72
7 274
8 Over limit time Over limit time 41489
9 Over limit time Over limit time Over limit time
10 1874
11 526
12 2718
13 834
14 Over limit time 25202
15 4365
16 2324
17 8285
18 76
19 239
20 1306
21 Over limit time 39158
22 6649
23 Over limit time 12792
24 1773
25 5945
26 1828
27 1110
28 623
29 145
30 2359
31 130
32 4967
33 878
34 252
35 826
100

situation, we cannot distinguish the difference them. We figured out two efficient methods to
decrease the solving time and increase the solving rate.
The first method is that we could give different seeds to the random number generators.
Different seeds mean that the random number generator could generate different number sequence.
This method works because in the simulation the random is pseudorandom. We use the different
seed to simulate the real random and we can find that some of the random sequence will
dramatically decrease the solving time. All the cases could be solved within threshold time if the
variable size is under 125. This 100% solving rate Due the simulation time limit, larger than 125
variable size will not be shown by simulation. After the real chips fabricated, testing on chip would
save more time to prove our predictions.
The second method is that we could give different sampling rates to the random number
generators. Different sampling rate would also lead to different path to the final solutions. All the
cases could be solved within threshold time if the variable size is under 125 by implementing this
method. Due the simulation time limit, larger than 125 variable size will also not be shown by
simulation. After the real chips fabricated, testing on chip would save more time to prove our
predictions.

20.5 Average Time Versus Variable Size Fitting
From the benchmark problems
222
, each variable size listed on the website has been simulated by
our circuit accelerator. Figures 20.11 (a) - (i) show the simulation results from 20 variables to 250
variables. The threshold time for 20 variables, 50 variables, 75 variables, 100 variables, 125
101

variables, 150 variables, 175 variable, 200 variables, 250 variables are 0.5us, 3us, 6us, 10us, 15us,
20us, 25us, 32us and 50us respectively. Each of them contains 16 successfully solved case.

102

103

Figure 20.11: (a) - (i) show the simulation results from 20 variables to 250 variables. The threshold
time for 20 variables, 50 variables, 75 variables, 100 variables, 125 variables, 150 variables, 175
variable, 200 variables, 250 variables are 0.5us, 3us, 6us, 10us, 15us, 20us, 25us, 32us and 50us
respectively.
104

Figures 20.12 (a) - (i) show the histograms of each size of SAT problems. From Figures
20.12, for every size of the problem, most of them would be solved within a short time range.
However, some of them needs much more time to be solved. Based on the discussion in the Chapter
20.4, these cases with long solving time could also be solved within a short time by implementing
different seeds for random number generator or different sampling rates methods.

Figure 20.12: (a) - (i) show the histograms of the simulation results from 20 variables to 250
variables.

105

From the overall data, average calculation time versus variable size relationship is figured
out. Figures 21.13 (a) – (c) shows the fitting using Linear Fit, Polynomial Fit and Exponential Fit.

Figure 21.13: Average calculation time versus variable size relationship. (a) Linear Fit. (b)
Polynomial Fit. (c) Exponential Fit.

By using Linear Fit method, Average calculation time T and variable size x shows:
𝑇 = 𝑎 + 𝑏 ∗ 𝑥 , 𝑎 = −2088.9, 𝑏 = 52.88
By using Polynomial Fit method, Average calculation time T and variable size x shows:
𝑇 = 𝑎 + 𝑏 ∗ 𝑥 + 𝑐 ∗ 𝑥 2
, 𝑎 = −942, 𝑏 = 28.9, 𝑐 = 0.090
By using Exponential Fit method, Average calculation time T and variable size x shows:
𝑇 = 𝑎 ∗ 𝑒 𝑟 ∗𝑥 + 𝑐 , 𝑎 = 11482, 𝑟 = 0.00303, 𝑐 = −12639
Table 20.4 show the fitting results. Two criteria are used here. We calculated the error at
zero point and the residue sum of square for each fitting method. The calculation time at zero point
should be zero based on the fundamental truth. The smaller residue sum of square means that the
smaller fitting error exists in the fitting type. From the table we can conclude that the average
calculation time shows polynomial fit increasing versus the variable size. Basically, the complexity
of the SAT problem is exponential increase with the variable size. The reason of our circuit
106

accelerator can achieve polynomial increasing calculation time can be explained as this: Although
the SAT problem complexity increases exponentially, for our circuit accelerator, for each time step,
the random switch part will generate a new circuit based on the choices of each switch at the
constraint circuit. The whole circuit then follows the connection to change the potential values of
each literal. We can think about under every connection way, the circuit should follow the circuit
law and the current conditions of each literal to change the states. A cost function exists and the
circuit will finally stabilize at a local minimum based on the connection of the circuit. If the random
switch function does not exist, the circuit will probably get stuck in one of the local minima and
cannot find the global minima, which is one of the solutions of this equation. By introducing the
random switch function, the circuit is always changing which means that the cost function is
always changing. A continuous changing cost function will prevent the circuit trapped into the
local minima. For each change within a time step, the whole circuit could change. This means that
even though the complexity of the circuit increases exponentially, each search step in our circuit
accelerator also increases exponentially. Based on this, finally we can get a polynomial calculation
time relationship versus variable size.

Table 20.4: Fitting performance of Linear fit, Polynomial Fit and Exponential Fit.

Linear Fit Polynomial Fit Exponential Fit
Residue Sum of Square 3.29E+06 1.55E+06 1.73E+06
Error at zero point 2089 942 1157
Performance Poor Good Medium
107

Chapter 21 Summary
In summary, we can claim that the circuit accelerator for Boolean Satisfiability problem has been
invented successfully. The simulation results show polynomial relationship between calculation
time and the variable size. This circuit accelerator will open a door to solve the SAT problem and
pave the way for accelerating all NP-complete problem.
In the future, my lab mate Zerui Liu will take charge of taping out the real chip and finish
this project. We anticipate that the circuit accelerator for SAT problem can be implemented soon
and be used for a broad spectrum of applications in the future.

108

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127

Appendix A
Publications & Patents
1. Deming Meng
†
, Zerui Liu
†
, Guangxu Su
†
, Pan Hu et al, Wei Wu*. “Ultrafast Early Warning
of Heart Attack through Plasmon-Enhanced Raman using Collapsible Nanofingers and
Machine Learning.” Small. (Featured on cover)
2. Yunxiang Wang, Buyun Chen, Deming Meng, Boxiang Song et al, Wei Wu*. “Hot Electron
Driven Photocatalysis using Sub-5 nm Gap Plasmonic Nanofinger Arrays.” Nanomaterials.
3. Deming Meng
†
, Max R. Lien
†
, Zerui Liu, Mashnoon A. Sakib, Yongkui Tang, Wei Wu, and
Michelle L. Povinelli*, “Experimental Characterization of a Silicon Nitride Photonic Crystal
Light Sail.” Optical Materials Express. (Featured on cover)
4. Deming Meng, Yifei Wang et al, Wei Wu*. “Optical metrology of characterizing wetting
states.” Journal of Vacuum Science & Technology B.
5. Buyun Chen, Hao Yang, Boxiang Song, Deming Meng, Xiaodong Yan et al, Wei Wu*. “A
memristor-based hybrid analog-digital computing platform for mobile robotics.” Science
Robotics.
6. Hao Yang, Buyun Chen, Boxiang Song, Deming Meng, Subodh C. Tiwari et al, Wei Wu*.
“Memristive Device Characteristics Engineering by Controlling the Crystallinity of Switching
Layer Material.” ACS Applied Electronic Materials.
7. Hao Yang, He Liu, Boxiang Song, Yuanrui Li, Deming Meng, Buyun Chen et al, Wei Wu*.
“Effects of roughness and resonant-mode engineering in all-dielectric metasurfaces.”
Nanophotonics.
8. Boxiang Song, Zhihao Jiang, Zerui Liu, Yunxiang Wang, Fanxin Liu, Stephen B. Cronin, Hao
Yang, Deming Meng, Buyun Chen et al, Wei Wu*. “Probing the Mechanisms of Strong
Fluorescence Enhancement in Plasmonic Nanogaps with Sub-nanometer Precision.” ACS
Nano.
9. Deming Meng*, Bingqian Li, Mengyan Zeng, Chenhui Li, Rucheng Dai. “Study on Optical
and Thermal Properties of Low-E Glass.” Advanced Materials Research.
10. Deming Meng*, Shaoling Su. “Experimental research on leaching characteristics of one high
arsenic-containing indissolvable gold ore.” Gold (in Chinese).
doi: 10.11792/hj20140513
11. Liantao Yu, Deming Meng, Shujuan Dai*, Zhigang Hu, Jiahong Han. “The flotation
experiment on a certain arsenic gold ore.” CHINA MINING MAGAZINE (in Chinese).
http://d.wanfangdata.com.cn/Periodical_zgky201405035.aspx
128

12. Mingte Xu, Deming Meng, Shujuan Dai*. “Research Status of Pretreatment Techniques for
Refractory Gold Ores.” NON-FERROUS MINING AND METALLURGY (in Chinese).
http://d.wanfangdata.com.cn/Periodical_ysky201402006.aspx
† equal contribution * Corresponding Author
13. Haitao Shen, Deming Meng, et al. A Two-Wheel Self-Balanced Electric Vehicle. China
Patent, CN 203381739 U, 2014.
14. Wei Wu, Deming Meng, Zerui Liu et al. Circuit Accelerator for Boolean Satisfiability. U.S.
Patent, 63,410,460; issued September 27
th
, 2022.

129

Appendix B
Code of Auto Generation Circuit by Cadence

// Library name: Deming_SAT
// Cell name: inverter
// View name: schematic
subckt inverter Input Output
M0 (Output Input 0 0) nch_mac l=60n w=120.0n multi=1 nf=1 sigma=1 \
sd=350.0n ad=3.45e-14 as=3.45e-14 pd=800n ps=800n nrd=1.45833 \
nrs=1.45833 sa=100n sb=100n sca=0 scb=0 scc=0 mismatchflag=1
M1 (Output Input vdd! vdd!) pch_mac l=60n w=360.0n multi=1 nf=1 \
sigma=1 sd=200n ad=6.3e-14 as=6.3e-14 pd=1.07u ps=1.07u \
nrd=0.277778 nrs=0.277778 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
ends inverter
// End of subcircuit definition.

// Library name: Deming_SAT
// Cell name: clause1
// View name: schematic
subckt clause1 p1 p2 p3
I284 (net36) rand_bit_stream tperiod=0.1n seed=2 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I285 (net29) rand_bit_stream tperiod=0.1n seed=1 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I280 (net30) rand_bit_stream tperiod=0.1n seed=1 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
I279 (net12) rand_bit_stream tperiod=0.1n seed=2 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
M633 (net40 net36 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M632 (net32 net29 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
130

M626 (net23 p1 net40 net40) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M630 (net17 p1 net39 net39) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M631 (net15 p1 net38 net38) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M625 (net39 net12 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M622 (net22 p2 net23 net23) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M623 (net16 p2 net17 net17) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M624 (net14 p2 net15 net15) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M621 (net38 net36 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M620 (net31 net30 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M616 (p3 p3 net22 net22) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M618 (p2 p3 net16 net16) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
131

sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M619 (p1 p3 net14 net14) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M617 (net37 net12 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
V96 (net9 0) vsource dc=1.2 type=dc
V97 (net8 0) vsource type=pulse val0=0 val1=1.2 period=2 delay=10n \
rise=10p fall=10p width=1
ends clause1
// End of subcircuit definition.

// Library name: Deming_SAT
// Cell name: clause2
// View name: schematic
subckt clause2 p1 p2 p3
V97 (net8 0) vsource type=pulse val0=0 val1=1.2 period=2 delay=10n \
rise=10p fall=10p width=1
I284 (net36) rand_bit_stream tperiod=0.1n seed=4 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I285 (net29) rand_bit_stream tperiod=0.1n seed=3 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I280 (net30) rand_bit_stream tperiod=0.1n seed=3 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
I279 (net12) rand_bit_stream tperiod=0.1n seed=4 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
M633 (net40 net36 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M632 (net32 net29 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M626 (net23 p1 net40 net40) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
132

nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M630 (net17 p1 net39 net39) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M631 (net15 p1 net38 net38) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M625 (net39 net12 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M622 (net22 p2 net23 net23) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M623 (net16 p2 net17 net17) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M624 (net14 p2 net15 net15) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M621 (net38 net36 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M620 (net31 net30 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M616 (p3 p3 net22 net22) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M618 (p2 p3 net16 net16) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
133

mismatchflag=1
M619 (p1 p3 net14 net14) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M617 (net37 net12 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
V96 (net9 0) vsource dc=1.2 type=dc
ends clause2
// End of subcircuit definition.

// Library name: Deming_SAT
// Cell name: clause3
// View name: schematic
subckt clause3 p1 p2 p3
M633 (net40 net36 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M632 (net32 net29 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M626 (net23 p1 net40 net40) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M630 (net17 p1 net39 net39) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M631 (net15 p1 net38 net38) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M625 (net39 net12 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
134

M622 (net22 p2 net23 net23) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M623 (net16 p2 net17 net17) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M624 (net14 p2 net15 net15) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M621 (net38 net36 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M620 (net31 net30 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M616 (p3 p3 net22 net22) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M618 (p2 p3 net16 net16) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M619 (p1 p3 net14 net14) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M617 (net37 net12 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
I284 (net36) rand_bit_stream tperiod=0.1n seed=6 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I285 (net29) rand_bit_stream tperiod=0.1n seed=5 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I279 (net12) rand_bit_stream tperiod=0.1n seed=6 vlogic_high=0 \
135

vlogic_low=1.2 tdel=10n trise=10p tfall=10p
I280 (net30) rand_bit_stream tperiod=0.1n seed=5 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
V96 (net9 0) vsource dc=1.2 type=dc
V97 (net8 0) vsource type=pulse val0=0 val1=1.2 period=2 delay=10n \
rise=10p fall=10p width=1
ends clause3
// End of subcircuit definition.

// Library name: Deming_SAT
// Cell name: initial
// View name: schematic
subckt initial _net0
V2 (net3 0) vsource type=pulse val0=0 val1=2 period=1 rise=10p \
fall=10p width=10n
W5 (_net0 net7 net3 0) relay vt1=0 vt2=1 ropen=1T rclosed=10.00m
V9 (net7 0) vsource dc=1 type=dc
ends initial
// End of subcircuit definition.

// Library name: Deming_SAT
// Cell name: clause4
// View name: schematic
subckt clause4 p1 p2 p3
I284 (net36) rand_bit_stream tperiod=0.1n seed=8 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I285 (net29) rand_bit_stream tperiod=0.1n seed=7 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I280 (net30) rand_bit_stream tperiod=0.1n seed=7 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
I279 (net12) rand_bit_stream tperiod=0.1n seed=8 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
M633 (net40 net36 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M632 (net32 net29 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M626 (net23 p1 net40 net40) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
136

sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M630 (net17 p1 net39 net39) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M631 (net15 p1 net38 net38) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M625 (net39 net12 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M622 (net22 p2 net23 net23) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M623 (net16 p2 net17 net17) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M624 (net14 p2 net15 net15) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M621 (net38 net36 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M620 (net31 net30 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M616 (p3 p3 net22 net22) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M618 (p2 p3 net16 net16) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
137

nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M619 (p1 p3 net14 net14) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M617 (net37 net12 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
V96 (net9 0) vsource dc=1.2 type=dc
V97 (net8 0) vsource type=pulse val0=0 val1=1.2 period=2 delay=10n \
rise=10p fall=10p width=1
ends clause4
// End of subcircuit definition.

// Library name: Deming_SAT
// Cell name: clause5
// View name: schematic
subckt clause5 p1 p2 p3
I284 (net36) rand_bit_stream tperiod=0.1n seed=10 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I285 (net29) rand_bit_stream tperiod=0.1n seed=9 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I280 (net30) rand_bit_stream tperiod=0.1n seed=9 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
I279 (net12) rand_bit_stream tperiod=0.1n seed=10 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
M633 (net40 net36 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M632 (net32 net29 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M626 (net23 p1 net40 net40) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M630 (net17 p1 net39 net39) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
138

sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M631 (net15 p1 net38 net38) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M625 (net39 net12 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M622 (net22 p2 net23 net23) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M623 (net16 p2 net17 net17) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M624 (net14 p2 net15 net15) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M621 (net38 net36 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M620 (net31 net30 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M616 (p3 p3 net22 net22) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M618 (p2 p3 net16 net16) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M619 (p1 p3 net14 net14) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
139

nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M617 (net37 net12 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
V96 (net9 0) vsource dc=1.2 type=dc
V97 (net8 0) vsource type=pulse val0=0 val1=1.2 period=2 delay=10n \
rise=10p fall=10p width=1
ends clause5
// End of subcircuit definition.

// Library name: Deming_SAT
// Cell name: clause6
// View name: schematic
subckt clause6 p1 p2 p3
I284 (net36) rand_bit_stream tperiod=0.1n seed=12 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I285 (net29) rand_bit_stream tperiod=0.1n seed=11 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I280 (net30) rand_bit_stream tperiod=0.1n seed=11 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
I279 (net12) rand_bit_stream tperiod=0.1n seed=12 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
M633 (net40 net36 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M632 (net32 net29 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M626 (net23 p1 net40 net40) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M630 (net17 p1 net39 net39) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M631 (net15 p1 net38 net38) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
140

sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M625 (net39 net12 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M622 (net22 p2 net23 net23) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M623 (net16 p2 net17 net17) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M624 (net14 p2 net15 net15) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M621 (net38 net36 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M620 (net31 net30 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M616 (p3 p3 net22 net22) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M618 (p2 p3 net16 net16) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M619 (p1 p3 net14 net14) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M617 (net37 net12 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
141

nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
V96 (net9 0) vsource dc=1.2 type=dc
V97 (net8 0) vsource type=pulse val0=0 val1=1.2 period=2 delay=10n \
rise=10p fall=10p width=1
ends clause6
// End of subcircuit definition.

// Library name: Deming_SAT
// Cell name: clause7
// View name: schematic
subckt clause7 p1 p2 p3
I284 (net36) rand_bit_stream tperiod=0.1n seed=14 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I285 (net29) rand_bit_stream tperiod=0.1n seed=13 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I280 (net30) rand_bit_stream tperiod=0.1n seed=13 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
I279 (net12) rand_bit_stream tperiod=0.1n seed=14 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
M633 (net40 net36 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M632 (net32 net29 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M626 (net23 p1 net40 net40) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M630 (net17 p1 net39 net39) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M631 (net15 p1 net38 net38) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M625 (net39 net12 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
142

sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M622 (net22 p2 net23 net23) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M623 (net16 p2 net17 net17) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M624 (net14 p2 net15 net15) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M621 (net38 net36 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M620 (net31 net30 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M616 (p3 p3 net22 net22) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M618 (p2 p3 net16 net16) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M619 (p1 p3 net14 net14) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M617 (net37 net12 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
V96 (net9 0) vsource dc=1.2 type=dc
V97 (net8 0) vsource type=pulse val0=0 val1=1.2 period=2 delay=10n \
143

rise=10p fall=10p width=1
ends clause7
// End of subcircuit definition.

// Library name: Deming_SAT
// Cell name: clause8
// View name: schematic
subckt clause8 p1 p2 p3
I284 (net36) rand_bit_stream tperiod=0.1n seed=16 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I285 (net29) rand_bit_stream tperiod=0.1n seed=15 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I280 (net30) rand_bit_stream tperiod=0.1n seed=15 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
I279 (net12) rand_bit_stream tperiod=0.1n seed=16 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
M633 (net40 net36 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M632 (net32 net29 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M626 (net23 p1 net40 net40) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M630 (net17 p1 net39 net39) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M631 (net15 p1 net38 net38) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M625 (net39 net12 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M622 (net22 p2 net23 net23) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
144

sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M623 (net16 p2 net17 net17) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M624 (net14 p2 net15 net15) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M621 (net38 net36 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M620 (net31 net30 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M616 (p3 p3 net22 net22) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M618 (p2 p3 net16 net16) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M619 (p1 p3 net14 net14) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M617 (net37 net12 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
V96 (net9 0) vsource dc=1.2 type=dc
V97 (net8 0) vsource type=pulse val0=0 val1=1.2 period=2 delay=10n \
rise=10p fall=10p width=1
ends clause8
// End of subcircuit definition.

145

// Library name: Deming_SAT
// Cell name: clause9
// View name: schematic
subckt clause9 p1 p2 p3
I284 (net36) rand_bit_stream tperiod=0.1n seed=18 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I285 (net29) rand_bit_stream tperiod=0.1n seed=17 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I280 (net30) rand_bit_stream tperiod=0.1n seed=17 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
I279 (net12) rand_bit_stream tperiod=0.1n seed=18 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
M633 (net40 net36 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M632 (net32 net29 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M626 (net23 p1 net40 net40) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M630 (net17 p1 net39 net39) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M631 (net15 p1 net38 net38) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M625 (net39 net12 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M622 (net22 p2 net23 net23) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M623 (net16 p2 net17 net17) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
146

sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M624 (net14 p2 net15 net15) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M621 (net38 net36 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M620 (net31 net30 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M616 (p3 p3 net22 net22) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M618 (p2 p3 net16 net16) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M619 (p1 p3 net14 net14) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M617 (net37 net12 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
V96 (net9 0) vsource dc=1.2 type=dc
V97 (net8 0) vsource type=pulse val0=0 val1=1.2 period=2 delay=10n \
rise=10p fall=10p width=1
ends clause9
// End of subcircuit definition.

// Library name: Deming_SAT
// Cell name: clause10
// View name: schematic
subckt clause10 p1 p2 p3
147

I284 (net36) rand_bit_stream tperiod=0.1n seed=20 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I285 (net29) rand_bit_stream tperiod=0.1n seed=19 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I280 (net30) rand_bit_stream tperiod=0.1n seed=19 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
I279 (net12) rand_bit_stream tperiod=0.1n seed=20 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
M633 (net40 net36 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M632 (net32 net29 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M626 (net23 p1 net40 net40) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M630 (net17 p1 net39 net39) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M631 (net15 p1 net38 net38) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M625 (net39 net12 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M622 (net22 p2 net23 net23) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M623 (net16 p2 net17 net17) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M624 (net14 p2 net15 net15) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
148

sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M621 (net38 net36 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M620 (net31 net30 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M616 (p3 p3 net22 net22) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M618 (p2 p3 net16 net16) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M619 (p1 p3 net14 net14) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M617 (net37 net12 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
V96 (net9 0) vsource dc=1.2 type=dc
V97 (net8 0) vsource type=pulse val0=0 val1=1.2 period=2 delay=10n \
rise=10p fall=10p width=1
ends clause10
// End of subcircuit definition.

// Library name: Deming_SAT
// Cell name: clause11
// View name: schematic
subckt clause11 p1 p2 p3
I284 (net36) rand_bit_stream tperiod=0.1n seed=22 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I285 (net29) rand_bit_stream tperiod=0.1n seed=21 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
149

I280 (net30) rand_bit_stream tperiod=0.1n seed=21 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
I279 (net12) rand_bit_stream tperiod=0.1n seed=22 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
M633 (net40 net36 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M632 (net32 net29 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M626 (net23 p1 net40 net40) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M630 (net17 p1 net39 net39) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M631 (net15 p1 net38 net38) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M625 (net39 net12 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M622 (net22 p2 net23 net23) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M623 (net16 p2 net17 net17) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M624 (net14 p2 net15 net15) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M621 (net38 net36 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
150

sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M620 (net31 net30 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M616 (p3 p3 net22 net22) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M618 (p2 p3 net16 net16) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M619 (p1 p3 net14 net14) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M617 (net37 net12 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
V96 (net9 0) vsource dc=1.2 type=dc
V97 (net8 0) vsource type=pulse val0=0 val1=1.2 period=2 delay=10n \
rise=10p fall=10p width=1
ends clause11
// End of subcircuit definition.

// Library name: Deming_SAT
// Cell name: clause12
// View name: schematic
subckt clause12 p1 p2 p3
I284 (net36) rand_bit_stream tperiod=0.1n seed=24 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I285 (net29) rand_bit_stream tperiod=0.1n seed=23 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I280 (net30) rand_bit_stream tperiod=0.1n seed=23 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
I279 (net12) rand_bit_stream tperiod=0.1n seed=24 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
151

M633 (net40 net36 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M632 (net32 net29 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M626 (net23 p1 net40 net40) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M630 (net17 p1 net39 net39) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M631 (net15 p1 net38 net38) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M625 (net39 net12 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M622 (net22 p2 net23 net23) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M623 (net16 p2 net17 net17) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M624 (net14 p2 net15 net15) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M621 (net38 net36 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M620 (net31 net30 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
152

sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M616 (p3 p3 net22 net22) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M618 (p2 p3 net16 net16) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M619 (p1 p3 net14 net14) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M617 (net37 net12 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
V96 (net9 0) vsource dc=1.2 type=dc
V97 (net8 0) vsource type=pulse val0=0 val1=1.2 period=2 delay=10n \
rise=10p fall=10p width=1
ends clause12
// End of subcircuit definition.

// Library name: Deming_SAT
// Cell name: clause13
// View name: schematic
subckt clause13 p1 p2 p3
I284 (net36) rand_bit_stream tperiod=0.1n seed=26 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I285 (net29) rand_bit_stream tperiod=0.1n seed=25 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I280 (net30) rand_bit_stream tperiod=0.1n seed=25 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
I279 (net12) rand_bit_stream tperiod=0.1n seed=26 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
M633 (net40 net36 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
153

M632 (net32 net29 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M626 (net23 p1 net40 net40) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M630 (net17 p1 net39 net39) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M631 (net15 p1 net38 net38) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M625 (net39 net12 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M622 (net22 p2 net23 net23) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M623 (net16 p2 net17 net17) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M624 (net14 p2 net15 net15) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M621 (net38 net36 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M620 (net31 net30 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M616 (p3 p3 net22 net22) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
154

sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M618 (p2 p3 net16 net16) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M619 (p1 p3 net14 net14) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M617 (net37 net12 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
V96 (net9 0) vsource dc=1.2 type=dc
V97 (net8 0) vsource type=pulse val0=0 val1=1.2 period=2 delay=10n \
rise=10p fall=10p width=1
ends clause13
// End of subcircuit definition.

// Library name: Deming_SAT
// Cell name: clause14
// View name: schematic
subckt clause14 p1 p2 p3
I284 (net36) rand_bit_stream tperiod=0.1n seed=28 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I285 (net29) rand_bit_stream tperiod=0.1n seed=27 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I280 (net30) rand_bit_stream tperiod=0.1n seed=27 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
I279 (net12) rand_bit_stream tperiod=0.1n seed=28 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
M633 (net40 net36 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M632 (net32 net29 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
155

M626 (net23 p1 net40 net40) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M630 (net17 p1 net39 net39) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M631 (net15 p1 net38 net38) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M625 (net39 net12 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M622 (net22 p2 net23 net23) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M623 (net16 p2 net17 net17) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M624 (net14 p2 net15 net15) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M621 (net38 net36 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M620 (net31 net30 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M616 (p3 p3 net22 net22) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M618 (p2 p3 net16 net16) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
156

sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M619 (p1 p3 net14 net14) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M617 (net37 net12 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
V96 (net9 0) vsource dc=1.2 type=dc
V97 (net8 0) vsource type=pulse val0=0 val1=1.2 period=2 delay=10n \
rise=10p fall=10p width=1
ends clause14
// End of subcircuit definition.

// Library name: Deming_SAT
// Cell name: clause15
// View name: schematic
subckt clause15 p1 p2 p3
I284 (net36) rand_bit_stream tperiod=0.1n seed=30 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I285 (net29) rand_bit_stream tperiod=0.1n seed=29 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I280 (net30) rand_bit_stream tperiod=0.1n seed=29 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
I279 (net12) rand_bit_stream tperiod=0.1n seed=30 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
M633 (net40 net36 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M632 (net32 net29 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M626 (net23 p1 net40 net40) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
157

M630 (net17 p1 net39 net39) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M631 (net15 p1 net38 net38) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M625 (net39 net12 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M622 (net22 p2 net23 net23) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M623 (net16 p2 net17 net17) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M624 (net14 p2 net15 net15) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M621 (net38 net36 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M620 (net31 net30 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M616 (p3 p3 net22 net22) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M618 (p2 p3 net16 net16) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M619 (p1 p3 net14 net14) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
158

sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M617 (net37 net12 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
V96 (net9 0) vsource dc=1.2 type=dc
V97 (net8 0) vsource type=pulse val0=0 val1=1.2 period=2 delay=10n \
rise=10p fall=10p width=1
ends clause15
// End of subcircuit definition.

// Library name: Deming_SAT
// Cell name: clause16
// View name: schematic
subckt clause16 p1 p2 p3
I284 (net36) rand_bit_stream tperiod=0.1n seed=32 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I285 (net29) rand_bit_stream tperiod=0.1n seed=31 vlogic_high=1.2 \
vlogic_low=0 tdel=10n trise=10p tfall=10p
I280 (net30) rand_bit_stream tperiod=0.1n seed=31 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
I279 (net12) rand_bit_stream tperiod=0.1n seed=32 vlogic_high=0 \
vlogic_low=1.2 tdel=10n trise=10p tfall=10p
M633 (net40 net36 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M632 (net32 net29 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M626 (net23 p1 net40 net40) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M630 (net17 p1 net39 net39) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
159

M631 (net15 p1 net38 net38) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M625 (net39 net12 net32 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M622 (net22 p2 net23 net23) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M623 (net16 p2 net17 net17) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M624 (net14 p2 net15 net15) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M621 (net38 net36 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
M620 (net31 net30 net9 net8) pch_mac l=60n w=7.2u multi=1 nf=1 sigma=1 \
sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u nrd=0.0138889 \
nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M616 (p3 p3 net22 net22) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M618 (p2 p3 net16 net16) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M619 (p1 p3 net14 net14) pch_mac l=60n w=1.8u multi=1 nf=1 sigma=1 \
sd=200n ad=3.15e-13 as=3.15e-13 pd=3.95u ps=3.95u nrd=0.0555556 \
nrs=0.0555556 sa=175.00n sb=175.00n sca=0 scb=0 scc=0 \
mismatchflag=1
M617 (net37 net12 net31 net8) pch_mac l=60n w=7.2u multi=1 nf=1 \
160

sigma=1 sd=200n ad=1.26e-12 as=1.26e-12 pd=14.75u ps=14.75u \
nrd=0.0138889 nrs=0.0138889 sa=175.00n sb=175.00n sca=0 scb=0 \
scc=0 mismatchflag=1
V96 (net9 0) vsource dc=1.2 type=dc
V97 (net8 0) vsource type=pulse val0=0 val1=1.2 period=2 delay=10n \
rise=10p fall=10p width=1
ends clause16
// End of subcircuit definition.

// Library name: Deming_SAT
// Cell name: auto_test
// View name: schematic
I33 (net34 net33) inverter
I25 (net26 net25) inverter
I21 (net22 net21) inverter
I35 (net36 net35) inverter
I37 (net38 net37) inverter
I27 (net28 net27) inverter
I29 (net30 net29) inverter
I23 (net24 net23) inverter
I39 (net40 net39) inverter
I31 (net32 net31) inverter
I34 (net33 net34) inverter
I26 (net25 net26) inverter
I22 (net21 net22) inverter
I38 (net37 net38) inverter
I36 (net35 net36) inverter
I30 (net29 net30) inverter
I28 (net27 net28) inverter
I24 (net23 net24) inverter
I40 (net39 net40) inverter
I32 (net31 net32) inverter
I1 (net2 net1) inverter
I17 (net18 net17) inverter
I9 (net10 net9) inverter
I5 (net6 net5) inverter
I3 (net4 net3) inverter
I19 (net20 net19) inverter
I13 (net14 net13) inverter
I11 (net12 net11) inverter
I7 (net8 net7) inverter
161

I15 (net16 net15) inverter
I2 (net1 net2) inverter
I18 (net17 net18) inverter
I10 (net9 net10) inverter
I4 (net3 net4) inverter
I6 (net5 net6) inverter
I20 (net19 net20) inverter
I12 (net11 net12) inverter
I14 (net13 net14) inverter
I8 (net7 net8) inverter
I16 (net15 net16) inverter
I56 (net31) initial
I55 (net29) initial
I54 (net27) initial
I53 (net25) initial
I52 (net23) initial
I51 (net21) initial
I50 (net19) initial
I49 (net17) initial
I48 (net15) initial
I47 (net13) initial
I46 (net11) initial
I45 (net9) initial
I44 (net7) initial
I43 (net5) initial
I57 (net33) initial
I58 (net35) initial
I59 (net37) initial
I60 (net39) initial
I42 (net3) initial
I41 (net1) initial
V274 (vdd! 0) vsource dc=1 type=dc
I61 (net20 net32 net9) clause1
I62 (net31 net12 net9) clause2
I63 (net34 net28 net36) clause3
I64 (net20 net30 net37) clause4
I65 (net2 net18 net36) clause5
I66 (net5 net13 net12) clause6
I67 (net26 net1 net11) clause7
I68 (net4 net32 net40) clause8
I69 (net13 net15 net35) clause9
162

I70 (net14 net19 net40) clause10
I71 (net3 net28 net34) clause11
I72 (net3 net1 net37) clause12
I73 (net13 net40 net2) clause13
I74 (net22 net1 net34) clause14
I75 (net5 net24 net37) clause15
I76 (net6 net26 net11) clause16
I77 (net26 net5 net24) clause1
I78 (net9 net14 net24) clause2
I79 (net39 net15 net32) clause3
I80 (net26 net12 net37) clause4
I81 (net10 net1 net27) clause5
I82 (net17 net10 net35) clause6
I83 (net24 net34 net2) clause7
I84 (net40 net32 net37) clause8
I85 (net23 net19 net22) clause9
I86 (net11 net14 net4) clause10
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Abstract (if available)

Abstract The thesis focuses on nano-engineered devices for optical application, biomedical detection and circuit accelerator. By combining the nano fabrication and the optical and electrical design, nano-engineered devices could solve many existing problems in research, industry and daily life.

Linked assets

University of Southern California Dissertations and Theses

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Asset Metadata

Creator Meng, Deming (author)

Core Title Nano-engineered devices for optical application, biomedical detection and circuit accelerator

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Degree Conferral Date 2022-12

Publication Date 11/30/2023

Defense Date 11/15/2022

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag acute myocardial infections,Boolean Satisfiability,Breaktrhough starshot,circuit accelerator,light sail,machine learning,nanofingers,nanoimprint,NP-complete,OAI-PMH Harvest,optical metrology,surface-enhanced Raman spectroscopy,wetting states

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Wu, Wei (committee chair), Cronin, Stephen (committee member), Nakano, Aiichiro (committee member)

Creator Email demingme@usc.edu,mengdeming1993@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC112542503

Unique identifier UC112542503

Identifier etd-MengDeming-11337.pdf (filename)

Legacy Identifier etd-MengDeming-11337

Document Type Dissertation

Format theses (aat)

Rights Meng, Deming

Internet Media Type application/pdf

Type texts

Source 20221201-usctheses-batch-993 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

Repository Email cisadmin@lib.usc.edu