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Nanophotonic light management in thin film silicon photovoltaics

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Nanophotonic light management in thin film silicon photovoltaics

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NANOPHOTONIC LIGHT MANAGEMENT IN THIN
FILM SILICON PHOTOVOLTAICS

A DISSERTATION
SUBMITTED TO THE FACULTY OF
THE USC GRADUATE SCHOOL
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF
DOCTOR OF PHILOSOPHY

Chenxi Lin
2013

 Copyright by Chenxi Lin 2013
All Rights Reserved

1

ABSTRACT
This thesis is about light-trapping in thin film silicon photovoltaic devices. Light-trapping allows
more light to be absorbed inside a smaller volume of photoactive materials, therefore reducing
the required active layer thickness for obtaining high optical absorption. The decrease in
thickness can not only bring down the material cost of solar cells based on high-purity single-
crystalline silicon, but also enable materials with poorer qualities, such as polycrystalline silicon
to be used for photovoltaics, reducing both the material cost and processing cost.
In this dissertation, we use three-dimensional full-vectorial electromagnetic simulation tools
to explore various light-trapping schemes based on sub-wavelength nanostructures arranged in
both periodic and partially-aperiodic fashion. In specific, periodic silicon nanowire and nanohole
arrays were found to absorb more sunlight than an equally-thick silicon slab, if the geometry of
the array is properly designed. The strong structural dependence of the optical absorption
performance can be attributed to the optimal condition for exciting guided resonance modes
within the nano-structured array. Furthermore, partially-aperiodic silicon nanowire/nanorod
arrays show significant enhancement in light-trapping and anti-reflection performance,
respectively, compared to their periodic counterparts in certain size regimes. Machine-based
optimal design algorithm was utilized to maximize the optical performance enhancement. In
order to verify the theoretically-predicted optical absorption enhancement effect, proof-of-
concept experimental demonstration has been carried out for free-standing silicon
nanomembranes patterned with both periodic and partially-aperiodic nanohole structures. Good
agreement between theory and experiment was obtained, suggesting the wide applicability of
electromagnetic simulations and optimal design techniques in the optical design of nano-
structured thin film solar cells. Finally, the effect of plasmonic particles on the optical absorption
in silicon nanowire arrays was numerically examined. It was found that due to the existence of

2

diffractive coupling scheme afforded by the nanowire array itself, the plasmonic particles do not
improve the optical absorption within the silicon nanowires.

3

ACKNOWLEDGMENTS
Firstly, I would like to thank my advisor, Professor Michelle Povinelli for her guidance, patience,
and support during these years. Her intelligence, knowledge, and experience make my PhD an
invaluable learning experience. She has the vision to map out the research directions and the
ability to explain complex, difficult subject matters in a very accessible way. She is also an
understanding advisor who truly cares about the well-being of her students. In addition, she is
always happy to share with us her professional activities as a professor, such as writing research
proposals. She also spent tremendous efforts in improving our scientific presentation skills and
repeatedly demonstrated how a good presentation is done during her talks. Last but not the least,
I am also thankful for her for creating a dynamic, multi-cultural working environment in our lab
by bringing in students and interns from all around the world.
I would also like to express my gratitude towards the faculty members in USC Electrophysics
department. Professor William Steier recruited me to USC in the first place. Professor Anothony
Levi’s special topic class on optimal design inspired and initiated the partially-aperiodic silicon
nanowire project. I also greatly benefit from the interactions with Professor Dan Dapkus and
Chongwu Zhou during the technical discussions in the Center of Energy Nanoscience (CEN)
meetings, as well as the collaboration involving GaAs nanowires. It was also my privilege to sit
in the class of Professor Dan Dapkus (Heterojunction Devices), Professor Anupam Madhukar
(Solid State Physics), Professor Aiichiro Nakano (Computational Phyics), and Professor Aluizio
Prata Jr. (Advanced Electromagnetics). I would also like to thank Professor Wei Wu for serving
on my thesis defense committee.
I would like to thank all the current and former members of Povinelli group. Jing (Maggie)
Ma, Eric Jaquay and I joined the group at the same time. We studied together for the screening
exam in the early days of our Ph.D.. Later when I started my experimental projects, they spent a
lot of time training me on different machines in the clean room. Eric also put in relentless efforts

4

in improving my oral English. Luis Javier Martinez, is an extremely enthusiastic postdoctoral
researcher in our group with a deep understanding of photonic crystals research and great work
ethics. The experimental demonstration part of this thesis would not have been possible without
his guidance and expertise in device fabrication and optical characterization. Mehmet Solmaz is
a hands-on experimentalist who equipped our optics lab with indispensable instruments.
Ningfeng Huang collaborated with me on the project involving III-V nanowires solar cells and I
was always impressed with his talents and productivity. He is always the “go-to” guy for
anything related to computer, Linux, and programming. Camilo Mejia is the only physics student
among us who can always come up with fascinating ideas and insightful questions during the
group meeting. I also enjoyed working with Patrick Anderson and Roshni Biswas on their
respective projects towards the end of my Ph.D..
It was also my great pleasure to interact with many bright and enthusiastic graduate students
and researchers at USC. Yunchu Li from Dr. Dapkus’s lab has been our good office neighbor for
years. Yunchu is an incredibly nice person who always surprised us with delicious home-made
food. He also gave me a lot of advices and help during my preparation of the Ph.D. qualifying
exam. I would also like to thank Maoqing Yao, Chunyung Chi, and Yenting Lin from Dr.
Dapkus’s group, Anuj Madaria from Dr. Zhou’s lab, Hari Mahalingam from Dr. Steier’s lab,
Jesse Theiss, Prathamesh Pavaskar, and Shermin Arab from Dr. Cronin’s group, He Liu from Dr.
Wu’s group, for their help and input at different stages of my Ph.D. We had a lot of fun talking
about each other’s research while working in the clean room. I learnt a great deal from each one
of them.
I am also grateful to our clean room supervisor, Donghai Zhu. His hard work and amazing
knowledge and skills keep the machines in the clean room up and running for most of the time. I
would also like to thank the wonderful team of research staff members in the Electrophysics
branch of the EE department, Kim Reid, Jaime Zelada, Lauren Villarreal, Marilyn Poplawski, as
well as my GAPP advisors Tracy Charles and Jennifer Gerson. They are all genuinely nice
people who have taken good care of me through these years. It was also my pleasure to work

5

with Danielle Hamra from USC Ming Hsieh Institute during my service as the MHI Ph.D.
scholar.
Last but not the least, I greatly acknowledge the generous support from various funding
agencies during my Ph.D. years: USC Provost Fellowship, USC Center for Energy Nanoscience,
Wen-hui Chen Endowment Fellowship from USC graduate school, and National Science
Foundation.
Finally, I am indebted to my parents, Jianfeng Lin and Rongqin Sun, and my wife, Xing Fang,
for their unconditional love and support during the completion of this thesis. I dedicate this thesis
to them.

6

TABLE OF CONTENTS
LIST OF PUBLICATIONS ...............................................................................................10
LIST OF FIGURES ...........................................................................................................12
CHAPTER 1 INTRODUCTION .......................................................................................17
1.1 SOLAR ENERGY RESOURCE ...........................................................................17
1.2 THIN FILM SILICON SOLAR CELLS ...............................................................17
1.3 LIGHT MANAGEMENT IN SOLAR CELLS .....................................................18
1.3.1 Anti-reflection ...............................................................................................18
1.3.2 Light-trapping ...............................................................................................19
1.4 OPTICAL MODELING METHOD ......................................................................22
1.4.1 Scattering matrix method ..............................................................................23
1.4.2 Finite-Difference Time-Domain (FDTD) method ........................................24
1.5 OVERVIEW OF THE THESIS .............................................................................25
CHAPTER 2 OPTICAL ABSORPTION ENHANCEMENT IN PERIODIC SILICON
NANWIRE AND NANOHOLE ARRAYS.................................................................27
2.1 INTRODUCTION .................................................................................................27
2.2 SIMULATION SETUP .........................................................................................28
2.3 SIMULATION RESULTS ....................................................................................30
2.3.1 Efficiency landscape .....................................................................................30
2.3.2 Optical spectra of SiNW arrays ....................................................................32
2.3.3 Optical spectra of SiNH arrays .....................................................................37
2.3.4 Comparison to Lambertian light trapping limit ............................................38
2.3.5 Angular response ..........................................................................................40
2.3.6 Height dependence ........................................................................................41
2.3.7 Effect of different lattice geometries ............................................................43
2.3.8 Detailed balance limit analysis .....................................................................44
2.4 CONCLUSIONS....................................................................................................49

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CHAPTER 3 OPTIMAL DESIGN OF APERIODIC SILICON NANOWIRE LIGHT-
TRAPPING STRUCTURES .......................................................................................51
3.1 INTRODUCTION .................................................................................................51
3.2 OPTIMAL DESIGN ..............................................................................................52
3.2.1 Simulation setup and optimization algorithm ...............................................52
3.2.2 Ultimate efficiency........................................................................................53
3.2.3 Absorption spectra inspection .......................................................................54
3.2.4 Absorption profile .........................................................................................55
3.2.5 Statistical study of random structures ...........................................................56
3.2.6 Effect of rod diameter and super cell size .....................................................57
3.2.7 Comparison to optimal periodic nanowire arrays .........................................58
3.2.8 Advanced optimization algorithm .................................................................58
3.3 SUMMARY ...........................................................................................................59
CHAPTER 4 EFFECT OF APERIODICITY IN SILICON NANOROD ANTIREFLECTING
STRUCTURES ............................................................................................................60
4.1 INTRODUCTION .................................................................................................60
4.2 SIMULATION SETUP .........................................................................................60
4.3 SIMULATION RESULTS ....................................................................................62
4.3.1 Periodic nanorod array ..................................................................................62
4.3.2 Comparison between periodic and aperiodic nanorod array .........................63
4.3.3 Reflection spectra..........................................................................................65
4.3.4 Angular dependence ......................................................................................67
4.3.5 Effect of super-cell size ................................................................................67
4.3.6 Other material systems ..................................................................................68
4.4 SUMMARY ...........................................................................................................68
CHAPTER 5 EXPERIMENTAL BROADBAND ABSORPTION ENHANCEMENT IN
SILICON NANOHOLE STRUCTURES WITH OPTIMIZED COMPLEX UNIT CELLS
......................................................................................................................................69
5.1 INTRODUCTION .................................................................................................69

8

5.2 DESIGN AND OPTIMIZATION..........................................................................69
5.3 FABRICATION METHOD...................................................................................71
5.4 MEASUREMENT SETUP ....................................................................................73
5.5 MEASUREMENT RESULTS ...............................................................................74
5.6 DISCUSSION ........................................................................................................76
5.6.1 Comparison between experiment and theory ................................................76
5.6.2 Spatial Fourier spectra ..................................................................................76
5.6.3 Comparison to the optimal periodic structure ...............................................78
5.6.4 Angular response ..........................................................................................79
5.6.5 Diffraction in the experimental setup ...........................................................80
5.7 SUMMARY ...........................................................................................................84
CHAPTER 6 FABRICATION OF TRANSFERRABLE, FULLY-SUSPENDED SILICON
PHOTONIC CRYSTAL MEMBRANES EXHIBITING VIVID STRUCTURAL
COLOR AND HIGH-Q GUIDED RESONANCE ......................................................86
6.1 INTRODUCTION .................................................................................................86
6.2 FABRICATION .....................................................................................................87
6.2.1 Fabrication of photonic crystal .....................................................................87
6.2.2 Wet transfer and alignment process ..............................................................89
6.2.3 Fabricated structure .......................................................................................91
6.3 OPTICAL CHARACTERIZATION .....................................................................92
6.3.1 Structural colors ............................................................................................92
6.3.2 High-Q guided resonance .............................................................................93
6.4 SUMMARY ...........................................................................................................94
CHAPTER 7 EFFECT OF PLASMONIC PARTICLES ON PHOTOVOLTAIC
ABSORPTION IN SILICON NANOWIRE ARRAYS ..............................................96
7.1 INTRODUCTION .................................................................................................96
7.2 SIMULATION SETUP .........................................................................................97
7.3 SIMULATION RESULTS ....................................................................................99
7.4 PHYSICAL MECHANISM.................................................................................101

9

7.5 SUMMARY AND DISCUSSION .......................................................................102
CHAPTER 8 CONCLUSIONS AND OUTLOOK .........................................................104
8.1 IMPACT OF EMISSION MODIFICATION BY NANOSTRUCTURES .........105
8.2 EXPERIMENTAL DEMONSTRATION OF DEVICE PERFORMANCE
IMPROVEMENT ................................................................................................105
BIBLIOGRAPHY ............................................................................................................107

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LIST OF PUBLICATIONS
1. C. Lin, L. J. Martinez, and M. L. Povinelli, “Experimental broadband absorption enhancement
in silicon nanohole structures with optimized complex unit cells”, Optics Express 21: A872
(2013).
2. C. Lin, L. J. Martinez, and M. L. Povinelli, “Fabrication of transferrable, fully-suspended
silicon photonic crystal membranes exhibiting vivid structural color and high-Q guided
resonance”, Journal of Vacuum Science and Technology B, 31: 050606 (2013).
3. N. Huang, C. Lin, and M. L. Povinelli, “Limiting efficiencies of tandem solar cells consisting
of III-V nanowire arrays on silicon”, J. Applied Physics 112: 064321 (2012).
4. A. Madaria, M. Yao, C. Chi, N. Huang, C. Lin, R. Li, M. L. Povinelli, P. D. Dapkus, and C.
Zhou, “Toward Optimized Light Utilization in Nanowire Arrays Using Scalable Nanosphere
Lithography and Selected Area Growth”, Nano Letters 12: 2839 (2012).
6. N. Huang, C. Lin, and M. L. Povinelli, “Broadband absorption of semiconductor naowire
arrays for photovoltaic applications”, Journal of Optics, special issue on Green Photonics, 14:
024004 (2012).
5. C. Lin, N. Huang, and M. L. Povinelli, “Effect of aperiodicity on the broadband refection of
silicon nanorod structures for photovoltaics”, Optics Express 20: A125 (2011).
7. C. Lin and M. L. Povinelli, “Detailed balance limit of silicon nanowire and nanohole array
solar cells”, Proc. SPIE 8111: 81110U (2011),
8. C. Lin and M. L. Povinelli, “Optimal design of aperiodic, vertical silicon nanowire structures
for photovoltaics”, Optics Express 19: A1148 (2011).
9. C. Lin and M. L. Povinelli, "The effect of plasmonic particles on solar absorption in vertically
aligned silicon nanowire arrays", Applied Physics Letters 97: 071110 (2010).

11

10. C. Lin and M. L. Povinelli, “Optical absorption enhancement in silicon nanowire and
nanohole arrays for photovoltaic applications”, Proc. SPIE 7772: 77721G (2010).
11. C. Lin and M. L. Povinelli, "Optical absorption enhancement in silicon nanowire arrays with
a large lattice constant for photovoltaic applications", Optics Express 17: 19371 (2009).

12

LIST OF FIGURES
Figure 1-1 (a) Maximal short circuit current density as a function of silicon slab thickness for
silicon films with (red) and without (black) light-trapping. The performance of
several record-efficiency silicon solar cells are also indicated by stars of different
colors. (b) Comparison of the absorptance spectra for a 20 μm thick silicon thin
film with (green) and without (red) light-trapping, compared to a 200 μm thick
silicon wafer. All the calculations assume a perfect anti-reflection coating on top
of the silicon film. ............................................................................................21
Figure 1-2 Refractive index (left axis) and absorption length (right axis) of crystalline silicon
from Ref. [29]. .................................................................................................23
Figure 2-1 Schematics of the simulated square lattice SiNW (a) and SiNH (b) structures. The
insets show the cross section of a single nanowire and nanohole, respectively.30
Figure 2-2 The ultimate efficiency of 2.33μm-thick, square lattice SiNW (a) and SiNH (b)
arrays as a function of the lattice constant for several different filling ratios. .31
Figure 2-3 Optical properties of the SiNW array with varying lattice constant. In the left
column, (a), (b), and (c) are the reflectance, transmittance, and absorptance,
respectively, in the SiNW array with lattice constant 100nm and 500nm. The
optical properties of a silicon thin film are plotted for comparison. In the right
column, (d), (e), and (f) are the reflectance, transmittance, and absorptance,
respectively, in the SiNW array with lattice constants 100nm, 150nm, and 200nm.
The optical properties of the Si thin film are also plotted................................35
Figure 2-4 The dispersive band structures of a SiNW array for (a) a = 100 nm (b) a = 500
nm. ...................................................................................................................35
Figure 2-5(a) Characteristic line shape of a guided resonance at 1.197eV (b) Top view of
electric field energy density distribution on the end surface of the SiNW array at
the resonance shown in (a). (c) Side view of electric field energy density
distribution inside the nanowires at the same resonance. ................................36

13

Figure 2-6 Absorptance spectra of square lattice SiNH arrays with a fixed filling ratio 0.50
and varying lattice constants. (a) Absorptance spectra for lattice constants a = 100
nm, 150 nm, and 200 nm. The absorptance spectrum of the thin film is shown for
reference. (b) Absorptance spectra for lattice constant a = 500 nm and 900 nm.
The absorptance spectra for the thin film and a = 100 nm SiNH array are shown
for comparison. ................................................................................................38
Figure 2-7 Absorptance spectra for a 2.33 μm-thick thin film (black), an equally-thick thin
film with perfect geometrical light trapping (red), the equally-thick optimal square
lattice SiNH array (blue) and SiNW array (green). .........................................40
Figure 2-8 The incidence angle dependence of ultimate efficiency for a 2.33μm-thick silicon
thin film with an optimized single-layer antireflection coating (black), the optimal
square lattice SiNW array with L=2.33μm (red), and the optimal square lattice
SiNH array with L=2.33μm (blue). (a) the result for TE polarization (b) the result
for TM polarization. .........................................................................................41
Figure 2-9 The ultimate efficiency of 100 μm-thick square lattice SiNW (a) and SiNH (b)
arrays as a function of lattice constant for several different filling ratios. ......42
Figure 2-10 The ultimate efficiency of 2.33μm-thick hexagonal lattice SiNW (a) and SiNH
(b) arrays as a function of lattice constant for several different filling ratios. The
incident light is TE-polarized, as shown in the inset. ......................................43
Figure 2-11 The ultimate efficiency of 2.33μm-thick hexagonal lattice SiNW (a) and SiNH
(b) arrays as a function of lattice constant for several different filling ratios. The
incident field is TM-polarized, as shown in the inset. .....................................44
Figure 2-12 The dependence of solar cell characteristics on lattice constant and filling ratio
for silicon nanowire (a, c, e) and nanohole (b, d, f) arrays. .............................48
Figure 3-1 Schematics of periodic (a) and aperiodic (b) silicon nanowire structures. ......52
Figure 3-2 Top views of initial periodic (a) and optimal aperiodic (b) silicon nanowire
structures. Dashed lines indicate boundaries between super cells. ..................53
Figure 3-3 (a) Solar absorptance spectra for periodic (blue dotted) and optimal aperiodic (red
solid) silicon nanowire structures. The absorptance spectrum for an equally-thick

14

silicon thin film (gray dashed) is also plotted for reference. (b) Reflectance (black
dotted), transmittance (red dashed), and absorptance (blue solid) of the optimal
aperiodic structure near 1.249 eV (992.3 nm). ................................................55
Figure 3-4 Absorption profiles of (a) periodic and (b) optimal aperiodic silicon nanowire
structures at a horizontal cross section 0.233 μm below the top surface of the
nanowire array. White dashed lines indicate boundaries between super cells.56
Figure 3-5 Histogram of ultimate efficiencies in 1000 randomly-selected, aperiodic silicon
nanowire structures. The ultimate efficiency of the initial periodic array (blue,
dashed line) is plotted for reference. ................................................................57
Figure 3-6 Absorptance spectra comparison between the best aperiodic silicon nanowire
structure (super cell length 800 nm, initial lattice constants a = 200 nm) and the
optimal periodic silicon nanowire array (a = 650 nm, d = 520 nm). ...............58
Figure 4-1Schematic diagrams of periodic (a), almost periodic (b), and random (c) anti-
reflection nanostructures ..................................................................................61
Figure 4-2 (a) Top view of one unit cell in a periodic structure. (b) Average reflection loss
(ARL) as a function of lattice constant and d/a ratio. ......................................62
Figure 4-3 Average reflection loss (ARL) as a function of nanorod diameter for periodic
structures, almost periodic structures (10% positional disorder), random aperiodic
structures, and optimally designed aperiodic structures. .................................63
Figure 4-4 Reflectance spectra for periodic, random aperiodic, and optimal aperiodic
structures, averaged over TE and TM polarizations. The nanorod diameters are 70
nm (a), 140 nm (b), and 210 nm (c), respectively............................................66
Figure 4-5 Angular dependence of ARL for both periodic and 50 random aperiodic silicon
nanorod structures for a nanorod diameter of 70 nm (a = 100 nm) and 175 nm (a =
250 nm). ...........................................................................................................67
Figure 5-1 Silicon nanohole structures with (a) simple periodic and (b) complex unit cell
geometries. (c) Calculated F.O.M.s as a function of the unit cell length in
structures with random (blue) and optimized (red) complex unit cells. The

15

F.O.M.s for the simple periodic unit cell case and an equally-thick thin film are
also shown for reference. .................................................................................70
Figure 5-2 Nanohole patterns with unit cells containing simple periodic (a), average complex
(b), and optimized complex (c) configurations of nanoholes. A total of 9 unit cells
are shown for each configuration. Red dashed lines are the borders between unit
cells. (d–f) show the corresponding SEM images of the fabricated patterns. The
white square denotes a unit cell and the scale bars are 200 nm. ......................72
Figure 5-3 Measured (left panel) and simulated (right panel) reflectance, transmittance, and
absorptance spectra of nanohole structures with simple periodic (red), average
complex (blue), and optimized complex (green) unit cell geometries, as shown in
Figure 5-2. The spectra for an equally-thick thin film are also shown for reference
(gray dashed line). ............................................................................................75
Figure 5-4 Real space configurations (a–c) and spatial Fourier spectra (d–f) of nanohole
structures with simple periodic ((a) and (d)), average complex ((b) and (e)), and
optimized complex ((c) and (f)) unit cell geometries. .....................................78
Figure 5-5 Absorptance spectra comparison between the optimal periodic nanohole array
(blue) and the nanostructures with the optimized complex, aperiodic unit cell (red)
..........................................................................................................................79
Figure 5-6 Incidence angle dependence of the F.O.M. for nanohole structures with an
optimized complex unit cell geometry (red), optimized simple unit cell geometry
(green), and an equally-thick thin film (blue) for p (a) and s (b) polarized incident
light, as well as the average F.O.M. between two polarizations (c). ...............80
Figure 5-7 Schematic of specular and diffractive reflection and transmission processes in a
one-dimensional periodically patterned slab ...................................................81
Figure 5-8 (a) Angle-averaged actual (black) and specular (red) absorptance spectra for the
optimized complex unit cell geometry, for an incident beam angular spread up to
10 degrees. The blue arrows indicate the diffraction thresholds wavelengths. Right
of the dashed line is our wavelength range of interest. (b) Angle-averaged

16

F.O.M.s for three different unit cell geometries, as a function of the incidence
beam angular spread. .......................................................................................84
Figure 6-1 Side view scanning electron microscopy image of holes etched into silicon wafer
after the ICP-RIE process. ...............................................................................88
Figure 6-2 Illustration of the wet-transfer and positioning process of the photonic crystal
nanomembrane. (a) The membrane just before the release (dimensions not to
scale). (b) The membrane was released from the silicon handle substrate in HF
and transferred to water. (c) The membrane was wet-transferred and positioned
over an opening in a host substrate. .................................................................90
Figure 6-3 (a) Perspective-view SEM picture of a fabricated silicon photonic crystal
nanomembrane. Blue ellipses indicate device regions. (b-c) Top-view SEM
images of a square lattice (b) and slot-graphite lattice (c) photonic crystals. ..91
Figure 6-4 Dark-field optical microscope images of a silicon nanomembrane patterned with
nine square lattice photonic crystals with varying lattice constants from 350 nm to
750 nm with 50 nm spacing. The scale bar is 100 µ m. ....................................93
Figure 6-5 Representative cross-polarization transmission spectra of the silicon
nanomembrane pattered with a slot-graphite photonic crystal. .......................94
Figure 7-1(a) Schematic of the SiNW array with hemispherical metal caps. (b) Cross
sectional view of a single nanowire. (c) Top view of a single nanowire. ........98
Figure 7-2 Absorption ratio for SiNW arrays with (a) gold, (b) copper, and (c) silver
hemispherical metal caps. ..............................................................................100
Figure 7-3 The length dependence of the integrated enhancement factor in the SiNW arrays
with the approximately optimal configuration (a=500nm, d=100nm), for three
different metallic hemispheres. ......................................................................101
Figure 7-4 The absorptance spectrum of bare (black) and silver capped (red) SiNW arrays
with L = 500 nm, d = 100 nm, a = 100 nm (a) and 450 nm (b). ....................102

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CHAPTER 1 INTRODUCTION
1.1 Solar energy resource
Solar energy is an important alternative energy source. It is abundant, renewable, and clean. The
vast potential of the solar energy can be seen by the following simple calculation. The total
global energy consumption in 2010 is around 1.5 TWh (1.5 x 10
9
kWh). In terms of power
(energy current), this correspond to 17 TW. The annual solar energy incident upon the surface of
the Earth can be estimated to be 1.5 x 10
18
kWh in energy and 1.7 x 10
5
TW in energy current,
given an average power density of 285 W/m
2
around the globe throughout the year. To put this
number in perspective, the solar energy received by the Earth within two hours will suffice to
power the whole world for a year.
We can further estimate the land area required if we want to power the whole world with solar
cells, which converts sunlight to electricity. If we assume a moderate power conversion
efficiency from sunlight to electricity of 15%, the total land area required to produce the global
energy demand in 2010 is 17 TW / (285 W/m
2
x 15%) = 4 x 10
11
m
2
= 400,000 km
2
. This is
approximately the area of the state of California and one thousandth of the surface area of our
Earth (assuming the Earth is a sphere with a radius of 6370 km).
1.2 Thin film silicon solar cells
Although the potential is vast, so far the cumulative installed photovoltaic capacity has just
exceeded the 100 GW milestones, a very small fraction of the global electricity generation. At
least one of the main obstacles for the large-scale utilization of solar energy is believed to be the
high cost of photovoltaics compared to traditional fossil-fuel based energy sources. Thin film
photovoltaic devices have the potential to significantly reduce both the material cost and
processing cost of solar cells. Among various popular material choices for thin film
photovoltaics, crystalline or polycrystalline silicon has several unique advantages, such as earth-
abundance (compared to In in CIGS solar cells and Te in CdTe solar cells), non-toxicity, and an

18

ideal band gap for photovoltaic conversion process. Unfortunately, however, crystalline silicon
does not efficiently absorb sunlight in the near-IR range due to its indirect band gap. Therefore,
very effective light management schemes have to be employed to improve the optical absorption
in a thin film of crystalline silicon so that a reasonable power conversion efficiency can be
achieved.
1.3 Light management in solar cells
The goal of light management for solar cells is to admit as much light as possible into the solar
cells as well as to maximize the absorption probability of the admitted sunlight inside the
photoactive materials. In this section, we will briefly review these two important aspects of light
management, namely, anti-reflection and light-trapping, which are the focuses of this
dissertation. A discussion of other light management strategies, such as light concentration and
photon-recycling [1], are beyond our scope.
1.3.1 Anti-reflection
Fresnel reflection can be a significant source of optical loss for high-index semiconductor
materials which are popular for photovoltaics. For example, for silicon, a simple Fresnel formula
gives a reflection of around 30% at the wavelength corresponding to the band gap of crystalline
silicon (1.1 µ m). When integrated over the entire solar spectrum, the reflection loss amounts to
35% of the maximum achievable photocurrent. Therefore, minimizing the reflectance from a
semiconductor surface is very important for making high-efficiency solar cells. The simplest
form of anti-reflection coating is to apply a quarter-wavelength-thick thin film with a refractive
index between the incident medium and absorbing medium. For conventional silicon solar cell, a
single-layer silicon nitride (Si
3
N
4
) with optimal thickness is typically applied as the anti-
reflection coating. However, the performance of this type of anti-reflection coating depends
strongly on the operating wavelength and the incidence angle. Another approach for reducing the
reflectance is to use micron-scale pyramidal surface texturing [2], which serve both anti-
reflection and light-trapping functionalities. Over the last decade, with the development of
nanofabrication techniques, various novel high-performance anti-reflection schemes based on

19

sub-wavelength nanostructures have been proposed and demonstrated [3]. These sub-wavelength
anti-reflecting structures are capable of providing a broadband, omni-directional anti-reflection
performance. Chapter 4 of this dissertation will systematically examine the anti-reflection
performance of silicon nanorod structures and the effect of positional aperiodicity on its
performance.
1.3.2 Light-trapping
The second important aspect of light management is to increase the interaction path length of the
light inside the absorbing material so that maximal amount of absorption can be achieved before
the light can escape out of the solar cell. This is the so-called “light-trapping” approach. The
simplest light-trapping scheme is to attach a mirror onto the back side of the solar cells, acting as
a back reflector and effectively doubled the optical path length. In order to further increase the
optical path length, textured surface, which randomizes the light propagation directions inside
the absorbing material, is typically used. Another benefit associated with randomization of the
light propagation direction is that some fraction of light will be totally-internally-reflected (TIR)
at the semiconductor-air interface and confined within the active material. These light-trapping
approaches have been widely employed in the development of conventional crystalline silicon
photovoltaics. However, the fundamental question is to what extent can an idealized light-
trapping scheme improve the optical path length and hence the optical absorption?
Lambertian light-trapping limit
In a seminal paper [4] published in 1982, a light trapping limit based on statistical ray optics was
derived. This is the so-called “Lambertian” light-trapping limit since it only strictly applies for
an ideal Lambertian scattering surface, which scatters light in an isotropic fashion. The authors
show that in the weak-absorption limit (single pass absorption is negligible), optical absorption
in a semiconductor film can be enhanced by a factor as large as 4n
2
, where n is the index of the
semiconductor slab. This enhancement factor can be understood intuitively considering a factor
of 2 path length enhancement from the back reflector, another factor of 2 path length
enhancement from the Lambertian randomization of light propagation direction, and a
significantly reduced light escaping probability of 1/n
2
, corresponding to strong light

20

confinement within the absorbing medium. The potential of this limit is significant, considering
the high refractive indices of semiconductor materials typically employed for solar cells. For
example, the refractive index of silicon is around 3.5 near its indirect band gap (around 1.1μm),
yielding an optical absorption enhancement factor of around 50. In order to appreciate the power
of effective light-trapping scheme, we plot in Figure 1-1(a) the maximum short circuit current
density for a crystalline silicon slab with and without ideal light-trapping scheme (a perfect back
reflector and a Lambertian scattering surface), as a function of the slab thickness. The top surface
of the silicon slab is assumed to be coated with a perfect anti-reflection coating. We can clearly
observe that light-trapping can give rise to an at least one-order-of-magnitude reduction in
absorbing material thickness while maintaining the same amount of the photocurrent output.
Figure 1-1(b) shows the comparison of absorptance spectra for a 20 μm silicon thin film with and
without light-trapping, compared to a 200 μm film without light-trapping. Light-trapping
significantly improves the optical absorption in the near-IR range, enabling the 20 μm film
absorb more sunlight than the 200 μm film with a ten-times-thinner thickness.
We have also indicated in Figure 1-1(a) the thicknesses and short-circuit current densities of
several world-record solar cells based on crystalline or polycrystalline silicon. Clearly, light-
trapping schemes are employed in these cells to increase the optical absorption and hence the
photocurrent. However, at least in theory, there is still room for improvement, especially for thin
film crystalline silicon solar cells, where the active layer thickness varies from a few µ m to a few
tens of µ m.

21

Figure 1-1 (a) Maximal short circuit current density as a function of silicon slab thickness for
silicon films with (red) and without (black) light-trapping. The performance of several record-
efficiency silicon solar cells are also indicated by stars of different colors. (b) Comparison of the
absorptance spectra for a 20 μm thick silicon thin film with (green) and without (red) light-
trapping, compared to a 200 μm thick silicon wafer. All the calculations assume a perfect anti-
reflection coating on top of the silicon film.
Light-trapping in the wave optics regime
In conventional crystalline silicon solar cells, micron-scale pyramidal surface texturing was
introduced for light-trapping purpose [2]. However, such approach is not compatible with thin
film solar cells, where the film thickness becomes comparable to the texture size. Therefore,
numerous recent studies have thus focused on light-trapping structures with sub-wavelength
dimensions for thin film solar cells. For example, in this dissertation, we will numerically and
experimentally investigate the optical absorption in thin film silicon nanowire and nanohole
arrays where the absorber material itself is being directly patterned.
Our work, together with a large body of theoretical [5-13] and experimental [14-21] efforts in
nano-photonic light-trapping architectures, has inspired researchers in the nanophotonic
community to re-examine the ultimate limit of light-trapping when the wave nature of light
becomes important. Important assumptions for deriving the Lambertian light trapping limit no
longer strictly apply for thin semiconductor films textured with sub-wavelength periodicity, such
as (1) the photonic density of states inside the absorbing semiconductor film is the same as the

22

bulk value (n
2
), and (2) the light bouncing within the semiconductor film is essentially
incoherent (“ray-optics” picture remains valid). As a result, the validity of 4n
2
limit needs to be
re-evaluated.
A recent paper [22] developed a statistical temporal coupled mode theory and derived a
modified light-trapping limit in the wave-optics regime which is much higher than the
Lambertian light-trapping limit. However, the Lambertian limit is only surpassed for near-
normal incidence. When integrated over all incidence angles (considering isotropic incidence),
the absorption enhancement factor is still bound by 4n
2
limit [10, 23, 24]. Later it was realized
that the angle-averaged absorption enhancement factor can only exceed the Lambertian limit
when the local photonic density of state is strongly elevated via surface plasmon polariton
modes, slow light modes, or slot waveguide modes [25, 26].
1.4 Optical modeling method
In order to accurately model the optical behavior of thin film solar cells with sub-wavelength
nanophotonics light-trapping scheme, we need to perform accurate, fully-vectorial calculations
of the electromagnetic field in complex nanophotonic geometries. In our work, we have used
both finite-difference time-domain method (FDTD) [27] and generalized scattering matrix
methods [28] for our calculations. These methods are known to give accurate solutions to
Maxwell’s equations that successfully predict experimental results. We will give a brief
introduction of the respective advantages and drawbacks of each method in the following two
sections.
The main input parameters for our simulations are the geometries of the nanostructures and
their optical constants. Most popular semiconductor photovoltaic materials are very dispersive in
the solar spectrum. For example, Figure 1-2 shows the frequency-dependent refractive index and
absorption length of crystalline silicon, taken from Ref. [29]. The real part of the refractive index
varies from 3.5 near the indirect band gap of silicon to around 7 in the high-frequency range.
Moreover, the absorption length can differ by orders of magnitude, from ~10 nm in the high-
frequency range, to ~ mm near the indirect band gap.

23

Figure 1-2 Refractive index (left axis) and absorption length (right axis) of crystalline silicon
from Ref. [29].
1.4.1 Scattering matrix method
Scattering matrix method [28] is a widely-used method for calculating the response of nano-
structured optical materials, such as photonic crystals. The basic working principle is to divide
the structure into uniform slices (referred to as “layers”) along the light propagation direction,
solve for the eigenmodes using plane-wave expansion within each layer, and finally match the
boundary conditions for electric and magnetic fields across the interfaces between layers. The
frequency-domain nature of the method is ideal for simulations involving dispersive materials,
since the experimentally-determined optical constants can be directly used as the input for the
program. Another advantage of this method is that the memory requirement does not depend
upon the thickness of each layer since the height dependence is purely analytical. Therefore, it is
very convenient to examine structures with the same in-plane geometry but drastically different
thickness [30]. One drawback of this simulation method is that it is not so convenient to deal
with complex, non-planar three-dimensional geometries, such as cones, pyramids, and spheres.

24

The code we used for our scattering matrix method calculation is ISU-TMM [31, 32],
developed by Dr. Zhiyuan Li and Dr. Ming Li in Dr. Kai-Ming Ho’s research group at Iowa
State University. The source code is written in Fortran and parallelized for calculating different
frequency points on different computation nodes. We run the code routinely on USC High
Performance Computing and Communications (HPCC) supercomputer.
The source code of ISU-TMM is available after purchase and can be modified to provide
additional calculation capabilities. For example, the optical absorption in each layer in a
multilayer structure can be calculated separately. This feature is very important for calculation of
the absorption in each sub-cell in a multi-junction stacked tandem cells [33]. Moreover, the
order-dependent reflection and transmission spectra can also be calculated, which gives us both
specular and diffuse spectra in one single calculation [34].
1.4.2 Finite-Difference Time-Domain (FDTD) method
Finite-difference time-domain (FDTD) method is another widely-used numerical method for
solving Maxwell equations by discretizing both time and space [27]. FDTD is capable of
simulating structures with arbitrarily complex geometries and the broadband response can be
obtained in one single simulation by using a narrow pulse excitation source and Fourier-
transforming the response signal in time domain. Furthermore, FDTD can be readily parallelized
for large-scale simulations. Another advantage of FDTD is that the spatially and spectrally
dependent electromagnetic field information can be obtained, which is required to obtain the
carrier generation profile as the input for coupled opto-electrical modeling [33]. However, since
it is inherently a time-domain method, the frequency-dependent optical constants of materials
need to be implemented by adding an auxiliary polarization field [35] in the constitutive relations
between the electric displacement vector D and the electric field E.
We use both Meep [35] and Lumerical FDTD solution [36] simulation package for our FDTD
simulations. Meep is a freely-available and open-source software which has been widely used in
the photonic crystal community. Lumerical FDTD solution is a commercially-available software
which supports several desirable features for simulations involving dispersive materials and
plasmonic structures. More specifically, it uses a “multi-coefficient model” for a more versatile

25

fitting of the experimentally-determined material optical constants over a wide wavelength
range. Moreover, FDTD solutions supports a graded, non-uniform meshing scheme for improved
simulation accuracy and reduced memory requirement, compared to the conventional uniform
meshing scheme. Both softwares are parallelized and can be run on the USC HPCC
supercomputers.
1.5 Overview of the thesis
Chapter 2 will focus on full-field electromagnetic simulations of optical absorption in periodic
silicon nanowire and nanohole arrays. It is found that structures with optimal geometrical
parameters can absorb more sunlight than an equally-thick silicon thin film, albeit with less
material usage. The physical mechanisms for the broadband absorption enhancement are also
discussed. In addition, nanohole arrays can offer higher performance than nanowire arrays.
Chapter 3 presents a systematic investigation of optical absorption in silicon nanowire
structures with partial positional aperiodicity. It is shown that positional aperiodicity is in general
beneficial for solar absorption. Furthermore, an optimization algorithm is used to deliberately
design the position of individual nanowires within a single super cell for maximizing the
absorption enhancement factor. Chapter 4 examines the role of positional disorder in silicon
nanorod anti-reflecting structures. Broadband reflection reduction can be achieved for nanorod
structures with smaller feature size, whereas the largest anti-reflection performance improvement
can be obtained via a machine-based optimization procedure.
Chapter 5 presents a proof-of-concept experimental demonstration for broadband absorption
enhancement effect in a silicon nanomembrane with nanohole patterns consisting of optimized
complex unit cells. Good agreement between theory and experiment was obtained, with the
optimized complex unit cell giving a 3.5 times enhancement in broadband optical absorption,
compared to an un-patterned silicon thin film. Chapter 6 details the fabrication process for
obtaining transferrable, fully-suspended, and deflectable silicon photonic crystal nanomembrane,
which is utilized in the experimental study in Chapter 5. The fabricated device will also be useful
for studying opto-mechanical interactions in photonic crystal platforms.

26

Finally, Chapter 7 numerically studies the effect of metallic nanoparticles on top of silicon
nanowires on the absorption of sunlight in silicon nanowire arrays. It is shown that contrary to
common beliefs, metallic nanoparticles do not improve or even degrade the optical absorption
within the nanowires they are situated on.
Chapter 8 will conclude this dissertation by providing an overview of main findings in this
work and a brief discussion of several interesting further research directions.

27

CHAPTER 2 OPTICAL ABSORPTION ENHANCEMENT IN
PERIODIC SILICON NANWIRE AND NANOHOLE ARRAYS
2.1 Introduction
In this chapter, we will numerically investigate the optical absorption properties of vertically-
aligned silicon nanowire (SiNW) and nanohole (SiNH) array. These two structures are both
promising candidates for nano-structured silicon thin film solar cells. Nanowire arrays are
reported to exhibit low reflection and strong broadband absorption and may be used as
antireflection coatings or as the active layer in solar cells. For an extensive review on silicon
nanowire solar cells, please refer to Ref. [37]. In particular, silicon nanowire arrays incorporating
radial p-n junctions provide additional advantageous optoelectronic properties [38] that relax the
quality requirement by decoupling the carrier collection direction and light propagation direction.
Several groups have demonstrated solar cells based on radial p-n junction SiNW arrays on
different substrates [39, 40], including silicon wafer and flexible metal foil. Another structure
that is of interest to experimentalist is the silicon nanohole (SiNH) array [41], whose porous
nature and two-dimensional in-plane periodicity resembles that of the SiNW array. Theoretical
understanding of optical absorption within SiNW and SiNH arrays will be critical to
understanding the upper bound of achievable device performance and guiding further solar cell
development.
In this chapter, we use the scattering matrix method (ISU-TMM) introduced in Chapter 1 to
calculate the optical properties of SiNW and SiNH arrays with varying wire/hole spacing (lattice
constant) and filling ratios. We show that for fixed filling ratio (defined as πd
2
/4a
2
, where d is the
nanowire diameter and a is the lattice constant), increasing the lattice constant of the SiNW and
SiNH array up to 600 – 700 nm range yields dramatic optical absorption enhancement in the
low-frequency range of the solar spectrum near the band gap of crystalline silicon. For proper
choice of lattice constant and filling ratio, we find that the overall absorption efficiency of both

28

SiNW and SiNH arrays can surpass that of a Si thin film of equal thickness and even that of an
equal-thickness Si thin film with an optimal single-layer AR coating. We have also checked the
validity of this conclusion for different nanowire/nanohole height and different periodic lattice
geometries. We optimize the optical absorption with respect to lattice constant and filling ratio
and calculate the dependence of absorption efficiency on incidence angle for the optimal
structure. We also compare the performance of our optimal structure to an equally-thick silicon
slab with ideal light trapping scheme. Finally, we use a modified detailed balance limit approach
to estimate the upper bound on the power conversion efficiency of solar cells based on SiNW
and SiNH arrays.
2.2 Simulation setup
Figure 2-1 illustrates the vertically aligned SiNW (a) and SiNH (b) array under study. Both
structures are illuminated from the top by sunlight, indicated by the red arrow. The electric field
of the incident light is x-polarized. Each array consists of a square lattice or hexagonal lattice
(not shown) of silicon nanowires or nanoholes, each with diameter d and period a. The nanowire
and nanohole has a length L of 2.33μm, comparable to the film thickness of polycrystalline
silicon thin film solar cells and allows us to compare our results to those in Ref. [5]. The lattice
constant a was varied from 100nm to 900nm. The filling ratio, defined as the area occupied by Si
in one unit cell, is given by (πd
2
/4a
2
) for SiNW arrays and (1- πd
2
/4a
2
) for SiNH arrays. The
filling ratio was varied from 0.20 to 0.79 for SiNW arrays and 0.50 to 0.97 for SiNH arrays. The
frequency-dependent refractive index and absorption length of crystalline silicon was taken from
Ref. [29]. We assume that the nanowires are lightly doped, so that both n-type and p-type regions
can be modeled using the same refractive index and absorption length as intrinsic crystalline
silicon. For solar cell applications, the frequency range of interest is 1.1eV – 4eV, from the band
gap edge of crystalline silicon (1.1eV) to where the solar spectral irradiance is negligibly small.
We focus on the optical absorption properties of SiNW and SiNH arrays. A convenient figure
of merit for characterizing the broadband optical absorption is the ultimate efficiency [42]
defined as:

29

310
4000
310
( ) ( )
()
g
nm
g
nm
nm
I A d
Id


  







where λ is wavelength, I(λ) is ASTM AM1.5 direct normal and circumsolar spectral irradiance of
sun [43], A(λ) is the calculated absorptance (ratio of the absorbed optical power to the input
optical power), and λg is the wavelength corresponding to the band gap of the nanowire material.
The ultimate efficiency gives the ratio of output electrical power to input optical power,
assuming each photon with energy above the band gap generates one electron-hole pair with
energy equal to the band gap energy, and all photo-generated carries can be collected by the
external circuit. Physically speaking, this figure of merit gives the power conversion efficiency
when the temperature of the solar cell is at absolutely zero degree Kelvin, under which condition
the open-circuit voltage of the solar cell is exactly equal to the band gap of the photovoltaic
materials. Considering the band gap of crystalline silicon is around 1127 nm, the maximum
ultimate efficiency achievable for crystalline silicon based solar cells is around 48.62% for the
AM1.5 direct solar spectrum and 48.64% for the AM1.5 global solar spectrum.
Another figure of merit that can be related to the actual performance of the solar cell is the
maximum short circuit current density J
sc
. In order to calculate this figure of merit, we assume
perfect carrier collection efficiency, i.e., every photo-generated carrier can reach the electrodes
and contribute to the photocurrent. The maximum short circuit current density is then given by:
4000
310 310
( ) ( ) ( )
g
nm
g
sc
nm nm
e
e
J I A d I d
hc hc
 

         


The maximum short circuit current density for crystalline silicon based solar cells is around
39.78 mA/cm
2
for the AM1.5 direct solar spectrum and 44.23 mA/cm
2
for the AM1.5 global
solar spectrum. The value for the global spectrum is slightly higher since the global spectrum
includes the contribution from both direct and diffuse sunlight.

30

Figure 2-1 Schematics of the simulated square lattice SiNW (a) and SiNH (b) structures. The
insets show the cross section of a single nanowire and nanohole, respectively.
2.3 Simulation Results
2.3.1 Efficiency landscape
Figure 2-2 shows the ultimate efficiency as a function of the lattice constant for several different
filling ratios for both 2.33μm-thick square lattice SiNW and SiNH arrays. For both arrays, the
ultimate efficiency tends to increase with increasing lattice constant up to 600 nm – 700 nm and
then decreases, for a given filling ratio. This trend arises from enhanced field concentration
within the active materials and the excitation of guided resonances, as we will discuss later.
For SiNW arrays, for a fixed lattice constant, the ultimate efficiency initially increases with
filling ratio but then decreases again. This trend can be explained by the fact that as the filling
ratio approaches one, the efficiency of the nanowire array should approach that of a thin film
(lower dashed line). The optimal filling ratio is in the range from 0.5 to 0.64. It is clear from the
graph that the ultimate efficiency of a SiNW array with lattice constant larger than 150 nm can
exceed that of an equally-thick Si thin film (lower dashed line), given proper choice of filling
fraction. Moreover, a SiNW array with lattice constant larger than 350 nm can exceed that of Si
film with a single layer antireflection (AR) coating (upper dashed line). We calculated the
efficiency of the AR-coated thin film assuming a single-layer coating of silicon nitride (Si
3
N
4
)

31

with frequency-dependent refractive index given in Ref. [44]. In the frequency range of interest,
Si
3
N
4
has negligible loss. We optimized the thickness of the AR-coating to maximize the
efficiency, yielding an efficiency of 20.34% at a thickness of 63 nm. Within the parameter range
shown, the optimal SiNW structure has a lattice constant of 650 nm and a diameter of 520 nm. It
can achieve an ultimate efficiency of 23.84%, 72.4% higher than the efficiency of a Si thin film
of equal thickness and 17.2% higher than an equal-thickness Si thin film with an optimal single-
layer AR coating.
On the other hand, the absorption of SiNH array improves with decreasing filling ratio and the
optimal filling ratio is 0.5, the smallest filling ratio studied. Moreover, unlike SiNW arrays,
SiNH arrays can be more absorptive than a silicon slab with equal thickness regardless of the
structure. Finally, the optimal SiNH array structure (a = 600 nm and d = 480 nm) can achieve a
higher ultimate efficiency of 26.04% than the optimal SiNW array.
In terms of maximum short circuit current density, the optimal SiNW and SiNH arrays can
offer a maximum short circuit current density of 19.87 mA/cm
2
and 21.31 mA/cm
2
, respectively,
compared to 16.64 mA/cm
2
and 11.32 mA/cm
2
for the equally thick thin films with and without
an optimal single-layer Si
3
N
4
AR coating.

Figure 2-2 The ultimate efficiency of 2.33μm-thick, square lattice SiNW (a) and SiNH (b) arrays
as a function of the lattice constant for several different filling ratios.

32

2.3.2 Optical spectra of SiNW arrays
We first examine the optical spectra of SiNW arrays. Figures 2-3 (a), (b), and (c) compare the
reflectance, transmittance, and absorptance of arrays with a=100nm and a=500nm for a fixed
filling ratio of 0.28. Data for a thin film are shown for comparison. The results for the SiNW
array with lattice constant a=100nm agree well with previous study [5]. The reflectance (R) in
Figure 2-3 (a) is much lower than that of the thin film throughout the entire spectral range.
Meanwhile, the transmittance (T) in Figure 2-3 (b) is much higher than the Si thin film in the
low-frequency range and approaches zero in the high-frequency range. The absorptance, shown
in Figure 2-3 (c), is given by A = 1 – R – T. In the high-frequency range, the low reflectance and
zero transmittance of the SiNW array lead to higher absorptance than the Si thin film. In the low-
frequency range, the SiNW array has a lower absorptance than the thin film. We calculated the
ultimate efficiency for both structures and found that the efficiency of the thin film (13.83%) is
higher than that of the SiNW array (7.62%). We note that these values are close but not identical
to those given in Ref. [5]; slight differences may be due to the use of different optical constant
data near the band gap or to differences in implementation of the TMM method. We have
verified that the ultimate efficiency of the thin film calculated using the TMM code agrees with
that calculated using the analytical formula for the transmittance and reflectance of a silicon slab
within 0.3%.
For a = 500 nm, narrow, irregularly-spaced peaks appear in the reflectance spectrum (Figure
2-3 (a)) that are qualitatively different than the Fabry-Perot-like features seen in the thin film and
a = 100 nm lattice constant SiNW structures in the low frequency range. The transmittance
spectrum (Figure 2-3 (b)) exhibits narrow dips, and the absorptance spectrum (Figure 2-3 (c))
exhibits numerous enhancement peaks. In the high-frequency range, narrow spectral features are
largely absent in the reflectance, transmittance, and absorptance data. This phenomenon can be
explained by the high intrinsic material absorption of silicon in this range. We have observed in
numerical experiments that increasing the absorption of the nanowire material tends to smooth
out guided resonance peaks.
These spectral features correspond to the excitation of the so-called “guided resonance”
modes or “quasi-guided” modes in a slab waveguide with periodic corrugation. Guided

33

resonance modes, also known as slow Bloch modes [8], have been extensively studied in
photonic-crystal slabs [45, 46]. These modes resemble the pure guided modes in an optical slab
waveguide but can be excited by normally incident plane wave due to the diffractive coupling
mechanism provided by the periodic corrugation. They are characterized by an increase in
electromagnetic field intensity within the photonic crystal slab. Therefore, it is expected that
when guided resonance modes are excited by incident sunlight, the optical absorption will be
strongly enhanced.

34

35

Figure 2-3 Optical properties of the SiNW array with varying lattice constant. In the left column,
(a), (b), and (c) are the reflectance, transmittance, and absorptance, respectively, in the SiNW
array with lattice constant 100nm and 500nm. The optical properties of a silicon thin film are
plotted for comparison. In the right column, (d), (e), and (f) are the reflectance, transmittance,
and absorptance, respectively, in the SiNW array with lattice constants 100nm, 150nm, and
200nm. The optical properties of the Si thin film are also plotted.
Guided resonance modes will only be present at frequencies within the solar spectrum when
the lattice constant is sufficiently large, as pointed out in Ref. [8] in the context of organic solar
cells. We illustrate the effect of changing the lattice constant in Figure 2-4 (a) and (b), where the
dispersive band structures of a = 100 nm and a = 500 nm SiNW arrays are shown side by side.
We plot both Z-even (TE-like) and Z-odd (TM-like) modes [47]. Guided resonance modes lie
within the shaded region, called the light cone. The figure shows that for energies up to 2.8eV,
guided resonance modes are not present for the a = 100 nm SiNW array. For the a = 500 nm
SiNW array, guided resonance modes appear at energies of 0.97eV and above. Modes at the 
point can be excited normal incident sunlight, if they satisfy the symmetry requirement [48, 49].

Figure 2-4 The dispersive band structures of a SiNW array for (a) a = 100 nm (b) a = 500 nm.
In Figure 2-5 (a), we show the reflectance, transmittance, and absorptance data for the a = 500
nm SiNW array in a narrow spectral region around 1.197eV. A transmittance dip is observed in
the spectra, accompanied by a reflectance peak. The absorptance exhibits an enhancement peak,
consistent with a relative increase in electromagnetic field intensity at the resonant frequency.
The electric field density distributions (ε|E|
2
) on the end surface of the SiNW and on a vertical

36

cross section of the nanowire structure are shown in Figures 2-5 (b) and (c), respectively. The
field density is concentrated in the absorptive SiNW region.

Figure 2-5(a) Characteristic line shape of a guided resonance at 1.197eV (b) Top view of electric
field energy density distribution on the end surface of the SiNW array at the resonance shown in
(a). (c) Side view of electric field energy density distribution inside the nanowires at the same
resonance.
Referring back to Figure 2-3 (c), an additional difference between the a = 100 nm and a = 500
nm data is visible. In addition to the presence of guided resonance peaks, the overall shape of the
a = 500 nm curve is shifted toward lower energies compared to the a = 100 nm curve. In order to
understand this trend, we plot the optical properties of SiNW arrays with intermediate lattice
constants for which guided resonance modes are not present.
Figures 2-3 (d), (e), and (f) show the results for a = 100 nm, 150 nm, and 200 nm. For a = 150
nm and 200 nm, the reflectance values in Figure 2-3 (d) remain low across the entire spectral
range. The transmittance curve, shown in Figure 2-3 (e), tends to shift towards lower energies
(higher wavelengths) as the lattice constant is increased. The transmittance in the high-frequency
range is close to zero for all three lattice constants. The absorptance curves (Figure 2-3 (f)) also
shift to lower energies, while the absorptance is high in the high-frequency range for all three
lattice constants. We calculated ultimate efficiencies of 7.62%, 12.34%, and 16.14% for the
SiNW arrays with lattice constants a = 100 nm, 150 nm, and 200 nm, respectively, compared to

37

13.83% for the Si thin film of equal thickness. The increase in absorptance with increasing lattice
constant (even in the absence of guided resonances) can be understood in terms of the field
concentration inside the silicon nanowires. We have verified via FDTD simulations that for fixed
filling ratio, the normalized electromagnetic field energy inside the silicon nanowire increases
with increasing lattice constant. Later, several papers have investigated this phenomenon using a
modal approach. The wavelength and diameter dependent absorption was found to correlate
qualitatively with the imaginary part of the effective index of the fundamental waveguide mode
(HE
11
) inside an isolated single nanowire [50-52]. In specific, there is a red shift of the effective
absorption band edge when the diameter of the nanowire is increasing, consistent with the trend
we observed here.
2.3.3 Optical spectra of SiNH arrays
The absorptance spectra of SiNH arrays show different characteristics than SiNW arrays. Figure
2-6 shows the absorptance spectra of 2.33μm-thick square lattice SiNH arrays with a fixed filling
ratio of 0.50 and varying lattice constants. From Figure 2-6(a), we can observe that the
absorptance spectra for SiNH arrays with relatively small lattice constants (a = 100 nm, 150 nm,
and 200 nm) resemble that of an equally-thick thin film, shown for reference. With increasing
lattice constant, the absorptance in the low frequency range improves by a small amount.
Moreover, in contrast to SiNW arrays, the absorptance in the high-frequency range increases
with increasing lattice constant. Overall, the broadband absorption improves with increasing
lattice constant. When the lattice constant is large enough, guided resonance induced absorption
enhancement peaks are also apparent in the low frequency range, as can be seen from the
absorptance spectrum for a = 500 nm and a = 900 nm SiNH arrays in Figure 2-6(b). However,
similar to the SiNW array, the SiNH array with a very large lattice constant of 900 nm shows
decreased absorptance in the medium and high frequency range, which leads to a decrease in the
ultimate efficiency.

38

Figure 2-6 Absorptance spectra of square lattice SiNH arrays with a fixed filling ratio 0.50 and
varying lattice constants. (a) Absorptance spectra for lattice constants a = 100 nm, 150 nm, and
200 nm. The absorptance spectrum of the thin film is shown for reference. (b) Absorptance
spectra for lattice constant a = 500 nm and 900 nm. The absorptance spectra for the thin film and
a = 100 nm SiNH array are shown for comparison.
2.3.4 Comparison to Lambertian light trapping limit
We also compare our results to the conventional light-trapping limit derived from ray optics (also
known as the Yablonovitch limit), introduced in Chapter 1, for both SiNW and SiNH arrays. In
order to calculate the maximum absorption that can be achieved under the conventional light-
trapping limit, we used the formula from Ref. [53], which incoherently sums up all the multiple
reflections of light inside a free-standing semiconductor film:
2
max 2
22
2
2
1
(1 )
1
l
ll
eT
A
n
e Te
n








in which α is the optical absorption coefficient of the semiconductor film, l is the thickness of a
solid film, T is the transmittance at a single semiconductor/surrounding medium interface given
by the Fresnel formula, n
1
and n
2
are the refractive indices of the photoactive material (silicon)
and the surrounding dielectric (air), respectively. In the absence of a back reflector, this formula

39

gives an optical absorption enhancement factor of 2n
2
in the low absorption limit (αl << 1), with
a perfect anti-reflection coating (T = 1).
Figure 2-7 shows the absorptance spectra of a 2.33 μm-thick solid silicon film with (red) and
without (black) perfect geometrical light trapping, assuming no anti-reflection coating was
applied. Significant absorption enhancement is observed in the low frequency range where
silicon is a poor absorber. Quantitatively, the ultimate efficiency and maximum short circuit
current density of the 2.33 μm-thick solid silicon film with perfect light-trapping are calculated
to be 24.86% and 20.35 mA/cm
2
, respectively. We also plot the absorptance spectra for the
equally-thick SiNW (green) and SiNH (blue) arrays with optimal structural parameters.
Compared to the conventional light trapping limit, optimal SiNW and SiNH geometries can both
provide higher absorptance in the medium and high-frequency range. In the low frequency range,
a collection of guided resonances induced absorptance peaks provide enhancement that can be
higher or lower than the light-trapping limit, depending on frequency. Overall, the SiNH array
with the optimal parameters provides a slightly higher ultimate efficiency of 26.04% and
maximum short circuit current density of 21.31 mA/cm
2
compared to 24.86% and 20.35 mA/cm
2

achieved under the conventional light-trapping limit. This fact reveals the great potential of light-
trapping in the wave-optics regime [22, 54].

40

Figure 2-7 Absorptance spectra for a 2.33 μm-thick thin film (black), an equally-thick thin film
with perfect geometrical light trapping (red), the equally-thick optimal square lattice SiNH array
(blue) and SiNW array (green).
2.3.5 Angular response
We have also examined the angular response of both the SiNW and SiNH arrays, which is
important for concentrator photovoltaic applications. We plot the ultimate efficiency as a
function of incidence angle for the 2.33μm-thick, square lattice, optimal SiNW and SiNH arrays.
For comparison, the angular response for the optimal AR-coated silicon thin film was also
plotted. Several trends can be observed. Firstly, both the optimal SiNW and SiNH arrays show
less degradation of absorption efficiency with increasing incidence angle for TM polarization
(shown in Figure 2-8 (b)) than for TE polarization (shown in Figure 2-8 (a)). Detailed
calculations showed that the difference in ultimate efficiency between TE and TM polarizations
can be attributed to higher reflectance of TM-polarized light in the high-frequency range. TE
reflectance increases with incidence angle in the high-frequency range, while TM reflectance
decreases. Secondly, the optimal SiNH array is more absorptive to TM-polarized incident light
than the optimal SiNW array for incidence angles up to 80 degree. For TE polarization, the
optimal SiNH array can be more absorptive than optimal SiNW array only up to 30 degree.

41

Thirdly, the conclusion that both the optimal SiNW and SiNH array can be more absorptive than
the optimal AR-coated silicon thin film holds for incidence angles up to 80 degrees for the TM
polarization and up to 60 degrees for the TE polarization.
The good angular response of the nanowire array would suggest it to be a good candidate for
high-efficiency concentrator photovoltaics with reduced material consumption. In fact, from the
figure above, the ultimate efficiency remains roughly the same as the normal incidence value for
incidence angle up to 30 degrees. Considering the solid angle extended by the sun is around 0.26
degree (half angle), this gives a concentration factor of around 12,000. In theory, this
concentration factor will give rise to a 244 mV increase in the open-circuit voltage of the solar
cells. Although significant, the actual performance improvement is limited by the increase in the
cell temperature under concentration.

Figure 2-8 The incidence angle dependence of ultimate efficiency for a 2.33μm-thick silicon thin
film with an optimized single-layer antireflection coating (black), the optimal square lattice
SiNW array with L=2.33μm (red), and the optimal square lattice SiNH array with L=2.33μm
(blue). (a) the result for TE polarization (b) the result for TM polarization.
2.3.6 Height dependence
Above, we have examined optically thin structures with a film thickness L = 2.33 μm, which is
much smaller than the absorption length of silicon at near infrared wavelengths. We have
verified that optically thick nanowire and nanohole arrays (L = 100 μm) can also exhibit higher

42

efficiencies than equal thickness solid films. Figure 2-9 shows the ultimate efficiency results for
100 μm-thick square lattice SiNW (a) and SiNH (b) arrays. We observe that both 100μm-thick
SiNW and SiNH arrays with certain parameters are more absorptive than an equally thick solid
film, even with an optimal single layer AR coating. The optimal parameter range is much
narrower than for the 2.33μm-thick structures. Numerically, the optimal SiNW structure (a = 400
nm, d = 200 nm) has an ultimate efficiency of 39.79% and a maximum short circuit current
density of 32.56 mA/cm
2
. The optimal SiNH structure (a = 600 nm, d = 480 nm) has an ultimate
efficiency of 39.14% and a maximum short circuit current density of 32.03 mA/cm
2
. The 100μm-
thick silicon thin film with and without the optimal single layer AR coating has an ultimate
efficiency of 38.54% and 27.15%, corresponding to a maximum short circuit current density of
31.53 mA/cm
2
and 22.22 mA/cm
2
, respectively. The enhancement factor relative to the solid film
is lower than that for the 2.33μm-thick structures, which might be expected considering that the
100 μm thick film is already a very good absorber. Both the optimal SiNW and SiNH structures
exceed the conventional light trapping limit, which corresponds to an ultimate efficiency of
30.65% and a maximum short circuit current density of 25.08 mA/cm
2
.

Figure 2-9 The ultimate efficiency of 100 μm-thick square lattice SiNW (a) and SiNH (b) arrays
as a function of lattice constant for several different filling ratios.

43

2.3.7 Effect of different lattice geometries
In addition to the square lattice, the hexagonal lattice is another popular choice of lattice type for
periodic arrays. We examine the effect of lattice type on the optical properties of SiNW and
SiNH arrays. We study two different polarizations of the incident light at normal incidence: TE
(electric field is along the ГХ direction of the hexagonal lattice), and TM (electric field is
perpendicular to the ГХ direction of the hexagonal lattice).
In Figure 2-10, we plot the ultimate efficiency for TE-polarized incident light for 2.33μm-
thick hexagonal lattice SiNW and SiNH arrays. The inset indicates the polarization of the
incident light. The ultimate efficiency exhibits a similar trend as a function of lattice constant to
that for the square lattice. The optimal filling ratio for SiNW and SiNH arrays are close. The
optimal SiNW structure (a = 650 nm and d = 540 nm) can achieve an ultimate efficiency of
23.70%, corresponding to a maximum short circuit current density of 19.39 mA/cm
2
. The
optimal SiNH array structure (a = 650 nm and d = 480 nm) can achieve a slightly higher ultimate
efficiency of 26.17%, corresponding to a maximum short circuit current density of 21.41
mA/cm
2
.

Figure 2-10 The ultimate efficiency of 2.33μm-thick hexagonal lattice SiNW (a) and SiNH (b)
arrays as a function of lattice constant for several different filling ratios. The incident light is TE-
polarized, as shown in the inset.

44

Figure 2-11 shows the ultimate efficiency for TM-polarized incident light for the same
hexagonal lattice SiNW and SiNH arrays. The optimal SiNW array (a = 700 nm and d = 520 nm)
has an ultimate efficiency of 23.91% and a maximum short circuit current density is 19.57
mA/cm
2
. The optimal SiNH array (a = 650 nm and d = 480 nm) has an ultimate efficiency of
25.16% and a maximum short circuit current density of 20.59 mA/cm
2
. These numbers are close
to both the hexagonal lattice results for TE polarization and the square lattice results.

Figure 2-11 The ultimate efficiency of 2.33μm-thick hexagonal lattice SiNW (a) and SiNH (b)
arrays as a function of lattice constant for several different filling ratios. The incident field is
TM-polarized, as shown in the inset.
2.3.8 Detailed balance limit analysis
Up to now, we use ultimate efficiency and maximum short circuit current density to quantify the
broadband optical absorption in SiNW and SiNH arrays. But what is the upper bound of the
power conversion efficiency if we make a solar cell out of SiNW and SiNH arrays?
The detailed balance limit [42] approach, also known as the “Schockley-Queisser limit”, gives
the fundamental physical limit of power conversion efficiency of solar cells by considering only
the intrinsic loss mechanisms. In the original analysis, the short circuit current is proportional to
the total number of photons above the band gap available for absorption, the radiative
recombination is assumed to be the only recombination mechanism, and an ideal diode
characteristic is used to describe the electrical properties of the solar cell. Here we modified the

45

original analysis by taking into account the realistic optical absorption spectrum of the structure
under study, instead of assuming perfect absorption above the band gap. In this way, we can
obtain a practical limiting efficiency for thin film solar cells, in which the active layer is too thin
to effectively absorb light. Moreover, such modified analysis allows us to compare the
performance between thin film nanostructured solar cells and their planar, unpatterned
counterparts.
Again, the short circuit current can be related to the absorptance by

310
( ) ( )
g
sc
nm
e
J I A d
hc

    

(1)
where λ
g
= 1127 nm is the band gap of silicon, and the solar irradiance becomes negligible below
310 nm. Eq. (1) assumes perfect carrier collection efficiency.
We use the J-V characteristic of an ideal diode to describe the electrical properties of the solar
cell:

00
()
( ) ln 1 ln 1 ,
junc
sc illu sc BB
junc illu
A
J J A J J k T k T
VJ
q J A q J A



     
        


  
 

(2)

in which J is the current density of the solar cell, V is the voltage between the terminals of the
cell, and J
0
is the reverse saturation current density. A
illu
is the illumination area, and A
junc
is the
junction area. In planar thin films, γ equals unity. In nanostructured thin films, γ depends upon
the specific junction geometry. Here we assume an axial p-n junction geometry, where the p and
n regions are vertically stacked. Therefore, γ is equal to the filling ratio of the array.
We take the value of the reverse saturation current density to be [55]:

2 2 2 2 2
0 32
2
( ) (2 2 )exp( )
g
T B B B B g g
B
E
q
J n n k T k T k TE E
h c k T

    
(3)
where n
T
and n
B
are the refractive indices of the superstrate and substrate of the solar cell, equal
to 1 (air). For crystalline silicon with a band gap of 1.1eV at T = 300K, the value of J
0
is 5.4 x
10
-13
mA/cm
2
.
By setting the total current J = 0, we obtain the open circuit voltage of the solar cell. Under
the assumption that J
sc
>> J
0
,

46

0 0 0
( 0) ln 1 ln ln ln
sc sc sc B B B B
oc
J J J k T k T k T k T
V V J
q J q J q J q


      
      
      

      
(4)
The power conversion efficiency is defined as
..
mpp mpp
oc sc
in in
VJ
V J FF
PCE
II
 (5)
where V
mpp
and J
mpp
are the voltage and current density that maximize the output electrical
power V x J(V), FF ≡ V
mpp
J
mpp
/ V
oc
J
sc
is the fill factor, and I
in
is the incident solar power density.
For the ASTM AM1.5 direct and circumsolar solar spectrum at one sun, I
in
is about 900 W/m
2
.
The power density contained in the AM1.5 global spectrum is around 1000 W/m
2
.
For a given nanowire or nanohole structure, the power conversion efficiency can be
determined numerically using Eq. (2) and the value of the short circuit current obtained from the
optical simulation.
Figure 2-12 shows calculation results for nanowire (a, c, e) and nanohole (b,d,f) arrays. We
plot the short circuit current density, open circuit voltage, and power conversion efficiency for
arrays with various structural parameters (lattice constant and filling ratio).
Figures 2-12 (a) and (b) show J
sc
as a function of lattice constant and filling ratio for nanowire
and nanohole arrays, respectively. In both cases, the maximum values of J
sc
are obtained for
lattice constants in the 600 nm – 700 nm range and moderate filling ratio (~0.5). The value of the
short circuit current density is higher than for a thin film with the same thickness. It is also
higher than the value for a thin film with a single-layer Si
3
N
4
AR coating.
Figures 2-12 (c) and (d) show V
oc
as a function of lattice constant and filling ratio. V
oc
increases with decreasing filling ratio for both nanowires and nanoholes. The variation in voltage
is small (<6%) over the range of parameters plotted. From Eq. (4), V
oc
scales as ln(J
sc
/γ), where γ
is the filling ratio. J
sc
depends on γ, as seen above in Figures 2-12 (a) and (b). Thus, the value of
the filling ratio that optimizes J
sc
does not necessarily optimize V
oc
. Inspection of Figures 2(a)
and 2(c) reveals that this is the case for nanowire arrays.
We found that the fill factor (Eq. 5) is approximately 86% over the range of lattice constants
and filling ratios considered.

47

Figures 2-12 (e) and (f) show the power conversion efficiency. The optimal nanowire
structure (a = 650 nm and d = 520 nm) has an efficiency of 15.98%. The optimal nanohole array
structure (a = 600 nm and d = 480 nm) has an efficiency of 17.18%. These values are higher than
for a silicon thin film with the same thickness (8.71%), and even for a thin film with an optimal
single-layer Si
3
N
4
AR coating (12.99%). The dependence of efficiency on lattice constant and
filling ratio is very similar to the short circuit current (Figures 2-12 (a) and (b)), which can be
attributed to the much more significant variation in the short circuit current density than the open
circuit voltage.

48

Figure 2-12 The dependence of solar cell characteristics on lattice constant and filling ratio for
silicon nanowire (a, c, e) and nanohole (b, d, f) arrays.

49

We have assumed an axial p-n junction geometry in our analysis. Another possible geometry
is the radial p-n junction [38]. We have calculated the power conversion efficiency of radial
junction geometries, and the values are generally lower. This is due to the increase in junction
area, corresponding to γ >> 1 in Eq. (4), which leads to a decrease in the open circuit voltage.
Further work may incorporate more detailed and realistic models of the electro-optical
properties of the cell. Above, we have assumed a constant value of the reverse saturation current
density, J
o
(Eq. 3). Due to the possibility of emission enhancement in nanostructured films [56],
J
o
may vary with the filling fraction and lattice constant of nanowire or nanohole arrays.
Moreover, we have assumed perfect carrier collection. It should be possible to place a stricter
bound on power conversion efficiency using detailed device physics models [57, 58].
2.4 Conclusions
To summarize, in this chapter, we use the scattering matrix method to numerically study the
optical absorption properties of SiNW and SiNH arrays with lattice constants varying from
100nm to 900nm, for two different periodic lattices (square and hexagonal). Our results show
that dramatic optical absorption enhancement occurs with increasing lattice constant up to 600 –
700 nm. For relatively small lattice constants, the absorption enhancement results from an
increase in the electromagnetic field concentration within the silicon nanowires. For larger lattice
constants, guided resonances are excited and serve as a supplemental enhancement mechanism.
However, when the lattice constant is too large, the absorptance in the medium and high
frequency range decreases, hence the ultimate efficiency suffers. It was found that both SiNW
and SiNH arrays with the optimal parameters can be more absorptive than an equally-thick
silicon solid film, even with an optimal single layer Si
3
N
4
AR coating. The optimal SiNH array
was found to be slightly more absorptive than the optimal SiNW array. Interestingly, the optimal
SiNH array can surpass the conventional light trapping limit under normal incidence. Similar
conclusions were also reached for 100 μm, optically thick structures. Another desirable
characteristic of SiNW and SiNH arrays is that they exhibit high efficiency over a broad angular
range. Finally, a modified detailed balance analysis was carried out based on the optical

50

modeling results. A photovoltaic power conversion efficiency up to 17% was predicted for the
optimal silicon nanohole geometry.
Although we focus our study on silicon nanowire arrays in this thesis, the conclusion that
semiconductor nanowire arrays with properly designed geometry can be more absorptive than an
equally-thick thin film is in fact more general. In a later publication from our group [30], we
have reached at the same conclusion for vertical nanowire arrays based on a wide range of
photovoltaic materials, including group III-V and II-VI compound semiconductor materials with
direct band gaps, such as GaAs and CdTe. Furthermore, this conclusion also holds for a wide
range of nanowire height, ranging from 100 nm to 100 µ m.
Another exciting avenue for research is multi-junction nanowire solar cells where
photovoltaic materials with desirable band gaps stack on top each of other and absorb different
portions of the solar spectrum [59]. A unique advantage of the nanowire structure is that its small
dimension can relax the strain built up between lattice-mismatched materials [60]. In such
structure, we need to carefully design the dimension of each nanowire segment so that the
current flowing through each sub-cell is the same and the total output power from the solar cell is
maximized. This procedure is called “current-matching”. Several groups, including ours, have
investigated current-matching in double junction [33, 61, 62] and triple junction [63] nanowire
solar cells.

51

CHAPTER 3 OPTIMAL DESIGN OF APERIODIC SILICON
NANOWIRE LIGHT-TRAPPING STRUCTURES
3.1 Introduction
In the last chapter, we calculated the optical absorption in perfectly periodic silicon nanowire and
nanohole arrays, which has been the subject of almost all recent theoretical studies. However,
under realistic fabrication conditions, a small amount of disorder inevitably exists [64-66].
Moreover, while lithography-free fabrication method [67, 68] can offer inexpensive, scalable
methods for nano-patterning, they tend to produce structures with a greater amount of structural
randomness. Therefore, investigating the effect of disorder, or randomness, on the optical
absorption in sub-wavelength nanostructures is of practical interest.
Recently, several research groups, including ours, have carried out calculations on models that
mimic disordered or random structures, which are aperiodic on smaller length scales, while
periodic on a larger scale [6, 24, 69-76] (typically on the order of a micron). The large-scale
periodicity provides a finite computational cell for calculations, making such structures amenable
to simulation and systematic study. In general, an optical absorption enhancement effect was
observed in disordered systems compared to their ordered counterparts. An interesting further
question to ask is whether it is possible to deliberately design “random” or “disordered”
structures that maximize solar absorption.
In this chapter, we use large-scale simulations and machine-based optimization techniques
[77-84] to design optimal, aperiodic nanowire structures with greater than 100% increase in
photovoltaic efficiency compared to their periodic counterparts.

52

3.2 Optimal design
3.2.1 Simulation setup and optimization algorithm
Figure 3-1 shows schematics of the nanowire structures we consider in this Chapter. Figure
3-1(a) illustrates the top view of the periodic, vertically-aligned silicon nanowire array. Incident
light propagates in the z-direction with the electric field polarized in the x-direction. The
nanowire diameter d is 65 nm. The nanowires are arranged in a square lattice with lattice
constant a = 100 nm and are surrounded by air. Each nanowire has a height of 2.33μm in the z-
direction. Calculations were performed using a 500 nm by 500 nm super cell, containing 25
nanowires. The size of the super cell was limited by computational feasibility. The boundary
conditions are periodic in x and y.

Figure 3-1 Schematics of periodic (a) and aperiodic (b) silicon nanowire structures.
Starting from the periodic configuration, we adjusted the positions of the nanowires within the
super cell one at a time to maximize the ultimate efficiency. An iterative random walk algorithm
was used for the optimization. At each iteration, a nanowire in the super cell was randomly
selected and moved to a new position. The new position was drawn from a uniform distribution

53

around its original position over the whole super cell, under the constraint that the selected wire
will not overlap with any other wire in the super cell after the move. The ultimate efficiency of
the new structure was then calculated by TMM. If the ultimate efficiency was higher than that
before the move, the new position of the selected wire was accepted and stored. Otherwise, the
move was rejected and the selected wire was moved back to its original position. The procedure
was iterated for 1000 times. The resulting structures, such as the one shown in Figure 3-2 (b), are
partially aperiodic. Within the super cell, the rods are arranged aperiodically. From super cell to
super cell, the aperiodic arrangement repeats.

Figure 3-2 Top views of initial periodic (a) and optimal aperiodic (b) silicon nanowire structures.
Dashed lines indicate boundaries between super cells.
3.2.2 Ultimate efficiency
We calculated the ultimate efficiency of the periodic structure of Figure 3-2 (a) to be 8.70%. The
efficiency is lower than that of a solid, silicon thin film with the same thickness (13.83%).
Aperiodicity provides dramatic absorption enhancement. The optimal, aperiodic structure in
Figure 3-2 (b) has an ultimate efficiency of 20.44%, 2.35 times higher than the periodic array. Its
efficiency is higher than a solid, thin film and also slightly higher than a solid, thin film with a
Si
3
N
4
antireflective coating (20.34% for an optimized coating thickness of 63nm). The fact that

54

the aperiodic structure is more absorptive than the thin film is notable, given that the volume of
absorbing material is three times less.
3.2.3 Absorption spectra inspection
We plot the absorptance spectrum for the periodic structure in Figure 3-3 (a). The absorptance
spectrum for the thin film is plotted for reference. The absorptance of the periodic array is higher
than the thin film in the high-energy range, which can be attributed to reduced reflection from
the top surface. However, the absorptance is lower in the low energy range, which contains a
large proportion of solar photon flux. As a result, the ultimate efficiency of the periodic array is
lower than that of the thin film.
The absorptance spectrum of the optimally-designed, aperiodic structure is also shown in
Figure 3-3 (a). In the high energy range, the absorptance is similar to that of the periodic array
and higher than that of the thin film. This is also due to the significantly reduced reflection from
the top surface. More importantly, it exhibits an overall shift towards the lower energy range
compared to the periodic array. In addition, numerous absorption enhancement peaks appear at
lower energies. From previous work, we know that these two spectral features are also
characteristic of periodic arrays with larger lattice constants (for example, a~500 nm and d~300
nm) [85]. In Chapter 2, we attributed these features to (1) an increase in field concentration
inside the nanowire, and (2) the excitation of guided resonance modes. In a sense, the aperiodic
structure can thus be said to mimic a periodic array with larger lattice constant. An absorption
enhancement peak of the optimal aperiodic structure is shown in Figure 3-3 (b). Strong
absorption corresponds to high reflectance and low transmittance, as observed previously for
guided resonances in periodic arrays [85].

55

Figure 3-3 (a) Solar absorptance spectra for periodic (blue dotted) and optimal aperiodic (red
solid) silicon nanowire structures. The absorptance spectrum for an equally-thick silicon thin
film (gray dashed) is also plotted for reference. (b) Reflectance (black dotted), transmittance (red
dashed), and absorptance (blue solid) of the optimal aperiodic structure near 1.249 eV (992.3
nm).
3.2.4 Absorption profile
In Figure 3-4, we plot the power loss rate (or absorption profile) inside the periodic (Figure 3-4
(a)) and the optimal aperiodic (Figure 3-4 (b)) structures, normalized to the maximal power loss
rate inside the periodic array. The incident wavelength is λ = 992.3nm, corresponding to a
resonant absorption enhancement peak inside the aperiodic structure as shown in Figure 3-3 (b).
The power loss rate is calculated as
1
2 ωε″|E|
2
, where ω is the frequency of the incident light, ε″
is the imaginary part of the dielectric constant, and |E|
2
is the local electric field intensity. The
power loss rate is only non-zero inside the silicon nanowires. The evaluation plane was located
0.233 μm beneath the top surface of the nanowire array. Figure 3-4 (b) shows several localized,
strongly enhanced absorption regions in the optimal aperiodic structure, consistent with the peak
in the absorption spectrum.
For periodic structures, guided resonances result from the coupling of normally incident light
to a superposition of modes propagating in the plane of the array. This mechanism decreases the

56

fraction of light escaping the structure (either through reflection or transmission) and increases
absorption. For the aperiodic structure, normally incident light excites localized resonances
within the structure. This mechanism serves a similar function of resonant absorption
enhancement.

Figure 3-4 Absorption profiles of (a) periodic and (b) optimal aperiodic silicon nanowire
structures at a horizontal cross section 0.233 μm below the top surface of the nanowire array.
White dashed lines indicate boundaries between super cells.
3.2.5 Statistical study of random structures
We next investigated whether aperiodic structures outperform the periodic array in general. The
ultimate efficiency was calculated for 1000 randomly selected aperiodic structures. Figure 3-5
shows the histogram of the calculation results. Interestingly, all of the aperiodic structures we
investigated had a higher ultimate efficiency than their periodic counterpart. For the randomly
selected structures, the ultimate efficiency has a mean value of 14.51% and a standard deviation
of 1.60%. The mean value is higher than the ultimate efficiency of a silicon thin film of the same
thickness(13.83%).

57

Examination of the solar absorptance spectra revealed that the two prominent spectral features
of the optimal aperiodic structure, an overall shift towards low energies and the appearance of
absorption enhancement peaks, were generally observed.

Figure 3-5 Histogram of ultimate efficiencies in 1000 randomly-selected, aperiodic silicon
nanowire structures. The ultimate efficiency of the initial periodic array (blue, dashed line) is
plotted for reference.
3.2.6 Effect of rod diameter and super cell size
For the diameter and filling fraction used here, randomly selected, aperiodic structures all had
higher ultimate efficiencies than the periodic array. We have also performed calculations on
other wire sizes, including d = 50 nm and d = 80 nm with initial lattice constant a = 100 nm in a
500 nm by 500 nm super cell, as well as d = 100, 130, 160 nm with initial lattice constant a =
200 nm in an 800 nm by 800 nm super cell. In all of these cases, all aperiodic structures had
higher ultimate efficiencies than their periodic counterparts.

58

3.2.7 Comparison to optimal periodic nanowire arrays
Interestingly, for certain large enough rod sizes, the aperiodic structure can have a higher
ultimate efficiency than the optimum periodic array. More specifically, we simulated rods with d
= 160 nm and an initial spacing of 200 nm in an 800 nm by 800 nm super cell and calculated the
ultimate efficiency of 100 randomly-selected configurations. The highest ultimate efficiency
found in this set was 25.69%. In comparison, previous work identified a = 650 nm and d = 520
nm as the approximate optimal values for periodic structures, yielding an ultimate efficiency of
24.28% [86]. The absorptance spectra of the two structures are shown in Figure 3-6. This result
suggests that the large design space might potentially lead to high performance configuration.

Figure 3-6 Absorptance spectra comparison between the best aperiodic silicon nanowire
structure (super cell length 800 nm, initial lattice constants a = 200 nm) and the optimal periodic
silicon nanowire array (a = 650 nm, d = 520 nm).
3.2.8 Advanced optimization algorithm
While the random walk algorithm used in this work is relatively easy to implement, it is not
guaranteed to reach the global optimum. In the literature, several other advanced optimization
algorithms were successfully applied to other photovoltaic architectures [24, 76]. We have also
tested several other popular optimization algorithms to our problem, including a micro-genetic
algorithm [87] and several other derivative-free global or local optimization algorithms

59

implemented in the numerical package NLopt [88], such as COBYLA (Constrained Optimization
by Linear Approximation). However, it was not clear from the optimization results which
algorithm performs better than others (in terms of the number of evaluations and the figure of
merit of the final configuration), possibly due to the complex, noisy nature of the figure of merit
function in the extremely large parameter space. Furthermore, the identification of “robust”
optima [89], or configurations of nanowires that exhibit both high ultimate efficiency and low
sensitivity to perturbations in the design parameters, is a challenging optimization problem for
future research.
3.3 Summary
In summary, we have demonstrated the optimal design of aperiodic, vertically-aligned silicon
nanowire structures for photovoltaic applications. An optimization procedure based on the
random walk algorithm enhanced the ultimate efficiency by 2.35 as compared to the periodic
array. The solar absorptance spectrum of the optimal aperiodic structure was found to resemble
that of a periodic array with larger lattice constant and higher ultimate efficiency.
An interesting future direction for research is to design completely disordered structure for
light trapping purposes [90-92]. Improved solar absorption compared to an un-patterned slab and
even the slab with periodic patterning was observed, with the additional benefit of insensitivity
to incidence angle and polarization. Although potentially a larger parameter space will become
accessible, the design and optimization of such structure remain a severe challenge, due to the
difficulty of simulating the electromagnetic fields of a truly aperiodic structure.

60

CHAPTER 4 EFFECT OF APERIODICITY IN SILICON
NANOROD ANTIREFLECTING STRUCTURES
4.1 Introduction
In the last chapter, we examined the role of partial positional disorder in the light-trapping
performance of silicon nanowires absorbers. Here we are going to examine whether partial
aperiodicity can affect the other important perspective of light management in solar cells, the
anti-reflection performance. One previous work [67] has suggested that height variations in
nanotip structures can improve antireflection performance. However, the effect of positional
randomness on the performance of subwavelength antireflective structures has not been modeled
systematically.
In this chapter, we use large-scale electromagnetic simulations to systematically investigate
the effects of aperiodicity on broadband reflection. We found that aperiodic nanorod structures
can exhibit significantly better antireflection performance than periodic ones. We perform
calculations of the solar-averaged reflection loss for hundreds of random configurations to
characterize the statistical effects of aperiodicity. Our results show that the effects of aperiodicity
vary with nanorod diameter. For smaller diameters, randomness is generally beneficial, while for
larger nanorod diameters, it degrades the anti-reflection performance. We further use optimal
design techniques [80] to identify optimal aperiodic structures that outperform their periodic
counterparts over a range of nanorod sizes.
4.2 Simulation setup
Figure 4-1 illustrates three different types of structures that we simulate in this chapter. Vertical
silicon nanorods are arranged periodically (Figure 4-1 (a)), almost periodically (Figure 4-1 (b)),
or randomly (Figure 4-1 (c)) on a semi-infinite silicon substrate. In the periodic structure, the
nanorods are arranged in a square lattice. In the almost periodic structure, the nanorods have a

61

small amount of positional disorder. In the random structure, the nanorods are randomly
positioned. The height of the nanorod is fixed to 120 nm.

Figure 4-1Schematic diagrams of periodic (a), almost periodic (b), and random (c) anti-reflection
nanostructures
We use scattering matrix method (ISU-TMM) to calculate the reflectance from various
structures. In order to characterize the reflection loss throughout the solar spectrum for a
structure under study, we define a figure of merit called average reflection loss (ARL).

1127
310
1127
310
( ) ( )
()
2
()
nm
TE TM
nm
nm
nm
RR
Id
ARL
Id

  
  





in which R
TE
(λ) and R
TM
(λ) are the surface reflectance for TE and TM polarization,
respectively. TE and TM polarized light have electric fields perpendicular or parallel to the
incidence plane, respectively. This figure of merit gives the ratio between the number of
unabsorbed photons due to reflection loss and the total number of available photons above the
band gap of crystalline silicon. It can also be understood as the percentage loss in the ultimate
efficiency due to non-perfect anti-reflection performance.

62

4.3 Simulation Results
4.3.1 Periodic nanorod array
First, we evaluate the anti-reflection performance of periodic silicon nanorod structures. The
periodic structure is defined by a lattice constant a and wire diameter d, as shown in Figure 4-2
(a). We calculated the ARL as a function of a and d/a, the diameter to lattice constant ratio. The
filling ratio of the array is related to the d/a ratio by π(d/a)
2
/4. The calculation results are plotted
in Figure 4-2(b). Clearly, there is an optimal range of parameter space that minimizes broadband
reflection. The optimal range for d/a is 0.6 to 0.8. In this range, lattice constants between 200 and
350 nm give the lowest ARL. The optimal periodic structure has an ARL of 4.64%, with lattice
constant of 270 nm and d/a of 0.7 (equivalent to a filling ratio of 0.38).

Figure 4-2 (a) Top view of one unit cell in a periodic structure. (b) Average reflection loss (ARL)
as a function of lattice constant and d/a ratio.

63

4.3.2 Comparison between periodic and aperiodic nanorod array
In Figure 4-3, we present a systematic comparison of reflection loss in periodic and various
aperiodic structures. The filling ratio is fixed to 0.38, and the nanorod diameter is varied. For
reference, the ARL values for a bare silicon substrate, for conventional pyramidal surface
texturing, and for an optimized single-layer Si
3
N
4
anti-reflection coating with a thickness of 80
nm are shown by dashed lines. The reflectance spectrum of the conventional pyramidal surface
texturing was calculated by a simple scalar approach, following Ref. [93].

Figure 4-3 Average reflection loss (ARL) as a function of nanorod diameter for periodic
structures, almost periodic structures (10% positional disorder), random aperiodic structures, and
optimally designed aperiodic structures.
Consistent with Figure 4-2, the ARL of the periodic structure (green line) decreases with
increasing lattice constant until the optimal diameter of 189 nm (corresponding to an optimal
lattice constant of 270 nm) is reached. The optimal periodic structure exhibits lower reflection
loss than either the single layer AR coating or pyramidal surface texturing.

64

Next, we determined the ARL for almost periodic structures. For each configuration, the rod
positions were determined by adding a random shift to the original position of each rod, where
the shift was drawn in each of the lateral directions from a uniform distribution with width equal
to 10% of the lattice constant. The number of nanorods within one super cell was 25 for the
smallest nanorod diameter (70 nm), and 16 for other structures. A total of 100 configurations
were calculated for each nanorod diameter. The symbols and error bars in Figure 4-3 indicate the
mean values and standard deviations of the ARL, respectively. The mean ARL lies slightly
below the value for the periodic structure for smaller nanorod diameters, and slightly above for
larger diameters. We conclude that overall, the anti-reflection performance of a periodic structure
is not particularly sensitive to slight perturbations in position, for example, due to fabrication
imperfections.
In contrast, completely random structures can exhibit very different reflectance from periodic
structures. Random structures were generated by randomly positioning each rod within the
supercell, subject only to the constraint that no two rods overlap. A total of 300 configurations
were calculated for each nanorod diameter. For nanorod diameters below 150 nm, the mean ARL
of the random structure is lower than that of the periodic structure. However, for larger rod
diameters, the mean ARL of the random structure is higher than the periodic one. In short, the
effect of aperiodicity on anti-reflection varies with feature size, and random structures are
generally beneficial for small, non-optimal nanorod diameters.
Finally, we consider how deliberate design of an aperiodic structure can further improve
antireflection performance. Starting from the periodic structure, we use a guided random-walk
optimization algorithm similar to Ref. [70] to obtain an aperiodic structure than minimizes the
ARL. At each iteration, a nanorod is randomly moved to determine whether the ARL decreases;
if so, the nanorod is kept in the new position. We ran 300 iterations for each nanorod diameter.
We found that regardless of nanorod size, our algorithm found optimized structures with lower
ARLs than the periodic structure. The ARL is also lower than the mean value of random
structures. The exception is a nanorod diameter of 210 nm. In this case, the algorithm failed to
identify an aperiodic structure with lower ARL than the starting periodic configuration. Since
random-search algorithms are not guaranteed to reach the global optimum, it may still be the

65

case that there is an aperiodic structure with lower ARL. Moreover, values of the ARL even
lower than those in Figure 4-3 (magenta line, “optimal”) may be possible with further
optimization.
The size-dependent role of aperiodicity can be explained in an intuitive manner.
Randomization of nanorod positions within the super cell will introduce additional effective
periodicities (spatial Fourier components). From Figure 4-2(b), we observe at fixed filling ratio,
the ARL decreases with increasing lattice constant and then increases again. For initial
periodicities smaller than the optimal value (270 nm), the additional larger effective periodicities
introduced by randomness tend to decrease the ARL. On the other hand, when the initial
periodicity is larger than the optimal value, the even larger effective periodicities increase the
ARL. We caution, however, that in the high index contrast structures studied here, the physical
picture of reflection as resulting from a sum of gratings corresponding to the spatial Fourier
components (effective periodicities) of the nanorod array [94, 95] may not strictly apply; further
work is required to develop an appropriate scattering model.
Figure 4-3 also shows that the effects of disorder and aperiodicity cannot be described using
simple effective medium theory. The nanostructured material is sometimes modeled with an
effective index that depends only on the filling ratio and the refractive indices of silicon and air
[96]. Reflection from the surface can then be calculated from a 1D problem, corresponding to a
substrate coated with a homogeneous layer with the given effective index. The results of Figure
4-3 show that structures with fixed filling ratio (and hence, the same effective index) can have
radically different ARL values. Even for structures with fixed nanorod diameter, periodic,
random, and optimal aperiodic structures have different values of ARL.
4.3.3 Reflection spectra
In order to gain insight into the role of aperiodicity in the anti-reflection performance, we plot in
Figure 4-4 the reflectance spectra of periodic, random, and optimized aperiodic structures for
different nanorod diameters. For random structures, the reflectance spectra of 300 different
configurations are shown. For a small, non-optimal nanorod diameter of 70 nm, the reflectance
spectra of all random structures lie below that of the periodic one across most of the solar

66

spectrum. The optimally designed aperiodic structure exhibits even lower reflectance. For a
larger nanorod diameter of 140 nm, closer to the optimal value for periodic structures, the
reflectance of the random structures can be lower, higher, or similar to that of the periodic
structure, depending on wavelength. Nonetheless, the reflectance of the optimized aperiodic
structure is still lower than the periodic one across the entire wavelength range. Eventually, when
the nanorod diameter increases to 210 nm, random aperiodic structures exhibit higher reflectance
than the periodic structure across the entire spectrum range. The above observations are
consistent with the results in Figure 4-3.

Figure 4-4 Reflectance spectra for periodic, random aperiodic, and optimal aperiodic structures,
averaged over TE and TM polarizations. The nanorod diameters are 70 nm (a), 140 nm (b), and
210 nm (c), respectively.

67

4.3.4 Angular dependence
We have investigated the dependence of ARL on incidence angle (zenith angle) for both periodic
and random aperiodic structures (see Figure 4-5). For each size, the ARLs for 50 random
structures are calculated for incidence angles up to 80 degrees. The qualitative trends observed in
Figure 4-3 continue to hold up to large incidence angles, namely, the random aperiodic structures
have lower reflection loss compared to their periodic counterparts for small nanorod sizes. For
close to optimal nanorod size, the random aperiodic structures have slightly higher ARL for
small incidence angles. However, for large incidence angles, aperiodic structures perform better
on average.

Figure 4-5 Angular dependence of ARL for both periodic and 50 random aperiodic silicon
nanorod structures for a nanorod diameter of 70 nm (a = 100 nm) and 175 nm (a = 250 nm).
4.3.5 Effect of super-cell size
In our study, the size of the super cell was chosen for the sake of computational feasibility.
However, we have also calculated the ARL for 100 random structures at each nanorod diameter

68

for four times the original supercell area. This set of simulations was done using the Lumerical
FDTD simulation package. Similar to Figure 4-3, random aperiodic configurations exhibit either
lower or higher average values of ARL than the periodic structure, depending on nanorod
diameter.
4.3.6 Other material systems
We have carried out similar calculations for GaAs-based structures with the same height and
similar dimensions. Although GaAs is about ten times more absorptive than silicon in the solar
spectrum, a size-dependent effect of positional aperiodicity similar to the Si case (Figure 4-3)
was observed. On average, random structures outperform periodic ones for small nanorod
diameters.
4.4 Summary
In summary, we have systematically investigated the effect of aperiodicity on the antireflection
performance of silicon nanorod structures. Our results have important implications for practical
device applications. First, for lithographically-defined periodic structures, fabrication errors in
the position of the nanorods do not significantly degrade the antireflection performance. In fact,
for small, non-optimal nanorod sizes, fabrication imperfections can slightly reduce the reflection
loss. Secondly, for nanorod diameters below 150 nm, random structures generally outperform
their periodic counterparts, suggesting that lithographic methods may not be necessary. Thirdly,
for larger nanorod diameters, perfectly periodic structures are preferred, which requires effective
lithographic methods to minimize the degree of structural randomness. However, for optimal
performance, well-controlled, deliberately-designed aperiodic structures will give the best
overall results.

69

CHAPTER 5 EXPERIMENTAL BROADBAND ABSORPTION
ENHANCEMENT IN SILICON NANOHOLE STRUCTURES
WITH OPTIMIZED COMPLEX UNIT CELLS
5.1 Introduction
In the last two chapters, we numerically investigate the effect of positional disorder on the
optical performance of silicon nanowire and nanorod structures. We found that partially-
aperiodic structures can yield significant absorption enhancement or reflection reduction
compared to their simple periodic counterparts. Moreover, maximal enhancement factor can be
achieved using machine-based optimization techniques. However, the experimental evidence of
the theoretically-predicted effect remains scarce so far.
Here we design structures with optimized complex unit cells consisting of nanoholes in a
silicon membrane that maximizes absorption over the solar spectrum. We then fabricate the
optimal structure and measure the absorption in the 600 – 1000 nm wavelength range. The
optimal structure absorbs about 3.5 times more light than a thin film of equal thickness, using
only 76% silicon volume. Our results show excellent agreement between theory and experiment,
suggesting the broad applicability of optimization techniques for photovoltaic structure design.
5.2 Design and optimization
Figures 5-1(a) and 1(b) illustrate the silicon nanohole structures under study. We consider a free-
standing silicon nanomembrane with thickness t = 310 nm patterned with holes of diameter d =
120 nm. The unit cell is a square with side length L and repeats in both the x and y direction. The
boundaries between the unit cells are indicated by the white dashed lines. Within each unit cell,
we position (L/200 nm)
2
holes in various fashion, including a simple periodic pattern (Figure
5-1(a)) and complex aperiodic geometries (Figure 5-1(b)). The silicon filling ratio is 71.7% for
all structures.

70

We define a figure of merit to quantify the broadband optical absorption within the solar
spectrum as follows:
max
min
max
min
( ) ( )
. . .
()
I A d
FOM
Id




   
  




in which λ is the wavelength, I(λ) is the ASTM Air Mass 1.5 direct and circumsolar solar
irradiance spectrum [43], and A(λ) is the absorptance spectrum of the structure averaged for two
orthogonal polarizations (s and p) at normal incidence. This F.O.M. represents the ratio between
the number of absorbed photons and the total number of incident photons in the incident solar
spectrum; λ
min
and λ
max
define the wavelength range of interest.

Figure 5-1 Silicon nanohole structures with (a) simple periodic and (b) complex unit cell
geometries. (c) Calculated F.O.M.s as a function of the unit cell length in structures with random
(blue) and optimized (red) complex unit cells. The F.O.M.s for the simple periodic unit cell case
and an equally-thick thin film are also shown for reference.

71

We first investigated structures with randomly positioned holes inside a unit cell, or random
complex unit cells. For each unit cell length, 100 different structures were generated by placing
holes at random positions within the unit cell. A minimum inter-hole distance of 40 nm was
enforced, due to fabrication constraints. The mean value and standard deviation of the F.O.M.
over the 100 structures are indicated by blue squares and error bars in Figure 5-1(c), respectively.
The F.O.M.s for the simple periodic unit cell (a = 200 nm, d = 120 nm) and an un-patterned
silicon thin film of equal thickness are also given for reference. On average, structures with
random complex unit cells outperform their simple periodic counterpart, regardless of the unit
cell size.
We next optimized the hole positions to maximize the broadband absorption. For each unit
cell length, we used a random walk optimization technique [70] to maximize the F.O.M.; starting
from the simple periodic unit cell, 100 updates of the algorithm were performed. Our simulation
results are shown by the red star symbols in Figure xx-1(c). Structures with optimized complex
unit cell geometries have significantly higher F.O.M.s than the mean values for structures with
random complex unit cells. The optimized structure with the highest F.O.M. has a unit cell
length of 600 nm.
5.3 Fabrication method
Drawing on the above analysis, we focus on structures with a unit cell length of 600 nm. The
patterns chosen for fabrication are shown in Figures 5-2 (a) – (c). Figure 5-2 (a) illustrates the
simple periodic unit cell. Figure 5-2 (b) is a structure with a F.O.M. closest to the mean value of
our 100 randomly generated configurations. We refer to this configuration as the average
complex structure. Figure 5-2 (c) shows the structure with the optimized complex unit cell
geometry.
We use electron beam lithography combined with inductively coupled plasma reactive ion
etching (ICP-RIE) to transfer the nanohole patterns into the device layer of a silicon-on-insulator
(SOI) wafer (SOITEC). Every pattern was defined within a circular region with a diameter of 50
µ m. After the pattern formation, a 6 mm by 6 mm silicon membrane area was defined by
standard UV photolithography and ICP-RIE. The center square part of the silicon membrane

72

with dimensions of 500 µ m by 500 µ m was aligned to overlap the nanohole patterns, while the
rest of the membrane was patterned with access holes to facilitate the wet etching of the buried
oxide (BOX) layer. Finally, the silicon membrane was released from the handle silicon wafer in
49% hydrofluoric acid (HF) and wet-transferred [97] to an oxidized silicon wafer. The device
area was centered over a perforated window in the carrier wafer to obtain a free-standing
membrane [98], so as to yield accurate measurements of absorption in the silicon layer. Chapter
6 provides a more detailed description of the fabrication process.
Figures 5-2 (d) – (f) show scanning electron microscope (SEM) images of fabricated
structures with simple periodic (d), average complex (e), and optimized complex (f) unit cell
geometries. The SEM images were taken in a JSM 7001F low-vacuum field emission scanning
electron microscope in the center for electron microscope and microanalysis (CEMMA) at USC.
Image processing software [66] revealed that the differences in silicon filling ratio between these
patterns are below 2%.

Figure 5-2 Nanohole patterns with unit cells containing simple periodic (a), average complex (b),
and optimized complex (c) configurations of nanoholes. A total of 9 unit cells are shown for each
configuration. Red dashed lines are the borders between unit cells. (d–f) show the corresponding
SEM images of the fabricated patterns. The white square denotes a unit cell and the scale bars
are 200 nm.

73

5.4 Measurement setup
We characterized the optical absorption in the fabricated samples in a customized white light
spectroscopy setup consisting of a 20W tungsten-halogen lamp (Ocean Optics, HL2000-HP) and
a fiber-coupled spectrometer (Ocean Optics USB 4000). The spectrometer relies on a diffraction
grating to disperse the incident white light signal to a Si CCD array and obtain the wavelength-
dependent light intensity. The grating we chose allows for detection of wavelength between 475
nm to 1100 nm, with the highest grating efficiency around 625 nm. The wavelength resolution of
the spectrometer is determined by entrance slit width, the number of pixel in the CCD array, and
the groove density of the equipped grating. In our spectrometer the approximate wavelength
resolution is about 0.9 nm (FWHM). The collimated, unpolarized incident light was focused by a
microscope objective (Mitsutoyo, 10x, N.A. = 0.26) to only illuminate the patterned area of
interest (circular area with 50 µ m diameter). The reflected light from the sample was collected
by the same objective, while the transmitted light was collected by an achromatic doublet lens
(Thorlabs, f = 30mm, N.A. = 0.39). The collected light was focused into multimode fibers
connected to the spectrometer for analyzing both the reflectance R
exp
(ω) and transmittance
T
exp
(ω) spectra. The experimental absorptance spectrum A
exp
(ω) can then be determined by
A
exp
(ω) = 1 - R
exp
(ω) - T
exp
(ω). We used a protected silver mirror (Thorlabs) as the reflection
reference while the transmission reference was air. We focus on the wavelength range from 600
nm to 1000 nm, in order to minimize the diffractive reflection and transmission, which can
escape the collection optics and lead to measurement errors. For a unit cell length of 600 nm,
wavelengths above 600 nm are prohibited from diffracting to air for a normally-incident plane
wave. For a weakly focused incidence beam as in our current experimental configuration,
diffraction happens above 600 nm. However, we have carefully examined this issue using
standard diffraction theory and numerical simulations (please find more details in the section
5.6.5). We have verified that the difference caused by diffraction between the actual and
measured broadband absorptance is negligible (less than 2% relative difference in terms of the
F.O.M.).

74

5.5 Measurement results
Our experimental results are shown in Figures 5-3(a)—3(c). Figure 5-3 (a) shows the reflectance.
The thin film (gray) exhibits characteristic Fabry-Perot fringes. The structure with a simple
periodic unit cell (red) also exhibits Fabry-Perot fringes, with an overall spectral shift to lower
wavelengths, corresponding to a reduced effective refractive index. The structure with the
average complex unit cell (blue) has a similar overall shape to the periodic structure, but with
notable peaks and dips in the spectra. These features are characteristic of guided resonance
modes [45, 85]. The structure with the optimized complex unit cell (green) has a much higher
number of the guided resonance features. Figure 5-3 (b) shows the transmittance. Fabry-Perot
and guided resonance features are again visible in the spectra. The optimized structure has a
significantly lower transmittance than the other structures. Figure 5-3 (c) shows the absorptance.
The F.O.M.s in the range between 600 nm and 1000 nm for the three structures are indicated by
the numbers on the plot. It can clearly be seen that the optimized structure has the highest F.O.M.
(29.60%), significantly higher than the average complex unit cell (16.85%) and 4.3 times higher
than the simple periodic unit cell (5.60%). Thus, merely by designing the geometry within the
unit cell, dramatic absorption enhancement occurs. We note also that the optimized structure has
3.5 times higher F.O.M. than a solid film with the same thickness (6.56%), with only 76% of the
silicon volume.

75

Figure 5-3 Measured (left panel) and simulated (right panel) reflectance, transmittance, and
absorptance spectra of nanohole structures with simple periodic (red), average complex (blue),
and optimized complex (green) unit cell geometries, as shown in Figure 5-2. The spectra for an
equally-thick thin film are also shown for reference (gray dashed line).

76

5.6 Discussion
5.6.1 Comparison between experiment and theory
We simulate the fabricated structures assuming a silicon membrane thickness of 328 nm and a
uniform nanohole diameter of 110 nm. The thickness was determined by fitting the measured
optical transmittance spectrum of an un-patterned area, and the nanohole size was found to give
the best agreement between simulation and measurement. The results are shown in Figures 5-3
(d)–(f). Overall, we observe excellent agreement between simulation and measurement. The
simulated spectra have somewhat sharper features than the experimental spectra. This is possibly
due to the fact that non-uniformity in the size and shape of nanoholes in the fabricated sample
may broaden the spectral features in experiment [99]. Another factor is the finite spread of angles
in the incident beam. In TMM simulations, we have observed that averaging the spectra over a
range of incidence angles yields smoother and broader spectral features. In addition, the
simulated F.O.M.s between 600 nm and 1000 nm for the three different structures are indicated
by numbers on Figure 5-3 (f). In comparison with the measured F.O.M.s, relatively good
agreement was obtained. The largest difference occurs for the optimized complex unit cell
geometry, possibly due to the high sensitivity of the optimized geometry to fabrication
imperfections.
5.6.2 Spatial Fourier spectra
In order to qualitatively explain why the optimized complex unit cell geometry gives higher
absorption than other unit cell geometries, we examine the spatial Fourier spectra. Figures 6-4 (a)
– (c) again show the real space dielectric functions for reference. Figures 6-4 (d) – (f) show the
corresponding spatial Fourier transforms of the dielectric function; the amplitudes are
normalized to the DC component. The Fourier transform of the simple periodic unit cell is a
square lattice, with discrete, non-zero components. The Fourier transform of the average
complex unit cell is more uniform than the simple periodic configuration. The spatial Fourier
transform of the optimized complex unit cell has larger nearest-zero Fourier components than the

77

average complex unit cell (
-1
( , ) (2 / 600,0)nm
xy
kk   or
-1
(0,2 / 600)nm   ); these are the Fourier
components corresponding to the unit cell periodicity.
We can relate the spatial Fourier transforms to the guided resonance modes of the structure.
For a periodic structure, there is an onset frequency for guided resonance modes that scales
linearly with the lattice constant [45]. Conversely, in terms of wavelength, a structure will
support guided resonance modes up to a maximum wavelength that increases linearly with lattice
constant. For the structure in Figure 5-2 (a), the periodicity is 200 nm, and guided modes are
visible in the spectrum at about 625 nm and 680 nm (Fig. 6-3(f)), but not above. The average
complex unit cell geometry in Figure 5-2 (b) has nonzero Fourier components at smaller wave
vectors than the simple periodic unit cell (
x
k and
1
3 (2 / 600)nm
y
k 

 ) corresponding to
effective lattice constants between 200 and 600 nm. Such Fourier components increase the
maximum wavelength for guided resonance modes: from Figure 5-3 (f), it can be seen that
guided resonance features appear up to wavelengths of 1000 nm, significantly increasing the
broadband absorption. The optimized complex unit cell geometry also gives guided resonance
features up to 1000 nm, and the overall absorption is the highest. The broadband absorption
depends upon the number of resonances, the spacing between resonances, and the external
coupling rate for each resonance [100-102]. The optimization procedure tends to select structures
with largest nearest-zero Fourier components, implying that these components correlate with the
optimal resonance conditions.

78

Figure 5-4 Real space configurations (a–c) and spatial Fourier spectra (d–f) of nanohole
structures with simple periodic ((a) and (d)), average complex ((b) and (e)), and optimized
complex ((c) and (f)) unit cell geometries.
5.6.3 Comparison to the optimal periodic structure
In a separate simulation, we optimized the lattice constant of a periodic nanohole array with the
same filling ratio as the structures above. The periodic nanohole array has only one nanohole in
the center of each unit cell. The highest F.O.M. (28.35%) was obtained for a lattice constant of
600 nm (hole diameter d = 360 nm). The structure with the optimized unit cell geometry in
Figure 5-2 (c) significantly outperforms this result (F.O.M. = 32.11%). The polarization-
averaged absorptance spectra for structures with the optimal periodic (blue) and optimized
complex, aperiodic (red) unit cell are plotted in Figure 5-5. It can be seen that the optimized
aperiodic unit cell has a higher density of resonance peaks, possibly by breaking the symmetry
within the unit cell and increasing the number of resonances that can couple to external radiation
[48, 49, 76, 102, 103].

79

Figure 5-5 Absorptance spectra comparison between the optimal periodic nanohole array (blue)
and the nanostructures with the optimized complex, aperiodic unit cell (red)
5.6.4 Angular response
We have also calculated the angular response of the nanohole structure with an optimized
complex unit cell. Results for incident light with two orthogonal polarizations (s and p) and their
average are shown in Figure 5-5. We found that it outperforms an un-patterned thin film with
equal thickness (310 nm) regardless of the incidence angle. Moreover, the polarization-averaged
F.O.M. for the optimized complex unit cell is higher than the optimized simple periodic unit cell
(a = 600 nm, d = 360 nm) at all angles. The better angular response for p-polarized incident light
(Figure 5-5 (a)) for all structures can be attributed to the lower reflection for p polarization at
large incident angles. Finally, the average F.O.M. for the optimized complex unit cell can remain
above 80% of the normal incidence value for an incidence angle as large as 70 degrees.

80

Figure 5-6 Incidence angle dependence of the F.O.M. for nanohole structures with an optimized
complex unit cell geometry (red), optimized simple unit cell geometry (green), and an equally-
thick thin film (blue) for p (a) and s (b) polarized incident light, as well as the average F.O.M.
between two polarizations (c).
5.6.5 Diffraction in the experimental setup
In our measurement setup, we use microscope objectives with a finite numerical aperture to
collect the light reflected from and transmitted through the patterned silicon membrane at normal
incidence. Therefore, the specular component of the reflection and transmission will always be
completely collected. However, diffractive reflection and transmission, which exist for
wavelengths below the diffraction threshold (see below), will likely escape the collection optics
and give an underestimation of the total reflectance R or transmittance T. As a result, the
absorptance A will be overestimated, since A is determined from A = 1 – R – T. In this section,
we carefully examine the diffraction phenomenon and quantify its effect on the measured
absorptance under current measurement conditions. Our simulation results predict a relative
difference of less than 2% between the measured and actual absorption, in terms of the F.O.M. in

81

the chosen wavelength range of interest (600 nm to 1000 nm). This difference is much less than
the difference in F.O.M. for different unit cell geometries.
We start by looking at a simple situation, where light with an incidence angle θ
i
strikes a one-
dimensional periodically-patterned slab with a lattice constant a, as shown in Figure 5-7. The
incident light will be specularly reflected and transmitted with an angle equal to the incidence
angle θ
i
, as dictated by Snell’s law. In addition, when the frequency of the incident light is high
enough, discrete diffractive reflection and transmission orders also occur, as shown by the green
dashed arrows in Figure 5-7. The diffraction angle θ
d
can be determined from the conservation of
photon energy and wave vector parallel to the slab interface (with the addition of multiple
reciprocal lattice vectors) [47]. In particular,
//
0
2 / sin / 2 /
arcsin arcsin
/
ii
d
i
k m a n c m a
k n c
   


    

   
   
,
where n
i
is the refractive index of the incidence and exit medium, θ
i
is the incidence angle, and m
is an integer indicating the diffraction order. It can be shown by setting θ
d
= -90 degrees and m =
-1 that the threshold wavelength λ
th
at which the first order diffractive reflection and transmission
appears is given by a/λ
th
=
) sin (
i i
n   1
1
. For wavelengths smaller than λ
th
, |θ
d
| < 90 degrees and

diffractive reflection and transmission will occur.

Figure 5-7 Schematic of specular and diffractive reflection and transmission processes in a one-
dimensional periodically patterned slab

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According to the diffraction threshold condition given above, for a perfect plane wave at
normal incidence (θ
i
= 0 ⁰) in air (n
i
= 1), the diffraction threshold condition is reduced to a/λ
th
=
1, which means diffraction is forbidden for wavelengths larger than the lattice constant (λ > λ
th
=
a, or a/λ < 1). It can easily be shown that the diffraction threshold condition for a two
dimensional square lattice array, as in the silicon nanohole structure, is the same as the one-
dimensional case, where a is now the lattice constant of the 2D square lattice. (The exact
diffraction threshold will also depend on the azimuthal angle φ, but the diffraction threshold
wavelength is the largest when φ is multiple of π/2, which gives the diffraction threshold of
1
(1 sin )
th i i
a
n 


). Therefore, in our nanohole structure, for wavelengths above 600 nm (the unit
cell length), no diffraction occurs for a plane wave at normal incidence.
In practice, however, we use a weakly-focused incidence beam that inevitably has a finite
angular spread. We can estimate the angular spread using the effective focal length f of the
focusing microscope objective (20 mm for our 10x objective), as well as the beam spot diameter
d at the entrance pupil of the objective (measured to be 4 mm). The half angle of the incident
cone of light is determined from θ
max
= atan(d/2f), which is approximately 5.7 degrees. With this
angular spread, the diffraction threshold condition gives a threshold wavelength λ
th
of around
660 nm, and diffraction occurs between 600 nm and 660 nm.
In order to quantify the diffraction loss, we performed scattering matrix method simulations
(ISU-TMM) to calculate the specular (zero
th
order) and diffractive (non-zero
th
orders) reflectance
and transmittance spectra for the three different unit cell geometries under study, for polar
incidence angles up to 10 degrees. The total reflectance and transmittance spectra can be readily
obtained by summing up the specular and diffractive components. Assuming a top-hat angular
power distribution [99], we can obtain the reflectance and transmittance spectra averaged over
incidence angles up to θ
max
, the half angle of the incidence cone of light. We can then determine
the incidence angle-averaged “actual” and “specular” absorptance from the total and specular-
only reflectance and transmittance, respectively. The specular spectra predict our measurement
results.

83

Calculation results for the optimized complex unit cell are shown in Figure 5-8 (a). As
expected, for a normally-incident plane wave (θ
max
= 0 degree), the actual absorptance spectra
for wavelength above the unit cell length (600 nm, indicated by the dashed line) are exactly the
same as the specular one. As the angular spread of the incidence beam increases (increasing
θ
max
), the wavelength at which the specular and actual absorptance coincide shifts upward, as
indicated by the blue arrows. We have confirmed that this wavelength is determined by the
diffraction threshold condition in air, given by a/λ
th
=
i
 sin 1
1

. Moreover, we observe that the
difference between the actual and specular absorptance spectra above 600 nm is small.
In order to estimate the effect of diffraction on the measured broadband absorption, we
evaluate the F.O.M.s from the actual and specular absorption spectra. The F.O.M.s evaluated for
wavelengths between 600 nm and 1000 nm are shown in Figure 5-8 (b). We observe that for the
simple periodic unit cell, the specular F.O.M. is equal to the actual one for an angular spread up
to 10 degrees. This is due to the absence of diffraction for the small periodicity (a = 200 nm). For
the average and optimized complex unit cells, the specular F.O.M. is equal to the actual one for a
zero angular spread, corresponding to a perfect plane wave. For a non-zero angular spread,
corresponding to a focused incidence beam, the specular F.O.M. is higher than the actual one due
to diffraction loss. Nevertheless, even for the optimized complex unit cell, which has the largest
discrepancy between the specular and actual F.O.M., the difference in F.O.M. is only 0.42%
(absolute value) for an angular spread of 6 degrees. This difference corresponds to the error in
the absorption measurement. However, the error is far less than the difference in F.O.M. between
the three unit cells (simple periodic, average complex, and optimized complex), and is therefore
negligible.

84

Figure 5-8 (a) Angle-averaged actual (black) and specular (red) absorptance spectra for the
optimized complex unit cell geometry, for an incident beam angular spread up to 10 degrees. The
blue arrows indicate the diffraction thresholds wavelengths. Right of the dashed line is our
wavelength range of interest. (b) Angle-averaged F.O.M.s for three different unit cell geometries,
as a function of the incidence beam angular spread.
5.7 Summary
In summary, we demonstrate that silicon nanohole membranes with complex unit cell geometries
can yield higher broadband optical absorption than an equally-thick silicon film. In particular, an
optimized complex unit cell geometry gives a significantly better performance (3.5 times in the
current study) than an un-patterned silicon slab, using only 76% of the absorbing material
volume.
Given the large parameter space of the optimization problem, our results may be understood
as a lower limit on the obtainable performance: further optimization may yield complex
structures with even higher broadband absorption. Reverse design approaches based on ideal
Fourier space distributions [72] and/or optimal resonant coupling conditions [100] are interesting
directions for future research.
Another topic that is worth further investigation is a systematic study on the effect of varying
degree of global disorder on the optical absorption. To accurately measure the optical absorption
in globally-disordered structures, an integrating sphere based measurement setup which can

85

collect all the diffuse components of the reflected and transmitted light is necessary. Another
alternative method is to fabricate photodetectors or solar cells whose photocurrent output is
directly determined by the optical generation inside the active area, therefore circumventing any
undesirable loss associated with optical measurement methods.

86

CHAPTER 6 FABRICATION OF TRANSFERRABLE, FULLY-
SUSPENDED SILICON PHOTONIC CRYSTAL MEMBRANES
EXHIBITING VIVID STRUCTURAL COLOR AND HIGH-Q
GUIDED RESONANCE
In Chapter 5, we use fully-suspended silicon nanomembranes with nanohole patterning as the
test beds for studying the light-trapping capabilities of various nanohole patterns. In this chapter,
we detailed the fabrication process for obtaining this structure. In the fabricated structures, we
observed vivid structural colors in dark-field optical images of square lattice photonic crystals
and measured a guided resonance mode with a quality factor as high as 5600 in a novel slot-
graphite photonic crystal. The good optical quality and the deflectable nature of the fabricated
structure make it also useful for studying opto-mechanical interactions in nanophotonic
structures.
6.1 Introduction
In previous chapters, we have utilized guided resonance modes in photonic crystal slabs (or
“nanohole array”) to improve the optical absorption within the semiconductor material. These
optical modes can strongly enhance the optical near field of the slab, couple to external radiation,
as well as give rise to characteristic, structure-tunable transmission or reflection line shapes,
known as the Fano line shape [45, 104]. Therefore, in addition to enhancing optical absorption,
these unique properties of guided resonance modes can also be exploited for realizing a wide
variety of compact, surface-normal optical components such as filters, mirrors, and sensors [105,
106]. Quite recently, it has been both theoretically-proposed and experimentally-demonstrated
that guided-resonance modes can also be leveraged for light-assisted, templated self-assembly of
nanoparticles [107-109].

87

Transfer of a photonic crystal slab to a foreign substrate can yield additional desirable
properties, such as transparency and flexibility [97, 110-112]. If the slab is fully suspended in air
instead (“air-bridged”) [99, 113-115], its deflectable nature enables numerous interesting
optomechanical applications [116-118]. Furthermore, the absence of semiconductor materials
above or below the photonic crystal slab can improve filtering functionality [115] and allow
accurate optical measurements in the visible range [99, 119].
In this chapter, we developed a fabrication process for making silicon photonic crystal
nanomembranes that are both transferrable and fully suspended, which is difficult using either an
oxide under-etching technique [99, 113-115] or a dry-transfer process with polydimethylsiloxane
(PDMS) stamp alone[110, 111]. The photonic crystal pattern was introduced into the silicon
device layer of a SOI wafer, using electron beam lithography combined with inductively coupled
plasma reactive ion etching (ICP-RIE). A membrane containing the photonic crystal pattern was
then defined by photolithography and released from the handle wafer in hydrofluoric acid.
Finally, we wet-transferred and positioned the membrane over an opening in a foreign substrate
to obtain a fully-suspended configuration. We observed vivid visible structural color in dark-
field mode optical microscopy and measured a high quality factor (~5,600) guided resonance
mode in the near infrared, confirming the excellent optical quality of the fabricated structure.
6.2 FABRICATION
6.2.1 Fabrication of photonic crystal
The fabrication process starts with a silicon-on-insulator (SOI) wafer (SOITEC) consisting of a
340 nm device layer and a 2 µ m buried oxide layer. We first spin coated the wafer with an
approximately 260 nm-thick layer of electron beam resist (PMMA-A4 950K). The resist was
pre-baked in an oven at 170 degrees for 70 minutes. We then performed electron beam
lithography with an electron acceleration voltage of 30 kV on a Raith 150 e-Line system to
define various photonic crystal patterns in the e-beam resist. Each photonic crystal pattern was
defined within a circular region with 50 μm diameter. Proximity effect correction was performed

88

by the NanoPECS module in the Raith software. After the e-beam exposure, we developed the e-
beam resist in a 1:3 mixture of methyl isobutyl ketone (MIBK) and isopropyl alcohol (IPA) and
then rinsed the sample in IPA. The sample was post-baked on a hot plate at 100 degrees for 2
minutes. In order to transfer the photonic crystal pattern from the e-beam resist to the silicon
device layer, we performed inductively coupled plasma reactive ion etching (ICP-RIE)
(PlasmaPro100 ICP180, Oxford Instruments) with a mixed-mode Pseudo-Bosch process [120],
in which the etching gas SF
6
and the passivation gas C
4
F
8
flow simultaneously into the etching
chamber. We optimized the etching recipe to obtain a smooth, vertical sidewall profile, which is
critical for the optical quality of the photonic crystals. Figure 6-1 shows a typical scanning
electron microscope (SEM) image of the etched side wall profile in silicon. The sidewall angle
determined from SEM inspection is around 90 degrees. The pseudo-Bosch process we use here is
known to produce a much smoother sidewall than the traditional Bosch process. In the literature,
a less than 5 nm surface roughness has been reported for nanoscale silicon nanowires etched with
a pseudo-Bosch process [120]. The parameters of the optimized recipe were 33 SCCM (standard
cubic centimeter per minute) of SF
6
and 57 SCCM of C
4
F
8
, 20 mTorr pressure, 600W ICP power,
and 30W RF forward power. These settings give a DC bias voltage of around 200V. Under these
conditions, the PMMA resist to silicon etching selectivity is around 1.8:1. After etching, the
remnant e-beam resist was removed in acetone followed by oxygen plasma stripping.

Figure 6-1 Side view scanning electron microscopy image of holes etched into silicon wafer after
the ICP-RIE process.
100nm
nmnm

89

6.2.2 Wet transfer and alignment process
After the fabrication of the photonic crystal pattern, we performed standard ultraviolet (UV)
photolithography to define a 6 mm by 6 mm square membrane region in the silicon device layer,
as shown in Figure 6-2 (a). The central square part of the membrane with dimensions of 500 µ m
by 500 µ m was aligned to overlap with the photonic crystal patterns (shown in blue in Figure 6-
2(a)), while the rest of the membrane was patterned with an array of circular access holes (40 µ m
in diameter, 500 µ m in pitch) to facilitate the wet chemical etching of the buried oxide (BOX)
layer in hydrofluoric acid (HF). Specifically, we spin coated our sample with AZ5214
photoresist and soft-baked the resist at 100 degrees for 2 minutes. After being exposed to UV
light in a mask aligner (Karl Suss MJB-3, 100 mJ/cm
2
), the photoresist was developed in
AZ400K (1:4 concentration) and post-baked at 170 degrees for 2 minutes. ICP-RIE etching was
again used to transfer the membrane pattern to the sample, using the same etch parameters as
above. The remaining photoresist was stripped in acetone and oxygen plasma.
In order to release the silicon membrane from the handle silicon substrate, we immersed the
sample in hydrofluoric acid (concentration 48% - 51%, Avantor-Macron Fine Chemicals) for a
few hours to completely remove the buried oxide layer. The released nanomembrane weakly
adheres to the underlying silicon handle wafer. When transferred to de-ionized (DI) water, mild
agitation of the water causes the membrane to detach from the substrate and float, as shown in
Figure 6-2(b). It is very important to use the hydrofluoric acid from this specific brand, otherwise
the membrane would tend to stick to the underlying substrate and the chance of release is very
low.
The final step of the process is to position the nanomembrane over a perforated window in a
host substrate. The host substrate can be chosen from a wide variety of materials, including glass,
plastic, and oxidized silicon. Here we focus on oxidized silicon. We start with a plain [100]-
oriented silicon wafer and perforate it using either mechanical drilling or wet chemical etching in
potassium hydroxide (KOH) solution. In the latter case, we first deposited 100 nm silicon nitride
(Si
3
N
4
) on silicon wafer by low pressure chemical vapor deposition (LPCVD, HTE Lab) to serve
as a wet-etching mask, and then defined a window pattern by UV photolithography and electron

90

cyclotron resonance reactive ion etching (ECR-RIE). After the KOH solution etched through the
entire silicon wafer, the silicon nitride mask was removed in hydrofluoric acid. Finally, a thin
layer (~50 nm) of thermal oxide was grown on the surface of the perforated silicon wafer in an
oxidation furnace. The purpose of this oxidation step is to ease the manipulation of the
nanomembrane on the surface of the host substrate due to the hydrophillicity of the silicon
dioxide.
The detailed wet transfer and positioning process is described as follows. First, the floating
membrane was picked up by a glass slide and transferred from water to isopropyl alcohol (IPA).
IPA has a lower surface tension and higher viscosity than water. We find that mild agitation of
the IPA can be used to dislodge the membrane, allowing repositioning on the substrate. The
membrane is extremely flexible, compared to a silicon wafer, and can be repositioned many
times without damage. We can therefore first pick up the nanomembrane using the host substrate
and then reposition the membrane until the central part containing the photonic crystals lies over
the perforated window (Figure 6-2 (c)). Finally, after the evaporation of IPA, we obtain a fully
suspended silicon photonic crystal nanomembrane.

Figure 6-2 Illustration of the wet-transfer and positioning process of the photonic crystal
nanomembrane. (a) The membrane just before the release (dimensions not to scale). (b) The
membrane was released from the silicon handle substrate in HF and transferred to water. (c) The
membrane was wet-transferred and positioned over an opening in a host substrate.

91

Using the process described above, we were able to obtain silicon nanomembrane with
thickness ranging from 2 µ m to 310 nm. However, for smaller membrane thickness such as 250
nm, the membrane adheres very strongly to the underlying silicon substrate and the wet transfer
process stops working. In such cases, dry transfer method involving peel-off of the silicon
nanomembrane with a PDMS stamp after the membrane release can be used.
6.2.3 Fabricated structure
A perspective scanning electron microscope (SEM) image of the fabricated silicon photonic
crystal nanomembrane is shown in Figure 6-3 (a). In this case, the silicon membrane was
positioned over a circular, mechanically-perforated opening in an oxidized silicon wafer. The
central square area of the membrane is patterned with nine different photonic crystal devices, as
indicated by blue circles. We have fabricated several different photonic crystal patterns,
including a square lattice (Figure 6-3 (b)) and a novel slot-graphite lattice (Figure 6-3 (c)). The
slot-graphite lattice is created by placing a rectangular slot in the center of each unit cell in the
regular graphite [121] photonic crystal structure. Our simulation results [122] show that such a
lattice supports a high-quality-factor Г-point guided resonance mode [45] (referred to as a “slot
mode”), which can couple to external plane waves in the vertical direction.

Figure 6-3 (a) Perspective-view SEM picture of a fabricated silicon photonic crystal
nanomembrane. Blue ellipses indicate device regions. (b-c) Top-view SEM images of a square
lattice (b) and slot-graphite lattice (c) photonic crystals.

92

6.3 OPTICAL CHARACTERIZATION
In order to assess the optical quality of the transferred photonic crystal nanomembranes, we
perform both dark-field reflection optical microscopy in the visible range and cross-polarization
optical transmittance measurement in the near infrared range.
6.3.1 Structural colors
Dark-field reflection optical microscopy was performed in a Nikon microscope with a 20x
objective. In dark-field mode, the microscope objective provides oblique incidence light and
collects scattered rather than directly-reflected light. Figure 6-4 shows the dark-field optical
microscope image of a free-standing silicon membrane consisting of nine different photonic
crystal patterns. The patterns are square lattice photonic crystals with lattice constants ranging
from 350 nm to 750 nm and a fixed radius to lattice constant ratio (r/a) of around 0.28. We can
clearly observe that the color of the photonic crystal pattern gradually changes from violet to
yellow with increasing lattice constant. The color originates from reflected diffraction orders
supported by the periodic lattice.

93

Figure 6-4 Dark-field optical microscope images of a silicon nanomembrane patterned with nine
square lattice photonic crystals with varying lattice constants from 350 nm to 750 nm with 50 nm
spacing. The scale bar is 100 µ m.
We have also observed vivid structural colors in bright-field optical microscope images, with
illumination from either the front or the back. We can observe that these colors differ greatly
from the color of the un-patterned area and vary significantly from one device to another. This is
because the observed colors in bright field are determined by the reflectance (for front-side
illumination) and transmittance (for back-side illumination) spectra of the illuminated photonic
crystal pattern, which are very different from those of equally-thick silicon thin films and
strongly structure dependent. The tunable structural colors observed here will be useful for
applications such as color filters [123] and refractive index sensors[124].
6.3.2 High-Q guided resonance
The optical transmittance measurement was carried out in a custom cross-polarization
transmission setup. In cross-polarization measurement mode [125, 126], the non-resonant path
through the photonic crystal membrane contributing to the Fabry-Perot background in the
transmission spectrum [45] is suppressed, while the resonant transmission at the resonance
frequency is readily detected. As a result, guided resonance modes appear as peaks in the
transmission spectrum.
The incident light from a fiber-coupled tunable semiconductor laser in the near infrared range
(1500 – 1620 nm) was first collimated and then focused by a microscope objective (Mitutoyo, 5x,
N.A.=0.14) to illuminate the photonic crystal area of interest. The transmitted light through the
photonic crystal nanomembrane was collected by an achromatic doublet lens (Thorlabs, f = 30
mm) and then focused into a single mode optical fiber connected to a photodetector. The
transmittance spectra were obtained by synchronizing the laser source and the photodetector in a
LABVIEW program. In order to perform the transmission measurement in cross-polarization
mode, two polarizers were inserted before the illuminating objective and after the collecting lens
to provide separate control on the polarization of the incident light and transmitted light.

94

We fabricated a slot-graphite lattice photonic crystal and adjusted the thickness of the
membrane by ICP-RIE etching [127] so that the slot mode was within the wavelength range of
our laser. Figure 6-5 shows a representative cross-polarization transmission spectrum of the slot-
graphite lattice photonic crystal pattern shown in Figure 6-3 (c). The resonance peak was fitted to
a Fano lineshape [126] and exhibited a high quality factor of around 5,600. The extended nature
of the mode [122] makes it a good indicator of the optical quality of the fabricated device
throughout the entire device area. The quality factor measured here was comparable to that of a
slot-graphite device with the same lattice but on oxide [122].

Figure 6-5 Representative cross-polarization transmission spectra of the silicon nanomembrane
pattered with a slot-graphite photonic crystal.
6.4 Summary
In summary, we have successfully fabricated transferrable, fully-suspended, and deflectable
silicon photonic crystal nanomembranes with good optical quality. We observed vivid structural

95

colors in a membrane patterned with square lattice photonic crystals in dark-field optical
microscopy. We also measured a guided resonance mode with a quality factor up to 5,600 in a
slot-graphite lattice photonic crystal. We expect the fabrication process reported here will be
useful for the study of optomechanical interactions based on photonic crystal slabs, as well as
characterizing the optical properties of semiconductor thin films with photonic crystal patterning
in the visible range.
In future work, we will investigate how we can improve the precision of the wet positioning
process, possibly with the assistance of an optical microscope (compared to the naked eye, used
in the current process), as well as a more controlled liquid flow for membrane manipulation. In
addition, the use of optical tweezers [128] or the pre-definition of embedded magnetic materials
in the nano-membrane [129] are interesting approaches for further research. Ultimately, we
expect the wet transfer and positioning technique can be used for the stacking of nanomembranes
with different photonic functionalities and enable a wide range of interesting applications [130].

96

CHAPTER 7 EFFECT OF PLASMONIC PARTICLES ON
PHOTOVOLTAIC ABSORPTION IN SILICON NANOWIRE
ARRAYS
7.1 Introduction
Up to now, we have demonstrated both numerically and experimentally the optical absorption
enhancement effect in both periodic and partially-aperiodic dielectric nanostructures. Another
important theme in nanophotonic light-trapping design is to utilize the unique properties of
metallic nanostructures to enhance the optical absorption in a thin sheet of semiconductor
materials [131-138]. Briefly speaking, the optical absorption enhancement effect can be
attributed to two mechanisms: (1) metal nanoparticles or nanogratings can assist diffractive
coupling of normally-incident light into optical guided modes in the semiconductor thin films,
which are otherwise inaccessible; this coupling process can be greatly facilitated by the large
scattering cross sections of metal nanostructures. (2) metallic nanoparticles or metallic back
reflectors support localized or propagating surface plasmon polariton modes. Once excited by
incident light, these modes can resonantly enhance the local electric field intensity in absorbing
semiconductors in the vicinity of the metallic nanostructures. In this chapter, we are going to
examine whether noble metal catalyst particles on top of the VLS-grown silicon nanowires [139,
140] can increase the optical absorption in the absorbing silicon nanowires. While enhanced near
fields near gold-capped nanowires have previously been studied for SERS or TERS [141], the
effect of metal caps on absorption has not been modeled in the photovoltaic context. Given the
large body of recent work on plasmon enhanced solar cells, it is an important question to ask
whether metal caps increase the optical absorption in silicon nanowire photovoltaics systems.
Here we carry out calculations to show that, in contrast to other photovoltaic devices, metallic
particles degrade the integrated optical absorption in vertically-oriented silicon nanowire array

97

solar cells. Our work contributes to understanding the efficiencies that can ultimately be
achieved in nanowire solar cells. Measured experimental efficiencies depend on both optical and
electronic transport properties. In addition to affecting absorption, metallic caps can introduce
impurity states into the nanowires or change the contact resistance. One recent experiment
demonstrated that a gold-capped silicon nanowire solar cell had higher short circuit current than
its counterpart with the caps removed [17]. By simulating metal-capped nanowire arrays, we
isolate the effect of metallic particles on absorption to understand the role of plasmonic effects.
Using finite-difference time-domain (FDTD) modeling, we study how the diameter and
spacing of the nanowires and the composition of the metal caps affect the integrated absorption
across the solar spectrum. We find that for a wide range of nanowire diameters and spacings,
metallic caps degrade the integrated absorption in the photoactive region. This conclusion holds
true even without considering additional parasitic absorption due to impurity states. We discuss
why the two common mechanisms for plasmonic enhancement in thin-film photovoltaic systems,
the excitation of localized particle resonances and the use of metallic particles to excite guided
modes, do not increase efficiencies in nanowires.
7.2 Simulation setup
Figure 7-1(a) illustrates the structure under study, a vertically-aligned silicon nanowire (SiNW)
array with hemispherical metal caps. The array is illuminated from the top by sunlight (red
arrow). The electric field of the incident light is polarized along the x-axis. The array consists of
silicon nanowires with diameter d and period a arranged in a square lattice, as shown in Figure 7-
1(b). Each nanowire has a hemispherical metal cap. The diameter of the cap is equal to the
diameter d of the SiNW beneath, as shown in Figure 7-1(c). The shape of the metallic particle is
similar to that seen in TEM pictures of VLS-grown silicon nanowires in the literature [142]. We
fixed the length L of the SiNWs to be 500 nm. The diameter was varied between 100 nm and 500
nm and the lattice constant was varied between 100 nm and 1050 nm.

98

Optical constants for silicon and metal were taken from the literature [143]. Gold, copper, and
silver particles were studied. All three noble metals have been used for VLS growth of silicon
nanowires [144].

Figure 7-1(a) Schematic of the SiNW array with hemispherical metal caps. (b) Cross sectional
view of a single nanowire. (c) Top view of a single nanowire.
We calculate the optical absorption of the nanowire array using the finite-difference time
domain (FDTD) method, using the commercial Lumerical package. We calculate the absorption
within the photoactive silicon region; increased absorption corresponds to higher photocurrent
and higher efficiency. We define a figure of merit equal to the photon flux absorbed in the SiNW
layer normalized by the total incident photon flux:

99

 

  

d I
hc
d A I
hc
M O F
nm
nm
nm
nm



1100
400
1100
400
) (
) ( ) (
. . .

in which λ is the wavelength, I(λ) is the spectral irradiance of the ASTM Air Mass 1.5 global
spectrum, and A(λ) is the absorptance inside the silicon calculated by FDTD. The sampling
interval in the numerical integration is 1nm.
To determine whether the metal caps increase or decrease absorption inside the SiNW layer,
we study the absorption ratio, defined as the ratio between the F.O.M. for the SiNW array with
and without metal caps.
7.3 Simulation results
Figure 7-2 shows the calculated absorption ratio for gold (a), copper (b), and silver (c) caps. We
observe that the absorption ratio for gold is always below 1; in other words, gold caps decrease
the absorption in the nanowires. Copper caps also decrease absorption and have the lowest
absorption ratio of the three metals. Bulk silver has lower loss than gold or copper in the solar
spectrum. We observe that silver caps provide slightly higher absorption ratios than gold or
copper. The highest absorption ratio is close to 1.

100

Figure 7-2 Absorption ratio for SiNW arrays with (a) gold, (b) copper, and (c) silver
hemispherical metal caps.
In order to find out whether the optimum absorption ratio for each metal is dependent upon
the wire length and possibly leads to higher absorption ratio, we also plotted in Figure 4 the
length dependence of the absorption ratio for the approximately optimal configuration
(a=500nm, d=100nm) for all three different metals. The length of the SiNWs was varied from
100nm to 2μm. It turned out that the absorption ratio shows strong length dependence for small
wire lengths and approaches unity for relatively large wire lengths. For the same wire length,
silver hemispheres provide the best performance among three noble metals, while copper
hemispheres are optically the worst choice. This trend agrees with previous observations.

101

Figure 7-3 The length dependence of the integrated enhancement factor in the SiNW arrays with
the approximately optimal configuration (a=500nm, d=100nm), for three different metallic
hemispheres.
7.4 Physical mechanism
To understand why metal caps degrade the absorption ratio, we compare absorbance spectra for
bare and capped nanowire arrays. Figure 7-4 (a) shows the spectrum for a silver-capped array
with d = a = 100 nm. In this case, the nanowire diameter is equal to the lattice constant, and the
metal caps touch. The silver-capped array exhibits lower absorptance than the uncapped array
across the entire spectrum. This case corresponds to a low overall absorption ratio (Figure 7-4
(c)). Figure 7-4 (b) shows results for a silver-capped array with a = 450 nm and d = 100 nm. In
this case, the nanowires are well separated. The absorptance spectrum for the silver-capped array
shows an enhancement peak around 840nm. We have verified by inspection of the near-field
electric field intensity that this peak is due to the excitation of a localized surface plasmon on the
cap. However, the absorptance spectrum for the capped array is lower than the bare array for
lower wavelengths. As a result, the absorption ratio is close to 1 (Figure 7-2 (c)).
The effect of plasmonic enhancement on the integrated absorption is weak for the metal-
capped nanowire geometry. In Figure 7-4(b), the plasmon resonance of the metal cap occurs in
the red/near-IR range. Compared to a metal cap in vacuum, the resonant wavelength is red-

102

shifted due to the presence of the silicon nanowire. As the nanowire diameter increases from 100
nm, the plasmon resonance shifts to higher wavelengths at which the solar irradiance is lower.
For spherical metal caps (not shown), we have observed that the plasmon wavelength is shorter,
yielding higher absorption ratios (1.2 at maximum).

Figure 7-4 The absorptance spectrum of bare (black) and silver capped (red) SiNW arrays with L
= 500 nm, d = 100 nm, a = 100 nm (a) and 450 nm (b).
We have also calculated the absorption ratio as a function of nanowire length for a
configuration with high absorption ratios, a = 500 nm and d = 100nm (not shown). We observed
that the absorption ratio decreases with decreasing wire length between 2μm and 100nm. For all
lengths, silver has the highest absorption ratio and copper has the lowest; all values are less than
or equal to 1.
7.5 Summary and Discussion
In this chapter, we have calculated the effect of gold, copper, and silver metallic caps on the
absorption in silicon nanowire arrays. In most cases, we find that the metal caps decrease
integrated absorption. We note that the effect of metallic impurities in the silicon, not considered
here, could further degrade performance.

103

Our result stands in contrast to a large body of work reporting on plasmonic enhancement of
optical absorption. We attribute this result to particular features of metal-capped silicon nanowire
arrays.
First, the metal caps resulting from VLS growth have a diameter equal to the nanowire
diameter. Under this constraint, the localized plasmon resonance of the cap occurs in the
red/near-IR range of the spectrum and does not provide enough enhancement to offset the lower
absorption at short wavelengths. Overall, the integrated absorption performance is similar to or
worse than a bare array. The plasmon resonance may be useful for near-IR photodetectors.
Second, while metal particles or gratings have often been used to couple light into the quasi-
guided modes of a photoactive layer, enhancing absorption, such an effect is not necessary here.
The silicon nanowire array itself, due to its two-dimensional periodicity, already provides this
coupling, as we have shown in previous work [85].
For silicon nanowire solar cells grown by VLS methods, the overall cell efficiency will not
only depend on the optical absorption properties, but also the electrical collection efficiency.
Further study will be required to untangle these effects. However, our results suggest that care
must be taken in applying the concept of plasmonic enhancement to solar cell designs; the
“plasmonic solution” is not universally valid. The nanowire geometry studied here provides an
illustrative example of how plasmonic particles can degrade optical performance.

104

CHAPTER 8 CONCLUSIONS AND OUTLOOK
In this dissertation, we use full-field electromagnetic simulations to investigate the optical
absorption properties of nano-structured silicon thin film solar cells. In specific, both periodic
silicon nanowire and nanohole arrays were found to be more absorptive than a silicon slab of
equal thickness, given that the structure of the array is optimized for coupling of incident
sunlight into the active materials. Excitation of the guided resonance modes within the nanowire
and nanohole arrays was identified as the critical mechanism for absorption enhancement.
Next we studied the effect of partial positional disorder on the light-trapping performance of
silicon nanowire structures and the anti-reflection performance of silicon nanorod structures.
Although the effect was found to be most beneficial for smaller nanowire/nanorod size,
structures with superior performance compared to the optimal periodic structure were also
identified. The performance enhancement can be maximized by carrying out machine-based
optimal design of individual nanowire/nanorod position.
In order to test the validity of our optical simulation and optimal design approach, we carried
out an experiment in which we measured the optical absorption in a free-standing silicon
nanomembrane patterned with nanohole structures with different configurations. The free-
standing silicon nanomembrane was fabricated by a wet-transfer and alignment technique we
developed. The measurement results show excellent match with simulation. A strongly
configuration-dependent broadband optical absorption was measured with an optimally-designed
structure showing a 3.5 times absorption enhancement compared to an un-patterned silicon thin
film.
We also examined numerically whether plasmonic nanoparticles on top of silicon nanowires
can improve the optical absorption. We found that these nanoparticles do not improve, if not
degrade, the optical absorption in silicon, for a wide range of array geometries.
Finally, we discuss two interesting future research directions that are worth further study.

105

8.1 Impact of emission modification by nanostructures
A solar cell is also a LED in the sense that the solar cell is forward-biased at the maximal power
point where it operates. By reciprocity, various nanophotonic light-trapping schemes studied
here will strongly modify the emission properties of the active layer in addition to its absorption
properties. Under the radiative limit, the emission of near-band-gap photons from radiative
recombination inside the solar cell will directly determine the reverse saturation current I
o
. From
the ideal diode equation introduced in Chapter 2, change in I
o
will affect open-circuit voltage V
oc

according to the relationship V
oc
= k
B
Tln(I
sc
/I
o
)/q. Therefore, restricting the emission of near-
band-gap photons can potentially increase the open-circuit voltage as well as the power
conversion efficiency of the solar cells. Recently, several research groups have examined both
theoretically [145-151] and experimentally [152, 153] the effect of placing energy and angular
constraint on the photons emitted from radiative recombination on the solar cell performance.
8.2 Experimental demonstration of device performance improvement
The ultimate question for the nanophotonic light-trapping schemes studied here is whether the
optical absorption enhancement effect demonstrated here both theoretically and experimentally
can boost the actual device performance, namely, a photocurrent enhancement in a photodetector
and a power conversion efficiency enhancement in a solar cell.
Here, the main concern is the enlarged surface area associated with nano-structures, especially
in the case of directly-patterned active layers such as nanowire solar cells. The optical benefit
brought by the nano-texturing might be offset by the increased surface recombination and hence
reduced carrier collection efficiency. Indeed, in the literature, the reported power conversion
efficiencies still remain relatively low. However, it has been demonstrated that effective surface
passivation scheme can significantly reduce the surface recombination for semiconductor
nanowires fabricated from bottom-up growth method [154, 155]. On the other hand, for
nanostructures fabricated from reactive-ion etching technique, the plasma-induced surface
damage resulting from ion bombardment during the etching can be effectively removed by a

106

surface damage removal etching [156, 157]. Proper surface treatment was also found to improve
the power conversion efficiency of surface-textured silicon solar cells using a wet chemical
etching process [68].

107

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Abstract (if available)

Abstract This thesis is about light-trapping in thin film silicon photovoltaic devices. Light-trapping allows more light to be absorbed inside a smaller volume of photoactive materials, therefore reducing the required active layer thickness for obtaining high optical absorption. The decrease in thickness can not only bring down the material cost of solar cells based on high-purity single-crystalline silicon, but also enable materials with poorer qualities, such as polycrystalline silicon to be used for photovoltaics, reducing both the material cost and processing cost. ❧ In this dissertation, we use three-dimensional full-vectorial electromagnetic simulation tools to explore various light-trapping schemes based on sub-wavelength nanostructures arranged in both periodic and partially-aperiodic fashion. In specific, periodic silicon nanowire and nanohole arrays were found to absorb more sunlight than an equally-thick silicon slab, if the geometry of the array is properly designed. The strong structural dependence of the optical absorption performance can be attributed to the optimal condition for exciting guided resonance modes within the nano-structured array. Furthermore, partially-aperiodic silicon nanowire/nanorod arrays show significant enhancement in light-trapping and anti-reflection performance, respectively, compared to their periodic counterparts in certain size regimes. Machine-based optimal design algorithm was utilized to maximize the optical performance enhancement. In order to verify the theoretically-predicted optical absorption enhancement effect, proof-of-concept experimental demonstration has been carried out for free-standing silicon nanomembranes patterned with both periodic and partially-aperiodic nanohole structures. Good agreement between theory and experiment was obtained, suggesting the wide applicability of electromagnetic simulations and optimal design techniques in the optical design of nano-structured thin film solar cells. Finally, the effect of plasmonic particles on the optical absorption in silicon nanowire arrays was numerically examined. It was found that due to the existence of diffractive coupling scheme afforded by the nanowire array itself, the plasmonic particles do not improve the optical absorption within the silicon nanowires.

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Asset Metadata

Creator Lin, Chenxi (author)

Core Title Nanophotonic light management in thin film silicon photovoltaics

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 12/01/2013

Defense Date 10/04/2013

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

Tag light-trapping,nanophotonics,nanowires,OAI-PMH Harvest,optimal design,plasmonics,solar cells,thin films

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Povinelli, Michelle L. (committee chair), Dapkus, Paul Daniel (committee member), Nakano, Aiichiro (committee member), Wu, Wei (committee member)

Creator Email chenxil@usc.edu,linchenxi.pkuee@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-352110

Unique identifier UC11288118

Identifier etd-LinChenxi-2188.pdf (filename),usctheses-c3-352110 (legacy record id)

Legacy Identifier etd-LinChenxi-2188.pdf

Dmrecord 352110

Document Type Dissertation

Rights Lin, Chenxi

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

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