optical optimization of the light and carrier collection management solar
TRANSCRIPT
The Pennsylvania State University
The Graduate School
Department of Engineering Science and Mechanics
OPTICAL OPTIMIZATION OF THE LIGHT AND CARRIER COLLECTION
MANAGEMENT SOLAR CELL ARCHITECTURE
A Thesis in
Engineering Science and Mechanics
by
Charles A. Smith
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Master of Science
August 2013
The thesis of Charles A. Smith was reviewed and approved* by the following:
Stephen J. Fonash
Kunkle Chair Professor of Engineering Science
Thesis Advisor
S. Ashok
Professor of Engineering Science
Wook Jun Nam
Assistant Professor, Department of Engineering Science and Mechanics
Judith A. Todd
P. B. Breneman Department Head
Head of the Department of Engineering Science and Mechanics
*Signatures are on file in the Graduate School
iii
ABSTRACT
The current reliance on fossil-based fuels has resulted in a number of negative environmental
impacts on air, land, and water resources. Divesting the global energy landscape from these ancient
forms of stored solar energy will help alleviate their accompanying problems. Specifically of interest
is the utilization of current, not ancient, sunlight. The energy that reaches Earth from the Sun far
surpasses humankind’s current consumption. The total world energy consumption in one year was
148,000 Terawatt-hours (or, to use a clever and possibly more comprehensible unit, the energy
contained in ~9.7 cubic miles of oil) as of 2008 [1], [2], which is anywhere from 0.003% to 0.01% of
the energy supplied to the Earth’s surface by incident sunlight in one year1. Clearly, collecting only a
small fraction of the sun’s electromagnetic radiation has the potential to offset the global dependence
on fossil fuels. Solar energy technologies currently account for only 0.2% of the electrical energy
generation in the U.S.A. The installation rate is increasing but needs assistance from low-cost solar
cell technology [3]. Higher performing solar cells that cost less on a dollar per watt basis than
contemporary cells are needed. Particularly, modules that reach a $0.50/W metric are the goal of the
U.S. Department of Energy’s SunShot Initiative [4]. The desire of this thesis is to identify solar cell
architectures that may be manufactured to achieve this.
The word photovoltaic, derived from the Greek φως (pronounced: phôs) meaning “light” [5]
and the surname of Alessandro Volta the Italian scientist credited with the creation of the first modern
battery [6], is synonymous with the term solar cell. To use a simple definition: a solar cell is a
combination of materials that directly produces electricity when placed in sunlight. More precisely,
the energy contained in the sunlight’s photons—the quantum of electromagnetic radiation—is
captured by the solar cell’s absorber layer and converted into charge carriers (electrons and holes) via
the photovoltaic effect. Thus, creating a solar cell that absorbs as many incident photons as possible
is one goal of all solar cell designs.
iv
This thesis focuses on better comprehending and optimizing a new solar cell architecture
called the light and carrier collection management (LCCM) system. Rather than the conventional
stack of planar materials, the LCCM design includes a material layer with nano-scale features which
creates undulations in the subsequent layers. Computer simulation was used to investigate both the
absorption of electromagnetic radiation in the new architecture and the effect of altering the many
geometric variables to further increase this absorption. Throughout the design optimization, a
dramatic increase in light absorption was witnessed in the LCCM cells relative to that of planar cells.
Short-circuit current densities as high as 35.5 milliamperes per square centimeter (mA/cm2) were
attained from simulation results of LCCM solar cells that utilized an ultra-thin nanocrystalline silicon
(nc-Si) absorber layer. This enhanced performance will yield cost benefits when manufacturing a
solar cell. If an ultra-thin device (<1000nm) is capable of absorbing wavelengths normally absorbed
by a very thick cell (~100,000nm), the consumer will profit from the reduction in required material.
Optimized LCCM solar cells attaining 30.2 to 35.5mA/cm2 were calculated to cost ~$0.02 for one
watt of power output; whereas, planar cells capable of reaching the same short-circuit current
densities were calculated to cost $0.20 to $0.60 per one watt of power. This thesis will cover the
many design variables investigated and show that the LCCM architecture holds the possibility of
greatly reducing the cost of modern solar cells.
1. The power in watts supplied by sunlight for one year can be approximately calculated by using the following
assumptions: either the AM1.5G daily power flux of 1000 W/m2 or the more conservative daily average irradiance of 250
W/m2, the total surface of the Earth (5.1×1014 m2), the number of hours in a day, and the number of days in a year.
v
TABLE OF CONTENTS
List of Figures .......................................................................................................................... vii
List of Tables ............................................................................................................................ x
Acknowledgements .................................................................................................................. xi
CHAPTER 1. Solar Cell Architecture ........................................................................................ 1
1.1 Planar Architecture .................................................................................................. 1 1.2 Multijunction Architecture ...................................................................................... 2 1.3 Light and Carrier Collection Management (LCCM) Architecture .......................... 3
CHAPTER 2. Motivation for Selected Design Parameters ........................................................ 5
2.1 Nano-element Material Choice: AZO ..................................................................... 5 2.2 Cell Configuration Choice: Substrate ...................................................................... 6 2.3 Nano-element Shape Choice: Nanocone ................................................................. 7 2.4 Absorber Layer Material Choice: Nanocrystalline Silicon (nc-Si) ......................... 9
CHAPTER 3. Numerical Analysis ............................................................................................. 11
3.1 Physical Optics versus Geometric Optics ................................................................ 11 3.2 Unit Cell Approach .................................................................................................. 11 3.3 Periodic Boundary Conditions ................................................................................. 12 3.4 Inputting Material Properties ................................................................................... 14 3.5 Mesh Generation ...................................................................................................... 15 3.6 Simulation Solution and Calculation of Jsc .............................................................. 17
CHAPTER 4. Optimizing the LCCM Architecture .................................................................... 19
4.1 Length and Thickness Study .................................................................................... 20 4.1.1 Jsc Results for L-t Study ................................................................................ 21 4.1.3 Spectrum Regions of Enhanced Absorption in L-t Study ............................. 23
4.2 Varying the Nano-element Shape ............................................................................ 25 4.2.1 Radius of Curvature Applied to Nanocone ................................................... 25 4.2.2 Sharp Apex Nanocones at Radius of Curvature Heights .............................. 27 4.2.3 Truncated Nanocone at Radius of Curvature Heights .................................. 29 4.2.4 Radius of Curvature, Sharp Apex, and Truncated Nanocones Compared .... 30 4.2.5 Radius of Curvature Applied at Control Height ........................................... 31
4.3 Nanocone Aspect Ratio Study ................................................................................. 33 4.3.1 Holding H Constant and Varying d .............................................................. 35 4.3.2 Varying both H and d in the t=300nm L=800nm LCCM Model .................. 36 4.3.3 Varying L with Altered (H:d) in the t=300nm L=800nm LCCM Model ..... 38 4.3.4 Varying both H and d in the t=600nm L=1100nm LCCM Model ................ 40
CHAPTER 5. Varying the Nano-element Material .................................................................... 42
5.1 Variation in Nanocone Material .............................................................................. 42 5.2 Using Ag Nanocones to Attain Enhanced Performance .......................................... 46
vi
CHAPTER 6. Solar Cell Price per Power Analysis ................................................................... 50
6.1 Assumptions Made .................................................................................................. 50 6.2 Price per watt for the Length and Thickness Study ................................................. 53 6.3 Price per watt for the Aspect Ratio (H:d) Studies ................................................... 56 6.4 Price per watt for the Cone Material Study ............................................................. 60
CHAPTER 7. Conclusion ........................................................................................................... 63
Appendix A : Material Data .................................................................................................... 65
Appendix B : HFSS™ Simulation Settings ............................................................................. 67
Appendix C : HFSS™ Script ................................................................................................... 72
Appendix D : Material Price Quotes ....................................................................................... 78
Appendix E : Averaged nc-Si Volume .................................................................................... 79
Appendix F : Model Details and Performance Results ........................................................... 84
References ............................................................................................................................... 89
vii
List of Figures
Figure 1-1: The solar cell on the left depicts an absorber layer that has been designed to
absorb all wavelengths with energies above its bandgap. The planar design on the right
uses the same absorber but has now been designed with the material’s charge carrier
collection length in mind. Adapted from [7]. ............................................................................ 2
Figure 2-1: At left, nanodomes are seen after deposition of TCO and a-Si:H on a Ag
nanocone array. Scale bar is 500nm; the inset shows a cross-section of the nano-array.
Adapted from [14]. At right, nanodomes are seen in cross-section after deposition of
AZO and a-Si:H on an AZO nano-column array. Adapted from [16]. ...................................... 7
Figure 2-2: The column at left shows the regions (highlighted yellow) where the integrity of
the nano-element may be compromised during the mold separation step. On the right, a
cone displays its advantageous aspects (highlighted in blue). .................................................... 8
Figure 3-1: At left, a microscopic view of an LCCM solar cell array model is seen with its
cross-section revealed; scale bar is 3μm. The image on the right shows the unit cell for
this solar cell; scale bar is 2μm. .................................................................................................. 12
Figure 3-2: At left, an arbitrary hexagonal prism unit cell is shown next to itself, now
transparent, with one set of master and slave boundaries identified. At right, the same
unit cell is repeated to show the pairing of master and slave boundaries. .................................. 13
Figure 3-3: The images at left show the unit cell as drawn in the 3-D modeling tool. The
middle images show a coarse mesh that will yield less accurate results. The images at
right show a very fine mesh that will produce desirable numerical analysis results. Scale
bars are 1μm. .............................................................................................................................. 16
Figure 4-1: All of the variables that are used to model an LCCM solar cell are expressed on
this cross-section of an arbitrary LCCM model. ........................................................................ 20
Figure 4-2: The Jsc increases and then decreases with changing L. The dashed lines
correspond to the Ltch for each t curve; the markers on the Ltch dashed line correspond to
the respective t curve. The top and bottom AZO film thicknesses used in these models
were 10nm and 30nm, respectively. ........................................................................................... 21
Figure 4-3: The Jsc for a planar nc-Si solar cell shows an increase based on the Beer-Lambert
law. Adapted from [7]. .............................................................................................................. 22
Figure 4-4: The absorption as a function of wavelength for the t=200nm LCCM models are
plotted against the planar t=200nm absorption curve. ................................................................ 24
Figure 4-5: The absorption as a function of wavelength for the t=200nm L=300nm LCCM
model is plotted against the planar t=200nm absorption curve. ................................................. 24
Figure 4-6: The absorption as a function of wavelength for the t=600nm L=1100nm LCCM
model is plotted against the planar t=600nm absorption curve. The LCCM absorption
curve is close to unity for a large portion of the spectrum. ........................................................ 25
viii
Figure 4-7: Increasing RoC is applied to the control nanocone (550:100) resulting in
decreased H. ............................................................................................................................... 26
Figure 4-8: Cross-sectional view of increasing RoC applied on the t=300nm L=600nm LCCM
control model’s nanocone. Scale bars are 700nm...................................................................... 27
Figure 4-9: Cross-sectional view of sharp apex nanocone at decreasing H applied in the
t=300nm L=600nm LCCM control model. Scale bars are 700nm. ........................................... 28
Figure 4-10: Cross-sectional view of truncated nanocones at decreasing H applied in the
t=300nm L=600nm LCCM control model. Scale bars are 700nm. ........................................... 29
Figure 4-11: Cross-sectional view of increasing RoC at H=550nm applied in the t=300nm
L=600nm LCCM control model. Scale bars are 700nm. ........................................................... 32
Figure 4-12: The original definition of R* used in the L-t, RoC, Sharp Apex, and Truncated
studies is seen on top. On the bottom is the definition to amend R* for aspect ratio
studies. ........................................................................................................................................ 34
Figure 4-13: Cross-sectional view of increasing d at H=550nm applied in the t=300nm
L=1000nm LCCM control model. Scale bars are 900nm. ......................................................... 35
Figure 4-14: The varying (H:d) unit cells are in rows according to H and columns according
to d. The control LCCM unit cell t=300nm L=800nm (550:100) is omitted; it would be
very similar to the control in Figure 4-13. Scale bars are 600nm. ............................................. 37
Figure 4-15: The dashed line indicates the new t=300 (400:300) models. The solid line
indicates the original (550:100) ratio in the model. The vertical lines correspond to the
Ltch for each (H:d) curve. ............................................................................................................ 39
Figure 4-16: The dashed line indicates the new t=300 (300:350) models. The solid line
indicates the original (550:100) ratio in the model. The vertical lines correspond to the
Ltch for each (H:d) curve. ............................................................................................................ 40
Figure 5-1: t=300nm L=600nm (550:100) LCCM models with AZO, Ag, factitious nc-Si, and
nc-Si nanocones are seen, respectively, from left to right. Scale bars are 700nm. .................... 43
Figure 5-2: The decreasing H values used in this study are shown. Only the t=300nm
L=600nm AZO nanocone (H:100) LCCM models are displayed. Scale bars are 700nm. ........ 43
Figure 5-3: The Jsc values are given for the t=300nm L=600nm (H:100) LCCM models with
increasing H for each nanocone material. ................................................................................... 44
Figure 5-4: The absorption as a function of wavelength for t=300nm L=600nm (400:100)
LCCM cells with varying nanocone materials. .......................................................................... 44
Figure 5-5: The rising and falling Jsc values as L increases is once again seen for these
t=300nm (550:100) LCCM models. The vertical dashed line indicates Ltch for both
model types. ................................................................................................................................ 46
ix
Figure 5-6: Varying aspect ratios are shown for Ag (left) and AZO (right) nanocone models.
The t=300nm and L=800nm for all. Scale bars are 800nm. ...................................................... 47
Figure 5-7: The Jsc curves for Ag and AZO nanocone models at t=300nm (300:300). The
increasing and decreasing trend is again seen. ........................................................................... 49
Figure 6-1: The trend of US$/Wcell for increasing t in planar cells. This uses Jsc values for nc-
Si from [7]. ................................................................................................................................. 54
Figure 6-2: The Jsc for LCCM cells from the L-t study are plotted against their US$/Wcell
values. ......................................................................................................................................... 54
Figure 6-3: The US$/Wcell and Jsc, plotted for each L-t LCCM curve, now with data points
showing planar cells with increasing t. The price per watt axis uses a logarithmic scale. ........ 55
Figure 6-4: The highest Jsc from each LCCM t in the L-t study is plotted and the planar cell
that would also reach that value is compared to see the reduction in price per watt. ................. 55
Figure 6-5: The US$/Wcell and Jsc plotted for each (H:d) in the t=300nm L=800nm unit cell. ......... 56
Figure 6-6: The US$/Wcell and Jsc plotted for each (H:d) in the t=600nm L=1100nm unit cell. ........ 57
Figure 6-7: The US$/Wcell and Jsc plotted for each (H:d) in the Ag nanocone t=300nm
L=800nm cell. ............................................................................................................................. 58
Figure 6-8: The US$/Wcell and Jsc plotted for each (H:d) in the AZO nanocone t=300nm
L=800nm cell (bottom AZO film=5mn). .................................................................................... 58
Figure 6-9: The US$/Wcell and Jsc plotted for each (H:d) in the t=300nm AZO nanocone
LCCM model. ............................................................................................................................. 59
Figure 6-10: The US$/Wcell and Jsc plotted for the t=300nm (300:300) AZO nanocone and
t=300nm (300:300) Ag nanocone LCCM models. Data point size reduced for clarity. ............ 60
Figure 6-11: The US$/Wcell and Jsc plotted for the t=300nm L=600nm (H:100) AZO, Ag, and
nc-Si nanocone LCCM models. The minimum US$/Wcell is displayed. ................................... 61
x
List of Tables
Table 1-1: The performance improvements in LCCM architecture are seen in the short-circuit
current density (Jsc) values, while the open-circuit voltage (Voc) is maintained [10]. ................ 4
Table 2-1: Price indicators as of February 2013 for three choices of nano-element stock
material are listed from [17], [18]............................................................................................... 6
Table 4-1: LCCM cells with highest Jsc compared to the planar control cells ................................... 22
Table 4-2: LCCM cells with highest Jsc compared to planar control cells at same Jsc ........................ 23
Table 4-3: Results of the LCCM models with increasing RoC applied to the nanocone. All
models have d=100nm. ............................................................................................................... 27
Table 4-4: Results of the LCCM models with sharp apex nanocones at decreasing H. All
models have d=100nm. ............................................................................................................... 28
Table 4-5: Results of the LCCM models with truncated nanocones at decreasing H. All
models have d=100nm. ............................................................................................................... 30
Table 4-6: Radius of Curvature, Sharp Apex, and Truncated Nanocone groups compared by
sorting according to H. ............................................................................................................... 31
Table 4-7: Results of the LCCM models with nanocones at H=550nm but increasing RoC
applied. ....................................................................................................................................... 32
Table 4-8: Using the t=300nm L=800nm LCCM model as an example, the original R*, R*a,
and R*b created by (550:100) are given. Two (H:d) changes are expressed to show the
change in R*b and R*. ................................................................................................................. 34
Table 4-9: Results of the LCCM models with increasing d at H=550nm. All models have
t=300nm, L=1000nm, and a sharp apex. .................................................................................... 36
Table 4-10: Results from the LCCM models with varying (H:d). The aspect ratios are
grouped according to H. All models have t=300nm L=800nm. ................................................ 37
Table 4-11: Results from the LCCM models with varying (H:d). The aspect ratios are
grouped according to H. All models have t=600nm L=1100nm. .............................................. 40
Table 5-1: Design parameters of the varying nanocone material models and their simulation
results. Each H grouping uses the respective AZO nanocone model as its control.
[t=300nm L=600nm (H:100)] ..................................................................................................... 45
Table 5-2: The results of the Ag and AZO nanocone (H:d) study grouped by descending H
and colored within each group according to (H:d). .................................................................... 48
xi
Acknowledgements
I would like to thank my mother Conni Harris Smith without whom I would not even have
the chance to write this thesis. My family, friends, and loved one also deserve recognition. Over the
years, they have been a supporting community that enabled me to reach this point in my path. I
would like to thank my former teachers, mentors, and professors from grade school to present day for
never stifling my curiosity and penchant for scientific thought. I owe many thanks to Dr. Stephen
Fonash. Without his astounding knowledge of the field, I would not know and understand the beauty
of nano-scale physics. My research group members also deserve recognition for aiding me in this
research. I owe sincere thanks to the National Science Foundation (NSF) for continuing to sponsor
young minds through their Graduate Research Fellowship program. This material is based upon work
supported by such a fellowship from the NSF under Grant No. DGE1255832.
1
Chapter 1. Solar Cell Architecture
Before the design optimization is detailed, a discussion should first be held. It is important to
understand the dominant solar cell architecture and how it limits certain aspects of designing a high-
performing photovoltaic device. Other design paradigms that attempt to improve on the leading
architecture will be discussed but are not amenable to mass production. However, a recent design
that manages the flow of incident light and the collection of photogenerated electron-hole pairs
provides a path toward low-cost, high-efficiency, and manufacturable solar cells.
1.1 Planar Architecture
Solar cells have been fabricated using a planar layer-on-layer approach since the beginning of
their mass production. This choice in architecture created competing design parameters for the solar
cell designer. The cell’s absorber layer must be thick enough to absorb the portion of the
electromagnetic spectrum that is capable of being absorbed (which is dictated by a material’s
absorption coefficient). At the same time, the absorber thickness must be made sufficiently thin to
allow photogenerated charge carriers (electrons and holes) to be collected by the external circuit.
These two thicknesses sometimes are at odds with each other, especially in many potentially
inexpensive absorber materials [7]. A charge carrier collection length may be on the nano-scale,
while the same material’s light absorption length may be on the micro-scale. If a cell is designed to
maximize light absorption and thus is relatively thick such as the left solar cell in Figure 1-1, charge
carriers will likely be wasted through bulk recombination mechanisms. Additionally, some absorber
material will be wasted as a result of attempting to absorb all concerned wavelengths. If a cell is
alternatively designed to maximize charge carrier collection and is thus relatively thin such as the
right solar cell in Figure 1-1, certain wavelengths may not be sufficiently absorbed by the cell’s
2
absorber thickness. However, these opposing length scales are merely consequences of the current
cell architecture.
Figure 1-1: The solar cell on the left depicts an absorber layer that has been designed to absorb all
wavelengths with energies above its bandgap. The planar design on the right uses the same absorber
but has now been designed with the material’s charge carrier collection length in mind. Adapted from
[7].
1.2 Multijunction Architecture
A technique used to alleviate these competing design paradigms is to combine two or more
planar cells in a tandem configuration. In these multijunction cells, the first planar cell absorbs the
shortest wavelengths of light while allowing longer wavelengths to pass through to the second cell.
The second absorbing layer then attenuates the longer wavelengths. Ideally, each cell’s absorber
thickness is manufactured so that a portion of the solar spectrum is optimally absorbed and maximum
charge carrier collection is achieved. Higher efficiencies are more easily attained with tandem cells
than with single junction cells. However, tandem cell manufacturing is inherently complex. Tunnel
junctions, complex active layer alloys, precise thicknesses of absorber layers, randomly textured
3
transparent conductive oxides (TCO), and current matching must be engineered to realize these
designs [8], [9].
Consequently, single junction cells that match the efficiency of their multi-junction brethren
are very appealing due to their relative ease of manufacturing. An exemplary way of achieving high
efficiencies in single junction cells is to minimize the absorber thickness to promote charge carrier
collection while maintaining a high level of light absorption. This design concept elicited the advent
of light management in solar cells. Until recently, the internal reflection of light was controlled with
less-than-precise methods by randomly texturing TCO layers. This surface finish often results in
textures that are on the scale of microns in height, a limiting factor to this form of light management.
This poses a problem when the solar cell designer wants to utilize absorber films of sub-micron
thicknesses.
1.3 Light and Carrier Collection Management (LCCM) Architecture
A more recent form of light management makes use of nano-scale elements. The inclusion of
these deliberately placed nano-elements acts toward the same goal as random texturing, i.e. total
internal reflection. The nano-features offer the solar cell designer latitude to create cells with sub-
micron absorber thicknesses. Additionally, the designer can tailor the array of nano-elements to her
choosing. Thus, light management using nano-arrays opens the door to photonics in solar cell design.
These photonic structures direct the light laterally or into the plane of the absorber layer rather than
allowing it to initially traverse the absorber thickness and subsequently reflect back through the
absorber film. An engineer can create a very thin absorber layer; one much thinner (and thus less
costly) than a typical solar cell but with equal or improved performance. It is this design that this
thesis explores.
If the nano-elements act as an electrode and are fabricated to project into the absorber
thickness, the design paradigm is altered. The placement of nano-arrays within an absorber layer
allows not only light management but also the management of charge carrier collection. Carriers will
4
now be able to enter the external circuit by traveling not only across the absorber’s thickness but also
by traversing laterally to the nearest nano-element. This enhanced proximity to an electrode and
simultaneous control over the flow of light liberates the solar cell designer from the length mismatch
of planar architecture. This new architecture is called the light and carrier collection management
(LCCM) system.
Solar cells designed with LCCM architecture are able to utilize potentially inexpensive
absorber materials that suffer from poor collection lengths [7]. By fabricating ultra-thin absorber
layers with a nano-array, the designer may be at ease in knowing that all photogenerated carriers have
a higher probability of avoiding bulk recombination. Recent work has proven that power conversion
efficiency (PCE) is enhanced in fabricated LCCM cells relative to their planar counterparts.
Superstrate cells using nano-columns embedded in hydrogenated amorphous silicon (a-Si:H)
outperformed equivalent planar cells. Table 1-1 adapted from [10] shows the experimental results.
The planar and LCCM cells had the same nominal thickness t deposited (t=400nm); the term
“nominal thickness” is defined as the thickness that would result from the absorber deposition if it
were done on a planar surface [11]. The LCCM architecture’s nano-column was created using the
TCO material aluminum-doped zinc oxide (AZO).
Table 1-1: The performance improvements in LCCM architecture are seen in the short-circuit current
density (Jsc) values, while the open-circuit voltage (Voc) is maintained [10].
Architecture Jsc (mA/cm2) Voc (V) Fill Factor (FF) PCE (%)
Superstrate Planar 11.44 0.69 0.44 3.38
Superstrate LCCM 12.71 0.71 0.50 4.52
5
Chapter 2. Motivation for Selected Design Parameters
2.1 Nano-element Material Choice: AZO
Additional work by other groups has investigated using metallic nano-elements [12–14].
These works utilized silver (Ag) in particular and were able to achieve PCE of up to 8.1% for a-Si:H
substrate cells. These cited articles created nano-elements other than nano-columns, which suggests
design opportunities. Metal nano-arrays are thought to contribute to improved device performance
through three ways: longer light path lengths from scattering, near-field enhancement in the absorber
layer, and scattering frequencies into both surface plasmon polariton and photonic modes [15]. In our
own research, PCE values of 8.17% were achieved in superstrate a-Si:H LCCM cells with t=400nm
[16]; this experimental design boasted a Jsc of 14.79mA/cm2. However, this higher PCE was attained
with AZO as the nano-column material, as opposed to a metal. These enhancements when using
AZO are believed to arise from advantageous refraction of the various wavelengths at the absorber-
AZO interface rather than a reflection at an absorber-metal interface. The refraction of the visible
wavelengths created by the presence of a TCO nano-element seemingly results in longer path lengths
for light inside the absorber thickness.
The decision to use a TCO nano-element arises not only from performance enhancements but
also cost considerations. The choice of AZO as compared to other standard TCO options such as
indium tin oxide (ITO) arises from the thrifty engineer who wisely keeps an eye on the cost of their
cell design. Viewing Table 2-1, the raw material cost of ingots (Zn, Al, In, Sn, and Ag) and the
refined material cost of sputtering targets (AZO, ITO, and Ag) from a leading material supplier point
to AZO being the least expensive of the three. Additionally, AZO does not react with the hydrogen
plasma inherent in the deposition process of a-Si:H and nc-Si films and yields reasonable optical
transmittance and electrical conductivity after the plasma process. This thesis primarily used AZO in
its modeling; simulations using Ag as the nano-array were done to reaffirm the choice in AZO.
6
Table 2-1: Price indicators as of February 2013 for three choices of nano-element stock material are
listed from [17], [18].
Price of Ingots on World Market ($/kg)
Zinc Aluminum Indium Tin Silver
~2.50 ~2.50 ~550.00 ~30.00 ~1300.00
Price of Refined Materials in Sputtering Targets ($/in3)
AZO (ZnO/Al2O3, 98/2 wt%) ITO (In2O3/SnO2, 90/10 wt%) Ag (99.99% pure)
~170.00 ~200.00 ~300.00
In addition to its use in the nano-element, AZO was placed above and below the absorber
layer in these optical simulations. While the author realizes that this would not be the most favorable
condition electronically, the frequency-dependent index of refraction for AZO is well-known and was
used as a placeholder. In production, another material should be chosen. AZO is very adept at
creating an Ohmic contact with n-type absorber materials, allowing electrons to flow from the
absorber into the external circuit while simultaneously blocking the transport of holes; however, it is
ineffective at performing the opposite operation. It is for this reason that a hole transport-electron
blocking layer should be chosen as the TCO for the p-type side.
2.2 Cell Configuration Choice: Substrate
Surveying the many design variables inherent to LCCM architecture, researchers began to
employ numerical analysis to simulate LCCM designs. Using a Maxwell’s equations solver, the
question of whether substrate or superstrate configuration exhibits higher Jsc in LCCM cells was
explored. Simulation work done with LCCM cells (a-Si:H thickness of 400nm, AZO nano-column)
revealed that substrate cells performed better than their superstrate analogs [9]. These substrate
designs enjoyed Jsc values as high as 17.09mA/cm2 (compared to the planar control’s Jsc of
12.48mA/cm2 and the superstrate LCCM design’s Jsc of 16.18mA/cm2) [9]. A thinner substrate cell
(thickness, t=200nm) was shown to theoretically achieve Jsc values (16.6mA/cm2) better than the
thicker superstrate LCCM cells. This finding that substrate LCCM cells outperform their
counterparts informed this thesis to focus exclusively on substrate cells.
7
2.3 Nano-element Shape Choice: Nanocone
This research group also explored the impact of nano-element shape on cell performance. As
previously noted, nano-columns are not the only option for the nano-element. However, a nano-
element with a high aspect ratio (defined as feature height to feature width) was found to be
preferable. Specifically, cones and columns were admired due to the result observed after depositing
an absorber layer. Since the absorber thicknesses are ultra-thin films, an undulation of the deposited
film occurs. These cresting and furrowing films can be thought of as nanodomes. Figure 2-1 shows
two examples of these nanodomes created after using nano-columns and nanocones. All previously
mentioned LCCM cells researched by this group used either nano-columns or nanocones.
Figure 2-1: At left, nanodomes are seen after deposition of TCO and a-Si:H on a Ag nanocone array.
Scale bar is 500nm; the inset shows a cross-section of the nano-array. Adapted from [14]. At right,
nanodomes are seen in cross-section after deposition of AZO and a-Si:H on an AZO nano-column
array. Adapted from [16].
The nanodomes are capable of being tailored. The observation was made that varying the
nano-elements’ distance from one another—known as pitch—created a variation in the undulations to
be either separated, touching, or overlapping. This additional variable proved desirable for
performance enhancements. One study which included LCCM models created by using nano-
columns or nanocones found that varying the nano-features’ pitch—thus making the nanodomes
overlap, touch, or separate—resulted in a range of Jsc values. An a-Si:H LCCM substrate cell
(t=200nm) made with AZO nano-columns was able to attain 17.3mA/cm2 after the column pitch was
varied [8]. This same study found identical cells modeled with AZO nanocones were able to reach Jsc
8
values of 17.1mA/cm2 after the cone pitch was varied. Additionally, the AZO nano-element cells
were compared to Ag nano-column models in this study. The metal columns attained a maximum
Jsc=15.9mA/cm2 after nano-column pitch was varied [8], and the conclusion that non-metallic nano-
arrays outperform metallic arrays was reinforced.
The choice to simulate nano-columns or nanocones was also informed by the intended
manufacturing process for these nano-arrays. While electron beam lithography was used for the
experimental devices created in this group, nanoimprint lithography (NIL) is ultimately the most
appealing design choice for its high-throughput capabilities and its assurance of high fidelity
replication of the nano-arrays [10], [15], [16]. NIL uses a mold to stamp a formable material (the
nano-array material in this study). A critical step in NIL is the release of the mold from the newly
embossed nano-features [19]. A column’s edges would suffer filleting or deformation from the mold
release. A conical shape—with the absence of a top edge and with the obtuse angle created by its
surface and its supporting plane—can be easily imagined to have higher shape integrity than a
columnar shape when the mold-array separation step occurs. Figure 2-2 demonstrates the geometric
features just discussed. As a result of both their ability to promote nanodome formation and their
enhanced manufacturability, nanocones were chosen for this study.
Figure 2-2: The column at left shows the regions (highlighted yellow) where the integrity of the nano-
element may be compromised during the mold separation step. On the right, a cone displays its
advantageous aspects (highlighted in blue).
9
2.4 Absorber Layer Material Choice: Nanocrystalline Silicon (nc-Si)
The studies discussed so far utilized a-Si:H as the absorber layer. However, any absorber
amenable to being deposited in a thin-film would be acceptable. Crystalline silicon (c-Si) cells which
are fabricated from ingots into rigid, brittle wafers cannot be conformally coated on nano-
architecture. Even though nano-architecture may be utilized in c-Si cells to increase light absorption
[20–23], these designs are achieved through etching portions of the relatively thick c-Si wafers,
wasting material that has required the input of great quantities of energy. To avoid squandering
energy-intensive materials and to take advantage of the LCCM’s nanodome, a material that can be
conformally deposited is desired.
A detriment to amorphous silicon is the degradation it experiences shortly after
manufacturing—called the Staebler-Wronski effect (SWE) [24]. While not completely understood,
the effect is most often attributed to the large number of bonding defects, a result of amorphous
structure. Hydrogenation relieves some of the deleterious effects caused by dangling bonds.
However, the efficiency suffers a decrease of 10-30% even with this hydrogenation [25]. A material
that can be conformally deposited but does not suffer from the SWE would be a shrewd choice.
Fortuitously, nanocrystalline silicon (nc-Si) does not suffer from the SWE and is also capable
of being conformally deposited. The tradeoff for choosing nc-Si is that a-Si:H absorbs
electromagnetic radiation stronger than nc-Si from roughly 2-3.5eV [7]. However, nc-Si absorbs
similarly or better than a-Si:H from 1-2eV which is important to note since nc-Si has a much lower
bandgap than a-Si:H (~1.11ev compared to ~1.55-2eV, respectively) [7], [26], [27]. This lower
bandgap affords the possibility of higher Jsc values being obtained from a nc-Si absorber layer than an
a-Si:H layer. In fact, preliminary LCCM modeling done by this group using nc-Si showed Jsc values
of 29.2mA/cm2 for t=800nm using an AZO nanocone [15]. Another research group modeled nc-Si
LCCM designs that resulted in Jsc=31mA/cm2 for t=500nm and Jsc=34mA/cm2 for t=1000nm [28].
However, this group used a tapered Ag nano-pillar for the array and miscalculated the absorption in
10
the models by including the absorption due to the Ag array. It is the aim of this thesis to identify
LCCM architectures that result in even better performance with even thinner absorber layers.
The simulation and experimental results when using nc-Si are preferable when evaluated
against the earlier a-Si:H LCCM study that only boasted 17.1mA/cm2 (t=200nm, AZO nanocone) [8].
The theoretical maximum Jsc for a-Si:H (~20mA/cm2) [7] is also a limiting factor that can be avoided
if nc-Si is chosen as the absorber material. Since it has been shown that the absorption of
electromagnetic waves can be independent from the absorber layer thickness, the possibility of
achieving high Jsc values (>30mA/cm2) with even thinner nc-Si films than has been reported is very
intriguing. It is especially appealing considering the Beer-Lambert law indicates these high Jsc values
are normally obtained by absorption lengths much larger than these ultra-thin absorber layers.
Another benefit of choosing nc-Si as the absorber layer, and accordingly choosing to include it in this
thesis’s modeling, is its single digit micro-scale carrier collection lengths (2-5μm), an order of
magnitude higher than a-Si:H collection lengths (~300nm) [7]. Knowing that the collection lengths
trump those of a-Si:H and knowing that we can achieve Jsc values normally attained at absorption
lengths of ~100μm at lengths approximately three orders of magnitude smaller (hundreds of
nanometers) [7], nc-Si was chosen as the absorber layer in the LCCM architecture.
To reiterate, the simulations utilized AZO for the nano-element array, cones as the shape of
the nano-element, and nc-Si for the absorber material in substrate configurations. These choices are
held constant unless otherwise noted. The preceding observations and remarks detailed the rationale
for these choices. However, subsequent design choices were introduced to this study after some
investigation down the initial design path. These will be detailed in the following text.
11
Chapter 3. Numerical Analysis
3.1 Physical Optics versus Geometric Optics
The numerical analysis used for the simulations reported in this thesis was executed using the
ANSYS HFSS™ software package. A three dimensional (3-D) full-wave electromagnetic field
simulator such as HFSS™ [29] is required to accurately simulate the interaction between visible light
and the complex architecture of the LCCM device. Geometric optics—bound by the representation
of light as rays—would be unable to accurately portray the interaction between light and the repeating
nano-scale structures present in the device. While physical optics simulate a far more accurate
picture of the light-device interaction than geometric optics, a 3-D full-wave electromagnetic
simulation allows one to solve Maxwell’s equations, resulting in the most accurate picture of a
device’s interaction with electromagnetic waves far before the fabrication stage.
3.2 Unit Cell Approach
Computer-aided design tools that incorporate Maxwell’s equations solvers such as HFSS™
make analyzing the effects of light interaction with nano-scale features possible. The software allows
the researcher to create 3-D models of a proposed solar cell design to scale. The creation of this
model relies on what is called a unit cell. This unit cell is the smallest repeatable unit of volume that
can represent the entire solar cell. A depiction of this is given in Figure 3-1.
12
Figure 3-1: At left, a microscopic view of an LCCM solar cell array model is seen with its cross-
section revealed; scale bar is 3μm. The image on the right shows the unit cell for this solar cell; scale
bar is 2μm.
The unit cell approach allows HFSS™ to decrease computation time. If an entire macro-scale
array were to be analyzed for electromagnetic wave absorption, the required processing time would
be far longer than a typical graduate student’s academic career. Thus, a unit cell approach allows the
numerical analysis of solar cell architecture to be achievable in a timely fashion. An astute reader
may ask, “How do you translate this unit cell approach to meaningful metrics such as Jsc?” To answer
this question, the curtains must first be lifted on HFSS™ to reveal some of the behind-the-scenes
programming.
3.3 Periodic Boundary Conditions
To model a macro-scale array using its smallest repeatable volume, periodic boundary
conditions must be applied to each face of the unit cell. The side faces of the unit cell—the faces that
would lie normal to the plane of the solar cell array—are deemed “master” and “slave” boundaries. A
periodic boundary condition in electromagnetic simulation matches the electric field pattern on the
slave face to the master face within a phase difference. The designation of which face is a “master”
and which face is a “slave” arises from repeating the unit cell to create the full array. Once an
13
arbitrary side face is deemed a master, the opposite parallel face will be selected as its slave; this
slave face would be mated to an adjacent unit cell’s corresponding master face if the unit cell were
repeated to create an array. Again, the reason for doing this is to model the periodicity of the electric
field. In order to use a unit cell to simulate a solar array, the periodic boundary conditions must
account for the flow of the electric field. The slave boundary that mates to the master boundary of the
hypothetical second unit cell matches the flow of the electric field (magnitude and direction) from
said master boundary.
Figure 3-2: At left, an arbitrary hexagonal prism unit cell is shown next to itself, now transparent,
with one set of master and slave boundaries identified. At right, the same unit cell is repeated to show
the pairing of master and slave boundaries.
Figure 3-2 helps illustrate how each face is designated. At left, an arbitrary unit cell is
displayed next to a transparent view of itself. One set of boundaries is identified. The right image
portrays the repetition of this unit cell to illustrate the logic behind why one boundary is a master and
14
its opposite face is a slave. The remaining faces may similarly be assigned master and slave
boundaries and the unit cell repeated in the respective directions to further illustrate the point.
The unit cell approach therefore requires the user to create a unit volume that is either a
parallelepiped or a hexagonal prism. There will be two master-slave pairs for a parallelepiped unit
cell and three master-slave pairs for a hexagonal prism unit cell. All of the LCCM designs in this
thesis were modeled using a hexagonal prism unit cell similar to that seen in Figure 3-2 to
accommodate the characteristic nano-features. All planar control designs were modeled using a
parallelepiped unit cell.
Additional boundaries are needed to act as the initiating and terminating sites of
electromagnetic wave propagation. These boundary conditions must be positioned such that the
radiation travels in the intended direction for the design (i.e. through the “bottom” for a superstrate
configuration or through the “top” for a substrate configuration). After applying the three master-
slave pairs to the hexagonal prism, the LCCM models have two remaining faces which can be
considered the top and the bottom of the unit cell. Since the LCCM designs in this study are
exclusively substrate cells, the top face of the unit cell must be an “excitation” boundary in order for
electromagnetic waves to be simulated properly. This is done to simulate sunlight entering the top
side of the solar cell. The other boundary which will be referred to as the bottom face is assigned a
boundary condition that absorbs any remaining electromagnetic waves. This is done so that the
bottom boundary condition represents an extension into infinity, or put another way, it does not let
any electromagnetic waves reflect and travel back through the device.
3.4 Inputting Material Properties
After creating a 3-D model and assigning the appropriate boundary conditions, the program
requires the input of material parameters. Specifically, HFSS™ requires the input of relative
permittivity and dielectric loss tangent values as a function of wavelength. These required
parameters are derived from more familiar optical and electrical properties: complex index of
15
refraction and complex permittivity . These two material characteristics are defined in Eq. 1 and
2 [30]. The relation between the two is expressed in Eq. 3 and 4 [30]. The quantities and are the
real parts of their respective equations, and they represent the phase speed of a given frequency and
the dielectric’s effect on an electromagnetic wave, respectively. While the quantities and are the
imaginary parts. The value is known as the extinction coefficient and describes the absorption of
electromagnetic waves. Similarly, expresses the dissipation of energy into a material.
Equation 1 - Complex Refractive Index
Equation 2 – Complex Permittivity
Equation 3
Equation 4
With these equations stated, the material parameters specific to HFSS™ may be calculated
and input. The real portion of complex permittivity must be divided by the permittivity of free
space as seen in Eq. 5 to obtain . The values which describe the absorption of energy in
dielectric material are attained by dividing by as seen in Eq. 6.
Equation 5 – Relative Permittivity
Equation 6 – Dielectric Loss Tangent
The complex refractive index or the complex permittivity for nanocrystalline silicon (nc-Si),
aluminum-doped zinc oxide (AZO), and silver (Ag) were obtained from the literature [26], [31], [32].
The tabulated material data for each is listed in Appendix A.
3.5 Mesh Generation
After supplying HFSS™ with the appropriate boundary conditions and desired material
parameters, a simulation setup can be created. Many nuances exist within the program’s simulation
settings. The overall goal when setting these options is to allow the computer to construct a 3-D
representation of the user-drawn unit cell model. This representation is constructed out of many
small tetrahedra and is called a mesh. This technique of deconstructing the drawn model into many
16
smaller, more easily computable pieces is known as the finite element method. The description and
underlying mathematics behind the finite element method (FEM) may be found elsewhere [33].
These tetrahedra, or elements, are what allow the electric field to be computed and characterized
throughout the structure. The division of the model into many small elements allows the computer to
solve Maxwell’s equations in each element in a piecewise fashion rather than trying to solve the
entire domain of the structure in a continuous fashion.
Figure 3-3: The images at left show the unit cell as drawn in the 3-D modeling tool. The middle
images show a coarse mesh that will yield less accurate results. The images at right show a very fine
mesh that will produce desirable numerical analysis results. Scale bars are 1μm.
It should be noted that the mesh profile on a slave boundary perfectly matches the mesh
profile seen on its corresponding master boundary. This means each tetrahedron surface that makes
up the master face has an identical tetrahedron surface on the slave face. The fact that the mesh
profiles match allows the computer to numerically analyze a periodic structure. Simulation settings
may be chosen that result in a poor, or coarse, mesh which will yield inaccurate results. A user gains
an understanding for what settings to apply to ensure a fine mesh. Creating a sufficiently fine mesh is
a crucial step that must be done before the unit cell is subjected to the simulated electromagnetic
waves. There is a tradeoff between a very fine mesh and a reasonable solution time, i.e. a finer mesh
17
creates a higher number of tetrahedra which yields a longer computational time. Figure 3-3 provides
a visual for understanding a coarse and fine mesh. Appendix B provides screen captures of the
simulation settings used in this work.
3.6 Simulation Solution and Calculation of Jsc
Once the simulation settings have been suitably adjusted, the actual simulation can
commence. HFSS™ begins by refining the mesh in accordance with the simulation settings. Once a
proper mesh resolution has been reached, the first frequency is propagated from the top excitation
boundary toward the solar cell material layers. Using the mesh created by FEM, Maxwell’s equations
are solved for each frequency step. For all models in this thesis, the range of frequencies was 200-
1000THz (300-1500nm) with a 10THz step between each frequency. This frequency sweep resulted
in 80 frequency steps for each model.
HFSS™ was then employed to extract the absorption values A(λ) for just the nc-Si absorber
layer. The program is able to do this since it has been supplied with the values and has solved for
the electric field values at each tetrahedron. Equation 7 shows the equation used to calculate A(λ)
where V is the volume of the nc-Si layer, c is the speed of light in vacuum, λ0 is the wavelength in
vacuum, and E is the electric field. A script was written to aid this task; an example is given in
Appendix C.
( ) ∫
( )| |
Equation Layer Specific Absorption
At last, the astute reader’s question can now be answered. The Jsc value is obtained by
integrating the product seen in Eq. 9 from 300 to 1110nm. The upper limit of the interval is chosen
based on the bandgap of the particular nc-Si material data used. However, the AM1.5G spectrum
( ) must first be converted as shown in Eq. 8. The product —where is Planck’s constant and
is frequency—transforms the quantity ( ) from power impinging per area per nanometer of
18
bandwidth (W/m2/nm) to the quantity ( ) number of photons per second per area per nanometer of
bandwidth (Nph/m2/s/nm).
( ) ∫ ( )
Equation Photon Flux
∫ ( ) ( )
Equation Short Circuit Current Density
The assumption is made that for every photon absorbed a charge carrier is collected by the
external circuit; so an internal quantum efficiency (IQE) of one is assumed. With this assumption, the
electric charge of an electron may be included into the product of Eq. 9 to produce Jsc in units of
milliamperes per square centimeter (mA/cm2). It should be noted that there are two additional unit
conversions necessary to obtain Jsc values in units of milliamperes per square centimeter. These
calculations were used to calculate the Jsc values for each model in this study.
19
Chapter 4. Optimizing the LCCM Architecture
To properly model the LCCM design, experimental prototypes were consulted. While layer
thicknesses were easily duplicated, the two separate radii of the nanodome required attention to detail.
The reason for the difference in thickness arises from the deposition of the conformal absorber layer.
The deposition rate in the vertical orientation experiences film growth just as a planar deposition
would; while the deposition rate in the lateral direction is slower. It can be assumed that the radius
from the tip of the nanocone to the top of the absorber layer, defined as R, is the same as the thickness
t found in the planar regions of the deposited film. The sidewall radius, defined as R*, is the length
measured at height t from the centerline of the nano-element to the point where the dome meets the
flat film. It is not the same thickness as the nominally deposited thickness. This fact was shown in
[16] when a-Si:H was deposited on nano-columns. However, there was a ratio of R to R* that was
shown to approximate the nanodome's spheroid form. This ratio is R/R*≅1.1 as observed in
experimental results.
The absorber thicknesses modeled in this thesis range from t=200-600nm in steps of 100nm.
Thicker films were not modeled since ultra-thin films that achieve similar or better performance than
their micro-scale counterparts were the goal of this optimization. Additionally, a t=800nm nc-Si
substrate cell had previously been modeled and shown to theoretically achieve Jsc=29.2mA/cm2 [15].
Thinner films than 200nm were also not modeled due to the concern of imprecisely modeling the R*
variable at such small thicknesses. As previously noted, the pitch of the nanocones can be adjusted,
and this variable is deemed L. For a given model, there is an L that results in the nanodomes just
touching; this is termed Ltch. Any L that is greater than Ltch will create a flat planar-like space between
the domes. Any L that is less than Ltch will create an array with truncated domes. The models in this
thesis ranged from L=200-1400nm. A smaller L was not modeled because the minimum nanocone
base diameter d utilized was 100nm. If a model were made with L=100nm, the nanocones would be
20
touching. This would result in an array that would be extremely hard to manufacture, regardless of
the lithography technique used. Figure 4-1 features the variables in the LCCM architecture.
Figure 4-1: All of the variables that are used to model an LCCM solar cell are expressed on this cross-
section of an arbitrary LCCM model.
4.1 Length and Thickness Study
Multiple L values have been simulated at each t of nc-Si to investigate the effect of nanocone
spacing. The minimum L value for each t was 200nm and the maximum L value used ranged from
800-1400nm. The reason for the range of maximum L values is due to the trend that developed for
each thickness, i.e. further simulations were not required to draw conclusions. Initially, d was set at
100nm and the nanocone’s height H was set at 550nm. This aspect ratio (H:d) was used in our
research team’s previous nc-Si study [15]. This opening investigation into the effects of varying t and
L used (550:100). Different aspect ratios that were explored will be discussed in a later section.
As previously stated, the absorber was positioned between two layers of AZO. The “top
AZO” coated the nc-Si undulations and was the first material layer to experience the simulated
electromagnetic waves. The thickness of this AZO layer was initially set at 10nm for the L-t study.
This material and thickness was placed not for optimized electrical properties but as an optical spacer.
The nano-cone array and its supporting film were also AZO. This film called “bottom AZO” was
initially set at 30nm for the L-t study and could be expected to perform appropriately as an Ohmic
21
contact between the nc-Si layer and the back Ag layer, i.e. block the flow of holes while allowing the
flow of electrons. The thickness of the Ag film was set at 50nm for this L-t study and every
subsequent study.
4.1.1 Jsc Results for L-t Study
Figure 4-2 displays Jsc versus L for t=200-600nm. A trend of increasing Jsc as L is increased
from L=200nm is seen. After the L values surpass their Ltch value, the Jsc begins to decrease. This
trend is seen in all thicknesses and is due to the fact that as L becomes extremely wide the solar cell
begins to approximate a planar cell, having only a few nano-features in an otherwise flat solar cell. A
Jsc=35.5mA/cm2 is found on the t=600nm curve at L=1100nm; this is the highest Jsc value for all t
modeled at the aspect ratio (550:100). This bests our research team’s previous nc-Si LCCM
investigation that used t=800nm to achieve Jsc=29.2mA/cm2 [15] and also tops the result in the
literature that used nc-Si on Ag nano-pillars to achieve Jsc=34mA/cm2 at t=1000nm [28].
Figure 4-2: The Jsc increases and then decreases with changing L. The dashed lines correspond to the
Ltch for each t curve; the markers on the Ltch dashed line correspond to the respective t curve. The top
and bottom AZO film thicknesses used in these models were 10nm and 30nm, respectively.
15
20
25
30
35
40
200 400 600 800 1000 1200 1400
Jsc
(m
A/c
m2)
L (nm)
Current Density Curves using AZO Nanocones at (550:100)
t=200nm
t=300nm
t=400nm
t=500nm
t=600nm
22
Figure 4-3: The Jsc for a planar nc-Si solar cell shows an increase based on the Beer-Lambert law.
Adapted from [7].
The LCCM results can be compared to the plot of increasing planar thicknesses in Figure 4-3.
It should be noted that this curve represents an optimistic scenario for nc-Si planar cells. Comparing
this curve with the graph seen in Figure 4-2 illustrates the LCCM’s outstanding improvement over
planar nc-Si Jsc values. Table 4-1 compares the highest Jsc from each t curve against the Jsc of the
planar control cells at the same t. Tables in this thesis use a color scheme to link columns (or rows)
that share a performance metric or design variable.
Table 4-1: LCCM cells with highest Jsc compared to the planar control cells
t (nm) LCCM L
(nm)
LCCM Jsc
(mA/cm2)
Planar Jsc
(mA/cm2)
Increase in Jsc
from Planar (%)
200 300 30.2 13.8 118.8
300 600 32.6 15.1 115.9
400 750 34.1 16.2 110.5
500 1150 34.3 17.1 100.6
600 1100 35.5 17.8 99.4
Alternatively, the reduction in needed absorber material can be shown. Figure 4-3 can be
used to identify a planar t that matches the maximum Jsc values from each LCCM t curve. Using the
planar t and the respective LCCM unit cell base area, a nc-Si volume can be calculated for the planar
cells that achieve the same Jsc values as the LCCM models. The nc-Si volume in LCCM cells can
then be compared with this newly calculated “planar volume.” The reduction in needed absorber is
shown in Table 4-2.
23
Table 4-2: LCCM cells with highest Jsc compared to planar control cells at same Jsc
Maximum
LCCM
Jsc (mA/cm2)
LCCM
t
(nm)
LCCM nc-Si Volume
(nm3)
in a cell of 1cm2 area
Planar nc-Si Volume
(nm3)
in a cell of 1cm2 area
Decrease in nc-Si
Volume from
Planar (%)
30.2 200 6.04×1016
1.50×1018
-96.0
32.6 300 5.75×1016 2.50×1018 -97.7
34.1 400 7.30×1016 3.75×1018 -98.1
34.3 500 7.02×1016 3.90×1018 -98.2
35.5 600 9.16×1016 5.50×1018 -98.3
4.1.3 Spectrum Regions of Enhanced Absorption in L-t Study
The enhancement in the LCCM architecture is due to the greater absorption of wavelengths
across the entire concerned spectrum (λ=300-1110nm) relative to planar cells. Figure 4-4 plots the
t=200nm LCCM models for L=200-800nm. This plot is provided not to overwhelm the reader but to
show that absorption is enhanced for all variations of L at this t. Similar plots for t=300-600nm
exhibit the same result and would be tedious to include.
Figure 4-5 shows the LCCM model with the highest Jsc for t=200nm. Both Figure 4-4 and
Figure 4-5 show that absorption approaches unity from approximately 400nm to 750nm, the visible
portion of the electromagnetic spectrum. Figure 4-6 shows the highest Jsc obtained from this L-t study
and reveals this structure absorbs above 90% of the incoming wavelengths from 400nm to 900nm.
The wavelengths greater than 750nm, while not absorbed as greatly, also experience increased
absorption relative to planar control cells. It is this superior absorption that produces the high Jsc
curves seen in Figure 4-2.
24
Figure 4-4: The absorption as a function of wavelength for the t=200nm LCCM models are plotted
against the planar t=200nm absorption curve.
Figure 4-5: The absorption as a function of wavelength for the t=200nm L=300nm LCCM model is
plotted against the planar t=200nm absorption curve.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
300 400 500 600 700 800 900 1000 1100
Ab
sorp
tion
λ (nm)
LCCM (550:100) and Planar Absorption, t=200nm
Planar LCCM L=300nm LCCM L=200nmLCCM L=250nm LCCM L=350nm LCCM L=380nmLCCM L=400nm LCCM L=450nm LCCM L=500nmLCCM L=550nm LCCM L=600nm LCCM L=800nm
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
300 400 500 600 700 800 900 1000 1100
Ab
sorp
tion
λ (nm)
LCCM (550:100) and Planar Absorption, t=200nm
Planar
LCCM L=300nm
25
Figure 4-6: The absorption as a function of wavelength for the t=600nm L=1100nm LCCM model is
plotted against the planar t=600nm absorption curve. The LCCM absorption curve is close to unity
for a large portion of the spectrum.
4.2 Varying the Nano-element Shape
4.2.1 Radius of Curvature Applied to Nanocone
The possibility that a nanocone may not be manufactured with a perfectly sharp apex led to
an investigation of what affect a “dulled” nanocone tip would produce. This was accomplished by
applying a radius of curvature (RoC) to the top of the H=550nm, d=100nm cone used in the L-t study.
The application of an RoC will result in a decrease in H. Figure 4-7 illustrates how an RoC is applied
to the model and the resulting decrease in H. The RoC chosen were 5-25nm in steps of 5nm. This
study used a single model from the L-t study as the control unit cell. In particular, it used the LCCM
model that achieved the highest Jsc from the t=300nm group. This LCCM cell had the following
variables: t=300nm, L=600nm, H=550nm, d=100nm. In this study, AZO was again used as the nano-
array and TCO film material in the same thicknesses as the L-t study.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
300 400 500 600 700 800 900 1000 1100
Ab
sorp
tion
λ (nm)
LCCM (550:100) and Planar Absorption, t=600nm
Planar
LCCM L=1100nm
26
Figure 4-7: Increasing RoC is applied to the control nanocone (550:100) resulting in decreased H.
The change in H is seen in Figure 4-8. Though the volume of the cone decreases and one
may think the nc-Si layer would gain volume, the absorber layer also diminishes due to the definition
of R. This creates three changing variables—cone tip shape, cone height, and nc-Si absorber volume.
It should be realized that changing the nano-element in any way will alter the absorber volume; so,
the absorber volume cannot be a controlled variable.
It was seen that the Jsc decreases slightly from the control value as the RoC is increased, a
result of the decreasing nc-Si volume. Though, the Jsc decrease was gradual considering the change in
nanocone feature. Table 4-3 lists the models’ features (H, nc-Si volume, Jsc) and the relative change
of the features for the RoC LCCM models. As a consequence of the multiple variables, further
studies were executed to understand the relationship between altering the nanocone and the LCCM
performance.
27
Figure 4-8: Cross-sectional view of increasing RoC applied on the t=300nm L=600nm LCCM control
model’s nanocone. Scale bars are 700nm.
Table 4-3: Results of the LCCM models with increasing RoC applied to the nanocone. All models
have d=100nm.
H (nm)
nc-Si Volume
(nm3)
Jsc
(mA/cm2)
Decrease in
nc-Si Volume
from Control (%)
Decrease in
Jsc from
Control (%)
Control 550 1.79×108 32.6 0.0 0.0
RoC=5nm 500 1.71×108 32.5 -4.4 -0.4
RoC=10nm 450 1.63×108 31.6 -8.9 -3.1
RoC=15nm 400 1.55×108 31.7 -13.3 -2.8
RoC=20nm 350 1.47×108 29.9 -17.7 -8.2
RoC=25nm 300 1.40×108 29.7 -22.0 -8.9
4.2.2 Sharp Apex Nanocones at Radius of Curvature Heights
To test only the effect of changing H, the control LCCM model was again used to make
models at each decreasing H seen in the RoC models, but these were made with the control model’s
nanocone apex—a “sharp apex.” Figure 4-9 shows the cross-sectional view of these models. The nc-
Si volume did decrease again but decreased almost the same amount as the RoC LCCM models; this
is seen when comparing Table 4-4 to Table 4-3. These sharp apex models also experienced the
decreasing Jsc values with decreasing H. In fact, the Jsc values in this sharp apex study were almost
28
exactly the same values seen in the RoC study. This observation reveals that while changing the
height of the nanocone in this control model does decrease the Jsc, slight deviations in the shape of the
nanocone tip at a given H do not affect the performance of the model.
Table 4-4: Results of the LCCM models with sharp apex nanocones at decreasing H. All models
have d=100nm.
H (nm)
nc-Si Volume
(nm3)
Jsc
(mA/cm2)
Decrease in
nc-Si Volume
from Control (%)
Decrease in
Jsc from
Control (%)
Control 550 1.79×108 32.6 0.0 0.0
Sharp Apex 500 1.71×108 32.5 -4.4 -0.2
Sharp Apex 450 1.64×108 31.7 -8.7 -2.8
Sharp Apex 400 1.56×108 31.6 -13.1 -3.3
Sharp Apex 350 1.48×108 29.9 -17.5 -8.3
Sharp Apex 300 1.40×108 29.5 -21.7 -9.4
Figure 4-9: Cross-sectional view of sharp apex nanocone at decreasing H applied in the t=300nm
L=600nm LCCM control model. Scale bars are 700nm.
29
4.2.3 Truncated Nanocone at Radius of Curvature Heights
To further test the effect of altering the nanocone shape, LCCM models with truncated
nanocones were created. A truncated nanocone was set at each of the H values from the RoC group.
The cross-sectional images of this group can be seen in Figure 4-10. The results again show that Jsc
decreases with decreasing H. Moreover, the values found for Jsc and the relative change in value
compared to the control cell nearly matched the values seen in Table 4-3 and Table 4-4. The results
of the truncated nanocone group can be viewed in Table 4-5. These three studies—models with RoC,
models with sharp apex nanocones at RoC H, and models with truncated nanocones at RoC H—
illustrate that the designer enjoys some latitude when manufacturing the nanocone tip. A unit cell
with an apex that unintentionally deviates from the control architecture will almost attain the Jsc of the
intended form.
Figure 4-10: Cross-sectional view of truncated nanocones at decreasing H applied in the t=300nm
L=600nm LCCM control model. Scale bars are 700nm.
30
Table 4-5: Results of the LCCM models with truncated nanocones at decreasing H. All models have
d=100nm.
H (nm)
nc-Si Volume
(nm3)
Jsc
(mA/cm2)
Decrease in
nc-Si Volume
from Control (%)
Decrease in
Jsc from
Control (%)
Control 550 1.79×108 32.6 0.0 0.0
Truncated 500 1.71×108 32.5 -4.4 -0.3
Truncated 450 1.63×108 31.6 -8.9 -3.1
Truncated 400 1.55×108 31.7 -13.3 -2.8
Truncated 350 1.47×108 29.9 -17.7 -8.4
Truncated 300 1.40×108 29.8 -22.1 -8.6
4.2.4 Radius of Curvature, Sharp Apex, and Truncated Nanocones Compared
If the three previous studies are compared in one table that is sorted according to H, the
significance of the three variations is more easily understood. Table 4-6 compiles Table 4-3 through
Table 4-5 in this manner. Within each H grouping, it can be seen that the nc-Si volume and Jsc values
for the three architecture variations (“RoC,” “Sharp Apex,” “Truncated”) are nearly the same. Not
surprisingly, the percent difference from the control model is largely the same within each H
grouping, as well. This observation means that for a given H the nanocone shape—within a
reasonable span of variation—does not determine the performance of the LCCM model. It was
observed that the nanodomes’ profiles were fairly constant within each H grouping while the nano-
element shape changed; this led to the realization that the nanodome’s spheroid geometry appears to
be the governing feature for enhanced absorption. However the importance of the nanocone—or any
high aspect ratio nano-element—should not be discounted. The nanodome—simply an undulation in
the subsequent layers—is developed only from the inclusion of these high aspect ratios.
31
Table 4-6: Radius of Curvature, Sharp Apex, and Truncated Nanocone groups compared by sorting
according to H.
H (nm) nc-Si Volume
(nm3)
Jsc
(mA/cm2)
Decrease in
nc-Si Volume
from Control (%)
Decrease in
Jsc from
Control (%)
Control 550 1.79×108 32.6 0.0 0.0
RoC=5nm 500 1.71×108 32.5 -4.4 -0.4
Sharp Apex 500 1.71×108 32.5 -4.4 -0.2
Truncated 500 1.71×108 32.5 -4.4 -0.3
RoC=10nm 450 1.63×108 31.6 -8.9 -3.1
Sharp Apex 450 1.64×108 31.7 -8.7 -2.8
Truncated 450 1.63×108 31.6 -8.9 -3.1
RoC=15nm 400 1.55×108 31.7 -13.3 -2.8
Sharp Apex 400 1.56×108 31.6 -13.1 -3.3
Truncated 400 1.55×108 31.7 -13.3 -2.8
RoC=20nm 350 1.47×108 29.9 -17.7 -8.2
Sharp Apex 350 1.48×108 29.9 -17.5 -8.3
Truncated 350 1.47×108 29.9 -17.7 -8.4
RoC=25nm 300 1.40×108 29.7 -22.0 -8.9
Sharp Apex 300 1.40×108 29.5 -21.7 -9.4
Truncated 300 1.40×108 29.8 -22.1 -8.6
4.2.5 Radius of Curvature Applied at Control Height
An additional study was done to investigate the effect of nanocone shape on LCCM
performance. This study compared the importance of the nanocone within the nanodome by holding
the base diameter and height constant (100nm and 550nm, respectively) but applying a RoC. The
increasing RoC from the earlier study was used (5-25nm, steps of 5nm). The increase in RoC results
in a nanocone that approaches the profile of a nano-column with a rounded top. See Figure 4-11 for
the cross-sectional view of these “RoC at H=550nm” models. Applying a RoC in this manner results
in some portion of the nc-Si volume being replaced by the wider nanocone volume; see Table 4-7 for
this small change. Though there is this small absorber volume decrease, the Jsc remains almost at the
same values as the control. The values only decrease by <2%. Table 4-7 also lists these results. It
should be noted that in this RoC at H=550nm study the nanodome’s spheroid geometry did not
change. Upon contemplation of these variations and their results, it was realized that, rather than
32
increasing and decreasing with the changing aspect ratio, R* remained constant in these models. R
also remained constant, but that consistency is appropriate due to the unchanging H. The meager
decrease in Jsc combined with the fact that the spheroid’s R* remained unchanged shows that the
nanodome architecture is a very important aspect to our LCCM design. The unchanging R* variable
is addressed in the following section.
Figure 4-11: Cross-sectional view of increasing RoC at H=550nm applied in the t=300nm L=600nm
LCCM control model. Scale bars are 700nm.
Table 4-7: Results of the LCCM models with nanocones at H=550nm but increasing RoC applied.
H (nm)
nc-Si Volume
(nm3)
Jsc
(mA/cm2)
Decrease in
nc-Si Volume
from Control (%)
Decrease in
Jsc from
Control (%)
Control 550 1.79×108 32.6 0.0 0.0
RoC=5nm at H 550 1.79×108 32.5 -0.1 -0.4
RoC=10nm at H 550 1.79×108 32.4 -0.2 -0.8
RoC=15nm at H 550 1.79×108 32.3 -0.3 -1.1
RoC=20nm at H 550 1.78×108 32.2 -0.4 -1.4
RoC=25nm at H 550 1.78×108 32.1 -0.6 -1.6
33
4.3 Nanocone Aspect Ratio Study
The observation that the nanodome not the nanocone shape was the main player in affecting
Jsc informed the next study. Since R* is defined as the radius at t from the nanocone centerline to the
point where the dome meets the flat film, the nanodome’s bottom diameter remained the same in the
four previous studies. This is not the most accurate modeling when the nano-element aspect ratio is
being varied as it was when H was changing in the RoC, Sharp Apex, and Truncated nanocone
studies. It can be imagined that the R* variable should change. Specifically, the portion of R* that
comprises the width from the centerline to the surface of the nanocone should increase or decrease
based on the new H and d. This is so because the R* variable was originally formulated from a
nanocone of H=550nm and d=100nm. Changing either of those variables should be met with a
change in R*. Specifically, if H=550nm is maintained and d is increased from 100nm, then R* should
increase (the converse is true—hold H constant and decrease d, then R* should decrease). Similarly,
if d=100nm is maintained and H is increased, then R* should increase (the converse is also true—
hold d constant and decrease H, then R* should decrease). The R variable is appropriately defined no
matter the change in nano-element. Figure 4-12 illustrates the way R* is previously defined and how
it may be better approximated for the next study.
In the top row, the fixed R* used in the previous studies is shown to not change even though
H is changing. The bottom row shows the approximation used for the following aspect ratio study.
R* is divided into two parts—R*a and R*b. The R*a length is a set number taken from the LCCM
models that contain the aspect ratio H=550nm and d=100nm for each t (200-600nm). R*a is defined
as the portion of R* from the nanocone’s surface to the dome-film vertex at height t. R*b is then
adjusted as either H or d are changed. Table 4-8 gives an example of how R*b and R* were adjusted
as the aspect ratio was varied from (550:100). A caveat to this new definition is that it is only
required when t is less than H. It is only when the film thickness is smaller than H that the new
definition should be used to approximate the effect of a widening or narrowing nanocone, which
34
would logically result in the dome-film vertex moving away or toward the centerline of the nanocone.
Appendix F lists some examples of R*a and R*b.
Figure 4-12: The original definition of R* used in the L-t, RoC, Sharp Apex, and Truncated studies is
seen on top. On the bottom is the definition to amend R* for aspect ratio studies.
Table 4-8: Using the t=300nm L=800nm LCCM model as an example, the original R*, R*a, and R*b
created by (550:100) are given. Two (H:d) changes are expressed to show the change in R*b and R*.
t (nm) L (nm) H (nm) d (nm) R* (nm) R*a (nm) R*b (nm)
300 800 550 100 275.0 252.3 22.7
300 800 400 100 264.8 252.3 12.5
300 800 400 400 302.3 252.3 50.0
While simulated cells should closely match the geometry of manufactured cells, there will
always be discrepancy between the two. Other approximations for adjusting R* to fit new aspect
ratios were explored, but these did not preserve the spheroid form of the nanodome. This form is
35
important since it has been witnessed in many experimental results [14], [16], [34]. For these
reasons, this varying R*b approximation was used for the following aspect ratio study.
4.3.1 Holding H Constant and Varying d
The R*=R*a + R*b definition was then used in LCCM models to evaluate cells with wider
nanocone base diameters that may offer more ease in manufacturing. The t=300nm LCCM models
with an aspect ratio of (550:100) were used again as the control model. H was held constant.
L=1000nm, rather than L=600nm, was used in this study to accommodate any expanse in the dome
and the increasing cone base. The d was increased from 100nm to 300nm in steps of 50nm to inspect
the effect on performance. Figure 4-13 shows the cross-section of the control model and the four
variations.
Figure 4-13: Cross-sectional view of increasing d at H=550nm applied in the t=300nm L=1000nm
LCCM control model. Scale bars are 900nm.
While the R*=R*a + R*b definition did help create more accurate models—seen by the
slightly increasing dome width in Figure 4-13—the absorber volume did still change. Table 4-9
displays this change and the other parameters of the models and their resulting performance. The
trend seen is that wider d results in higher Jsc when compared to the original aspect ratio in this
particular LCCM model. These results were very promising considering a smaller aspect ratio
(550:300) is more amenable to manufacturing than a high aspect ratio (550:100).
36
Table 4-9: Results of the LCCM models with increasing d at H=550nm. All models have t=300nm,
L=1000nm, and a sharp apex.
H (nm) H (nm) nc-Si Volume
(nm3)
Jsc
(mA/cm2)
Increase in
nc-Si Volume
from Control (%)
Increase in
Jsc from
Control (%)
550 100 3.46×108 28.6 0.0 0.0
550 150 3.51×108 29.9 1.6 4.7
550 200 3.56×108 29.7 3.1 3.9
550 250 3.61×108 30.5 4.4 6.6
550 300 3.65×108 31.7 5.7 8.4
4.3.2 Varying both H and d in the t=300nm L=800nm LCCM Model
The improvement in Jsc in the t=300nm L=1000nm LCCM models with aspect ratios other
than (550:100) pointed the way toward more manufacturable LCCM unit cells with similar or
enhanced performance. Varying both H and d in an LCCM model offered another potential for
optimization by allowing the designer to control the ease of manufacturability by identifying a
smaller aspect ratio to imprint. The t=300nm L=800nm (550:100) LCCM model was used as the
control. This particular model was chosen to see if its Jsc=29.8mA/cm2 could be enhanced to the
maximum seen on the t=300nm Jsc-L curve (32.6mA/cm2). The model’s aspect ratio was varied using
H=300-500nm in steps of 100nm and d=300-400nm in steps of 50nm. R* was adjusted to accurately
portray the change in (H:d) for each model. Cross-sectional images of the aspect ratio variants are
displayed in Figure 4-14.
37
Figure 4-14: The varying (H:d) unit cells are in rows according to H and columns according to d. The
control LCCM unit cell t=300nm L=800nm (550:100) is omitted; it would be very similar to the
control in Figure 4-13. Scale bars are 600nm.
Table 4-10: Results from the LCCM models with varying (H:d). The aspect ratios are grouped
according to H. All models have t=300nm L=800nm.
(H:d) nc-Si Volume
(nm3)
Jsc
(mA/cm2)
Change in
nc-Si Volume
from Control (%)
Change in
Jsc from
Control (%)
(550:100) 2.5×108 29.8 0.0 0.0
(500:400) 2.6×108 30.7 5.0 2.8
(500:350) 2.6×108 31.4 3.9 5.2
(500:300) 2.6×108 30.8 2.6 3.3
(400:400) 2.3×108 30.9 -8.9 3.6
(400:350) 2.3×108 31.3 -8.9 5.1
(400:300) 2.3×108 31.9 -9.0 6.9
(300:400) 1.9×108 29.8 -21.8 -0.2
(300:350) 2.0×108 30.7 -20.9 3.0
(300:300) 2.0×108 30.2 -20.2 1.3
38
Table 4-10 displays the variable information for each model along with the resulting Jsc
values. The first group with H=500nm—close to the control’s H=550nm—experienced increased Jsc
values as d was increased. The second grouping with H=400nm also enjoyed increased Jsc values.
The Jsc results of this group indicated smaller aspect ratios may offer designs that may be more easily
manufactured while maintaining similar Jsc values. It can be seen in the last group (H=300nm) that
substantially altering the nanocone from the high (550:100) aspect ratio does not necessarily diminish
the Jsc. Though there was a decrease in Jsc for the (300:400) aspect ratio, all three of the models in
that H grouping experienced a pronounced decrease in the volume of nc-Si absorber used.
4.3.3 Varying L with Altered (H:d) in the t=300nm L=800nm LCCM Model
Varying the aspect ratios while holding t and L constant provided the insight that Jsc values
can be improved. Varying L at one of the new (H:d) ratios held the possibility of further
improvement in Jsc. With this prospect, two aspect ratios from the previous study were chosen to
witness the effect of varying L. The (400:300) LCCM unit cell was used as the first new aspect ratio
since it expressed the highest improvement in Jsc in the aspect ratio study. L was varied between 300-
1000nm. The behavior of Jsc while varying L at this (H:d) resulted in the same trend seen in Figure
4-2—increasing Jsc as L approaches Ltch, followed by a gradual decrease in Jsc after L is made greater
than Ltch. The results are given in Figure 4-15. The solid line shows the Jsc-L curve from Figure 4-2;
this model used t=300nm and (550:100). The dashed line is the same t=300nm model with the new
(400:300) aspect ratio. As Table 4-10 showed, there is an increase in Jsc for the model with the new
aspect ratio at L=800nm. Though there are diminished Jsc values exhibited for smaller L values, the
smaller (400:300) aspect ratio outperforms the (550:100) model at wide L. This is advantageous for
manufacturing and cost-savings since a wide nanocone pitch avoids stringent NIL features and
requires less material. For this analysis of varying L at a new (H:d), the (400:300) L=800nm data
point proved to be an idyllic model. Its Jsc nearly equals the maximum seen in the t=300nm (550:100)
models.
39
Figure 4-15: The dashed line indicates the new t=300 (400:300) models. The solid line indicates the
original (550:100) ratio in the model. The vertical lines correspond to the Ltch for each (H:d) curve.
The t=300 (300:350) model was the second new aspect ratio chosen to investigate the effect
of changing L. It was varied between 400-1000nm; L=300nm was not modeled as it was in the last
comparison since d is now 350nm and it would result in overlapping cones. This aspect ratio from
Table 4-10 was chosen because it showed modest improvement in Jsc even though its volume of nc-Si
was greatly reduced. Figure 4-16 shows a similar trend to what is seen in Figure 4-15. However, of
the models simulated, only the L=800nm data point shows improved Jsc. The solid line again shows
the t=300 (550:100) Jsc as a function of L curve that was seen in Figure 4-2. The dashed line shows
the new aspect ratio of (300:350) modeled at varying L. Again, the L=800nm (300:350) model
attains the highest value seen. The slight enhancement in Jsc indicates L=800nm as a possible
enviable structure for manufacturing.
20
22
24
26
28
30
32
34
300 400 500 600 700 800 900 1000
Jsc
(m
A/c
m2)
L (nm)
Current Density Curves using AZO Nanocones at (550:100) and (400:300)
(550:100)
(400:300)
40
Figure 4-16: The dashed line indicates the new t=300 (300:350) models. The solid line indicates the
original (550:100) ratio in the model. The vertical lines correspond to the Ltch for each (H:d) curve.
4.3.4 Varying both H and d in the t=600nm L=1100nm LCCM Model
An additional study of varying H and d was done using the model with the highest Jsc
(35.5mA/cm2) seen in Figure 4-2. The t=600nm L=1100nm was varied from the original (550:100) in
the same fashion—H=300-500nm in steps of 100nm and d=300-400nm in steps of 50nm. Again, R*
was adjusted according to the R*=R*a + R*b definition. Table 4-11 lists the results.
Table 4-11: Results from the LCCM models with varying (H:d). The aspect ratios are grouped
according to H. All models have t=600nm L=1100nm.
(H:d) nc-Si Volume
(nm3)
Jsc
(mA/cm2)
Change in
nc-Si Volume
from Control (%)
Change in
Jsc from
Control (%)
(550:100) 9.2×108 35.5 0.0 0.0
(500:400) 9.2×108 34.4 -3.7 -3.1
(500:350) 9.3×108 34.0 -3.2 -4.1
(500:300) 9.3×108 34.0 -2.7 -4.0
(400:400) 8.7×108 33.7 -9.9 -5.1
(400:350) 8.7×108 33.5 -9.4 -5.4
(400:300) 8.7×108 33.3 -9.1 -6.2
(300:400) 8.1×108 32.6 -15.9 -8.0
(300:350) 8.1×108 32.5 -15.6 -8.3
(300:300) 8.1×108 33.3 -15.3 -6.2
20
22
24
26
28
30
32
34
300 400 500 600 700 800 900 1000
Jsc
(m
A/c
m2)
L (nm)
Current Density Curves using AZO Nanocones at (550:100) and (300:350)
(550:100)
(300:350)
41
Just as in Table 4-10, the new aspect ratios are grouped by H. Interestingly, every new aspect
ratio model resulted in a decrease in absorber volume. Unfortunately, all the simulated variations in
aspect ratio resulted in a decrease in Jsc. This second study into varying H and d in an LCCM model
revealed that altering the nanocone’s aspect ratio does not necessarily give immediate benefits in Jsc.
Since the nc-Si volume diminished along with the relatively small decrease in Jsc, the designer may
find that one of these aspect ratio models results in the maximum price per watt from this thesis. This
analysis will be performed in the last chapter.
42
Chapter 5. Varying the Nano-element Material
5.1 Variation in Nanocone Material
Though the choice of AZO as the nano-element material was made for reasons cited in
Chapter 2, the exploration of using materials with different optical properties was done to see the
effects on light absorption. Using nanocone materials other than AZO and altering only one
geometric variable allowed insight into the performance of various materials in the LCCM
architecture. All variables (t, L, R, R*, d) were held constant except H to provide this insight. The six
H values from the RoC study (300-550nm) were employed again. AZO nanocones were compared
against Ag, nc-Si, and factitious nc-Si nanocones. The factitious nc-Si’s relative permittivity and
dielectric loss tangent were calculated by using nc-Si’s complex refractive index with the extinction
coefficient k set to be identically zero. The resulting dielectric loss tangent is also identically zero for
the factitious nc-Si, which results in a material that does not absorb electromagnetic radiation. This
material was concocted to investigate what role the nanocone’s optical properties play in absorbing
incident light. Each material slightly altered the optical properties of the nanocone in the LCCM
models. Transitioning from a TCO or metal nanocone (which refracts or reflects light at the absorber-
nanocone boundary) to a factitious material (which does not refract nor reflect light at the absorber-
nanocone boundary and which does not absorb light) to a nc-Si nanocone (which is in effect merely
an additional volume of nc-Si that will not refract nor reflect light but will absorb it) allowed insight
into this shifting behavior.
Ag nanocones were included in the study to reaffirm earlier statements of their inferiority in
enhancing light absorption and as a basis to seek a potentially improved Ag nanocone LCCM
configuration. Figure 5-1 shows cross-sectional images of the LCCM architecture with each type of
nanocone material. The factitious nc-Si nanocone is shown as an opaque red colored cone; the nc-Si
nanocone model is shown as a continuation of the undulating nc-Si absorber layer in Figure 5-1.
Figure 5-2 serves as a reminder of the varying H used in this study. Only the AZO nanocone is
43
displayed in this figure; the other materials would be the same with their respective nanocone
materials in place of the green colored AZO. It should be noted that the original R* definition was
used for this study. This was done to hold as many variables constant as possible. An additional note
should be made on a trivial inaccuracy in the Ag nanocone models. A 30nm thick bottom AZO film
was included just as it had been in every other model; however, it was modeled underneath the Ag
nanocone. While this would have ideally been modeled as a conformal AZO coating, the results still
served their purpose of informing the present study on the effect of using Ag nanocones.
Figure 5-1: t=300nm L=600nm (550:100) LCCM models with AZO, Ag, factitious nc-Si, and nc-Si
nanocones are seen, respectively, from left to right. Scale bars are 700nm.
Figure 5-2: The decreasing H values used in this study are shown. Only the t=300nm L=600nm AZO
nanocone (H:100) LCCM models are displayed. Scale bars are 700nm.
In Figure 5-3, the Jsc results are plotted against increasing H values for each of the nanocone
materials used. Ag nanocone models exhibit inferior Jsc for all models simulated. The AZO
nanocone models perform well but also experience decreased Jsc as H is made smaller, just as the
other model types do. Intriguingly, the nc-Si and factitious nc-Si nanocone models perform similarly
44
to the AZO nanocone models. The decreased performance of the Ag nanocone models shows that an
LCCM nano-element that reflects traveling light is not as desirable as one that refracts it (as in the
case of the AZO nanocones) or as one that allows continued propagation (as in the case of the nc-Si
and factitious nc-Si nanocones). The congruence of the nc-Si and factitious nc-Si models arises from
the fact that the two model types only differ by the absorbing volume of the nc-Si nanocones. Figure
5-4 uses the (400:100) LCCM models to compare the absorption profiles arising from the use of the
different nanocone materials.
Figure 5-3: The Jsc values are given for the t=300nm L=600nm (H:100) LCCM models with
increasing H for each nanocone material.
Figure 5-4: The absorption as a function of wavelength for t=300nm L=600nm (400:100) LCCM cells
with varying nanocone materials.
28
29
30
31
32
33
300 350 400 450 500 550
Jsc
(m
A/c
m2)
H (nm)
Jsc Performance of Varied Nanocone Material
AZO ConeAg ConeFactitious nc-Si Conenc-Si Cone
0
0.2
0.4
0.6
0.8
1
300 400 500 600 700 800 900 1000 1100
Ab
sorp
tion
λ (nm)
Absorption Data for Varying Nanocone Material, t=300nm (400:100)
AZO NanoconeAg NanoconeFactitious nc-Si Nanoconenc-Si Nanocone
45
To varying degrees, each of the Ag nanocone models experiences decreased absorption which
manifests itself in the decreased Jsc values. As is demonstrated in Figure 5-4, wavelengths ranging
from roughly 650-950nm are not absorbed by the Ag nanocone models to the same degree as the
other models. The details of each model in this study are listed in Table 5-1. The models are grouped
according to H. Within each group, the AZO nanocone model is used as the control for the other
three models. The volume of nc-Si is constant within each group, except for the nc-Si nanocone
models which gain the volume contained in the nanocone.
Table 5-1: Design parameters of the varying nanocone material models and their simulation results.
Each H grouping uses the respective AZO nanocone model as its control. [t=300nm L=600nm
(H:100)]
Nanocone Material H (nm) nc-Si Volume
(nm3)
Jsc
(mA/cm2)
Change in nc-Si
Volume from
Control (%)
Change in
Jsc from
Control (%)
AZO (Control) 550 1.8×108 32.6 0.0 0.0
Ag Nanocone 550 1.8×108 31.3 0.0 -4.1
Factitious nc-Si 550 1.8×108 32.5 0.0 -0.2
nc-Si 550 1.8×108 32.6 0.7 0.1
AZO (Control) 500 1.7×108 32.5 0.0 0.0
Ag Nanocone 500 1.7×108 31.0 0.0 -4.6
Factitious nc-Si 500 1.7×108 31.9 0.0 -2.1
nc-Si 500 1.7×108 31.9 0.8 -2.0
AZO (Control) 450 1.6×108 31.7 0.0 0.0
Ag Nanocone 450 1.6×108 30.6 0.0 -3.4
Factitious nc-Si 450 1.6×108 32.4 0.0 2.4
nc-Si 450 1.6×108 32.4 0.7 2.3
AZO (Control) 400 1.6×108 31.6 0.0 0.0
Ag Nanocone 400 1.6×108 29.9 0.0 -5.4
Factitious nc-Si 400 1.6×108 31.3 0.0 -0.7
nc-Si 400 1.6×108 31.4 0.7 -0.6
AZO (Control) 350 1.5×108 29.9 0.0 0.0
Ag Nanocone 350 1.5×108 29.5 0.0 -1.3
Factitious nc-Si 350 1.5×108 30.3 0.0 1.3
nc-Si 350 1.5×108 30.3 0.6 1.5
AZO (Control) 300 1.4×108 29.5 0.0 0.0
Ag Nanocone 300 1.4×108 28.7 0.0 -2.7
Factitious nc-Si 300 1.4×108 28.9 0.0 -2.1
nc-Si 300 1.4×108 29.0 0.6 -1.9
46
The study ultimately showed that a model’s Jsc benefits from a nanocone with optical
properties that allows either refraction or propagation of light at the absorber-nanocone boundary.
The models with AZO, nc-Si, and factitious nc-Si nanocones outperformed those with Ag because
light was able to travel a longer path length (and thus have a higher opportunity to be absorbed).
Though Ag showed inferior performance as a nanocone material in this study, a brief investigation
into its use and whether enhancement could be obtained was subsequently performed.
5.2 Using Ag Nanocones to Attain Enhanced Performance
The first study using Ag nanocones repeated the L-t study previously done with AZO
nanocones. This was done to see if the same trend—increasing Jsc as L approaches Ltch, followed by a
gradual decrease in Jsc after L is made greater than Ltch—would arise. The study utilized the same
t=300nm (550:100) Ag nanocone model used in the previous study; this model contained the planar
layer of AZO underneath the Ag nanocone. Figure 5-5 displays the t=300nm curve from Figure 4-2
that used AZO nanocones and shows that the same trend does in fact arise when using Ag. The Ltch
value is the same since there was no change in R* between the two model types.
Figure 5-5: The rising and falling Jsc values as L increases is once again seen for these t=300nm
(550:100) LCCM models. The vertical dashed line indicates Ltch for both model types.
28
30
32
34
400 600 800 1000
Jsc
(m
A/c
m2)
L (nm)
AZO and Ag Nanocone Jsc Comparison, t=300 (550:100)
AZO Nanocone
Ag Nanocone
47
Interestingly, there are two points in Figure 5-5 that show better Jsc performance when using
the Ag nanocone models. This is promising for the designer who wants to utilize Ag nano-elements.
The models used in the next study included a conformal AZO coating on top of the Ag nanocones to
better approximate a manufactured cell’s material layers. A brief study using 0, 5, 15, and 30nm of
AZO was done to determine what thickness the conformal bottom coating should be. A thickness of
5nm was determined to be the least advantageous for facilitating the absorption of light; it resulted in
the lowest Jsc value. This AZO thickness was chosen with the thought that even higher performance
may subsequently be achieved if decent enhancements are first found using this thin layer. To test
this, a wide variety of architectures was desired. Therefore, the nanocone aspect ratio study was
repeated with the AZO-coated Ag nanocones. The H and d were again varied between 300-500nm
and 300-400nm, respectively. To appropriately compare this group’s performance, a batch of LCCM
models was created using AZO nanocones in the same varying aspect ratio but with a 5nm bottom
AZO film, rather than the usual 30nm. Figure 5-6 displays the cross-sectional images of the Ag and
AZO nanocone models; the 5nm bottom AZO layer is indiscernible at this scaled down view.
Figure 5-6: Varying aspect ratios are shown for Ag (left) and AZO (right) nanocone models. The
t=300nm and L=800nm for all. Scale bars are 800nm.
The use of the R*=R*a + R*b definition kept the nc-Si absorber volume constant for each
(H:d) variation. The Ag nanocone models experienced smaller Jsc values for all simulated models.
The results of the two batches are given in Table 5-2.
48
Table 5-2: The results of the Ag and AZO nanocone (H:d) study grouped by descending H and
colored within each group according to (H:d).
Nanocone Material (H:d) nc-Si Volume (nm3) Jsc (mA/cm2)
AZO (500:400) 2.6×108 31.4
Ag (500:400) 2.6×108 28.4
AZO (500:350) 2.6×108 31.7
Ag (500:350) 2.6×108 28.6
AZO (500:300) 2.6×108 31.7
Ag (500:300) 2.6×108 28.0
AZO (400:400) 2.3×108 31.3
Ag (400:400) 2.3×108 29.7
AZO (400:350) 2.3×108 31.8
Ag (400:350) 2.3×108 28.8
AZO (400:300) 2.3×108 31.8
Ag (400:300) 2.3×108 28.4
AZO (300:400) 1.9×108 30.8
Ag (300:400) 1.9×108 27.5
AZO (300:350) 2.0×108 29.7
Ag (300:350) 2.0×108 27.1
AZO (300:300) 2.0×108 29.4
Ag (300:300) 2.0×108 27.5
An additional study to investigate whether Ag nanocones could be used to fabricate a device
with enhanced absorption was performed by selecting a model from the (H:d) study and varying its L.
The selected model was the t=300nm L=800nm (300:300) Ag nanocone model. The L was varied
from 300-1200nm. This variation in L was compared with AZO nanocone models by selecting the
corresponding unit cell from the previous study—5nm bottom AZO film, t=300nm L=800nm
(300:300) AZO nanocone LCCM model—and varying L in the same fashion. The Jsc results are
shown in Figure 5-7. LCCM models that include AZO nanocones outperform those with Ag
nanocones yet again. However, there are two points where the Jsc values are very similar (L=410nm
and L=600nm) and one point where Ag nanocone models surpass the AZO models (L=300nm). This
reveals that while AZO nanocones largely enjoy enhanced performance when compared to Ag,
specific architectures using Ag nanocones do exist that result in higher or similar performance
enhancements. However, the practicality of manufacturing these designs lies in process constraints (a
small L such as 300nm may be inadvisable) and in cost savings (elevated cost per watt when using Ag
49
nanocones). The next chapter investigates the potential cost benefits or detriments of using Ag or
AZO as the nanocone material.
Figure 5-7: The Jsc curves for Ag and AZO nanocone models at t=300nm (300:300). The increasing
and decreasing trend is again seen.
20
22
24
26
28
30
32
300 600 900 1200
Jsc
(m
A/c
m2)
L (nm)
AZO and Ag Nanocone Jsc Comparison, t=300nm (300:300)
AZO Nanocone
Ag Nanocone
50
Chapter 6. Solar Cell Price per Power Analysis
6.1 Assumptions Made
The cost of a solar installation is often more important to solar energy stakeholders than
properties like the short circuit current density of a cell. However, the cost of a photovoltaic system
is directly related to the desired power output which itself is tied to the performance of each solar cell
in the system. Linking these interests, the price per peak watt (US$/Wp) metric is often used by
stakeholders when selecting a solar module technology. The power used to calculate this metric is the
peak power possible from the combined output of a module’s cells; this corresponds to the maximum
power point on a cell’s experimental current density-voltage (J-V) characteristic curve. The capital
costs are used to determine the US$/Wp for a module and are calculated by companies once a solar
module’s manufacturing process has been finalized and constituent materials have been procured.
Thus, it is a very realistic approximation of the cost a consumer will pay for one watt of power from a
solar module, excluding costs related to the system’s installation, required power electronics, and
“balance of system” components.
Understandably, this thesis cannot account for the resulting power from a module since
design details such as number of cells per module, placement of metal contact fingers, and inter-cell
wiring specifications are not yet determined. It also cannot account for the total cost of a module
(glass, wiring, metal contacts, supporting frame) outside of the materials modeled in HFSS™.
However, it can approximate the US$/Wp metric for a single solar cell by using the calculated Jsc
values and the material volumes in each unit cell. This cost per watt in an individual solar cell will be
abbreviated as US$/Wcell to differentiate from the commonly used notation. This form of cost
analysis still proves very useful if the same evaluation is done for planar cells. The resulting
US$/Wcell disparity between the two architectures will be shown.
While this thesis only deals with optimizing the solar cell’s light absorption via altering the
material and architecture, the US$/Wcell values can be detailed after some assumptions and
51
declarations are made. Firstly, the maximum power point—the point where the product of voltage
and current density is maximized—is needed. Ideally, the J-V curve would be simulated for each
model to obtain the maximum power point; however, HFSS™ does not provide the capability of
numerically analyzing the transport physics of electrons and holes. But, a relation between Jsc and the
maximum power point exists [7] and is seen in Eq. 10 where Jmp and Vmp signify the maximum power
point’s current density and voltage, respectively. To use this, one value for fill factor (FF) and one
value for open-circuit voltage (Voc) were chosen.
Equation 10 – Maximum power point relation
The limitation of choosing one Voc and FF is less than ideal, but if these choices are used for
all LCCM models and planar comparisons, the results of the price per watt values will offer a glimpse
at the cost-savings possible when using the LCCM architecture. In the literature, a FF of ~0.6 and a
Voc of ~0.5V is often reported for nc-Si solar cells of ~1000nm [35], [36]. These two values (FF=0.6,
Voc=0.5V) were used to calculate all of the following US$/Wcell values. It should be noted that the FF
and Voc increase as the t of a planar cell decreases. This trend implies that LCCM architecture may
enjoy higher FF and Voc than the assumed values used here since ultra-thin absorber films have been
modeled, which will result in an even lower US$/Wcell.
While US$/Wp is calculated by tallying all capital costs related to a particular solar module,
the US$/Wcell values will account for all of the material needed to create each unit cell’s architecture.
The cost of Ag, AZO, and nc-Si feedstock materials were quoted by commercial vendors. The
material volumes or masses requested in the price inquiries were chosen to mimic the economies of
scale enjoyed at a manufacturing scale. The Ag and AZO prices are $18.26/cm3 and $10.22/cm3; the
price quotes and material details are listed in Appendix D. Since prices were quoted for orders of
single units, there is the possibility that multiple units per order could result in cost-savings. An
additional assumption made for the cost of each material was that the entire feedstock will be utilized.
This means that the Ag and AZO sputtering targets used to define the material price are assumed to
be completely incorporated in the solar cell layers and completely consumed during manufacturing.
52
To determine the cost of the nc-Si layer, the mass density ρ must be defined since the
production of nc-Si is achieved through chemical vapor deposition of silane gas (SiH4). The gas is
sold based on mass rather than volume to avoid confusion over what amount is being purchased.
Since the HFSS™ unit cells are defined by modeling volume not mass, the ρ must be used to estimate
the given mass in the absorber layer. nc-Si can be considered a triphasic (comprised of three phases)
material with a crystalline Si portion, a hydrogenated amorphous Si portion, and a portion comprised
of voids [37]. The nc-Si’s mass density is determined by the fractions of crystalline material and of
amorphous material (the void fraction will be considered an inherent part of the amorphous phase). A
greater crystalline fraction will bring the film’s mass density closer to that of c-Si. Crystalline
fractions in deposited nc-Si films vary greatly depending on the deposition technique and parameters,
but the range is often between 70-80% of the total film volume [38–42]. The ρ of a-Si:H has been
shown to range from approximately 1.75-2.29g/cm3 [27], [43], [44]; whereas, the ρ of c-Si is
2.33g/cm3 [45]. Calculating nc-Si ρ using these values gives a range of 2.16-2.32g/cm3 which agrees
with experimental measurements of nc-Si (2.22-2.31g/cm3) [44]. To be conservative, 2.31g/cm
3 was
used for nc-Si mass density. This high-end of the nc-Si density range was chosen so that the absorber
layer would be comprised of the highest amount of material. If a lower density was chosen, this
would essentially state that a smaller amount of nc-Si was required to achieve the high Jsc values in
this study. The nc-Si price is defined by assuming the entire mass of SiH4 gas in a canister is
completely incorporated into a nc-Si film, which may not be factual since SiH4 and its radicals are by-
products of the process [46]. This assumption will be used for both LCCM and planar cells to
maintain consistency. The quoted price of SiH4 is $0.52/g which is $1.20/cm3 after using nc-Si’s ρ.
Appendix D lists the price quote and material details for SiH4. A note should be made that a dilution
of hydrogen is often used to create nc-Si rather than a-Si:H layers [46]; however, this cost was not
included in the cost analysis since the manufacturing process design required to know the dilution
falls outside of the scope of this thesis.
53
Using these material prices and the power calculation, the cost per watt US$/Wcell values can
be found for all of the models reported in the previous chapters. Equation 11 details the calculation,
where VAg, VAZO, and Vnc-Si are the volumes for Ag, AZO, and nc-Si, respectively, in a given unit cell.
The Jsc is converted from milliamperes to amperes in the denominator and the unit cell area (units of
square centimeters) is used in the numerator to render Jsc as the short circuit current (Isc) in units of
amperes. The US$/Wcell values are given with three decimal places to provide two significant figures
to display the change from model to model.
[(
)( ) (
)( ) (
)( )]
( )( )( )(
)(
) Equation 11 – Price per watt for a cell
If the reader prefers to see just the reduction in nc-Si volume needed to attain high Jsc values
or feels that the preceding cost analysis calculations are suspect, please refer to Appendix E. That
supplement provides graphs that plot LCCM models and planar models based on Jsc and “averaged
nc-Si volume”. This averaged volume is the result of dividing the nc-Si volume in a unit cell by the
unit cell’s base area. This yields t for planar cells and an effective thickness for LCCM cells.
6.2 Price per watt for the Length and Thickness Study
The LCCM models analyzed in Section 4.1 are the first to be analyzed for cost
improvements. But first, the planar control models’ US$/Wcell values are listed in Figure 6-1 for
increasing t. The figure uses the Jsc values from Figure 4-3 which, as was noted, is an optimistic view
for planar cells. The lowest US$/Wcell is seen at t=800nm and is $0.05/Wcell; it is indicated on the
graph by a black outlined data point. Figure 6-2 plots the Jsc values from the LCCM L-t study against
their respective US$/Wcell values and is given to show a clearer view of the data points which are also
used in the subsequent figure. Figure 6-3 combines the data from Figure 6-1 and Figure 6-2 to show
the improvement in both Jsc and US$/Wcell when using the LCCM architecture. The cluster of data
points from the LCCM L-t study approach an optimal region on the graph—low cost and high
performance. It should be noted that Figure 6-2 uses a linear scale for US$/Wcell, while Figure 6-3
54
uses a logarithmic scale. Figure 6-4 selects the highest Jsc value from each LCCM t batch and
compares the price disparity needed to reach these values when using planar and LCCM architectures.
Appendix E lists the design variables of every model along with their respective Jsc and US$/Wcell and
uses a color gradient “heat map” to express the optimum values for each metric.
Figure 6-1: The trend of US$/Wcell for increasing t in planar cells. This uses Jsc values for nc-Si from
[7].
Figure 6-2: The Jsc for LCCM cells from the L-t study are plotted against their US$/Wcell values.
$0.05/Wcell
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.1 1 10 100
Pri
ce p
er w
att
(U
S$
/Wce
ll)
t (μm)
Planar US$/Wcell for Increasing t
16
20
24
28
32
36
0.01 0.02 0.03 0.04 0.05 0.06
Jsc
(m
A/c
m2)
Price per watt (US$/Wcell)
“L-t” Study Cost Analysis
t=200nm t=300nm t=400nm t=500nm t=600nm
55
Figure 6-3: The US$/Wcell and Jsc, plotted for each L-t LCCM curve, now with data points showing
planar cells with increasing t. The price per watt axis uses a logarithmic scale.
Figure 6-4: The highest Jsc from each LCCM t in the L-t study is plotted and the planar cell that would
also reach that value is compared to see the reduction in price per watt.
0
4
8
12
16
20
24
28
32
36
40
0.01 0.10 1.00
Jsc
(m
A/c
m2)
Price per watt (US$/Wcell)
“L-t” Study Cost Analysis
t=200nm t=300nm t=400nm t=500nm t=600nm Planar t=0.2-100um
30
32
34
36
0.01 0.10 1.00
Jsc
(m
A/c
m2)
Price per watt (US$/Wcell)
LCCM compared against Planar at Maximum LCCM Jsc
Planar t=200nm t=300nm t=400nm t=500nm t=600nm
87.7% decrease in price
92.8% decrease
94.9% decrease
95.3% decrease
96.2% decrease
56
Figure 6-3 displays a large grouping of exemplary data points with US$/Wcell≅$0.02/Wcell
and Jsc>30mA/cm2. The planar cells from t=0.2-100μm are also displayed to show the relatively large
price required to reach similar Jsc values to the LCCM cells. Figure 6-4 illustrates these cost savings.
At short-circuit current density values greater than 30mA/cm2, the price to produce one watt is
reduced 87.7-96.2%. This clearly shows the benefit of using the LCCM solar cell architecture.
6.3 Price per watt for the Aspect Ratio (H:d) Studies
The same price per watt analysis can be done for the study in Section 4.3.2 that varied (H:d)
in the t=300nm L=800nm LCCM cell. The graph in Figure 6-5 shows Jsc versus US$/Wcell. The
pattern of each circle corresponds to a single aspect ratio; these patterns will be used in subsequent
graphs for consistency. The solid circle is the original t=300nm L=800nm (550:100) model from the
L-t study. Figure 6-5 reiterates Table 4-10; the (H:d) variations largely enjoy better Jsc than the
original (550:100) LCCM model. Figure 6-5 supplements this by showing that the US$/Wcell of the
(H:d) variations is very near, the same, or better than the original’s value (Note the price per watt axis
values). In each H grouping, the lowest d yields the lowest US$/Wcell.
Figure 6-5: The US$/Wcell and Jsc plotted for each (H:d) in the t=300nm L=800nm unit cell.
28
30
32
34
0.02 0.03
Jsc
(m
A/c
m2)
Price per watt (US$/Wcell)
The "Varying (H:d) at t=300nm L=800nm" Study
(550:100) (500:400) (500:350) (500:300) (400:400)
(400:350) (400:300) (300:400) (300:350) (300:300)
57
A similar graph is seen in Figure 6-6 for the second varying (H:d) study that was done in
Section 4.3.4 with the t=600nm L=1000nm LCCM cell. The smallest d in each H grouping again
contains the lowest US$/Wcell; however, only the (300:300) model achieves a better US$/Wcell value
than the original (550:100) unit cell. It should be remembered that t=600nm L=1100nm (550:100)
attained the highest Jsc (35.5mA/cm2) in this thesis. So, while this study did not achieve a higher Jsc, it
does contain models that best the t=600nm L=1100nm (550:100) in the realm of price per watt.
Figure 6-6 displays unit cells that surpass the highest-Jsc model’s US$/Wcell while nearly matching the
35.5mA/cm2.
Figure 6-6: The US$/Wcell and Jsc plotted for each (H:d) in the t=600nm L=1100nm unit cell.
The same style of graph is displayed in Figure 6-7 for the variation in aspect ratio when using
Ag nanocones (from Section 5.2). Again, the smallest d in each H grouping results in the most
advantageous US$/Wcell. It should be remember that these Ag nanocone models have a 5nm
conformal coating of AZO on top of the Ag film and Ag nanocone. While the US$/Wcell values for
Ag nanocone models are competitive with the values seen so far in the AZO nanocone models, the Jsc
values are consistently lower in the Ag nanocone models. Compare the relative position of the
spheres in Figure 6-7 with the AZO nanocone models in Figure 6-8 to see the disparity in Jsc. The
32
34
36
0.02 0.03
Jsc
(m
A/c
m2)
Price per watt (US$/Wcell)
The "Varying (H:d) at t=600nm L=1100nm" Study
(550:100) (500:400) (500:350) (500:300) (400:400)
(400:350) (400:300) (300:400) (300:350) (300:300)
58
AZO nanocones in Figure 6-8 are the same reported in Section 5.2, models with only 5nm of bottom
AZO film thickness.
Figure 6-7: The US$/Wcell and Jsc plotted for each (H:d) in the Ag nanocone t=300nm L=800nm cell.
Figure 6-8: The US$/Wcell and Jsc plotted for each (H:d) in the AZO nanocone t=300nm L=800nm cell
(bottom AZO film=5mn).
26
28
30
32
34
0.01 0.03
Jsc
(m
A/c
m2)
Price per watt (US$/Wcell)
The "Ag Nanocone (H:d) Variation" Study
(500:400) (500:350) (500:300) (400:400) (400:350)
(400:300) (300:400) (300:350) (300:300)
26
28
30
32
34
0.01 0.03
Jsc
(m
A/c
m2)
Price per watt (US$/Wcell)
The "AZO Nanocone (H:d) Variation" Study
(500:400) (500:350) (500:300) (400:400) (400:350)
(400:300) (300:400) (300:350) (300:300)
59
Another investigation into the price per watt is done for models presented earlier in Section
4.3.3 in Figure 4-15 and Figure 4-16. These models varied L in the altered (H:d) t=300nm LCCM
cells. The two AZO nanocone aspect ratios reported earlier were (400:300) and (300:350). Both
altered aspect ratios have models that enjoy lower US$/Wcell than the original (550:100) AZO
nanocone LCCM models. Looking at the data added by the (400:300) and (300:350) models, it
should be perceived that these data points are approaching the green highlighted region of Figure 6-2.
The abscissa in this graph is the same as that in the earlier graph. This gradual advance from the large
cluster seen in Figure 6-2 to the green highlighted region indicates adjusting the aspect ratio of the
nanocone results in LCCM architecture that produces preferable performance.
Figure 6-9: The US$/Wcell and Jsc plotted for each (H:d) in the t=300nm AZO nanocone LCCM
model.
The graph in Figure 6-10 displays a similar study to that of Figure 6-9, contrasting the
performance of the AZO nanocone (300:300) model with that of a Ag nanocone (300:300) model.
This is the study where the AZO nanocone model included the 5nm of bottom AZO. The green data
points represent the US$/Wcell values for the models where L was varied in the t=300nm (300:300)
Ag nanocone LCCM models (Section 5.2). Again, the fill pattern of the data points is provided to
20
25
30
35
0.01 0.02 0.03 0.04 0.05 0.06
Jsc
(m
A/c
m2)
Price per watt (US$/Wcell)
The "Varying L with Altered AZO (H:d) in t=300nm" Study
(550:100) AZO (400:300) AZO (300:350) AZO
60
identify the nanocone aspect ratio. While the Ag nanocone models result in neither a lower minimum
US$/Wcell nor a higher Jsc, the values found when using the Ag nanocone models are still relatively
close to those of the AZO nanocone models.
Figure 6-10: The US$/Wcell and Jsc plotted for the t=300nm (300:300) AZO nanocone and t=300nm
(300:300) Ag nanocone LCCM models. Data point size reduced for clarity.
It should be remembered that the intention of varying L in this Ag nanocone (300:300) model
was to try to achieve better performance than the initial L=800nm Ag nanocone (300:300) model did
in Figure 6-7. The data point in that earlier figure had Jsc=27.5mA/cm2 and US$/Wcell=$0.021. So,
while two of the Ag unit cells surpassed it in Jsc, none of the present Ag nanocone (300:300) models
attained a significantly lower US$/Wcell value. As a reminder, Appendix E lists all of the models
variables along with performance metrics for each simulated unit cell in this thesis.
6.4 Price per watt for the Cone Material Study
The final investigation into the price per power is done for the study where the nanocone was
changed from AZO to Ag to nc-Si. The factitious nc-Si models are excluded to focus on the three
genuine materials. The effect on US$/Wcell supports the earlier assertions that AZO is a more
preferred nanocone material than Ag. Figure 6-11 displays the three nanocone material types for the
20
25
30
35
0.01 0.02 0.03 0.04 0.05 0.06
Jsc
(m
A/c
m2)
Price per watt (US$/Wcell)
The "Varying L with Altered Ag (H:d) in t=300nm" Study
(300:300) AZO (300:300) Ag
61
models from Section 5.1; it bears repeating that the R* definition used for the creation of these
models was the original definition and not the more accurate R*=R*a + R*b. For this reason, the
trends seen in the graph are more important than the actual minimum values for each material type.
The high price of silver certainly affects the competiveness of the Ag nanocone models.
Interestingly, the use of nc-Si nanocones (effectively the absence of a nanocone) does not enjoy a
greater decrease in US$/Wcell than may be expected. These could be expected to enjoy very low price
per watt values since they avoid the use of expensive Ag and AZO, but the relatively little volume—a
(H:100) nanocone’s worth—of material being replaced does not greatly affect the bottom line.
Figure 6-11: The US$/Wcell and Jsc plotted for the t=300nm L=600nm (H:100) AZO, Ag, and nc-Si
nanocone LCCM models. The minimum US$/Wcell is displayed.
Looking back through the many price per power values displayed in this chapter, the lowest
value seen is $0.017/Wcell in the t=300nm L=800nm LCCM models with AZO nanocones of
(300:300) displayed in Figure 6-10. However, it must be noted that this is one of the models that uses
only 5nm of AZO for the bottom film. If these AZO nanocone models with the very thin TCO layer
are excluded, then the minimum US$/Wcell becomes $0.021/Wcell for the t=300nm L=1000nm
(300:300) Ag nanocone LCCM model shown in Figure 6-10. If the choice of not using Ag is desired
28
30
32
34
0.020 0.025
Jsc
(m
A/c
m2)
Price per watt (US$/Wcell)
The "Variation in Nanocone Material" Study
AZO Cone Ag Cone nc-Si Cone
62
or the 5nm of bottom AZO on the Ag nanocone models is undesirable, the minimum value is still
found to be $0.021/Wcell by using the t=300nm L=800nm (300:350), t=300nm L=800nm (300:300), or
t=300nm L=1000nm (400:300) AZO nanocone LCCM models presented in Figure 6-5 and Figure
6-9. These models have the thicker 30nm of AZO as the bottom film. If the high aspect ratio
(550:100) AZO nanocone models are used, the price per watt becomes $0.022/Wcell. Again,
Appendix E displays the performance enhancements as averaged nc-Si volume for those readers who
wish to disregard the cost analysis, and Appendix F lists all of the models variables along with
performance metrics for each simulated unit cell in this thesis.
63
Chapter 7. Conclusion
In summary, the LCCM architecture was explored in detail and its performance compared
against that of planar solar cells. The L-t study of Section 4.1 proved that very high Jsc values can be
obtained when using nanodomes and nanocone features. The highest Jsc (35.5mA/cm2) in this thesis
was found in Figure 4-2 in a t=600nm L=1100nm (550:100) model. Section 6.2 showed that a
minimum US$/Wcell is not found where Jsc is maximized; see Appendix E for a heat map table to
compare the various models’ maximums and minimums. The alteration of the nanocone tip in
Section 4.2 was shown to not affect the performance greatly. This revealed the importance of the
nanodome more so than the nanocone; though, the nanocone is an elegant way of achieving the
characteristic undulation.
Nanocone aspect ratios were explored in Section 4.3 and proved to be a path to enhance the
performance of the LCCM architecture while also alleviating the complications of the manufacturing
process. Smaller aspect ratios—(400:300) and (300:350)— produced better Jsc values than the
original (550:100) LCCM models did. The master mold-substrate release step in nanoimprint
lithography should benefit from these smaller aspect ratios since they are less severe than high aspect
ratio features. The possibility of varying L at any of the altered (H:d) ratios exists and a few studies
were done in Section 4.3 to see this effect. The trend of increasing Jsc as L increases toward Ltch
followed by a gradual decline in Jsc as L is increased greater than Ltch was again seen when aspect
ratios other than the original (550:100) were used. Additionally, modest improvements in Jsc were
achieved by varying L at the (H:d) variations.
Utilizing materials besides AZO in the nanocone proved to be both deleterious and beneficial.
It was seen in Section 5.2 that the choice of Ag often results in performance that is lower than when
using AZO; however, through varying L and (H:d), similar performance to the AZO nanocone models
can be attained. An interesting prospect arose when the nanocone material was altered to be a
semiconductor in Section 5.1. The performance of the nc-Si nanocone models (actually the absence
64
of a nanocone) matched or bested the performance of AZO nanocone models. With these insights, it
is up to the designer to choose which material he or she uses. Compared to Ag nanocone models, the
AZO and nc-Si nanocone models offered an easier path to create an architecture that attains high
performance. This should be kept in mind when selecting a nanocone material.
The cost analysis of the price per watt metric in Chapter 6 showed that the LCCM
architecture outcompetes the planar cells not only in Jsc but also in US$/Wcell. The fact that LCCM
solar cells can attain very high Jsc (>30mA/cm2) while costing 87.7-96.2% less than conventional
planar cells shows that the LCCM architecture is a very promising solar cell architecture that must be
developed further. The solar electric industry yearns for an innovation in solar cell technology; the
LCCM cells only need to answer the call.
65
Appendix A: Material Data
Ag
AZO
Photon Energy (eV) n k
Wavelength (nm) n k
0.64 0.24 14.08
300 2.42 0.600
0.77 0.15 11.85
325 2.42 0.600
0.89 0.13 10.10
350 2.41 0.690
1.02 0.09 8.828
370 2.35 0.620
1.14 0.04 7.795
375 2.30 0.460
1.26 0.04 6.992
390 2.20 0.000
1.39 0.04 6.312
400 2.19 0.000
1.51 0.04 5.727
423 2.02 0.006
1.64 0.03 5.242
444 1.98 0.003
1.76 0.04 4.838
477 1.95 0.002
1.88 0.05 4.483
512 1.92 0.001
2.01 0.06 4.152
558 1.90 0.001
2.13 0.05 3.858
613 1.88 0.001
2.26 0.06 3.586
681 1.86 0.001
2.38 0.05 3.324
770 1.84 0.002
2.50 0.05 3.093
879 1.80 0.004
2.63 0.05 2.869
1061 1.76 0.014
2.75 0.04 2.657
1179 1.75 0.018
2.88 0.04 2.462
1200 1.75 0.020
3.00 0.05 2.275
1300 1.74 0.031
3.12 0.05 2.070
1500 1.72 0.080
3.25 0.05 1.864
1800 1.68 0.180
3.37 0.07 1.657
2200 1.60 0.300
3.50 0.10 1.419
2500 1.50 0.400
3.62 0.14 1.142
3.74 0.17 0.829
3.87 0.81 0.392
3.99 1.13 0.616
4.12 1.34 0.964
4.24 1.39 1.161
4.36 1.41 1.264
4.49 1.41 1.331
4.61 1.38 1.372
4.74 1.35 1.387
4.86 1.33 1.393
4.98 1.31 1.389
5.11 1.30 1.378
5.23 1.28 1.367
5.36 1.28 1.357
5.48 1.26 1.344
5.60 1.25 1.342
5.73 1.22 1.336
5.85 1.20 1.325
5.98 1.18 1.312
6.10 1.15 1.296
6.22 1.14 1.277
6.35 1.12 1.255
6.47 1.10 1.232
6.60 1.07 1.212
66
nc-Si nc-Si (continued) nc-Si (continued)
Photon
Energy
(eV)
ε' ε''
Photon
Energy
(eV)
ε' ε''
Photon
Energy
(eV)
ε' ε''
0.73373 12.43157 0 2.23020 18.01446 2.183356 3.73490 14.74330 28.46642
0.76074 12.46608 0 2.25870 18.20056 2.322616 3.75760 14.12776 28.80225
0.78981 12.50502 0 2.29210 18.42428 2.495267 3.79210 13.15896 29.29084
0.81983 12.54728 0 2.32210 18.63033 2.659495 3.81540 12.47899 29.60344
0.84932 12.59087 0 2.34850 18.81501 2.811063 3.85090 11.40174 30.04549
0.87943 12.63759 0 2.38000 19.04064 3.002063 3.87500 10.64305 30.31666
0.91009 12.68758 0 2.40780 19.24314 3.179135 3.91170 9.441892 30.67690
0.93939 12.73772 0 2.44100 19.49068 3.403183 3.93650 8.598655 30.87882
0.97065 12.79390 0 2.47010 19.71300 3.611870 3.97440 7.273129 31.11086
1.00000 12.84932 0 2.50000 19.94523 3.837824 4.00000 6.352038 31.21050
1.02900 12.90687 0 2.53060 20.18777 4.083000 4.02600 5.404975 31.26000
1.05980 12.97100 0 2.56200 20.44103 4.349713 4.06560 3.945036 31.22987
1.09010 13.03750 0 2.58870 20.66058 4.590386 4.09240 2.953485 31.13427
1.11960 13.10595 0 2.62160 20.93424 4.903662 4.11960 1.955069 30.97464
1.15080 13.18260 0 2.64960 21.17103 5.187661 4.14720 0.956299 30.74884
1.18090 13.26214 4.96E-05 2.67820 21.41572 5.494917 4.17510 -0.03487 30.45606
1.20980 13.34435 0.002439 2.70740 21.66795 5.827793 4.21770 -1.49227 29.89156
1.24000 13.43518 0.008682 2.73730 21.92757 6.189547 4.24660 -2.43298 29.43419
1.27050 13.53057 0.018695 2.76790 22.19376 6.583240 4.27590 -3.34060 28.91547
1.29980 13.62539 0.031707 2.79910 22.46559 7.012716 4.30560 -4.20935 28.33898
1.33050 13.72770 0.048782 2.83100 22.74155 7.482130 4.33570 -5.03272 27.71013
1.35960 13.82769 0.068210 2.85710 22.96395 7.889617 4.36620 -5.80671 27.03382
1.39010 13.93478 0.091747 2.89040 23.24166 8.443351 4.39720 -6.52664 26.31676
1.42040 14.04369 0.118336 2.91770 23.46130 8.925452 4.42860 -7.19008 25.56487
1.45030 14.15378 0.147720 2.95240 23.72843 9.581755 4.46040 -7.79488 24.78491
1.47970 14.26448 0.179624 2.98080 23.93234 10.15400 4.47650 -8.07490 24.38650
1.51030 14.38225 0.215993 3.00970 24.12307 10.77173 4.50910 -8.59024 23.57646
1.54040 14.50011 0.254734 3.03920 24.29548 11.43828 4.54210 -9.04599 22.75443
1.56960 14.61732 0.295452 3.06930 24.44326 12.15647 4.57560 -9.44346 21.92578
1.60000 14.74155 0.340872 3.10000 24.55890 12.92876 4.59260 -9.62067 21.51106
1.62940 14.86442 0.387963 3.13130 24.63350 13.75665 4.62690 -9.93381 20.68296
1.66000 14.99444 0.440047 3.16330 24.65685 14.64046 4.64420 -10.0701 20.27128
1.68940 15.12223 0.493388 3.18770 24.63389 15.33840 4.67930 -10.3045 19.45406
1.71980 15.25735 0.552022 3.22080 24.53961 16.31298 4.71480 -10.4899 18.64931
1.74890 15.38913 0.611344 3.24610 24.41449 17.07274 4.73280 -10.5652 18.25262
1.77900 15.52824 0.676178 3.28040 24.16578 18.11643 4.75100 -10.6296 17.85988
1.81020 15.67532 0.747134 3.30670 23.91235 18.91500 4.78770 -10.7269 17.08854
1.83980 15.81769 0.818110 3.34230 23.47979 19.98730 4.82490 -10.7852 16.33779
1.87030 15.96797 0.895422 3.36960 23.08260 20.78759 4.84380 -10.8008 15.97048
1.89890 16.11191 0.971745 3.39730 22.62391 21.57536 4.88190 -10.8068 15.25322
1.93150 16.27901 1.063085 3.43490 21.92136 22.59391 4.90120 -10.7981 14.90345
1.95890 16.42318 1.144233 3.46370 21.33220 23.32611 4.94020 -10.7591 14.22247
1.99040 16.59173 1.241834 3.49300 20.69666 24.02615 4.96000 -10.7295 13.89130
2.01950 16.75160 1.337110 3.52270 20.02112 24.69252 5.00000 -10.6523 13.24784
2.04960 16.91990 1.440251 3.55300 19.31171 25.32579 5.02020 -10.6053 12.93566
2.08050 17.09718 1.552052 3.58380 18.57296 25.92883 5.06120 -10.4960 12.33022
2.10880 17.26286 1.659488 3.61520 17.80776 26.50558 5.08200 -10.4345 12.03686
2.14160 17.45918 1.790500 3.63640 17.28289 26.87795 5.12400 -10.2989 11.46908
2.17160 17.64316 1.916978 3.66860 16.47147 27.42182 5.14520 -10.2255 11.19449
2.19860 17.81194 2.036193 3.70150 15.62733 27.95076 5.16670 -10.1486 10.92596
67
Appendix B: HFSS™ Simulation Settings
Figure B-1: Every simulation was set up to sweep through frequencies ranging from 200-1000THz
(equivalent to ~300-1500nm). Though, only the portion from 300-1110nm was used in Jsc
calculations. The step size in frequencies was 10THz.
68
Figure B-2: Each simulation was solved using a solution frequency of 1000THz. Since this is the
highest frequency in the sweep, using it to create the tetrahedral mesh will result in the finest mesh for
all swept frequencies. A maximum number of passes (refining steps) was chosen as 12. It was seen
that if a model had not adapted its mesh to meet the convergence criteria (explained in Figure B.3) by
12 passes, then manual examination of the meshing was required by the researcher. This did not
happen frequently. A “maximum delta S” of 0.01 was chosen. This value represents the maximum
change in the scattering parameter (hence, S) between two consecutive mesh refinement steps. The
0.01 value proved to be a very strict parameter that resulted in a high degree of meshing and
consequently high accuracy in simulating the reflection, absorption, and transmission of the
electromagnetic waves.
69
Figure B-3: The selection of using “lambda refinement” simply tells the program to refine the mesh
based on the material-dependent wavelength and is a default. The “maximum refinement per pass”
informs the program how many tetrahedral should be added at the beginning of each refinement step;
30% of the previous step is the default value. “Minimum number of passes” is associated with the
maximum number of passes from Figure B.2; it is set at one because the “minimum converged
passes” will drive the number of refining steps. The converged passes value is set at only two
because the maximum delta S value is so strict. These two values work together to push the adaptive
meshing process through enough passes to refine the mesh to an appropriate degree.
70
Figure B-4: Floquet port is the name of the top and bottom boundaries that emitted and absorbed the
simulated electromagnetic radiation, mentioned in Section 3.3. A number of modes must be selected
to accurately simulate incident visible light. The number of modes used was always at least two to
include both transverse electric and transverse magnetic polarization states. However, the model’s
structure and solution frequency (1000THz) sometimes necessitated that additional modes be
included to obtain the highest accuracy possible. To check if more modes were needed, there is a
modes calculator that generates 1-100 modes and their polarization state, m and n values, and
attenuation. All modes with attenuation equal to zero should be kept for the most accurate result.
However, a high number of modes (14+) results in long solution times. Most models required only
two modes. A number of models requiring 14+ modes were simulated both with the high number of
modes and just two. The difference in results was negligible and not large enough to warrant the
drastically increased solution times.
71
Figure B-5: Within the HFSS Options tab, the number of processors and the RAM limit used to
simulate can be set. This dialogue box is given to show the large number of both used to complete
the many simulations in this thesis in a year’s time.
72
Appendix C: HFSS™ Script
' ----------------------------------------------
' Script Recorded by Ansoft HFSS Version 13.0.0
' 12:39:20 PM Mar 29, 2012
' ----------------------------------------------
Dim oAnsoftApp
Dim oDesktop
Dim oProject
Dim oDesign
Dim oEditor
Dim oModule
Set oAnsoftApp = CreateObject("AnsoftHfss.HfssScriptInterface")
Set oDesktop = oAnsoftApp.GetAppDesktop()
oDesktop.RestoreWindow
Set oProject = oDesktop.SetActiveProject("Type name of HFSS file here")
Set oDesign = oProject.SetActiveDesign("HFSSDesign1")
Set oModule = oDesign.GetModule("FieldsReporter")
oModule.CalcStack "clear"
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "200000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "210000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "220000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "230000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "240000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "250000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "260000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "270000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "280000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "290000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
73
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "300000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "310000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "320000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "330000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "340000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "350000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "360000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "370000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "380000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "390000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "400000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "410000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "420000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "430000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "440000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
74
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "450000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "460000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "470000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "480000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "490000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "500000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "510000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "520000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "530000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "540000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "550000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "560000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "570000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "580000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "590000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "600000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
75
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "610000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "620000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "630000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "640000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "650000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "660000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "670000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "680000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "690000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "700000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "710000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "720000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "730000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "740000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "750000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
76
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "760000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "770000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "780000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "790000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "800000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "810000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "820000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "830000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "840000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "850000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "860000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "870000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "880000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "890000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "900000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "910000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
77
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "920000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "930000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "940000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "950000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "960000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "970000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "980000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "990000GHz", "Phase:=", "0deg")
oModule.CopyNamedExprToStack "Volume_Loss_Density"
oModule.EnterVol "ActiveLayer"
oModule.CalcOp "Integrate"
oModule.ClcEval "Setup1 : Sweep", Array("Freq:=", "1000000GHz", "Phase:=", "0deg")
78
Appendix D: Material Price Quotes
Material: Aluminum-doped zinc oxide sputtering target
Company: Kurt J. Lesker Company
Date Quoted: February 19, 2013
Quantity
ZnO/Al2O3
Composition
(wt%)
Purity
(%)
Diameter
(in)
Thickness
(in)
Price
(US$)
Price/
Volume
(US$/in3)
1 98/2 99.999 8 0.25 2355.00 187.40
1 98/2 99.999 3 0.25 625.00 353.68
1 98/2 99.999 3 0.125 590.00 667.74
1 98/2 99.999 1 0.125 365.00 3717.86
1 98/2 99.99 8 0.25 2105.00 167.51
1 98/2 99.99 3 0.25 590.00 333.87
1 98/2 99.99 3 0.125 560.00 633.79
1 98/2 99.99 1 0.125 295.00 3004.85
Material: Indium tin oxide sputtering target
Company: Kurt J. Lesker Company
Date Quoted: February 19, 2013
Quantity
ZnO/Al2O3
Composition
(wt%)
Purity
(%)
Diameter
(in)
Thickness
(in)
Price
(US$)
Price/
Volume
(US$/in3)
1 90/10 99.99 8 0.25 2560.00 203.72
1 90/10 99.99 4 0.25 650.00 206.90
1 90/10 99.99 4 0.125 645.00 410.62
1 90/10 99.99 3 0.25 565.00 319.72
1 90/10 99.99 3 0.125 430.00 486.66
1 90/10 99.99 1 0.25 360.00 1833.46
1 90/10 99.99 2 0.25 325.00 413.80
1 90/10 99.99 2 0.125 292.00 743.57
Material: Silver sputtering target
Company: Kurt J. Lesker Company
Date Quoted: February 19, 2013
Quantity Purity
(%)
Diameter
(in)
Thickness
(in)
Price
(US$)
Price/
Volume
(US$/in3)
1 99.99 8 0.25 3760.00 299.21
1 99.99 6 0.25 2840.00 401.78
1 99.99 4 0.25 1626.00 517.57
1 99.99 4 0.125 1045.00 665.27
1 99.99 3 0.25 787.00 445.35
1 99.99 3 0.125 485.00 548.91
1 99.99 2 0.25 415.00 528.39
1 99.99 2 0.125 300.00 763.94
1 99.99 1 0.25 235.00 1196.85
1 99.99 1 0.125 215.00 2189.97
Material: Silane gas bottle
Company: Praxair
Date Quoted: April 1, 2013
Mass (g) Purity (%) Praxair Part # Price (US$)
10,000 99.99 SI 4.0SP 5197.50
79
Appendix E: Averaged nc-Si Volume
16
20
24
28
32
36
0 200 400 600 800 1000 1200
Jsc
(m
A/c
m2)
Averaged nc-Si Volume (nm3/nm2)
“L-t” Study, Reduction in nc-Si Volume
t=200nm t=300nm t=400nm t=500nm t=600nm
0
4
8
12
16
20
24
28
32
36
40
100 1,000 10,000 100,000
Jsc
(m
A/c
m2)
Averaged nc-Si Volume (nm3/nm2)
“L-t” Study, Reduction in nc-Si Volume
t=200nm t=300nm t=400nm t=500nm t=600nm Planar t=0.2-100um
80
30
32
34
36
100 1,000 10,000 100,000
Jsc
(m
A/c
m2)
Averaged nc-Si Volume (nm3/nm2)
LCCM compared against Planar at Maximum LCCM Jsc
t=200nm t=300nm t=400nm t=500nm t=600nm Planar t=0.2-100um
96.0% decrease in nc-Si Volume
97.7% decrease
98.1% decrease
98.2% decrease
98.3% decrease
28
30
32
34
300 350 400 450 500
Jsc
(m
A/c
m2)
Averaged nc-Si Volume (nm3/nm2)
The "Varying (H:d) at t=300nm L=800nm" Study
(550:100) (500:400) (500:350) (500:300) (400:400)
(400:350) (400:300) (300:400) (300:350) (300:300)
81
32
34
36
700 800 900 1000
Jsc
(m
A/c
m2)
Averaged nc-Si Volume (nm3/nm2)
The "Varying (H:d) at t=600nm L=1100nm" Study
(550:100) (500:400) (500:350) (500:300) (400:400)
(400:350) (400:300) (300:400) (300:350) (300:300)
26
28
30
32
34
300 350 400 450 500
Jsc
(m
A/c
m2)
Averaged nc-Si Volume (nm3/nm2)
The "Ag Nanocone (H:d) Variation" Study
(500:400) (500:350) (500:300) (400:400) (400:350)
(400:300) (300:400) (300:350) (300:300)
82
26
28
30
32
34
300 350 400 450 500
Jsc
(m
A/c
m2)
Averaged nc-Si Volume (nm3/nm2)
The "AZO Nanocone (H:d) Variation" Study
(500:400) (500:350) (500:300) (400:400) (400:350)
(400:300) (300:400) (300:350) (300:300)
20
25
30
35
200 400 600 800 1000
Jsc
(m
A/c
m2)
Averaged nc-Si Volume (nm3/nm2)
The "Varying L with Altered AZO (H:d) in t=300nm" Study
(550:100) AZO (400:300) AZO (300:350) AZO
83
20
25
30
35
300 400 500
Jsc
(m
A/c
m2)
Averaged nc-Si Volume (nm3/nm2)
The "Varying L with Altered Ag (H:d) in t=300nm" Study
(300:300) AZO (300:300) Ag
28
30
32
34
400 500 600
Jsc
(m
A/c
m2)
Averaged nc-Si Volume (nm3/nm2)
The "Variation in Nanocone Material" Study
AZO Cone Ag Cone nc-Si Cone
84
Appendix F: Model Details and Performance Results
Planar Study
Table E-1: The variation from red to green shows the transition from an undesired to a desired value,
respectively, for each performance metric. All planar models were assumed to have the same 10nm of top AZO
and 30nm of bottom AZO to mimic the material layer thicknesses seen in the LCCM studies.
Top AZO (nm) Bottom AZO (nm)
10 30
t (nm) Jsc (mA/cm2) US$/Wcell
200 7.7 0.068
300 9.8 0.057
400 11.5 0.052
500 12.4 0.052
600 13.2 0.052
700 14 0.051
800 15.1 0.050
900 15.8 0.051
1000 16.3 0.052
2000 19.9 0.062
3000 22.3 0.074
4000 24.1 0.085
5000 25.1 0.097
6000 26.5 0.107
7000 27.1 0.120
8000 28 0.130
9000 28.5 0.142
10000 28.9 0.154
20000 32.1 0.263
30000 33.3 0.374
40000 34.4 0.478
50000 35 0.584
60000 35.9 0.681
70000 36.5 0.780
80000 36.8 0.882
90000 37 0.985
100000 37.1 1.091
85
LCCM L-t Study
Table E-2: The variation from red to green shows the transition from an undesired to a desired value,
respectively, for each performance metric. All models in this study have AZO nanocones. The original R*
definition is used in these models but is accurate since the original (H:d) is also used.
t (nm) (H:d) Top/Bottom
AZO (nm) t (nm) (H:d)
Top/Bottom
AZO (nm) t (nm) (H:d)
Top/Bottom
AZO (nm)
200 (550:100) 10/30 300 (550:100) 10/30 400 (550:100) 10/30
L (nm) Jsc (mA/cm2) US$/Wcell L (nm) Jsc (mA/cm2) US$/Wcell L (nm) Jsc (mA/cm2) US$/Wcell
200 23.5 0.037 200 20.2 0.045 200 19.3 0.049
250 26.8 0.030 400 28.9 0.028 400 23.5 0.036
300 30.2 0.026 450 30.4 0.026 450 25.8 0.032
350 29.9 0.027 500 29.7 0.026 500 27.6 0.030
380 29.3 0.027 525 31.5 0.025 550 31.2 0.026
400 29.2 0.026 550 32.5 0.024 600 31.2 0.027
450 29 0.024 570 32.3 0.024 650 31.1 0.026
500 29 0.023 600 32.6 0.023 700 32.4 0.025
550 29.5 0.022 650 32.3 0.022 750 34.1 0.023
600 27.8 0.023 700 30.7 0.023 770 33.2 0.024
800 25.6 0.023 750 30.7 0.022 800 32.6 0.024
800 29.8 0.022 850 32.7 0.023
1000 28.6 0.022 900 32.3 0.023
1200 25.6 0.024 950 32.6 0.022
1000 32.5 0.022
1200 31.2 0.022
t (nm) (H:d) Top/Bottom
AZO (nm) t (nm) (H:d)
Top/Bottom
AZO (nm)
500 (550:100) 10/30 600 (550:100) 10/30
L (nm) Jsc (mA/cm2) US$/Wcell L (nm) Jsc (mA/cm2) US$/Wcell t (nm) R* (nm)
200 19.2 0.051 200 20.2 0.051
200 180
400 21.9 0.040 400 21.4 0.043
300 275
600 29.6 0.029 600 26.2 0.034
400 375
650 30.5 0.028 800 31 0.028
500 450
700 30.8 0.027 1000 34.7 0.025
600 550
750 32.3 0.026 1050 33.9 0.025
800 33.5 0.025 1100 35.5 0.024
850 33.4 0.025 1120 34.8 0.024
900 33.2 0.025 1150 34.2 0.024
920 32.3 0.025 1200 34.8 0.024
950 32.5 0.025 1300 34.2 0.023
1000 33.6 0.023 1400 34.8 0.022
1050 33.8 0.023
1100 33 0.023
1150 34.3 0.022
1200 33.2 0.022
1300 33.1 0.022
1400 31.4 0.023
86
LCCM Varying (H:d) Studies
Table E-3: The variation from red to green shows the transition from an undesired to a desired value,
respectively, for each performance metric. The R*=R*a + R*b definition was used for these models. R*a and
R*b are given for each aspect ratio variation. Note that when H is smaller than t, the original R* definition does
not require alteration.
AZO Nanocone AZO Nanocone
t
(nm)
L
(nm)
Top/Bottom
AZO (nm)
R*a
(nm)
t
(nm)
L
(nm)
Top/Bottom
AZO (nm)
R*a
(nm)
300 800 10/30 252.3 600 1100 10/30 550
(H:d) Jsc
(mA/cm2)
US$/
Wcell
R*b
(nm) (H:d)
Jsc
(mA/cm2)
US$/
Wcell
R*b
(nm)
(550:100) 29.8 0.022 22.7 (550:100) 35.5 0.024 0
(500:400) 30.7 0.026 80.0 (500:400) 34.4 0.026 0
(500:350) 31.4 0.024 70 (500:350) 34.0 0.026 0
(500:300) 30.8 0.024 60 (500:300) 34.0 0.025 0
(400:400) 30.9 0.024 50 (400:400) 33.7 0.025 0
(400:350) 31.3 0.023 43.8 (400:350) 33.5 0.025 0
(400:300) 31.9 0.022 37.5 (400:300) 33.3 0.025 0
(300:400) 29.8 0.023 0 (300:400) 32.6 0.025 0
(300:350) 30.7 0.021 0 (300:350) 32.5 0.024 0
(300:300) 30.2 0.021 0 (300:300) 33.3 0.024 0
AZO Nanocone Ag Nanocone
t
(nm)
L
(nm)
Top/Bottom
AZO (nm)
R*a
(nm)
t
(nm)
L
(nm)
Top/Bottom
AZO (nm)
R*a
(nm)
300 800 10/5 252.3 300 800 10/5 252.3
(H:d) Jsc
(mA/cm2)
US$/
Wcell
R*b
(nm) (H:d)
Jsc
(mA/cm2)
US$/
Wcell
R*b
(nm)
(500:400) 31.4 0.023 80 (500:400) 28.4 0.028 80
(500:350) 31.7 0.021 70 (500:350) 28.6 0.026 70
(500:300) 31.7 0.020 60 (500:300) 28.0 0.025 60
(400:400) 31.3 0.021 50 (400:400) 29.7 0.024 50
(400:350) 31.8 0.020 43.8 (400:350) 28.8 0.024 43.8
(400:300) 31.8 0.019 37.5 (400:300) 28.4 0.023 37.5
(300:400) 30.8 0.019 0 (300:400) 27.5 0.023 0
(300:350) 29.7 0.019 0 (300:350) 27.1 0.023 0
(300:300) 29.4 0.019 0 (300:300) 27.5 0.021 0
87
LCCM Varying L at (H:d) Studies
Table E-4: The variation from red to green shows the transition from an undesired to a desired value,
respectively, for each performance metric. Please see previous page for R*a and R*b for each model.
AZO Nanocone AZO Nanocone
t (nm) (H:d) Top/Bottom
AZO (nm) t (nm) (H:d)
Top/Bottom
AZO (nm)
300 (400:300) 10/30 300 (300:350) 10/30
L (nm) Jsc
(mA/cm2) US$/Wcell L (nm)
Jsc
(mA/cm2)
US$/
Wcell
300 21.2 0.053 400 25.3 0.039
400 25.3 0.039 600 29.6 0.025
600 30.6 0.026 800 30.7 0.021
800 31.9 0.022 1000 27.9 0.022
1000 29.9 0.021
AZO Nanocone Ag Nanocone
t (nm) (H:d) Top/Bottom
AZO (nm) t (nm) (H:d)
Top/Bottom
AZO (nm)
300 (300:300) 10/5 300 (300:300) 10/5
L (nm) Jsc
(mA/cm2) US$/Wcell L (nm)
Jsc
(mA/cm2) US$/Wcell
300 21.7 0.051 300 20.6 0.043
410 25.1 0.038 410 25.5 0.033
525 28.2 0.026 525 30.7 0.022
600 29.1 0.025 600 29.2 0.021
800 27.5 0.021 800 29.4 0.017
1000 25.8 0.021 1000 26.9 0.020
1200 22.9 0.023 1200 24.9 0.021
88
LCCM Nanocone Material Study
Table E-5: The variation from red to green shows the transition from an undesired to a desired value,
respectively, for each performance metric. Original R* definition was used for these models (R* = 275nm)
rather than more accurate R*=R*a + R*b. The bottom AZO layer in the Ag and nc-Si nanocone models is only a
flat 30nm film beneath the nanocones, not a conformal layer over the cones.
AZO Nanocone Ag Nanocone nc-Si Nanocone
t (nm) L (nm) Top/Bottom
AZO (nm) t (nm) L (nm)
Top/Bottom
AZO (nm) t (nm) L (nm)
Top/Bottom
AZO (nm)
300 600 10/30 300 600 10/30 300 600 10/30
H
(nm)
Jsc
(mA/cm2)
US$/
Wcell
H
(nm)
Jsc
(mA/cm2)
US$/
Wcell
H
(nm)
Jsc
(mA/cm2)
US$/
Wcell
550 32.6 0.020 550 31.3 0.023 550 32.6 0.022
500 32.5 0.022 500 31.0 0.023 500 31.9 0.022
450 31.7 0.022 450 30.6 0.023 450 32.4 0.022
400 31.6 0.022 400 29.9 0.023 400 31.4 0.022
350 29.9 0.023 350 29.5 0.023 350 30.3 0.022
300 29.5 0.022 300 28.7 0.023 300 29.0 0.022
89
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