Selectively Transparent and Conducting Photonic Crystals and their Potential to Enhance the

Performance of Thin-Film Silicon-Based Photovoltaics and Other Optoelectronic Devices

By

Paul G. OBrien

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

Graduate Department of the Faculty of Materials Science and Engineering, University of Toronto

Copyright 2011 by Paul G. OBrien

ii

Selectively Transparent and Conducting Photonic Crystals and their Potential to Enhance the Performance of Thin-Film Silicon-Based Photovoltaics and Other

Optoelectronic Devices

Doctorate of Philosophy (2011)

Paul G. OBrien

Graduate Department of the Faculty of Materials Science and Engineering, University of Toronto

Abstract

The byproducts of human engineered energy production are increasing atmospheric CO2

concentrations well above their natural levels and accompanied continual decline in the natural

reserves of fossil fuels necessitates the development of green energy alternatives. Solar energy is

attractive because it is abundant, can be produced in remote locations and consumed on site.

Specifically, thin-film silicon-based photovoltaic (PV) solar cells have numerous inherent

advantages including their availability, non-toxicity, and they are relatively inexpensive.

However, their low-cost and electrical performance depends on reducing their thickness to as

great an extent as possible. This is problematic because their thickness is much less than their

absorption length. Consequently, enhanced light trapping schemes must be incorporated into

these devices. Herein, a transparent and conducting photonic crystal (PC) intermediate reflector

(IR), integrated into the rear side of the cell and serving the dual function as a back-reflector and

a spectral splitter, is identified as a promising method of boosting the performance of thin-film

iii

silicon-based PV. To this end a novel class of PCs, namely selectively transparent and

conducting photonic crystals (STCPC), is invented. These STCPCs are a significant advance

over existing 1D PCs because they combine intense wavelength selective broadband reflectance

with the transmissive and conductive properties of sputtered ITO. For example, STCPCs are

made to exhibit Bragg-reflectance peaks in the visible spectrum of 95% reflectivity and have a

full width at half maximum that is greater than 200nm. At the same time, the average

transmittance of these STCPCs is greater than 80% over the visible spectrum that is outside their

stop-gap. Using wave-optics analysis, it is shown that STCPC intermediate reflectors increase

the current generated in micromorph cells by 18%. In comparison, the more conventional IR

comprised of a single homogeneous transparent conducting oxide film increases the current

generated in the same cell by just 8%. Moreover, the benefit of using STCPC IRs in building

integrated photovoltaics is also presented.

iv

Acknowledgements

I extend my gratitude to Professor Kherani for giving me the opportunity to work under

his supervision and thank him for all the inspiration and guidance he has provided. I

acknowledge and extend my appreciation to Professor Ozin for collaborative support and insight.

I would like to thank Dr. Alongkarn Chutinan for his invaluable insight about photonic

crystals. Without his knowledge and assistance in modeling thin-film solar cells integrated with

photonic crystal structures this work would not have been possible. I would also like to express

my gratitude towards Keith Leong, Dr. Davit Yeghikyan, and Dr. Tome Kosteski for sharing

their knowledge and experience in the laboratory. I would also like to thank Danny Puzzo for

insights regarding nanoparticle films. I am also grateful to the University of Toronto, the Department of Materials Science and

Engineering, Natural Sciences and Engineering Research Council of Canada, Ontario Centres of

Excellence, and the Ontario Research Fund Research Excellence, a tripartite program, for their

financial support.

v

Table of Contents

Ch 1 Introduction: Photonic crystal thin-film silicon-based solar cells for a better Anthropocene................................................1

Ch 2 Photonic crystal background theory.............................. 9 2.1 A brief introduction to photonic crystals................................................. 9 2.2 Opaline photonic crystals......................................................................... 13 2.3 Confining light at photonic crystal surfaces............................................ 16

Ch 3 Utilizing photonic crystals to enhance light trapping in thin-film silicon-based photovoltaics...... 18

3.1 General light trapping strategies used for crystalline silicon solar cells.. 19 3.1.1 Anti-reflection coatings............. 19 3.1.2 Randomly texturing crystalline silicon solar cells................................. 20

3.2 Light trapping strategies for thin-film a-Si:H cells.................................. 25 3.2.1 Integrating photonic crystals at the front surface of thin-film cells to enhance

light in-coupling..................... 29

3.2.2 Periodically structuring the active region of thin-film cells to strategically tailor their photonic density of states..................................................... 31

3.2.3 Minimizing parasitic absorption losses in thin-film cells by structuring their rear contacts in the form of a photonic crystal..

34

3.3 Photonic crystal rear-contacts that function as solar spectrum splitters... 36

Ch 4 Investigating certain photonic crystal intermediate reflectors for micromorph solar cells. 40

4.1 Modeling details for micromorph cells with certain intermediate reflectors............................................................................... 42

4.2 A single ZnO film functioning as the intermediate reflector.................... 48 4.3 A Bragg-reflector functioning as the intermediate reflector.................... 49 4.4 An inverted ZnO opal photonic crystal functioning as the intermediate

reflector..................................................................................................... 52

4.5 Intermediate reflector performance as a function of incident angle......... 54

vi

4.6 Performance of the intermediate reflectors as a function of the upper a-Si:H cell thickness.................................................................................... 56

4.7 Concluding remarks about the intermediate reflector photonic crystal structures investigated herein............................................................... 59

Ch 5 Selectively transparent and conducting photonic crystals... 62 5.1 Fabrication of selectively transparent and conducting photonic crystals. 63 5.2 Optical properties of selectively transparent and conducting photonic

crystals...... 66 5.3 Electrical properties of selectively transparent and conducting photonic

crystals...................... 75

Ch 6 Silica nanoparticle based selectively transparent and conducting photonic crystals for intermediate reflectors in micromorph solar cells.79

6.1 Fabrication of silica nanoparticle based selectively transparent and conducting photonic crystals.................................................................... 80

6.2 Infiltration of ITO into silica nanoparticle films............................. 86 6.3 Comparing selectively transparent and conducting photonic crystals

comprised of ATO and SiO2 nanoparticle films... 89 6.4 Optical characterization of SiO2 nanoparticle based selectively

transparent and conducting photonic crystals....88 6.5 Electrical and optical properties of selectively transparent and

conducting photonic crystals prepared at lower temperatures.. 91 6.6 Enhancing the pass-band transmission of selectively transparent and

conducting photonic crystals 96 6.7 Optical performance of selectively transparent and conducting photonic

crystals as intermediate reflectors in micromorph cells.... 100

vii

Ch 7 Selectively transparent and conducting photonic crystals for building integrated photovoltaic applications......... 105

7.1 Modeling details for a-Si:H cells with selectively transparent and conducting photonic crystal rear contacts for building integrated photovoltaic applications.......................................................................... 108

7.2 Performance of a-Si:H cells with STCPC rear contacts for BIPV applications... 113

7.3 Designing BIPV panels with STCPC rear contacts.. 117

7.4 Experimental results towards BIPV panels with STCPC rear contacts120

Ch 8 Novel mesoporous transparent and conducting nanocomposite films and their use as building-blocks to fabricate entirely mesoporous selectively transparent and conducting photonic crystals.. 125

8.1 Fabrication of mesoporous transparent and conducting films... 128

8.2 Optical Properties of mesoporous transparent and conducting films... 132

8.3 Electrical properties of mesoporous transparent and conducting films 135

8.4 Entirely mesoporous STCPCs.. 136

Ch 9 Concluding comments and future outlook. 1399.1 Summary... 139 9.2 Future work ..142

9.2.1 Structuring selectively transparent and conducting photonic crystals in a variety of different forms...

142

9.2.2 Fabricating STCPCs from a variety of different materials 143 9.2.3 Other potential applications of selectively transparent and conducting

photonic crystals.144

List of Publications and Other Contributions 147

References.. 149

viii

List of Acronyms

1D one-dimension(al) 2D two-dimension(al) 3D three-dimension(al) AFM atomic force microscopy ALD atomic layer deposition AR anti-reflection coating a-Si:H hydrogenated amorphous silicon ATO antinomy-tin oxide BIPV building integrated photovoltaics c-Si crystalline silicon DSC dye-sensitized solar cell EISA evaporation-induced self-assembly EL electroluminescent FCC face-centered cubic FWHM full-width at half-maximum IR intermediate reflector ITO indium-tin oxide MOCVD metallorganic chemical vapour deposition OLED organic light emitting diode OPV organic photovoltaics PBG photonic band-gap PC photonic crystal PG Porous glass PIR parallel interface refraction PV photovoltaic PV/T photovoltaic-thermal RF radio-frequency SOIR ultra-violet STCPC quantum efficiency TOF-SIMS time-of-flight secondary-ion mass-spectroscopy TCO transparent conducting oxide TIR total internal reflection

c-Si micro-crystalline silicon

ix

List of Figures

Figure 1.1 The AM1.5 solar spectrum and absorption length for silicon........................... 7

Figure 2.1 An example of a 1D, a 2D and a 3D photonic crystal........................... 9

Figure 2.2 Frequency versus wavevector in a homogeneous medium......... 10

Figure 2.3 Electromagnetic waves at the stop-gap band edges in a 1D PC............................ 11

Figure 2.4 Yablonovite, the first experimentally demonstrated PC with a complete PBG.................... 13

Figure 2.5 Fabrication of an opaline photonic crystal.........................13

Figure 2.6 The photonic band diagram of an opaline photonic crystal...15

Figure 2.7 The internal [110] facet of a silicon inverse opal.. 16

Figure 2.8 Surface states in a 1D PC...16

Figure 3.1 Using ARCs to reduce Fresnel reflection from a c-Si wafer............................. 19

Figure 3.2 Light trapping behavior in textured c-Si wafers.... 21

Figure 3.3 Dielectric profile of a textured surface approximating a graded index coating.................... 22

Figure 3.4 Light trapping in c-Si wafers with grated surfaces....... 24

Figure 3.5 Light behavior in a thin homogeneous Si slab...................... 27

Figure 3.6 Light behavior in a thin homogeneous Si slab with a shallow grating.............................. 30

Figure 3.7 Light behavior in a thin homogeneous Si slab with a deep grating.............................. 32

Figure 3.8 Light behavior in a thin homogeneous Si slab coupled to an opaline PC. 35

Figure 4.1 The ideal partitioning of the AM1.5 solar spectrum into a micromorph cell........................ 41

Figure 4.2 2D representation of modeled structures within the micromorph cell...... 44

Figure 4.3 Indices of refraction and extinction coefficients for the ZnO, a-Si:H and c-Si:H used to perform the calculations in Chapter Four..........

45

Figure 4.4 Schematic diagram and performance of a micromorph cell with a homogeneous ZnO film functioning as its IR ..

48

Figure 4.5 Schematic diagram and performance of a micromorph cell with a Bragg-reflector comprised of alternating layers of c-Si:H and ZnO functioning as its IR...

51

Figure 4.6 Schematic diagram and performance of a micromorph cell with an inverted ZnO opal functioning as its IR...

53

Figure 4.7 Current generated in various micromorph cell structures as a function of the incident angle of the solar irradiance......

55

x

Figure 4.8 Performance of micromorph cells with various different IRs as a function of the upper a-Si:H cell thickness.........

58

Figure 5.1 A cross-sectional SEM image of a 1D STCPC. 64

Figure 5.2 The reflectance and transmittance from a set of 1D STCPCs... 66

Figure 5.3 Reflectance spectra of a green, a yellow and a red 1D STCPCs ...... 68

Figure 5.4 An optical micrograph exemplifying the quality of a 1D STCPC.68

Figure 5.5 Ellipsometry measurements performed on a 1D STCPC...... 70

Figure 5.6 The index refraction of the ATO and ITO reference films compared to the effective index of refraction of the ATO and ITO layers within 1D STCPCs... 71

Figure 5.7 SEM images comparing STCPCs comprised of ITO layers of different thicknesses....... 73

Figure 5.8 Water adsorption isotherm of an ATO nanoparticle film...... 76

Figure 5.9 The sheet resistance of various 1D STCPCs plotted alongside that of certain reference films... 76

Figure 6.1 TOF-SIMS analysis of ITO interpenetration and diffusion into silica nanoparticle films 85

Figure 6.2 XRD patterns of ITO films annealed at different temperatures.86

Figure 6.3 A comparison of STCPCs comprised of ATO and SiO2 nanoparticle films. 88

Figure 6.4 SEM cross-sectional images of STCPCs comprised of SiO2 nanoparticle films and their reflection and transmission spectra89

Figure 6.5 Comparison of the optical and electrical properties of STCPCs that underwent annealing at different temperatures....

91

Figure 6.6 Comparison of the optical properties of SiO2 nanoparticle and sputtered ITO reference films annealed at different temperatures and of the measured and modeled reflection of STCPCs comprised of SiO2 nanoparticle films ...........................................................

93

Figure 6.7 Water adsorption isotherms and AFM images for SiO2 nanoparticle reference films.. 94

Figure 6.8 Cross-sectional SEM images and transmission spectra of silica based STCPCs with different stacking sequences. 99

Figure 6.9 Schematic diagram of the modeled micromorph cell incorporating a STCPC IR and its optical performance...

102

Figure 7.1 Schematic diagram of the a-Si:H superstrate cells modeled for BIPV applications. 109

Figure 7.2 Index of refraction and extinction coefficient for the a-Si:H films deposited onto the STCPC rear contacts.. 112

Figure 7.3 The transmitted power and current generated as a function of texture height for certain a-Si:H cell configurations considered for BIPV applications...114

xi

Figure 7.4 Contour plots of the photo-induced current density, the transmitted solar irradiance and the transmitted solar lumens for a-Si:H cells with STCPC rear reflectors as a function of their texture height and the Bragg-peak positions of the STCPCs

115

Figure 7.5 The absorption spectra for the various a-Si:H cell configurations considered for BIPV applications

116

Figure 7.6 The solar photon flux and solar lumens transmitted through the various a-Si:H cell configurations considered for BIPV applications..

117

Figure 7.7 Transmittance measurements of the solar photon flux and solar lumens transmitted through a-Si:H films with STCPC rear contacts

121

Figure 7.8 A coin photographed through STCPCs with differing Bragg-peak positions... 122

Figure 8.1 SEM images and TOF-SIMS depth profiling of mesoporous nanocomposite films.131

Figure 8.2 SEM image of a silica nanoparticle film with 10nm of ITO deposited onto its surface 132

Figure 8.2 The transmittance spectra of mesoporous nanocomposite films... 134

Figure 8.3 Resistance measurements for mesoporous nanocomposite films...... 135

Figure 8.4 A cross-sectional SEM image of an entirely nanoporous STCPC comprised of five alternating bi-layers of SiO2 and TiO2 nanoparticle films... 137

Figure 8.5 Reflection and transmission spectra of an entirely mesoporous STCPC.. 137

Figure 9.1 Schematic diagram of the expected 3D STCPC structures... 143

Figure 9.2 A schematic diagram of an OLED device with an STCPC anode.....146

xii

List of Tables

4-1 The current generated in the a-Si:H and c-Si:H cells within micromorph cells with different IRs and the corresponding current losses due to reflection and parasitic absorption occurring in the IR .. 53

4-2 The incident angle of the solar irradiance at which micromorph cells with different IRs become bottom limited and the corresponding generated current 56

4-3 The thickness of the upper a-Si:H cell at which micromorph cells with different IRs become bottom limited and the corresponding generated current ... 58

7-1 Summary of results for the optimal cases of the various cell configurations considered as well as the design case. 119

7-2 Experimentally measured transmitted power and lumens through 100nm thick a-Si:H films with different rear contacts.. 121

8-1 Resistivity of mesoporous nanocomposite films. 136

1

Chapter One

Introduction: Photonic crystal thin-film silicon-based solar cells for a better Anthropocene

Humanity is now entering the Anthropocene, and is inevitably losing its grasp on the

comforts of the Holocene. During the Holocene, the warm interglacial period that extended over

the last ten to twelve millennia, the earth regulated its own climate conditions which were

favorable for terrestrial life to flourish. In the present day Anthropocene, which commenced

with the industrial revolution, human activities are the cause of the major factors that drive

changes in the global environment.1 Crutzen states that in the Anthropocene we are largely

treading on terra incognita meaning that humanity does not know what climatic changes their

actions will bring forth. A current endeavor to keep the global environment of the Anthropocene

similar to that of the Holocene has scientists attempting to identify a set of planetary

boundaries that define acceptable limits of human induced climatic changes.2 Thus far, at least

nine categories have been identified that require planetary boundaries, some of which include

stratospheric ozone depletion, ocean acidification, global fresh-water use, and change in land

use. As a specific example, it has been proposed that changes in atmospheric CO2 concentrations

should not be permitted to exceed 350 parts per million by volume. The current atmospheric CO2

concentration is 387 p.p.m.v., signaling an immediate need to curb human CO2 emissions.

The byproducts of human energy production are the major factors pushing the

atmospheric CO2 concentration as well as other climatic metrics beyond their planetary

boundaries. For example, energy related activities accounted for 86.7% of the total greenhouse

2

gas emissions in the U.S. during 2009 and 81% of these greenhouse gas emissions was CO2.3

These statistics on greenhouse gas emissions are more or less comparable throughout the rest of

the world and the climate over the course of the Anthropocene will be determined by how

humans produce their energy.

To maintain the current favorable climate, humanity must adopt renewable forms of

power such as wind, solar and geothermal energy. Of these green energy alternatives solar

energy is an attractive option because it is abundant, can be produced in remote locations and,

since it can be consumed when and where it is produced, energy storage and transportation costs

are often avoided. Although solar power cannot be produced incessantly its availability often

coincides with human energy demands; the greatest amount of power is required during midday

when the solar radiance is the most intense. Furthermore, photovoltaic equipment is easy to

install, requires little maintenance and operates silently. However, the biggest disadvantage

preventing widespread use of electrical power generated from photovoltaic cells is its high cost.

For decades the photovoltaics (PV) industry has preached about the holy grail of "Grid

parity", which refers to the point when the decreasing cost of solar power becomes equal to that

of power derived from fossil fuels. As the story goes, upon reaching grid parity rooftops

everywhere will be covered with PV panels and fortunes will be made as the smoggy skies begin

to clear. However, grid parity has already been achieved, at least in certain places and at certain

times. For example, in Hawaii the cost of diesel generated electricity approaches US$0.30/kWh

and, given the sunny climate, PV arrays often provide the most economical power. Moreover,

other locations such as Italy, Spain, Australia, Germany, Japan, and certain states in Southern

U.S. are expected to reach grid parity within the next five years. Nonetheless, in five years PV

will not be the primary source of electrical power in any of these regions.

3

As we arrive at the point of grid parity it becomes increasingly clear that it is the not the

holy grail it was originally claimed to be. Some argue that calling grid parity the holy grail was

nothing more than a single-minded idea, yet a necessary one designed to focus widespread

efforts on the noble task of producing more efficient and inexpensive photovoltaic systems.

Others propose a new holy grail, stating that widespread PV electric power generation will be

unshackled when energy storage methods, such as lithium-ion batteries and other alternatives,

are improved.4 Still others argue that grid parity is a fallacy since it is based on a comparison

between energy produced from photovoltaic panels and fossil fuels, but does not consider the

negative externalities associated with fossil fuels such as smog, acid rain and climate change.5

But perhaps the best explanation comes from Dr. Narayanan, who describes grid parity as a

wave that breaks across markets over time, with the potential for surges and retreats.6

Although grid parity is an excellent achievement it is not a resting place or the final destination

for the PV industry. Instead, we are at a point when grid parity will come and go as material

costs, consumer electric rates, and the weather fluctuate.

The wave analogy of grid parity captures the diversity of the human energy

consumption problem. We depend on different forms of energy for tasks such as heating,

lighting, and a variety of other domestic and industrial applications. We also require energy in

different spaces such as remote locations and in transport. The PV market strives to respond to

the diverse nature of human energy usage with a range of different products.

The PV market is currently dominated by crystalline silicon based PV cells, which are

classified according to whether they are monocrystalline or multicrystalline. These cells have the

highest conversion efficiencies and are the best choice when space is limited, which is often the

case for rooftop installations. For example, SunPower Corporation, a leading manufacturer of

4

monocrystalline silicon photovoltaics, has reported a minimum efficiency rate of 22%. Also, JA

Solar has recently developed multi-crystalline solar cells with a conversion efficiency of 18.2%,

and commercial production of these cells will commence in the second half of 2011. However,

the drawback of these cells is their high costs and during the mid 2000s there was a polysilicon

bottleneck that reduced the supply of crystalline silicon solar cells causing prices to inflate even

higher. At this time, major investments and entrepreneurial activities were directed towards thin-

film solar cells. In fact, the thin-film market share rose from 5% in 2002 to 17% in 2009 and is

expected to make up as much as 25% in the near future.7 The mainstream types of thin-film PV

cells are cadmium telluride (CdTe), copper indium gallium (di)selenide (CIGS), hydrogenated

amorphous (a-Si:H) and microcrystalline ( c-Si:H) silicon, as well as organic photovoltaics

(OPV) and dye-sensitized solar cells (DSC).

Currently, the largest thin-film PV manufacturer is CdTe producer First Solar, who

generated over 1.1 GW in 2009 at an industry leading cost of 83 cents per Watt (at the complete

panel level). Moving forward, limited availability of tellurium may cause prices to increase,

however this may be offset by further thinning of CdTe cells down to 2 2.5nm.8 CIGS

producers have encountered technical issues in manufacturing but are expected to show an

exponential improvement in costs from 2010 to 2012 due to the commercialization of high-

throughput roll-to-roll processes and may reach costs as low as 80 cents per Watt. Other than

First Solar, the only thin-film company to produce more than 100MW annually is United Solar,

who manufactures triple-junction amorphous silicon cells. However, by 2012 silicon tandem

junctions are expected to generate electric power at a cost of $0.80 to $1.20 per Watt and will be

more representative of the thin-film silicon market. OPV and DSC technologies offering low-

cost, high-volume roll-to-roll production are just beginning to move towards commercialization.

5

However, their low conversion efficiencies and poor longevity will prevent them from entering

the mainstream PV markets. Instead, in order for these technologies to succeed, they must carve

out their own niche PV applications. For example, on account of their transparent properties,

they could be integrated into architectural glass to serve as building integrated photovoltaic

(BIPV) panels. In summary, it is predicted that the world-wide annual production for thin-film

PV will exceed 10 GW by the end of 2012. Of this 2.47 GW and 2.11 GW will be CdTe and

CIGS based cells, respectively, while the majority will be comprised of 5.65GW of silicon-based

cells. More details pertaining to amorphous and microcrystalline silicon cells are provided

below.

Thin-film Silicon (Si) based photovoltaics (PV) is a compelling material choice given its

non-toxicity, its relative abundance, its technological mature state, and its amenability to large

scale terrestrial applications. PV cells wherein the active region is a-Si:H have the advantage of

a high optical absorption coefficient as well as the possibility of large-area Si-diode deposition at

low temperatures (T ~ 200C). However, the thickness of the a-Si:H cells must be kept to a

minimum, typically less than 300nm and preferably much lower, in order to mitigate the effects

of light induced degradation by means of the Staebler-Wronski effect,9 and to ensure a large

internal electric field.10 PV cells made from c-Si:H can also be deposited at low temperatures,

and their typical thickness of ~2 m or less is not limited by the Staebler-Wronski effect,

however it is also desirable to keep these cells as thin as possible to avoid lengthy deposition

times. Thus, in order to maximize the efficiency of a-Si:H cells and to minimize the costs of c-

Si:H cells they must be made as thin as possible. However, as these cells are thinned the portion

of the solar irradiance they absorb decreases.

6

The ASTM AM1.5 (Global tilt) solar spectrum is plotted in Figure 1.1(a).11 The

absorption edge of amorphous silicon varies depending on the deposition conditions but is often

in the vicinity of 1.7 eV, or 730nm. Thus, a-Si:H cells can potentially absorb all the solar

photons in the yellow shaded area shown in Figure 1.1(a). Similarly, the absorption edge of c-

Si:H is approximately 1.1 eV, or 1130nm and these cells have the potential to absorb solar

photons in either both the yellow and red shaded area shown in Figure 1.1(a). The less energetic

portion of the solar irradiance with wavelengths greater than 1130nm, that is the spectral region

shaded in light orange in Figure 1.1(a), are not absorbed in thin-film Si-based solar cells and do

not contribute to the output current.

The absorption length, defined as the distance into a material at which the probability that

a photon has been absorbed is 1/e (or ~37%), is plotted for c-Si, an indirect gap material, and a-Si, a direct-gap-like material, as a function of wavelength in Figures 1.1(b) and 1.1(c),

respectively. Here it can be noted that the absorption length of c-Si:H may be approximated by

assuming a two-phase mixture with appropriate volume fractions of a-Si:H and c-Si.12 In

comparing the plots shown within Figure 1.1 it is apparent that the absorption length for both a-

Si and c-Si is much greater than their corresponding cell thicknesses in the spectral region just

above their absorption edge. For example, the absorption length for a-Si for photons of

wavelength slightly greater than 700nm is over 500nm while cell thicknesses must be kept less

than 300nm. Also, the absorption length of c-Si at a wavelength of 1000nm is greater than

100 m which is 50 times greater than the aforementioned cell thickness of ~2 m. In order to achieve high levels of absorption in the thin-film silicon PV cells enhanced light-trapping

schemes must be implemented. One possibility which is the focus of this work may be to use

photonic crystals (PCs).

7

Figure 1.1 (a) the AM1.5 solar spectrum. The absorption length plotted as a function of wavelength for (b) crystalline silicon and (c) amorphous silicon.

PCs are a novel class of materials in which the periodicity of the index of refraction is

engineered to obtain optical properties that have not been achieved in any other type of material.

Some interesting optical phenomena inherent to PCs that could be utilized to enhance light

trapping in thin-film silicon based photovoltaics include photonic band-gaps (PBGs), parallel

interface refraction, and slow photons. Thus, the objective of this thesis is to investigate and

further develop the potential utilization of PC structures to enhance the performance of thin-film

silicon based PV. To this end, the relevant background theory pertaining to PCs is presented in

Chapter Two, while Chapter Three reviews the subject of light-trapping in thin-films in order to

answer the question What is the best way to utilize PCs for the purpose of enhancing the

performance of thin-film Si-based photovoltaics? In this chapter a transparent and conducting

0

200

400

600

800

1000

300 500 700 900 1100AbsorptionLength(m)

Wavelength(nm)

cSi( m)(b)

0

0.2

0.4

0.6

0.8

1

300 400 500 600 700

Absorptio

nLength(m)

Wavelength(nm)

aSi( m)(c)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

280 480 680 880 1080 1280 1480 1680 1880

SpectralIrradian

ceW

m2nm

1

Wavelength(nm)

(a)

8

PC situated at the rear side of the cell serving the dual function of a back-reflector and a spectral

splitter is identified as the potentially most valuable item. For example, a transparent and

conducting PC could serve as a highly effective intermediate reflector in tandem junction cells or

as a back reflector for building integrated photovoltaic (BIPV) panels. In Chapter Four

theoretical calculations are performed to determine which PC structures are most suitable to

serve as an intermediate reflector (IR) in micromorph tandem junction solar cells (the name for

the dual junction micromorph cell comes from the fact that its bottom cell is a microcrystalline Si

solar cell while its top cell is an amorphous Si solar cell). The results indicate that a one-

dimensional PC, or a simple Bragg-reflector, is an excellent starting point to design photonic

crystals that are both transparent and conducting. Chapter Five presents a novel type of PC,

namely selectively transparent and conducting photonic crystals (STCPCs). Chapter Six presents

improved STCPCs and their application as intermediate reflectors in micromorph solar cells. The

utilization of STCPC rear contacts in thin-film silicon-based cells for BIPV applications is

presented in Chapter Seven. Chapter Eight presents transparent and conducting mesoporous

nanocomposite films that can potentially be used as AR coatings that block UV light. Moreover,

Chapter Eight also shows how these nanocomposite films can be used to fabricate entirely

mesoporous STCPCs. The conclusions and an outlook towards future work and technologies are

presented in Chapter Nine.

9

Chapter Two

Photonic crystal background theory

The purpose of this chapter is to introduce photonic crystals (PCs) and to provide the

relevant background theory pertaining to PCs. To this end, appropriate examples of PCs are

presented to familiarize the reader with certain attributes that are applicable to the PC structures

investigated herein and their utilization for enhanced light harvesting in thin-film silicon-based

photovoltaics. Specific topics considered in this chapter include opaline photonic crystals

(Section 2.1) and photonic behavior at the surface of PCs (Section 2.2). Although all of the

necessary background required to follow the contents of this thesis is provided in this section, the

description of PCs given here is by no means complete. More information about PCs is available

in the literature.13, 14, 15

2.1 A brief introduction to photonic crystals

A PC is a medium in which the index of refraction is periodic in either one (1D), two

(2D) or three dimensions (3D) as shown in Figure 2.1.16

Figure 2.1 An example of a (a) 1D, (b) 2D and (c) 3D PC.

a b c

10

The invention of the PC is attributed to both Sajeev John and Eli Yablonovitch, who in

1987 independently suggested that a medium with an index of refraction that is periodically

structured in 3D could completely prevent an electromagnetic wave from propagating in any

given direction. John suggested the existence of a range of frequencies over which all photonic

modes are localized in a slightly disordered 3D periodic structure.17, 18 It was suggested that this

range of frequencies is bounded above and below by extended states that can be described by

geometric optics and states that exhibit Rayleigh scattering, respectively. Yablonovitch

suggested that 3D periodic structures that completely inhibit photon propagation over a range of

frequencies that overlaps the electronic band edge could be used to inhibit spontaneous photon

emission in direct band-gap semiconductors.19 The ability to inhibit photon propagation for the

simplest case of the one-dimensional PC is presented subsequently with a discussion that follows

that by Joannopoulos.15

The frequency, , associated with an electromagnetic wave in a homogeneous medium

varies inversely with its wavelength as shown in Figure 2.2.

Figure 2.2 Frequency, , versus wavevector, |k|=2/ where is the wavelength, in a homogeneous medium.

/a /ak

k

11

However, introducing a periodic refractive index contrast into a homogeneous medium

creates a discontinuity in the dispersion relation. For example, when the wavelength of an

electromagnetic wave is at a critical value, namely twice the periodicity of the PC, it is possible

to shift the wave such that the electric field exists almost entirely in either the medium of high or

low index of refraction as shown in Figure 2.3. In either case the wavevector, k, associated with

the electromagnetic wave is the same, however, when the electric field exists predominantly in

the medium of high index of refraction the energy of the electromagnetic wave is lower than for

the case in which the electromagnetic field resides in the medium of low index of refraction.

Figure 2.3 Two electromagnetic waves with similar wavevectors but different energies in a 1D PC (left). Frequency plotted as a function of wavevector (right). At the critical frequencies, k = +/- /a, the allowed modes are separated by a stop-gap in the normal direction.

For wavevectors in the vicinity of the critical values, k = +/- /a, electric field modes

existing primarily in the medium of high index of refraction, corresponding to a lower field

12

energy, comprise what has been termed the dielectric band. Alternatively, electric field modes

existing predominantly in the medium of low index of refraction, corresponding to higher field

energy, form what is referred to as the air-band. As can be seen in Figure 2.3, propagation of

electromagnetic waves of energy between that of the dielectric band and air-band is forbidden

and this range of energy is referred to as the stop-gap. For the case of a 3D PC, when

propagation is forbidden in all directions, the stop-gap is referred to as a complete photonic band

gap (PBG). Also, the optical features of PCs scale with both their periodicity and the refractive

indices of their constituent materials. Consequently, the size of a PBG is often reported as the

gap to mid-gap ratio, /c, rather than just the actual gap itself, = a - d, where a and d

represent the frequency at the edges of the air band and dielectric band, respectively. This model

is analogous to the electronic band structure of a semiconductor in which the conduction (air)

band is separated from the valence (dielectric) band by an energy gap in which electron (photon)

propagation is forbidden.

The first 3D structure to exhibit a complete PBG is shown in Figure 2.4. This structure,

often referred to as Yablonovite,20 was experimentally demonstrated by Yablonovitch in 1991

and possesses a complete PBG over microwave wavelengths. Yablonovite was fabricated by

drilling a triangular array of holes in a macroscopic piece of stycast-12. At each opening three

holes are drilled at an angle of 35.26 off the normal and at angles which are separated azimuthally by 120.

13

Figure 2.4 The first experimentally demonstrated PC with a complete PBG. This structure has beennamed Yablonovite, after its inventor E. Yablonovitch.20 Copyright American Physical Society.

2.2 Opaline photonic crystals

The opal, which is the most frequent example of a PC found in nature, is an iridescent

gem comprised of silica spheres that exist in a tightly packed structure.21 Opals are best known

for their array of bright colours, which is determined by the size of the silica spheres as well as

the nature of their packing. Herein, PCs with a dielectric periodicity structured in the form of a

3D close-packed array of spheres are referred to as opaline PCs.

Figure 2.5 Fabrication of an opaline PC. (a) An electron micrograph of silica spheres synthesized usingStbers method.23 (b-c) Opaline films are grown onto a glass substrate which is placed in a colloidalsuspension of silica spheres in ethanol. The silica spheres organize into a tightly packed face-centered-cubic (FCC) structure within the meniscus at the ethanol-air interface. As the ethanol evaporates the meniscus descends down the substrate and an opaline PC is grown onto the glass substrate. (d) A cross-sectional electron micrograph of a planar opal made of silica spheres having a diameter of 1m.22

Copyright Elsevier (figure a) and John Wiley and Sons (figures b, c and d).

14

The most common example of an opaline PC is a 3D array of silica spheres that are

close-packed into a face-centered-cubic (FCC) crystal structure.22 To fabricate this opaline PC a

solution of monodisperse silica spheres in ethanol is first prepared using a modified Stber

method.23, 24 The silica spheres are subsequently deposited onto a flat substrate using the vertical

deposition technique.25 The vertical deposition technique is initiated by placing the substrate in

an upright position in the solution containing the silica spheres, as shown in Figure 2.5. As the

ethanol evaporates, silica spheres within the meniscus at the interface between the air and the

solution deposit onto the substrate in a tight packed FCC structure. As the ethanol continues to

evaporate the meniscus line descends down the substrate and eventually the entire substrate is

coated with the opaline PC. The number of layers of silica spheres in this opaline PC is

determined by the concentration of spheres in the initial ethanol solution. That is, the final

number of layers in the opaline PC can be increased by increasing the concentration of spheres in

the initial solution.

The dispersion relation inside an opaline PC comprised of close-packed dielectric spheres

in the [111] and [100] directions is shown in Figure 2.6. Opaline PCs do not possess a full PBG

but, as can be seen in Figure 2.6, there is a small pseudo-gap (/ = 5.5%) between the second

and third photonic bands in the [111] direction. One of the characteristics of opaline PCs

deposited using the vertical deposition method is that the [111] direction in the PC is aligned

with the normal direction of the surface on which the PC is deposited.

15

Figure 2.6 Photonic band diagram of an opaline PC along the -L ([111]) and -K ([110]) directions. and are the sphere diameter and photon wavelength respectively. The small stop-gap, /c = 5.5%, in the [111] direction has been shaded grey.26 Copyright American Chemical Society.

Shortly after their invention the potential utilization of PCs as the infrastructure for

optical circuits was investigated. However, to design efficient optical circuits, PCs having a

complete PBG at near-optical wavelengths were required. Opaline PCs possessing a complete

PBG in this region were first fabricated by Ozin et al.27 Working in conjunction with S. John, by

initially employing a chemical vapour deposition process, using disilane (Si2H6) as a precursor,

the voids in an opaline PC comprised of silica spheres were infiltrated with silicon (Si), and the

silica spheres were subsequently removed using a fluoride-based etching procedure. The

resulting inverted-opal structure, shown in Figure 2.7, has a complete PBG near 1.5m.

16

Figure 2.7 A scanning electron micrograph image of the internal [110] facet of a Si inverse opal.27

Copyright Nature Publishing Group. 2.3 Confining light at photonic crystal Surfaces

Considering that an ideal crystal is a periodic structure extending to infinity in all

directions, the planar surface of a PC can actually be regarded as a 2D crystal defect.

Accordingly, it is interesting to note that as in the case of defects introduced into the bulk of a

PC,28 light can also be localized at the PC surface. For example, electromagnetic waves can

propagate in localized states along the surface of periodically layered media, otherwise referred

to as 1D PCs.29, 30 The amplitude of the electric field associated with these surface states is

understood to exist as a standing wave with an exponentially decaying envelope in the PC and to

decay exponentially in the homogeneous medium outside the PC (see Figure 2.8).

Figure 2.8 Surface states in a 1D PC. The calculated transverse intensity distribution for the fundamental surface mode in a periodic layered medium consisting of 0.5m thick GaAs and AlGaAs layers. The dotted line is the observed intensity distribution.29 Copyright American Institute of Physics.

1m

17

As previously mentioned in Section 2.1 PCs can be designed to possess a photonic stop-gap or a

full PBG, a range of frequencies over which photon propagation is inhibited. This point raises

the question as to what happens when an incident light wave, with a frequency within the

photonic stop-gap of the PC, impinges onto its surface. This question can be answered with

reference to Figure 2.8. In general, photonic states that exhibit exponential decay with distance

from a boundary are referred to as evanescent states. For example, the surface mode for the 1D

PC shown in Figure 2.8 is evanescent in both the PC and the air and is thus confined to the

surface. A photon impinging onto the surface of a PC, with a frequency within its PBG, would

reside in a photonic state that is extended in the ambient medium outside the PC but is

evanescent within the PC. Furthermore, if the PC is comprised of non-absorbing materials then

the light energy in the evanescent photon states will eventually be completely reflected after

traversing some distance through the PC. On the other hand, if the PC is comprised of absorbing

materials than some portion of the light energy coupled into the evanescent states within the PC

will be absorbed. The next chapter of this thesis discusses the potential utilization of PCs to

enhance light trapping in thin-film silicon-based photovoltaic devices.

18

Chapter Three

Utilizing photonic crystals to enhance light trapping in thin-film silicon-based photovoltaics

Utilizing photonic crystals (PCs) to enhance light trapping in thin film photovoltaics (PV)

is a relatively new field wherein the majority of the research has been conducted over the past

few years. The objective of this chapter is to provide a thorough review of the relevant

theoretical and experimental subject matter in order to assess the best research avenue to pursue

in utilizing PCs to enhance the performance of thin film solar cells. More specifically, this

chapter aims to answer the question What is the best way to utilize PCs for the purpose of

enhancing the performance of thin-film Si-based photovoltaics? Also, it is noted that the best

PC-PV integration will not only depend on the enhanced light-trapping performance of the cell

but also on its electrical performance as well as any additional material or fabrication costs.

The theory surrounding light trapping in thin-film Si cells evolved from the study of the

optical behavior in their thicker counterpart, namely crystalline silicon (c-Si) cells. Although the

optical behavior of c-Si cells is analytically simpler and can almost always be described using

ray optics, whereas the optical behavior of thin-film cells requires a wave-optics based analysis,

there are certain similarities that should be elucidated. Thus, this chapter begins with a review of

the light trapping strategies used for c-Si solar cells in order to set the stage for a subsequent

discussion about light-trapping in thin-film Si-based cells. The discussion focuses primarily on

light trapping in hydrogenated amorphous silicon (a-Si:H) cells but also touches on hydrogenated

microcrystalline ( c-Si:H) solar cells.

19

3.1 General light trapping strategies used for c-Si cells 3.1.1 Anti-reflection coatings A simple homogeneous layer

Reflection from the top surface of c-Si solar cells causes a significant loss in their

efficiency. These losses occur because solar radiation arriving from the ambient, having an index

of refraction equal to na = 1, undergoes Fresnel reflection at the surface of the c-Si solar cell. The

index of refraction of c-Si ranges from nc ~ 3.5 in the spectral region just above its absorption edge at 1.1 eV to nc ~ 5 for photons of energy 4eV.31 Fresnel reflection (see Figure 3.1(a)) is consequent of the dielectric discontinuity at the boundary and increases as the dielectric contrast

between the two media increases. An anti-reflection coating (ARC) is commonly deposited on

top of c-Si cells to reduce their reflectance. In its simplest form, an ARC is a homogeneous film

with thickness tar and an intermediate index of refraction nar (see Figure 3.1(b)). In general, as

long as the index of refraction of the ARC is between that of the substrate and the adjacent media

it will reduce the reflectance by easing the dielectric transition. That is, for the case in which

solar radiation is incident onto c-Si solar cells, na < nar < nc.32 Such an ARC can be fabricated to

eliminate the reflectance at a given wavelength, , by setting its thickness to tar = /(4nar), where

nar = na nc)1/2 is the index of refraction of the optimal ARC. This optimized ARC is commonly

known as a quarter-wave stack.

Figure 3.1 Schematic illustration of (a) Fresnel reflection at the front surface of a c-Si wafer (b) a c-Si wafer with an ARC and (c) a c-Si wafer with a graded ARC.

nanar

ns

na

nc

(b) (c)na

nc

(a)

20

A graded index coating

The dielectric transition between two media can be smoothened to a greater extent by

employing a linearly graded ARC (see Figure 3.1(c)). Pertaining to c-Si cells, the index of

refraction of the ARC would be na at the upper surface and increases linearly to nc at the

interface between the ARC and the cell. In this configuration the index of refraction profile is

continuous across the boundary. Moreover, an ARC with a cubic or quintic index profile can

further reduce the reflectance because the refractive index profile is everywhere continuous up to

its first or second derivatives, respectively.33

3.1.2 Randomly texturing crystalline silicon PV Cells

The reflectance from a silicon cell can also be reduced by randomly texturing its surface.

The extent to which the reflectance is reduced depends on the topography and feature size of the

surface texture. Moreover, the nature of the interaction between impinging light and the Si

surface depends on the texture feature size, h, in comparison to the wavelength of the incident

photons, .

Textured features larger than the wavelength of the incident light

C-Si solar cells are commonly textured using an anisotropic wet-etching process. For

example, the etch rate of the Si (111) plane in KOH-based etchants is typically two orders of

magnitude slower than that of the other crystallographic planes.34 In practice, c-Si etched in

KOH-based etchants produces a random pyramidal surface texture wherein the surfaces of these

pyramids are the Si (111) crystallographic planes. The texture feature size of these random

pyramids is typically on the order of a few microns or larger. Thus, in this case the texture

feature size is greater than the wavelength of the impinging solar irradiation and the behavior of

21

the light within the cell can be described using ray-optics. As shown in Figure 3.2(a), incident

light may undergo a double-bounce at a pyramidal surface, where reflected light strikes the

surface a second time, thereby increasing its chance of entering the cell.35 Furthermore, scattered

light entering the cell has a greater chance of being absorbed on account of its increased path

length. Also, light scattered into the cell approaches the rear surface at an off-normal direction

and thus has an increased probability of being reflected and undergoing a double-pass through

the cell (see Figure 3.2(b)).36 The effects of randomly texturing solar cell surfaces have also been

studied theoretically. Specifically, Yablonovitch has used statistical ray optics to calculate an

upper bound of 2n2 on the optical intensity enhancement that can be attained in a dielectric film

with a refractive index of n.37 This upper limit is commonly referred to as the geometric optics

limit or the Yablonovitch limit. The Yablonovitch limit is achieved when the top-side of the cell

is a Lambertian surface, which scatters light isotropically into all directions (see Figure 3.2(c));

an angular integral in 3D gives an average optical path length of twice the film thickness, thus

yielding an optical intensity enhancement factor of 2n2. In the limit of low absorption, and

considering a further enhancement factor of 2 that occurs when the rear-side of the cell is a

perfect reflector, an optical absorption enhancement factor of 4n2 is realized at the Yablonovitch

limit.

Figure 3.2 Schematic illustration of incident light (a) undertaking a double-bounce at the textured c-Si surface (b) undergoing a double-pass through a textured c-Si wafer and (c) being isotroptically scattered into the textured c-Si cell.

Yablonovitch Limit 4nc2

(c)(a)

Doublebounce

(b)

Doublepass

22

Textured features that are small in comparison to the wavelength of the incident light

For the case in which the height of the textured surface features is small compared to the

incident light (i.e. h

23

HAuCl4. Au nanoparticles produced in the solution act as catalysts that etch a nanoporous layer

into the surface of the wafer. This nanoporous region is a few hundred nanometers thick and

functions as a graded ARC. These cells had an NREL confirmed efficiency of 16.8% which is

the highest reported for a Si solar cell without a deposited ARC. However, recombination

occurring in the nonporous layer currently limits the possibility of higher conversion

efficiencies.41 More recently, black Si has been prepared using a novel laser processing

technique.42 The black Si was prepared by exposing a Si wafer to 0.6 mJ pulses from a Ti-

sapphire laser system. The duration and repetition rate of the pulses was 130 fs and 1 kHz,

respectively. By appropriately scanning the laser pulses over the Si wafer a uniform distribution

of silicon nanostructures are formed over its surface. The effective index of refraction of these

nanostructures provides the desired graded index coating and the reflectance of the Si surface is

reduced to less than 3% over the entire solar spectrum. Solar cells with efficiencies in excess of

14% have been fabricated using black Si prepared in this manner.

As described in Section 3.2, alternate methods can be used to achieve textured surfaces

with small feature heights in thin-film Si-based cells such that the dielectric profile at the front

interface approximates a graded ARC.

Periodically texturing crystalline silicon PV Cells

As previously mentioned, wet-etching processes are commonly used to form random

pyramidal structures on the surface of c-Si solar cells. In order to model the performance of these

cells their surfaces are often assumed to be Lambertian. In the limit of weak absorption, and for

a c-Si wafer with an index of refraction n, and a perfect reflector on its rear side, a Lambertian

surface enhances the path length of light by a factor of 4n2 compared to the case of a plane wafer.

It is possible to improve upon this path length enhancement factor of 4n2 over certain specified

24

spectral regions and/or ranges of incident angles by periodically texturing the surfaces of the c-Si

cell. For example, compared to a Lambertian surface, ray optics analysis reveals that the

perpendicular slat configuration shown in Figure 3.4(a) has superior light-trapping

performance for light incident from within 30 to 45 from the normal of the original substrate. 36 Moreover, gratings can be etched into the surfaces of c-Si cells in order diffract weakly absorbed

light into off-normal diffraction orders that propagate in directions almost parallel to the plane of

the wafer (see Figure 3.4(b)). For example, weakly absorbed normally incident light near the

absorption edge of silicon ( = 1100nm) can be strongly diffracted into the planar direction by etching a rectangular grating into the rear side of the c-Si cell with a height and periodicity of

70nm and 610nm, respectively.43 The path length enhancement of light diffracted into these

laterally propagating modes is far greater than 4n2, however it should be noted that this

enhancement occurs only over a small spectral region in the vicinity of 1100nm.

Figure 3.4 Schematic illustration of light trapping in a c-Si wafer with (a) a perpendicular slat texture and (b) a rear-side diffraction grating which also shows the order of diffraction.

Thus, periodic surface textures can be strategically designed to enhance the path length of

light beyond the Lambertian limit of 4n2 over weakly absorbed spectral regions near the Si

25

absorption edge. As discussed in the next sub-section, periodic structuring can also be used to

enhance absorption in thin-film Si cells.

3.2 Light trapping strategies for thin-film a-Si:H cells

Light-trapping schemes are more important and yet less effective in thin-film cells

compared to their thick-film counterparts. In fact, the absorption enhancements in thinner cells

always fall short of the Yablonovitch limit.44 Firstly, in order to achieve Yablonovitchs

enhancement factor of 4n2 incident light must be isotropically scattered such that all the photonic

states in the absorbing medium are filled equally. However, the texture feature size of a

Lambertian surface must be larger than the wavelength of the impinging light. For thin-film a-

Si:H cells, which are typically less than 300nm thick, texturing is achieved by depositing them

onto roughened ZnO films.45 The ZnO film, which also serves as an electrical contact in the cell,

typically has a root-mean-square roughness between 40-150nm. In operation, the nano-rough

interface between the a-Si:H and ZnO diffuse light and also acts as an effective ARC because of

its graded effective refractive index profile. However, due its small feature size, it does not

function as a Lambertian surface that evenly scatters the impinging solar irradiance into the

photonic states within the cell. Moreover, there is a greater degree of light-matter interactions at

the lossy metal contacts in thin-film cells and this increases parasitic absorption.

Besides the aforementioned technical difficulties, Agrawal has recently delineated that

the fundamental reason for the poor performance of light-trapping schemes in thin-film cells is

their reduced density of local photonic states.44 Absorption is a local phenomenon that is

proportional to the local electric field intensity. In turn, the electric field intensity is proportional

to the local density of photonic states and their occupancy. As previously discussed with

26

reference to the Yablonovitch limit, the density of photonic states in a medium of index of

refraction n is n2 times greater than that in the ambient. However, this relation refers to the bulk

density of states. The local density of photonic states46 in thin film cells is significantly reduced

compared to that in bulk media with an equivalent refractive index. For example, the local

density of photonic states in a 400nm thick a-Si:H film is 10% lower than the bulk density of

photonic states over the weakly absorbing spectral region just above the a-Si:H absorption edge.

Moreover, the local density of photonic states in this spectral region rapidly decreases as the

thickness of the a-Si:H film is reduced below 400nm; for example, at 100nm thickness the

photonic density of states is ~25% lower than the bulk counterpart for frequencies just above the a-Si:H absorption edge. Thus, in principle, it is difficult to enhance absorption in thinner solar

cells because there are fewer photonic states to host incident light.

Herein, the subject of light trapping is simplified by assuming that an amorphous silicon

cell is a homogeneous slab with an index of refraction of na-Si:H( ), and extinction coefficient, ka-

Si:H ( ). Further, given the typical orientation of solar panels solar light is predominantly

centered within a small cone about the normal. As shown in Figure 3.5, incident light undergoes

partial reflection before entering the slab with a propagation direction within the escape cone.

The escape cone includes all directions between the substrate normal and the critical angle, c. The critical angle is determined using Snells law and, for the case at hand, is defined by the

equation c = Sin-1(1/na-Si:H). The escape cone is quite narrow for the plain amorphous silicon slab, for example assuming that na-Si:H ~ 4 then c ~ 14.5. Thus, light entering an amorphous silicon slab is confined to propagate within a small range of directions centered about the normal

direction. This scenario is highly unfavorable for efficient absorption since the path length of the

light through the cell is very short. Moreover, although light entering the escape cone may

27

undergo several passes through the slab, each time it is reflected off of the upper and lower

surfaces some light will be coupled out of the slab. Also, in an actual cell multiple passes

increases unwanted interactions between the light and the lossy rear contacts.

Figure 3.5A thin film may be viewed as a homogeneous slab. Incident light entering the slab propagates in a direction within the escape cone (left). Within the slab, light propagating in directions outside the escape cone undergo total internal reflection at the inner cell surface (right).

As shown in Figure 3.5 the plain homogeneous slab also hosts totally internal reflected

(TIR) modes. These TIR modes, which propagate along directions outside the escape cone, are

completely reflected at the internal surfaces and are confined within the a-Si:H slab. These

modes are highly favorable for light trapping on account of their long path length through the

cell and suggest a route to achieve efficient light trapping in thin-film cells. That is, the solar

irradiance can be efficiently absorbed in thin-film cells through coupling into photonic modes

that have a long dwell time within the slab.

A more quantitative analysis of these ideas has been presented by Chutinan et al.47 In

general the slab may be regarded as an optical cavity that hosts an infinite number of cavity

modes. A quality factor, Q, is associated with each of these modes. The quality factor is a

measure of the rate at which light energy escapes the photonic mode and is defined by the

equation E(t) = E(0)exp(-t/ ) E(0)exp(- 0t)/Q, where t represents time and ,E and 0 are the decay time, the energy and angular frequency of the mode, respectively. Moreover, the quality

factor can be broken down to distinguish the different decay mechanisms. The quality factor

28

associated with absorption can be denoted as Qabs 0 abs and the quality factor associated with

light leaking out of the cavity may be represented as Qcav 0 cav, where abs and cav are the

decay times for absorption and for light exiting the cavity, respectively.

For photonic modes within weakly absorbed spectral regions Qabs is relatively large. In

order to boost absorption light must reside in these modes for a sufficiently long period of time

and thus Qcav must also be large. However, in as much as a large Qcav value implies that it is

difficult for light to escape the cavity, it also means that it is equally difficult for light to enter the

cavity. For example, if ka-Si:H( ) = 0 such that the slab were a non-absorbing medium, then the

value of Qcav for the previously mentioned TIR modes is infinite. However, these modes are not

useful for light harvesting because light cannot be coupled into them. It turns out that, for a

given value of Qabs there is an optimal value of Qcav that maximizes absorption. To facilitate the

following discussion, herein photonic modes of frequencies within the weakly absorbed portion

of the solar spectrum that have large and near-optimal values of Qcav are referred to as high

quality modes. Since there are less photonic modes in thin-film cells, efficient light trapping

depends on utilizing these high quality photonic modes to as great an extent as possible.

PC structures could potentially be utilized to create and manipulate the flow of light into

high quality photonic modes in thin-film Si based cells. With regards to the simplified model of

the homogeneous slab, PCs could be integrated into its upper surface to reduce Fresnel reflection

and enhance light in-coupling. Moreover, the bulk of the slab could be periodically structured to

strategically tailor its photonic density of states thereby increasing the number of available high

quality photonic modes. Also, high quality photonic modes can be preserved by integrating PC

structures into the rear side of thin-film Si-based cells to reduce parasitic absorption losses in the

rear contact. The following sub-sections discuss both practical and novel methods of integrating

29

PC structures into the top surface, the active region and the rear contact of the thin-film Si-based

cells.

3.2.1 Integrating PCs at the front surface of thin-film cells to enhance light in-coupling

In the superstrate configuration a-Si:H cells are commonly deposited onto textured ZnO

front contacts. As previously mentioned these ZnO contacts typically have a root-mean-square

roughness between 40-150nm. Within the cell, the roughened interface between the ZnO contact

and the p- i- n- region of the cell functions as an ARC with a graded effective index and also

scatters light to some degree into the planar direction. Thus, in the context of the homogeneous

a-Si:H slab, a random texture with small feature sizes reduces Fresnel reflection and increases

light-coupling into the cell. PCs can be used to further enhance light coupling into thin-film Si-

based cells either by depositing a transparent periodic structure, such as a monolayer of close-

packed silica spheres, onto their surface or by using lithographic techniques to pattern their front

surface in the form of a diffraction grating.

It has recently been proposed that a hexagonally close-packed monolayer of silica

nanospheres can be deposited onto an untextured a-Si cell to enhance light in-coupling.48 Finite-

difference-time-domain based calculations show that for a sphere size of 600nm the current

density in the cell is increased by 12% compared to the reference case without the addition of the

silica spheres. Furthermore, it is reported that over almost the entire wavelength range, the

spectral current density is higher with the spheres than without the spheres. This broad band

enhancement is attributed to the monolayer of spheres behaving as a textured ARC. The addition

of the spheres also cause an absorption enhancement peak of over 100% over a narrow spectral

region centered about 665nm. This peak is attributed to whispering gallery modes resonating

30

through the periodic monolayer of silica spheres that couple light at the resonant frequency into

the a-Si cell. Although a relative increase in the current density of 12% is encouraging, it should

be noted that the reference case is a flat cell with an 80nm thick ITO front contact functioning as

an ARC, as opposed to an optimized ARC which itself could be textured.

The optical effects of forming a grating at the surface of thin-film Si-based cells depend

on the grating depth in comparison to the thickness of the cell. The addition of a shallow grating

has certain similarities with the aforementioned effects of the textured ZnO contact. That is, the

guided modes within the slab are only slightly perturbed and the grating enhances light coupling

into these modes because its dielectric profile approximates a graded refractive index (see Figure

3.6(a)). Also, for a rectangular grating profile, the height may be designed to reduce reflection by

functioning as an impedance matching layer (see Figure 3.6(b)).49 Moreover, in comparison to

random texturization, there is the added benefit that the profile and periodicity of the grating may

be designed to optimally couple its diffraction channels into the guided Fabry-Prot resonances

in the slab.

Figure 3.6 The dielectric profile of (a) a shallow pyramidal periodic texture in a homogeneous slab approximates a linearly graded refractive index that facilitates light in-coupling (b) a rectangular grating profile approximates an impedance matching layer and can couple light into high quality photonic modes.

31

The photonic modes in the homogeneous slab are slightly perturbed when a shallow

grating is applied to its surface. However, for gratings with depths that are comparable to the slab

thickness (see Figure 3.7) the structure approximates a photonic crystal slab. The photonic

density of states in the slab depends on the periodicity of the grating through Blochs theorem.

Thus, deep gratings can be implemented to strategically tune the photonic density of states in the

absorbing medium and are appropriately described in the next sub-section.

3.2.2 Periodically structuring the active region of thin-film cells to strategically tailor their photonic density of states

It is well known that photonic states can be shifted from one spectral region to another

by tuning the periodicity of the refractive index in an absorbing medium. Thus, light trapping

strategies for a-Si:H thin-film cells often involve periodically structuring the absorbing medium

such that it hosts a large number of high-quality photonic modes over the weakly absorbing

spectral region just above the a-Si:H absorption edge. In this context, one has a certain degree of

control over the spectral and angular distribution of the density of photonic states within the

photonic crystal slab through appropriate design of its periodicity. Thus, in principle, a thin-film

solar cell could be periodically structured to increase its photonic density of states over weakly

absorbing spectral regions. It may be noted that the total number of photonic states, integrated

over all frequencies and angles, is constant. However, from an engineering viewpoint, photonic

states may be shifted from spectral regions below the absorption edge of an absorbing medium

to a weakly absorbing region just above the absorption edge, thereby creating high quality

photonic modes. This light-trapping strategy was initially investigated almost three decades ago

by Sheng et al., wherein a thin-film a-Si:H cell was shaped in the form of a diffraction grating.50

In this work, the height and depth of the rectangular grating was theoretically optimized in order

32

to increase the density of photonic states in the a-Si:H cell in the spectral region between 600nm-

800nm. An enhancement of 2mA/cm2 and 3.5-4 mA/cm2 was calculated for an optimal one- and

two-dimensional grating, respectively.

Figure 3.7 A homogeneous slab with a grating comparable to its thickness can be approximated as a photonic crystal (left). The dielectric profile at the boundaries of this slab may approximate a graded index for longer wavelengths such that the slab has a high degree of transparency over the infrared region (right).

As an added benefit, it is interesting to note that the grated slab shown in Figure 3.7 may

have a high degree of transparency for light of wavelengths that are large compared to the

thickness of the cell. This high level of transparency arises because the dielectric profile of the

grated surfaces approximates a linearly graded index which, as discussed in Section 3.1, reduces

the Fresnel reflection at the surface of the slab. For example, considering that the slab is an a-

Si:H cell with thickness on the order of a couple of hundred nanometers, the transmission of light

in the near infrared spectral region increases significantly as the grating height approaches the

cell thickness. This benefit is exploited in Chapter Seven wherein the potential of enhancing

building integrated photovoltaic (BIPV) panels by integrating PC structures into their design is

investigated.

Since the work of Sheng et al., John17 and Yablonovitch19 independently proposed the

concept of photonic crystals. Shortly thereafter the concept of using periodic structures to

33

engineer the density of photonic states in solar cells was extended beyond gratings to structuring

the active region itself in the form of a PC. For example, an a-Si:H slab could be structured as a

one-dimensional PC with a stop-gap and band edge positioned just below and above the a-Si:H

absorption edge, respectively. Thus, similarly to the aforementioned case of the deep diffraction

grating, photonic modes can be shifted from the non-absorbing spectral region just below the

absorption edge to the spectral region just above the absorption edge. To this end, Gee

considered tailoring the photonic states in an ideal one-dimensional PC comprised of alternating

layers of Si and SiO2.51 An absorption enhancement factor of 4x was calculated for the case of a

quarter wave stack with a resonant frequency at 3000nm and photonic band-edge at ~1100nm, which is the absorption edge of Si. Gee also pointed out that the 4x enhancement factor should

be regarded as a lower limit since the calculations did not consider the possibility of diffracting

photons into off-normal modes, which have a longer optical path length through the absorbing

medium. Indeed, it has since been shown that slow-group-velocity modes having a Bloch vector

pointing along the plane of the slab are more effective in enhancing absorption.

It has also been theoretically shown that photonic crystal slabs with certain three-

dimensional periodic structures can effectively couple incident light into slow-photon-modes that

propagate in the planar direction of the slab. This optical phenomenon is referred to as parallel-

interface refraction (PIR). Specifically, a slab with a cubic lattice that is just a few unit cells thick

can support the PIR effect over a spectral range of at least 15% relative to the center frequency

and within a cone of 50 of incident angles, normal to the slab.47 Moreover, another periodically structured slab featuring an inverted pyramid type taper was designed to couple light into lateral

resonant modes that have a Bloch vector pointing along the plane of the slab. Theoretical

calculations show an absorption enhancement factor in excess of 40% over a cone of about 35

34

normal to the slab. It is also shown that a 250nm thick a-Si:H cell structured in this form has an

absorption enhancement factor of 1.5 over the spectral region ranging from 580nm to 780nm. It

can be noted that this approaches the Yablonovitch limit of 1.6 over this spectral region for an a-

Si:H cell of similar thickness.44, 52

3.2.3 Minimizing parasitic absorption losses in thin-film cells by structuring their rear contacts in the form of a PC

The rear surface of thin-film Si-based cells must perform multiple tasks, all of which are

vital to their performance. Specifically, the rear surface must contribute to the cells overall light-

trapping scheme to enhance absorption in the active region while simultaneously minimizing

parasitic absorption losses in the rear contact. As previously discussed in Section 3.2.1, a

diffraction grating at the top-side of a thin-film can couple incident light into high quality

photonic modes that propagate in the lateral direction. A similar effect can be achieved by

structuring the rear surface of the thin-film in the form of a diffraction grating. In this construct

light transmitted through the front surface of the cell can be diffracted into planar resonant

modes by a diffraction grating at the rear surface. Although a rear-side diffraction grating can

effectively trap light in thin films it is undesirable to texture thin-film Si-based cells for

numerous reasons. For example, regarding thinned crystalline Si solar cells, texturing may hinder

the ability to effectively passivate the Si surface and it is especially important to minimize back-

surface recombination in these Si cells.53 Furthermore, the effective surface area of the cell

increases as the texture feature size increases and this may lower the open circuit voltage owing

to an effective increase in the reverse saturation current density.54 On the other hand, Si cells that

are deposited in vacuum do not possess a high degree of crystallinity and thus cannot be

35

effectively textured by alkaline etching. Also, in this case the amount of Si removed should be

kept very small to avoid lengthy deposition times.

An alternative approach to diffract light at the rear side of thin-film Si-based cells may be

to structure the back contact itself in the form of a non-absorbing PC. The surface of a PC can be

regarded as a planar crystal defect (see Chapter Two) and it has recently been shown that the

periodic surface of two- and three-dimensional PC back-reflectors can couple incident light into

the planar direction in thin Si films. Specifically, opaline photonic crystal back-reflectors

optically coupled to thin a-Si:H films were shown to contribute to enhanced absorption in the

film by two different mechanisms. Firstly, the PC back-reflector behaves as a perfect mirror,

exhibiting nearly 100% reflection over its stop-gap frequencies. Secondly, the periodicity at the

PC-film interface couples incident light into high quality photonic modes that propagate in the

planar direction55 (see Figure 3.8).

Figure 3.8 Schematic illustration of a homogeneous a-Si:H slab with an opaline PC back-reflector. Incident light is diffracted at the PC-film interface into resonant modes that propagate along the plane of the slab.

Two- and three- dimensional PC back-reflectors can potentially be used for efficient light

trapping schemes in untextured thin-films. However, incorporating PC back-reflectors into actual

PV devices presents some design challenges since the space immediately adjacent to the rear

36

surface of the cell is occupied by an electrical contact. One solution may be to insert a thin

transparent conducting oxide (TCO) film between the active region of the cell and the PC back-

reflector. However, disrupting the PC-film interface reduces its ability to couple light into the

planar direction within the film.56 Nevertheless, this type of solution was recently implemented

in a 1.5 m thick p-i-n c-Si single-junction cell with ZnO contacts on both its upper and lower

surfaces.57 A porous aluminum membrane was used to deposit a Si/SiO2 diffraction grating onto

the rear ZnO contact. Subsequently, a one-dimensional Bragg-reflector comprised of five bi-

layers of Si and SiO2 was deposited onto the Si/SiO2 diffraction grating. Numerical simulations

showed that if the periodicity of the diffraction grating is around 300nm, then diffracted light

would not contribute to enhanced light absorption. This was attributed to the 400nm thick ZnO

contact situated between the c-Si cell and the grating. However, for a grating periodicity of

600-700nm, significant absorption enhancements were predicted, despite the rear ZnO contact.

Experimental results exhibited a 21% relative improvement in the overall efficiency for cells

comprised of the PC-based back-reflector compared to cells with no light trapping scheme.

3.3 Photonic crystal rear-contacts that function as solar spectrum splitters

This chapter has highlighted three different techniques to utilize PCs to enhance

absorption in thin-film Si cells. Firstly, PCs can be incorporated into the front surface of thin

film cells to facilitate light in-coupling. Secondly, the active region itself may be structured into

the form of a PC to favorably tailor the density of photonic states to enhance absorption in the

cell. Also, PCs may be integrated into the rear-side of the cell to ideally function as a lossless

back-reflector with the added benefit of diffracting light into high quality photonic modes that

propagate along the planar direction in the cell. The focus of this is section is to answer the

37

question posed at the beginning of this chapter: What is the best way to utilize PCs to enhance

thin-film Si-based photovoltaics?

Of the three aforementioned techniques structuring the active region of thin-film Si-based

cells in the form of a PC is perhaps the most fascinating way to enhance its optical performance.

However, the geometry of the PC may increase the series resistance of the cell and the large

surface area of the PC may also function as a recombination site for photo-generated carriers. For

example, actual three-dimensional thin-film silicon based solar cells have recently been

fabricated in the form of 5 m thick inverted opal films. Inverted p- and n- doped silicon opals

were successfully fabricated, however, the prototype p-i-n cells had an efficiency of just

0.32%.58 Moreover, designs that involve structuring the active region in the form of a PC would

require additional processing steps. It is unclear whether or not any efficiency enhancements

achieved from the enhanced optical performance of the cell with the PC structure would

outweigh the electrical losses associated with the increased surface to volume ratio and the

additional fabrication costs.

The other two options, wherein PCs are integrated either at the front or rear surface of the

cell to enhance light in-coupling or to function as a back-reflector, respectively, are attractive

because they could easily be incorporated into existing fabrication processes. In this regards,

techniques that integrate PCs at the front surface would most easily be incorporated into a-Si:H

cells fabricated in the substrate configuration. Likewise, fabrication techniques that integrate PC

back-reflectors would most easily be incorporated into a-Si:H cells that are fabricated in the

superstrate configuration. As previously mentioned in Section 3.2.1, theoretical calculations

show that the current density in an a-Si cell is increased by 12% when a close-packed monolayer

of silica spheres is deposited onto its surface. However, it is uncertain as to what extent light in-

38

coupling could be further enhanced using PC structures; although there is great potential to

improve light in-coupling over a narrow spectral region the PC integration at the upper surface of

the cell would likely interfere with and hinder in-coupling over other spectral regions. On the

other hand, as discussed in Section 3.2.3, p-i-n c-Si single-junction cells comprised of PC-based

back-reflectors exhibited a 21% relative improvement in their overall efficiency compared to

cells with no light trapping scheme. Moreover, thin film Si-based cells are most often fabricated

in the superstrate configuration.

The points presented in the preceding paragraphs suggest that the most promising

technique to pursue is the integration of PCs at the rear side of thin-film Si-based cells. Further to

the point, PC back-reflectors possess another inherent advantage that clearly distinguishes them

as the best way to utilize PCs for the purpose of enhancing the performance of thin-film Si-based

photovoltaics; they can be designed to serve the dual purpose of reflecting and transmitting

photons with energy above and below the cells absorption edge, respectively. As discussed in

Section 3.2.3, PC rear contacts should be fabricated from materials with both low absorptivity

and high conductivity such as transparent conducting oxides (TCOs). In this configuration the

periodicity of the PC can be tuned to position its stop-gap in the spectral region just above the

absorption edge of the cell. At the same time the dielectric band at the edge of the stop-gap can

be positioned near the absorption edge of the a-Si:H such that light in the spectral region below

the absorption edge of the cell is transmitted. Thus, the PC could function as a spectral splitter, or

an intermediate reflector, and the transmitted light could be converted to usable energy either in

the bottom cell of a tandem cell configuration (see Chapter Six) or in a photovoltaic/thermal

(PV/T) or BIPV system (see Chapter Seven).