Advanced Planar Light Guide Solar Concentrators

by

Michael J. Brown

Submitted in Partial Fulfillment of the

Requirements for the Degree

Doctor of Philosophy

Supervised by Professor Duncan T. Moore

The Institute of Optics

Arts, Sciences, and Engineering

Edmund A. Hajim School of Engineering and Applied Sciences

University of Rochester

Rochester, New York

2013

ii

Biographical Sketch

Mick Brown was born in Glendale, California. He attended Oberlin College, and graduated with a

Bachelor of Arts degree in Physics and Chemistry. He began his doctoral studies in Optics at the

University of Rochester in 2007. He received the Master of Science in Technical Entrepreneurship

and Management from The Simon School of Business, University of Rochester in 2012. He

pursued his research in Optics under the direction of Duncan T. Moore.

The following publications were a result of the work conducted during this doctoral study:

M. Brown, D. Moore, G. Schmidt, and B. Unger, "Measurement and Characterization of

Dimpled Planar Light Guide Prototypes," in International Optical Design Conference, OSA Technical

Digest (CD) (Optical Society of America, 2010), paper JMB45P

US Patent #8,189,970 B2 “Light Collecting and Emitting Apparatus, Method, and

Applications.” 2012

US Patent Application #13/462,047 “Light Collecting and Emitting Apparatus, Method, and

Applications.” 2013

iii

Acknowledgements

I would like to thank my advisor, Duncan Moore, for his guidance and support throughout

my graduate studies.

I would like to thank Professor Roger McWilliams for teaching me for many summers. The

experience in his lab was critical to my interest and growth as a scientist.

I would like to thank Greg Schmidt for his boundless ingenuity and kindness. His guidance

provided on this project and in all other areas of my graduate career was extremely valuable.

I would like to thank Blair Unger for his pioneering work on dimpled light guide

concentrators. Without his persistence, creativity, and communication abilities, this project never

would have gotten started.

I would like to thank Dan Williams, Pete McCarthy, Rebecca Berman, Eric Christensen, and

Xinye Liu both for their contributions to this project and for making the office as pleasant as it was.

I would like to thank Lynn Doescher for all her help with scheduling and logistics and

Evelyn Sheffer for keeping track of all the financial transactions of the group.

I would like to thank Tim McCollum, Gregg Podojil, and all the other members of the

Rambus team for their hard work and long hours spent fabricating the prototypes.

I would like to thank Ed White for helping connect me to his wide network of vendors and

resources.

I would like to thank my parents Sidford and Amy for their consistent support and

guidance through my graduate work and all the rest of my life. I would like to thank my brother

Casey for consistent support and empathy as we went through grad school.

I would like to thank my wonderful girlfriend Ellie Kilpatrick for her many years of support

and encouragement through this process.

I would like to thank Hans Hovanitz and all the rest of my friends back home in Los Angeles

for providing such rejuvenating respite from the rigors of my work in Rochester.

I would like to thank my friends in Rochester, specifically Talor Walsh, Tim Baran, Andrea

Baran, and Adam Heiniger for making my time in Rochester infinitely more pleasant than it would

have otherwise been.

iv

Abstract

Commercially viable solar energy is a critical part of meeting the energy needs of society

while sustaining the environment. Concentrating Photovoltaics provide a capability to produce

more power for a given area with a potentially lower cost. Dimpled light guide concentrators

couple a large input area to a small strip of solar cell. Several of the advantages for this type of

concentrator will be discussed. Following the pioneering work done earlier by Blair Unger, three

new designs of dimpled light guide concentrator are presented, each with distinct advantages and

drawbacks. Ray tracing models are described that illuminate the optical potential of each of these

three design families. In addition to optical performance, lifetime and durability models are

developed to inform material selection and cost modeling. Component parts of all three novel

designs are measured and characterized. Three concentrator prototypes are fabricated and

assembled into functional solar modules. The measured optical performance of these systems

shows geometric concentrations ranging from 60x to 71x with optical efficiencies ranging from

19% to 33%. It is expected that this efficiency can be improved through well known processes in

future iterations. In one of the designs, a small portion of the input aperture was found that

coupled 89.6% of the light to the cell, demonstrating the potential for optical performance of

future systems.

v

Contributors and Funding Sources

This work was supervised by a dissertation committee consisting of Professors Duncan

Moore, James Zavislan, and Julie Bentley of the Institute of Optics and Mitchell Anthamatten of

the Chemical Engineering Department at University of Rochester. The initial work described in

Chapter 1 was funded by Abengoa Solar under Award Number 052809-001 and describes

prototypes built in collaboration RPC Photonics. This work is described in more detail in the

doctoral thesis of Blair Unger, who contributed much of the data described in Chapter 1.

Investigation of the gradient index solar concentrator was done with funding from the DARPA

Manufacturable Gradient Index (MGRIN) project under Contract HR0011-10-C-0111. The research

presented in Chapter 3 was done with support from Rambus International Ltd. under Award

Number – 056105-002The team at Rambus fabricated the critical components of the concentrator

prototypes.

vi

Contents 1 Introduction ................................................................................................................................ 1

1.1 Solar Power Overview ......................................................................................................... 4

1.2 Photovoltaic Market Landscape .......................................................................................... 6

1.2.1 Current Photovoltaic Technologies ............................................................................. 9

1.3 CPV Systems ...................................................................................................................... 12

1.3.1 Concentrator Theory ................................................................................................. 13

1.3.2 CPV Families .............................................................................................................. 15

1.3.3 Critical Components of HCPV Systems ...................................................................... 18

1.3.4 Current HCPV concentrators ..................................................................................... 25

1.4 Light Guide Concentrators ................................................................................................ 28

1.4.1 Alternative Light Guide Concentrators...................................................................... 28

1.4.2 Dimpled Light Guide Concentrators .......................................................................... 31

2 Modeling and Design ................................................................................................................. 37

2.1 Overview ........................................................................................................................... 37

2.1.1 Modeling Software .................................................................................................... 37

2.1.2 Modeling Methods .................................................................................................... 39

2.1.3 General System Parameters ...................................................................................... 40

2.2 Concentrator Optical Design and Performance Modeling ................................................ 43

2.2.1 Phase Space Performance metric ............................................................................. 43

2.2.2 Lenslet Design ........................................................................................................... 48

2.2.3 Dimple Tree Performance and Sensitivity ................................................................. 51

2.2.4 Two Stepped Guide Performance and Sensitivity ..................................................... 59

2.2.5 Axial Index Variation Performance and Sensitivity ................................................... 64

2.2.6 Wedged Stepped Concentrator ................................................................................ 67

2.3 Material Durability and Lifetime Modeling ....................................................................... 73

2.3.1 Ultraviolet and Infrared Absorption Models ............................................................. 75

2.4 Integrated Module Performance Modeling ...................................................................... 85

2.4.1 Cell Models ................................................................................................................ 87

2.4.2 Yearly Energy Output Simulations ............................................................................. 89

vii

3 Fabrication and Testing ............................................................................................................. 91

3.1 Overview ........................................................................................................................... 91

3.2 Lenslet Arrays .................................................................................................................... 93

3.2.1 Lenslet Interferometer .............................................................................................. 94

3.2.2 Refractive Lenslet Arrays for Stepped Systems ....................................................... 100

3.2.3 Reflective Lenslet Arrays for Dimple Tree Systems ................................................. 109

3.3 Dimple Arrays .................................................................................................................. 115

3.3.1 Wedged Stepped Dimple Arrays ............................................................................. 116

3.3.2 Two Stepped Dimple Arrays .................................................................................... 126

3.3.3 Dimple Tree Arrays .................................................................................................. 131

3.4 Assembled Concentrators ............................................................................................... 136

3.4.1 Concentrator Module Testing Methods .................................................................. 137

3.4.2 Acrylic Wedged Stepped Concentrator ................................................................... 143

3.4.3 Polymer on Glass Wedged Stepped Concentrator .................................................. 147

3.4.4 Reflective Dimple Tree Concentrator ...................................................................... 158

4 Conclusion and Future Work ................................................................................................... 164

4.1 Improving Concentrator Prototypes ............................................................................... 164

4.2 Material Research ........................................................................................................... 167

4.2.1 Gradient Index Material Research .......................................................................... 167

4.3 Lifetime Durability and Performance Degradation ......................................................... 170

viii

Table 1-1: LCOE projections for several competing energy technologies. ......................................................... 3

Table 1-2: Standard cost breakdown of a solar installation. ............................................................................ 24

Table 2-1: Development of reflective dimple tree light guide variants showing an optimal design and then

tracking various concessions for manufacturing purposes. The results of the earlier Generation 2.5 light

guide prototypes are also shown for comparison purposes. ........................................................................... 55

Table 3-1: The shunt and parasitic series resistances were calculated for the three solar cells integrated into

the concentrator modules. Ideally a solar cell will have a high shunt and low series resistance value, so

LG003 was the best of this cell batch. ............................................................................................................ 141

Table 3-2: The various sources of loss for the acrylic wedged stepped concentrator. The facet scattering was

the dominant loss mechanism, though the defocus caused substantial losses. ............................................ 147

Table 3-3: Summary of loss mechanisms for glass wedged stepped concentrator. ...................................... 157

Table 3-4: Summary of loss mechanisms for the reflective tree concentrator prototype. ............................ 162

ix

List of Figures

Figure 1-1: Energy consumption broken down by source. Renewables form a small fraction of the total

energy used by the United States. Reproduced with copyright permission of EIA. .......................................... 1

Figure 1-2: A photothermal trough from Acciona Solar (left, picture reproduced with copyright permission)

and a power tower from Abengoa Solar (right). ................................................................................................ 5

Figure 1-3: Regional breakdown of installed PV capacity. Image reproduced with permission of copyright

holder NPD Solarbuzz. Image available from http://www.solarbuzz.com ........................................................ 7

Figure 1-4: Global Demand Stack for PV materials. Image reproduced with permission of copyright holder

Greentech Media. Image available at http://www.greentechmedia.com/ ...................................................... 9

Figure 1-5: Production of PV systems by technology type in 2010. Crystalline Silicon is dominant, with CdTe

being the other material appropriating the greatest market share. Image reproduced with permission of

copyright holder Greentech Media. Image available at http://www.greentechmedia.com/ ......................... 11

Figure 1-6: Two example low concentration systems. The system on the left relies on flat mirrors to reduce

silicon use by approximately 2x(image reproduced with permission of copyright holder Zytech Inc.), while

the system on the right is a truncated CPC with a concentration of 3.5x(Image reproduced with permission

of copyright holder Intech Inc.). ....................................................................................................................... 16

Figure 1-7: A mid concentration photovoltaic module. The system only requires one tracking axis and uses a

trough mirror to focus incident light onto the solar cell. Image reproduced with permission of copyright

holder SunPower Inc. Image available at us.sunpowercorp.com ................................................................... 17

Figure 1-8: A schematic of a generic concentrating system. Assumptions are made about the other

components to inform targets for the concentrator that is developed in this thesis (component 3). ............ 19

Figure 1-9: The efficiency improvement of several different families of cells. Rapid growth, especially in the

multijunction cells, is continuing. Image reproduced with permission of copyright holder National

Renewable Energy Laboratories(NREL). Image available at http://www.nrel.gov.......................................... 23

Figure 1-10: The ideal Fresnel lens (left) will suffer from a minimum draft angle (center) and rounding of the

ideally sharp corners (right) which will substantially reduce optical efficiency. .............................................. 27

Figure 1-11: A large dish concentrator. This was a test module in Phoenix, AZ that is approximately 75 feet

in diameter. Image reproduced with permission of copyright holder Southwest Solar Technologies ........... 28

x

Figure 1-12: A schematic for the Morgan Solar rotationally symmetric concentrator system. ....................... 30

Figure 1-13: A schematic of the UCSD light guide concentrator. Light is focused onto coupling prisms that

redirect light to either side of the light guide. Image reproduced with permission of copyright holder The

Optical Society. ................................................................................................................................................. 31

Figure 1-14: Schematics for a refractive and reflective dimpled light guide system. ...................................... 32

Figure 1-15: A schematic of a dimple for use in a dimpled light guide. The injection prism is shielded from

light injected upstream by a bypass prism. ...................................................................................................... 33

Figure 1-16: When fabricated, the knife edge prototype had a rounded tail, substantial drafts on the side

walls, which were also rough. This substantially degraded performance. ...................................................... 34

Figure 1-17: The second generation light guide prototype (top), the designed dimple geometry (bottom left),

and an SEM image of the fabricated second generation dimple structure (bottom right). ............................. 35

Figure 2-1: A lenslet feature is created in Solidworks and then patterned appropriately using LightTools. ... 39

Figure 2-2: Tracker Accuracy is dependent on wind loading (left) and the acceptance angle determines the

fraction of energy available (right). Image reproduced with permission of copyright holder Green Mountain

Engineering. ...................................................................................................................................................... 41

Figure 2-3: ASTM G173-03 Direct Component. This is a standard spectrum representative of peak irradiance

in the United States .......................................................................................................................................... 42

Figure 2-4: The angular spectrum a) 1mm, b) 18mm, c) 36mm, and d) 52mm from the injection element.

The angular spectrum 1mm from the guide is that injected by the lenslet. The angular spectrum expands as

light travels further down the guide, and any light travelling with too large an angle (outside the blue

rectangle) is lost from the system. ................................................................................................................... 46

Figure 2-5: Offsetting the lenslet aperture causes the central ray to be deviated from normal to the plane

(Left). If the central ray is not deflected to travel in the plane of the guide the effective injection angular

spread will be much larger (Upper Right) than if it is deflected directly parallel to the plane of the guide

(Lower Right) .................................................................................................................................................... 49

Figure 2-6: A lenslet geometry designed to cater to a manufacturing process where the sag depth is

restricted. Allowing customized aperture shapes allows improved injection and guiding efficiencies. ......... 50

xi

Figure 2-7: Optimal optical performance requires a conic surface shape for the lenslets to achieve a tight

focal spot (left). A spherical lenslet surface will leave a large amount of spherical aberration and reduce

performance (right). ......................................................................................................................................... 51

Figure 2-8: The first generation "knife edge" dimple has been fused into a long strip to avoid the problems

associated with manufacturing the knife edge geometry. ............................................................................... 52

Figure 2-9: The dimple geometry of the "dimple tree" family of light guide concentrators. The injection

facets are highlighted in teal. ........................................................................................................................... 53

Figure 2-10: The efficiency fall off for various dimple tree light guide concentrators as the geometric

concentration increases. .................................................................................................................................. 56

Figure 2-11: The angular spread of a reflective dimple tree light guide with nearly ideal manufacturing

parameters (1µm fillet radii, 1° draft angle). The angular spectrum expands almost entirely laterally, with

the vertical expansion being due to the draft angles and fillets. The red rectangle shows the boundaries for

TIR containment in the light guide structure. .................................................................................................. 58

Figure 2-12: A Schematic of horizontal stepping. This represents a top view with the light purple squares

representing the lenslet apertures, the dark purple squares representing the injection facets, and the red

rectangles representing the chips. The relative size of the lenslets and injection facets determines both

concentration and how many horizontal steps can be taken. Shown are a 36x concentrator with 6 steps

(left), a 9x concentrator with 3 steps (center) and a 4x concentrator with 2 steps (right) .............................. 60

Figure 2-13: A schematic of vertical stepping. The guide layer increases in thickness so that each injection

facet will not interfere with light injected upstream. In this schematic, the thickness of the lenslet layer is

decreasing to compensate for the increased guide layer thickness. ............................................................... 61

Figure 2-14: A schematic of a two stepped guide. When a horizontal step would interfere with an upstream

injection facet, a vertical step is taken. ............................................................................................................ 62

Figure 2-15: The effect on the angular spectrum of a two stepped light guide for various levels of

manufacturing defects. More precise manufacturing tolerances allow isolation of vertical and horizontal

angles. .............................................................................................................................................................. 64

Figure 2-16: An axial index variation will reroute a ray injected with a steep angle to travel more directly

down the guide. This can be done with a mismatched guide layer or a GRIN in the guide layer. .................. 66

Figure 2-17: A model of a wedged stepped concentrator. The injection facets are joined to the facet directly

downstream by a slight wedge. This concentrator geometry uses horizontal stepping. ................................ 68

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Figure 2-18: The modeled optical efficiency for light injected into the guide at given distances. Overall the

system was designed to be 600mm long with a geometric concentration of 750x. Absorption and

manufacturing imperfections both reduce performance. ............................................................................... 71

Figure 2-19: The angular spectrum for a gradient index light guide. Manufacturing errors will circularize the

spectrum and reduce guiding efficiency of the device. .................................................................................... 72

Figure 2-20: The modeled effects of both a mismatched guide layer and gradient index guide layer compared

to the homogenous design ............................................................................................................................... 73

Figure 2-21: The UV transmission characteristics of PMMA compared with the solar spectrum incident on

the surface. The chain scission peak will cause damage to the material, but a radical scavenger can be added

to absorb this UV. ............................................................................................................................................. 76

Figure 2-22: The spectral overlap between solar radiation hitting the Earth's surface and PMMA. PMMA

shows excellent transmission in the visible, but significant absorption in the infrared at wavelengths longer

than 1100 nm. .................................................................................................................................................. 78

Figure 2-23: The thermal effects of a cone of light focusing onto an injection facet in PMMA. The

temperature differential is not projected to be more than a degree, even at the focal spot. ........................ 80

Figure 2-24: Simplified model of light guide IR absorption. Light is assumed to be injected evenly traveling

towards the chip at the left. ............................................................................................................................. 81

Figure 2-25: Heat dissipation by various lengths of PMMA light guide concentrators. Most of the absorption

is in the infrared. The absorption approaches the solar spectrum with a characteristic length determined by

the material absorption of the guide layer. ..................................................................................................... 83

Figure 2-26: Thermal model of temperature increase due to infrared absorption of a PMMA two stepped

light guide. In this model, the only means of dissipating heat is convection from the bottom surface

interacting with 300K air. ................................................................................................................................. 84

Figure 2-27: Characteristic summer and winter days in Phoenix (top) and Chicago (bottom). Phoenix has

much less cloud cover, and thus much more direct sunlight. High concentration systems are primarily only

able to collect direct sunlight. .......................................................................................................................... 86

Figure 2-28: Schematic for a triple junction solar cell. Each successive layer efficiently absorbs and converts

the appropriate spectral region while allowing lower energy light to pass through to the cells underneath.

Image courtesy of Solar Junction ..................................................................................................................... 88

xiii

Figure 2-29: Averaged monthly output from the system with insulation data taken in Phoenix in 2005. There

is substantial variability between the months, as this particular year had a unique distribution of weather in

addition to the annual seasonal variability. ..................................................................................................... 89

Figure 3-1: The wedged stepped concentrator model and illustrative schematic of the wedged stepped

concentrator (a), the two-stepped concentrator model and schematic (b), and the reflective concentrator

model and dimple schematic (c). ..................................................................................................................... 92

Figure 3-2: Definition of angles and transverse direction. The blades of lenslets were combined together to

form a master. .................................................................................................................................................. 94

Figure 3-3: Schematic of custom Twyman-Green interferometer used to characterize lenslet arrays. .......... 96

Figure 3-4: The output of a sample patch of the reference lenslet array. The Y Error is selected and shows no

notable systematic errors and a fairly small random variation. The phase profile is presented on the right,

from which an RMS error can be calculated. ................................................................................................... 99

Figure 3-5: The systematic spacing error can be seen in the reference lenslet array. The original

measurement showing an X spacing mismatch is shown on the right, and the left shows a consistent spacing

mismatch when the sample was rotated 90° and remeasured...................................................................... 100

Figure 3-6: A small patch of the refractive stepped lens array. The lenses have a rectangular aperture and

the optical axis is offset from the center of the lens aperture. In this picture, the light will be guided toward

the left. ........................................................................................................................................................... 101

Figure 3-7: White light interferometer measurement of the refractive stepped master. The red vertical line

on the surface map is fitted to both a variable radius and to the designed radius. While there is a slight

discrepancy, this only represents the 15% of the lenslet aperture near the apex. The microroughness of

these surfaces is approximately 10nm. .......................................................................................................... 102

Figure 3-8: An exaggerated schematic of the bowing of the lenslet array. This is the direction of bow as can

be seen visually. This will cause a focal shift in the Z direction as seen by the green arrow and will reduce the

X spacing shown by the black arrows. ............................................................................................................ 104

Figure 3-9: The surface profile of a representative refractive lenslet and the calculated RMS surface error of

each measured lenslet at the best focus. Both color scales are in mm. ....................................................... 105

Figure 3-10: The focus error in both Z (top) and X (bottom) directions. The Z error shows a low central

region consistent with a bowed array, while the X error shows a consistent spacing mismatch being too close

together. Both of these profiles are dominated by the bow in the lenslet array as expected. .................... 107

xiv

Figure 3-11: The Y coordinate error was dominated by an imperfection between the third and fourth row.

This is indicative of an imperfection preventing the two rows during assembly. .......................................... 108

Figure 3-12: The fitting of the bow of the refractive lenslet. This fit should yield a Z error of approximately

240µm at the corners of the lenslet array...................................................................................................... 109

Figure 3-13: The surface map near the apex of a reflective lenslet master (right) and the profile of a slice

through the apex. The surface roughness is quite low, and the fitting of the curvature shows a slightly

weaker curve than designed. ......................................................................................................................... 111

Figure 3-14: The RMS of the reflective lenslet array when used as a refractive system. The error is

dominated by the fourth row. It is believed that a scratch along the lenslet array caused a failure of the

phase unwrapping algorithm. ........................................................................................................................ 112

Figure 3-15: The RMS profile of a lenslet not in the fourth row. Substantial tooling marks can be seen in the

bottom section of this figure, but the profile is very good. There are highly visible tooling marks on the

bottom section of the lenslet, which is consistent with the two regions separated by the discontinuity in the

fourth row. ..................................................................................................................................................... 113

Figure 3-16: X (top) and Y (bottom) position errors of the focal spot for the reflective lenslet array. The Y

error is dominated by a scratch on the fourth row, while the X error is dominated by a bowing in the system.

........................................................................................................................................................................ 114

Figure 3-17: The first attempt at an injection facet (left) showed an obvious ripple. After refining

manufacturing parameters, the injection features were improved significantly (right). ............................... 117

Figure 3-18: Schematic showing dimple layer for the purposes of orienting white light interferometer

measurements. The colors of the channel are consistent with respect to height differences. .................... 118

Figure 3-19: White light interferometer measurements of a central region of an acrylic wedged stepped

dimple layer. The surface roughness of each channel in this region is approximately ±5nm. ...................... 119

Figure 3-20: An SEM image of the final wedged stepped dimple geometry. The feature replication is quite

good, though there is a considerable amount of debris that can be seen on the part. ................................. 120

Figure 3-21: White Light Interferometer measurements of polymer on glass wedged stepped dimple

geometry. Both the middle region and the high region are very smooth surfaces. The casting on glass

process introduces some roll off near steam height transitions, as can be seen in the bottom figure near the

abrupt height transition. ................................................................................................................................ 122

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Figure 3-22: White light measurement of facets of wedged stepped dimple array cast onto glass. Substantial

variations are observed from facet to facet, but there are several regions that will have a small amount of

scattering. ....................................................................................................................................................... 124

Figure 3-23: Scattering fraction from injection facet surface is a function of RMS surface roughness. ........ 125

Figure 3-24: A small patch cut of the two stepped dimple geometry. Channels are still visible, but the flat

regions are relatively consistent. ................................................................................................................... 127

Figure 3-25: White light interferometer measurements of the two stepped patch cut. The flat region has

clearly defined channels separated by a fraction of a micron while the injection facet cut shows signs of tool

wear. ............................................................................................................................................................... 129

Figure 3-26: The master cut for the two stepped dimple geometry showed substantial damage. The deeper

cut appears to have ripped away the base substrate through the nickel coating, and caused deep gouges

over a substantial portion of the dimple layer. .............................................................................................. 130

Figure 3-27: An SEM image of the dimple tree patch cut. While there is substantial debris and visible marks

ear the facets, the geometry is roughly correct. ............................................................................................ 131

Figure 3-28: The first cuts of the reflective tree design showed substantial ringing along the guiding axis and

a sharp height transition along the transverse axis. There was a substantial portion of the cut in which these

errors were much more pronounced and scattering from this section of the part was easily visible with the

naked eye (bottom). ....................................................................................................................................... 133

Figure 3-29: The final dimple tree cut showed substantial dampening of the ringing near the facets. While

the magnitude is not substantially lower for the master, the distance covered by the ringing will be

substantially reduced. The low frequency also will reduce the scattering effect. ........................................ 134

Figure 3-30: The injection facet of the reflective tree guide system showed substantial roughness, mostly

along the guiding direction (right to left in this figure). The marks were consistent from facet to facet. .... 135

Figure 3-31: The three final concentrator modules that were fabricated and characterized for this thesis.

The acrylic wedged stepped guide (left), acrylic reflective tree guide (center), and polymer on glass wedged

stepped guide (right). ..................................................................................................................................... 137

Figure 3-32: A schematic of the University of Rochester Solar Simulator. This produces an approximately

uniform 20cm diameter beam that matches both the spectral content and angular extent of the sun. ...... 138

Figure 3-33: The dual diode model of a solar cell. Image from pveducation.org .......................................... 139

xvi

Figure 3-34: Dark IV curves for the three silicon solar cells mounted to the three light guide concentrators.

The cells were chosen as the closest to ideal fits from an available batch of silicon cells. ............................ 140

Figure 3-35: Scanning the illuminated slit allows determination of how far injected light has propagated

within the concentrator before reaching the solar cell at the output face. ................................................... 141

Figure 3-36: The apparatus for measuring optical efficiency at different sections of the concentrator input

aperture. Two rotation axes and a translation axes are automated. ............................................................ 142

Figure 3-37: The optical efficiency falloff of the acrylic wedged stepped prototype. A small slit aperture

illuminated a small portion of each lenslet array and found the optimum pointing to determine the efficiency

falloff. ............................................................................................................................................................. 144

Figure 3-38: The field of view of the acrylic wedged stepped concentrator at the front lenslet array (15 mm

from cell) and at the rear lenslet array (90mm from cell). The profile is fairly broad and the center moves

substantially from lenslet to lenslet. .............................................................................................................. 145

Figure 3-39: The optical efficiency falloff for the polymer on glass wedged stepped guide. ......................... 149

Figure 3-40: The normalized field of view from a slit aperture of the polymer on glass wedged stepped guide.

The field of view much more closely resembled the design specifications than for the other prototypes. .. 150

Figure 3-41: The model of the bowed lenslet array. The bowing of the lenslet array was approximated from

the unattached lenslet array measured in the lenslet interferometer. The amount of delamination was

controlled by changing the thickness of the low index layer. ........................................................................ 151

Figure 3-42: The optical efficiency of each lenslet in the array for a system with the observed bowing defect

and no others. The observed immersed region covers slightly more than half the aperture....................... 152

Figure 3-43: The optical efficiency of the glass wedged stepped design near the sweet spot. The variation in

efficiency within the immersed region of a lens array is caused by a substantial randomness in the injection

facet roughness. ............................................................................................................................................. 153

Figure 3-44: Detailed field of view of sweet spot measured with collumated HeNe beam. The field of view

very closely resembled the designed system, and there is relatively little variation within the injection facet.

........................................................................................................................................................................ 154

Figure 3-45: Laser Scans at the front and back of the glass wedged stepped system. The guiding loss from

the best facet near the back of the guide to the best facet found near the front of the guide was 22.7%. .. 156

xvii

Figure 3-46: Efficiency falloff for reflective tree concentrator system, taken at optimum pointing angle. ... 159

Figure 3-47: Normalized field of view of acrylic reflective tree concentrator for the lenslet array closest to

the cell (left) and farthest from the cell (right). ............................................................................................. 160

Figure 3-48: The small slit scan of the field of view for the front lenslet of the reflective tree concentrator.

The field of view is substantially blurred, indicating a focal length error, but the center moves almost a full

degree and systematically, indicating a clocking error. ................................................................................. 161

Figure 4-1: A representative injection facet of the two stepped light guide system. The pattern of scratches

was consistent over all facets measured on this part and is thought to be due to tool wear. ...................... 166

Figure 4-2: A comparison of the clarity of the undiffused glass (right), the diffused GRIN sample pretreated

with K+ ions(center), and the diffused GRIN sample without pretreatment (left). Photo by G. Schmidt ..... 168

Figure 4-3: Surface heights at the edge of 2mm thick slab of glass that has not been diffused (left),

pretreated for 6 hours (center), and pretreated for 16 hours (right). The 2D plots show the vertical and

horizontal slices of the data represented by the corresponding line color.................................................... 169

Figure 4-4: Fringe pattern and calculated refractive index profile for diffused GRIN sample. ...................... 170

1

1 Introduction

One of the critical challenges to be confronted in the near future is sustainably generating

sufficient electrical power to meet the rapidly increasing demand of modern society. Demand for

electrical power continues to accelerate as the population increases and society modernizes. This

demand is largely met by consumption of fossil fuel reserves, primarily coal, natural gas, and

petroleum. These sources are not sustainable, as natural reserves are finite and become less

efficient to extract as they are depleted. The use of these power sources also poses an

environmental hazard with potentially dire negative consequences.

Development of renewable sources of energy is critical to fill the void that will be left by the

depletion of natural fossil fuel reserves. Renewable energy sources also help to alleviate the

environmental strain that consumption of fossil fuels creates. Renewable sources currently

account for a small fraction of energy generation, as shown in Figure 1-11. In order to make a

greater impact, renewable energy technologies must be advanced to the point where they can be

Figure 1-1: Energy consumption broken down by source. Renewables form a small fraction of the total energy used by the United States. Reproduced with copyright permission of EIA.

2

cost competitive with fossil fuel sources. There are many different sources of renewable power,

and the economic viability and scalability of each is currently uncertain. Thus concurrent

development of many potential technology pathways is critical to the widespread use of

renewable power generation.

Renewable energy sources have only captured a small fraction of the energy market, as they

are not currently cost competitive with current electricity generation methods. The number of

competing technologies that have potential for utility scale electricity generation makes

quantitative comparison somewhat uncertain. Forecasting energy prices in the future is imprecise,

as the behavior of coal and gas varies dramatically depending on the source of the information. In

addition, a number of disruptive technologies might cause substantial price fluctuations if they

should achieve cost parity first. While determining actual commercial viability is an extremely

complicated process, it is impractical to calculate accurately for a developing technology, and thus

a simpler metric is useful for guiding the development process.

The Levelized Cost of Energy (LCOE) is designed to measure the cost of generating power

over the expected lifetime of a plant ($/kWh). This is fairly simple to calculate for a given system

and provides a simple means of quantitatively comparing two systems. This provides a useful

target for development, as any competitive system must surpass the LCOE of currently available

power generation techniques in order to achieve widespread adoption. The LCOE is calculated by

3

where N is the expected life time of the plant in years, AO is the Annual Operations Cost, DR is the

discount rate, RV is the residual value, and SDR is the system degradation rate.2 This takes into

account the performance and costs of the plant over the course of its life time, and provides an

approximate scalar metric that can be compared with other technologies.

The Energy Information Administration has released projections for the LCOE of several

different technologies assuming plants coming online in 2017. These were based off a set of

assumptions taking into account current trends in each of these technologies3. Any disruptive

technology must at least meet these projections, and thus this provided a useful target for

designing and developing a system. The projections are given in Table 1-1.

Table 1-1: LCOE projections for several competing energy technologies.4

Minimum Average Maximum

90.5 97.7 114.3

102.5 110.9 124

107.2 111.4 118.7

77 96 112.2

57.8 88.9 147.6

119 152.7 238.8

176.1 242 386.2

Advanced Nuclear

Renewables

Wind

Hydro

Photovoltaic

Photothermal

Advanced Combined

Cycle Natural Gas

59.5 66.1 81

56.8 63.1 76.4

Cost Range for Total System Levelized Costs

(2011 $/MWh) for plants entering service in 2017

Dispatchable Technologies

Conventional Coal

Advanced Coal

Plant Type

Conventional Combined

Cycle Natural Gas

4

Current projections have natural gas-fired plants being the dominant source of energy

with an expected average cost of just over $0.06 per kWh. This is used as a goal for developing the

system described in this dissertation and provides a baseline for comparing alternative

technologies and assessing viability for future research and development. This is a long term

target for any power technology that aims to achieve grid parity in the near future, but before

widespread adoption in the utility scale market, many of these technologies can leverage other

advantages to penetrate smaller markets. This dissertation focuses on the development of a

specific solar technology, and follows the development efforts aiming at initially competing with

other solar power technologies with a proposed path toward competitive utility scale generation.

1.1 Solar Power Overview

Solar power encompasses a wide variety of technologies designed to convert the sun’s

energy into electricity. The two primary families for solar power are photovoltaics, which convert

the sun’s energy directly into electricity using the photoelectric effect, and photothermal, which

uses the sun’s energy to heat an intermediate to run a thermal engine. These two technologies

are growing areas of research and are being deployed with increasing frequency and scale.

Current levels of development and deployment show uncertain, though promising, potential for

both families of technology. The two technologies rely on fundamentally different scientific

principles, each with its own merits and drawbacks for commercial use.

Photothermal technologies rely on a concentrator to focus light onto a heat exchanging

medium. There are many different incarnations of photothermal technologies, but the most

common are the trough receiver and the power tower. Photothermal troughs are designed to

focus light at a relatively low (approximately 20x) concentration onto a tube containing an

5

absorbing fluid, which is then used to run a heat engine.5 These typically have efficiencies of

between 12% and 18% due to the relatively low temperature differential they can achieve with

these concentrations. The advantages of these systems are that they only require one tracking

axis, which substantially simplifies mounting and installation, and these systems can be scaled to

relatively small installations. The power tower employs a large area of mirrors designed to focus

light onto a receiver situated atop a tower in the center of the mirror array, which is heated to

temperatures of up to 1,000 °C. These power towers are much more efficient, as the efficiency

scales with the temperature differential. These plants can achieve efficiencies in the range of 22-

26%.

Photovoltaics rely on the photoelectric effect to excite an electron into the conduction

band of a semiconductor. A junction of p-type and n-type semiconductor cause the excited charge

carriers to flow preferentially in one direction which creates a voltage across the junction. The

spectral region that excites a carrier and the energy that is gained from each exciting photon are

intrinsic properties of the semiconductor junction used. A material with a higher band gap more

efficiently extracts energy out of the high energy region of the sun’s spectrum, but lower energy

Figure 1-2: A photothermal trough from Acciona Solar (left, picture reproduced with copyright permission) and a power tower from Abengoa Solar (right).

6

photons do not excite an electron, and thus cannot be converted into electricity. In order to

optimally convert as much of the sun’s energy as possible, different PV junctions can be stacked

(multijunction cell), so that each junction utilizes the part of the spectrum it can optimally convert.

PV systems comprise a much larger market currently than photothermal systems due to

several key advantages. PV systems have a much wider range in the scale at which they can be

deployed. For many applications such as remote stations, residential, or portable power,

photothermal systems are too large to be practical. PV systems also do not require the large heat-

to-electricity conversion infrastructure. The primary advantage of photothermal systems is that

the heated medium can be stored much more easily than the power generated by a PV system,

which must be stored in a battery or some other means. This allows the capacity factor of the

photothermal system to be much higher, as the power is available for use when needed for a

lower price than storage for PV systems.

1.2 Photovoltaic Market Landscape

While photovoltaics have not become a major player in the utility scale power market,

they are being used currently in a wide variety of smaller markets. Photovoltaics are

advantageous for off grid applications and distributed generation, as they scale down to almost

arbitrarily small size. Thus PV materials are currently being used be the construction and

transportation industries for powering small installations where grid connectivity is impractical.

On a smaller scale, PV materials are frequently used to power consumer electronics that have low

power consumptions such as calculators and watches.

7

The market for photovoltaics has continued to grow rapidly, with new technologies and

manufacturing development continuing to drive industry growth. As of 2011, slightly over 37GW

of installed PV capacity existed around the world. Most of installed PV capacity has been centered

in Europe, where strong government support has driven widespread implementation, especially in

Germany. This dominance was expected to weaken over the coming decades as the markets in

North American and Asia expand while economic uncertainty was slowing adoption in Europe.

Figure 1-3 shows the regional breakdown of installed PV capacity.6

Figure 1-3: Regional breakdown of installed PV capacity. Image reproduced with permission of copyright holder NPD

Solarbuzz. Image available from http://www.solarbuzz.com

The price of solar energy varies substantially by region, technology employed, and

financing agreements. Many photovoltaic technologies are relatively immature, and thus it is

difficult to get an accurate levelized cost of energy from these systems. It is difficult to accurately

quantify the performance over the lifetime of many PV technologies, and thus the value of

implementing these technologies is uncertain. An alternative performance metric is the cost per

8

watt produced during peak conditions. This metric does not take into account the lifetime or

degradation of the plant and also fails to consider performance at suboptimal conditions.

Problems with this metric can make comparisons misleading, but it provides a simple and readily

calculated approximation to judge performance.

PV systems provide advantages beyond strict power generation, and thus there is still

demand for PV modules even though the system is more expensive than alternative fuels. These

systems have been adopted at remote locations where grid connectivity is unavailable and some

other specialized applications. Customers who are sensitive to environmental impacts or seeking

to market a “green” image may choose photovoltaics even if more expensive than alternative

forms of power generation. The demand for photovoltaics increases as the price decreases and

more markets become viable. The demand stack for PV systems shown in Figure 1-47 illustrates

the increase in demand for each region as the price of this energy varies.

9

Figure 1-4: Global Demand Stack for PV materials. Image reproduced with permission of copyright holder Greentech

Media. Image available at http://www.greentechmedia.com/

In order to compete with conventional fuel sources, PV technologies must surpass $1/W.

The US government launched the Sunshot Initiative in 2011 with the goal of reaching this cost

target for PV systems.8 If this cost target can be eclipsed, then PV technology can begin to

penetrate the utility power generation market, which expands the potential greatly. To compete

on a utility scale, more accurate information about the lifetime performance of a solar plant will

have to be gathered and compared with alternatives.

1.2.1 Current Photovoltaic Technologies

A great deal of research and development is being focused on new solar technologies, yet

the dominant technology for terrestrial solar power, both residential and utility, remains flat plate

10

silicon. Silicon is a fairly mature technology that has been used for solar cells for decades.

Advances in processing have increased the efficiency of deployed modules9, but most of the

development has been aimed at improving manufacturing methods in order to reduce costs.

Flat plate silicon modules efficiently convert photons with wavelengths between 500nm

and 1100nm and typically have efficiencies of approximately 15% when deployed in the field. This

technology is relatively mature, and thus the risks associated with deployment are minimal and

well known. The relatively high conversion efficiency and process maturity are the primary

reasons that silicon continues to dominate most PV applications. The cost of silicon is primarily in

the actual material and material processing, and thus the module price will continue to be tied

closely to that of raw silicon. This has been an extremely volatile commodity, as silicon is widely

used by the electronics industry, creating extreme fluctuations in price.

The maturity of Silicon photovoltaics is an advantage and a limitation, as the performance

is approaching a fundamental theoretical maximum. The cost is unlikely to be dramatically

reduced, as the primary cost driver is the cost of the raw Si. Other technologies aim to avoid these

limitations, and thus potentially dramatically lower the cost of producing solar power. The

technology that has reached the most widespread deployment is Cadmium Telluride (CdTe) films

deployed primarily by First Solar10.

CdTe has substantially lower conversion efficiency when compared to Silicon, but requires

only a thin film of material to be deposited on the substrate, and thus the cost of producing a

module is drastically reduced. This is a much newer technology than flat plate silicon, and thus

research continues to increase the efficiency11. These systems have achieved substantially lower

$/W than available Si modules, but the lifetime of these systems is unclear, and thus the LCOE is

11

uncertain. Active research is continuing in quantifying and extending the lifetime of these systems,

though they are still deployed on a large scale (Approximately 22% of the PV systems in the US).

Silicon and CdTe account for the vast majority of solar power plants that are currently

running. Other systems are primarily still in the pilot plant phase while the manufacturing

readiness level increases towards large scale production. Concentrating Photovoltaics are among

these fledgling technologies that have only been deployed in small demonstration facilities. Figure

1-5 shows the installation level of key solar technologies, and highlights the dominance of Silicon,

with CdTe being the only competing technology to appropriate significant market share.

Figure 1-5: Production of PV systems by technology type in 2010. Crystalline Silicon is dominant, with CdTe being the

other material appropriating the greatest market share. Image reproduced with permission of copyright holder

Greentech Media. Image available at http://www.greentechmedia.com/

12

1.3 CPV Systems

Concentrating photovoltaic systems aim to achieve parity with alternative systems by

concentrating incident light onto a relatively small area of active photovoltaic material. The

primary driving cost of current PV technologies is the cost of the actual photovoltaic material.

CPV systems aim to reduce the material cost and employ relatively inexpensive optical

components to collect sunlight and concentrate onto the reduced area of photovoltaic material.

In order to surpass conventional flat plate PV technologies, the benefits of concentrating

systems must make up for the added system complexity and costs. The cost savings comes in the

form of reduced chip area, and thus cost. If the concentration is high enough, more efficient cells

become cost effective. Though these materials would never be viable in a flat plate system with

no concentration, but if the required area can be reduced by a factor of several hundred, the

increased efficiency can make up for the increased cost.

Concentrating systems add a varying degree of complexity to the system, and the costs of

these additional components must be minimized to make CPV systems viable. The concentrator

optics constitute an additional cost, though different designs of concentrator can vary orders of

magnitude in cost per area. The mount for a concentrating system is much more expensive than

for traditional flat panel systems, as many designs require some sort of active tracking mechanism

to maintain their alignment with the sun. Many systems also require a thermal management

system to keep the temperature of the PV material and potentially other components within a

designed operating temperature range.

13

1.3.1 Concentrator Theory

One of the critical system design decisions for CPV systems is the design of the concentrator,

specifically what level of geometric concentration to operate at. The concentration ratio

(collected area/PV chip area) dramatically affects what PV materials can be used in the system, as

high efficiency cells are expensive enough that they only become cost effective at high

concentrations. The primary drawback for high concentration systems is that a high concentration

dictates a system with a small acceptance angle. High concentration systems must be mounted

onto a tracking system to keep them aligned with the sun. This adds an additional cost to the

system that can be a driving cost for the system in many cases.

The tradeoff between concentration and acceptance angle is a physical limit described by

Étendue. Étendue is a property that takes into account both the spatial and angular extent of light

travelling through an optical system. Given a ray passing through an entrance plane at (x,y) with

direction cosines (L,M,N) in a material with refractive index n, the beam passing through the

system can be described by a ray bundle with spatial shifts (dx,dy) and angular shifts (dL,dM). The

generalized étendue is described by

Let the same be true of the exit space, with coordinates and material being represented by the

same symbols prime (‘). For a nearby ray with coordinates (x+dx, y+dy, L+dL, M+dM), the

generalized étendue is invariant, and thus for a lossless system, the étendue at the input plane

and the output plane will be equal.

14

An illuminating way to interpret étendue conservation is by combining the direction

cosines and index of refraction into an “optical momentum”. The flux through an optical system

can then be considered as a volume in the 4 dimensional space given by (x,y,p,q). This has been

likened to a four dimensional space in fluid dynamics, and thus has taken the name phase space.

As this input beam travels through an optical system, the volume cannot be compressed in phase

space, though it can be distorted and/or diluted.

The goal of an optical concentrator is to transfer an input plane with a large area and a

comparatively narrow angular spread to an output space with a small area and a larger angular

extent. For a simple system in which the angular extent is spatially invariant at both entrance and

exit surface, the concentration is given by the equation below, with the maximum concentration

occurring when the angular extent at the output face is a full 2π steradians.

The major implication of this equation for CPV systems is that increasing the concentration

ratio necessitates a smaller system acceptance angle. The sun itself has a fairly small angular

extent (approximately ±0.26°), but the rotation of the earth causes the sun to effectively sweep

over a large range of angles. Concentrating systems must either have a large enough acceptance

angle to produce power at various times throughout day, which requires a low concentration ratio,

or the system must be mounted on a tracker that adjusts the pointing of the module to maintain

the module’s alignment with the sun. Higher concentration systems have narrower acceptance

angles, and thus demand more accurate trackers. These high precision trackers are substantially

more expensive.

15

1.3.2 CPV Families

While CPV systems can have geometric concentrations anywhere from just over one up to

potentially several thousand, most systems under investigation fall into one of three different

families. There are reasons to investigate each of these different concentration regimes, and each

has potential for success and barriers that must be overcome before widespread deployment.

1.3.2.1 Low Concentration Photovoltaics (LCPV)

Low concentration systems are closely related to flat panel systems. The sun typically only

covers most of the East-West range in the sky over the course of a day, but the North-South

variation of the sun is defined mostly by the tilt of the Earth’s rotation axis. This limited variation

allows a small degree of concentration without any tracking systems. With a static mount, the

large angular variation of the sun dictates that concentration ratios must be low, and these

systems typically operate between 1x and 3x concentration.

The primary advantage of this family of designs is the possibility of incorporating advances

from current flat panel technology. These systems do not require different mounts, different cells,

or additional thermal management, and thus can act as a simple retrofit for flat panel systems that

reduces the amount of actual PV material required. To be cost effective, these optical systems

must be extremely inexpensive and thus the optical design of these concentrators tends to be

relatively basic. A few sample LCPV systems are shown below in Figure 1-6. Simple TIR

concentrators that can be made through high volume processes such as injection molding are

common.

16

Figure 1-6: Two example low concentration systems. The system on the left relies on flat mirrors to reduce silicon use by approximately 2x

12(image reproduced with permission of copyright holder Zytech Inc.), while the system on the

right is a truncated CPC with a concentration of 3.5x13

(Image reproduced with permission of copyright holder Intech Inc.).

The viability of these systems is critically linked to the success of flat panel systems.

Currently, the cost of a Silicon flat plate module is heavily influenced by the cost of the actual PV

material, but the price of silicon is expected to drop relatively rapidly. The potential savings of

LCPV designs are in reducing the actual chip cost by a factor of up to three, but if the cell cost is no

longer the driving cost of the module, these systems lose the advantage over the simpler flat plate

technologies.

1.3.2.2 Mid concentration Photovoltaics

Mid concentration designs aim to balance the added complexity required for a

concentrating system with the potential benefits of more efficient cells. A key parameter in

determining the optimal concentration to design the system for is the future cost of high efficiency

solar cells. Projections of the cost of these cells are highly uncertain, and cost estimates can vary

by more than an order of magnitude. Mid concentration systems usually seem to employ a higher

17

efficiency cell to gain added power. An example of mid concentration designs that is being further

investigated is shown in Figure 1-7.14 This system uses a shaped trough reflector to concentrate

light onto the PV material and requires only one tracking axis.

Figure 1-7: A mid concentration photovoltaic module. The system only requires one tracking axis and uses a trough

mirror to focus incident light onto the solar cell. Image reproduced with permission of copyright holder SunPower

Inc. Image available at us.sunpowercorp.com

Mid concentration systems seek to gain the benefit of higher efficiency cells with

dramatically reduced cell costs while balancing the expenses of adding complexity to the optical

system and tracker. This family of systems operates in the general range of 25x to 75x

concentration. By keeping a moderate concentration, these systems place lower demands on the

tracking system, and thus either a single axis or simple two axis tracking system can be used. This

can keep mounting costs lower and can still use relatively simple high volume optical systems.

18

This concentration also frequently allows the use of passive cooling systems which are much less

expensive than active cooling systems.

Mid concentration systems frequently rely on projections that higher efficiency solar cells

will be available at a dramatically reduced cost. Advances in producing high efficiency cells make

this assumption plausible, but there are obstacles that must be overcome before these cells are

available at a cost that would be feasible at this concentration level.

1.3.2.3 High Concentration Photovoltaics (HCPV)

High concentration systems use much more complicated optics to achieve concentration

ratios between 150 and 1,000. Dramatically reducing the amount of PV material allows these

systems to use the highest efficiency chips available and not have the chip be the driving cost of

the system. These modules have to be mounted on precision solar trackers to precisely maintain

alignment to the sun for the system to produce significant power. These systems can harvest less

than 5% of diffuse sunlight, and are thus inefficient when the direct solar radiation is blocked.

High concentration systems provide a completely different cost structure to currently

available flat plate technologies, and the development of a new high concentration optical system

is the focus of this thesis.

1.3.3 Critical Components of HCPV Systems

The research presented here is focused around a concentrator design aimed for use in

high concentration photovoltaic (HCPV) systems. These are inevitably complex systems with a

large array of components working together to produce power. This research focuses on the

concentrator system. In order to justify performance and cost goals, information about the cost

19

and specifications of the other components of the system is necessary. Active research continues

in several areas aimed at both improving performance and lowering cost of other components of

the HCPV system, and these dramatically affect the cost competitiveness of the final system

incorporating the proposed light guide concentrator. A brief overview of the system components

is described below in order to inform the performance goals of the concentrator.

Figure 1-8: A schematic of a generic concentrating system. Assumptions are made about the other components to inform targets for the concentrator that is developed in this thesis (component 3).

1.3.3.1 Land for System Deployment

By targeting the utility market, the location for these systems should be inexpensive and

have as much direct sunlight as possible. An ideal location for these systems is the desert in the

Southwest United States. An ideal location for a solar power plant is on extremely inexpensive

land with high direct solar incidence that is near a population center to minimize transmission

losses and keep component transportation costs down. States such as Nevada and Arizona are

actively seeking solar projects to provide clean power, and these represent ideal locations for

constructing a solar plant.

20

The annual cost to rent a parcel of land for a solar power plant varies substantially by

location. According to the Bureau of Land Management, the annual cost to rent land in

designated “solar areas” ranges between $15 and $315 per acre per year. This represents a

negligible cost compared to the rest of the installation, as this is equivalent to between 0.3¢ and

7.8¢ per square meter, while the cost of the system is orders of magnitude greater.15 The final

location of a solar power plant is more heavily influenced by legislative policy decisions and tax

incentives.

1.3.3.2 High Precision Solar Tracker

High concentration photovoltaics must be mounted on a precision solar tracker in order to

maintain alignment with the sun over the course of time. When working with concentrations of

several hundred suns, the system is limited to a two axis tracker. The two critical specifications

that the tracker will place on the concentrator are the pointing error that the concentrator must

be able to compensate for and the weight that the tracker is capable of bearing while maintaining

its alignment.

The accuracy of commercially available solar trackers varies based on the manufacturer

and the location of installation. Wind loading causes substantial pointing errors, and thus any

concentrator mounted on these trackers must have an acceptance angle that can compensate for

this misalignment. While the accuracy of several trackers is quoted to be 0.3° or less, this is

frequently just the drive accuracy and does not take into account misalignments from wind or

other factors. From a study conducted by Green Mountain Solar, the measured pointing error on

current commercially available solar trackers is determined to be approximately 1.2°. Ongoing

research has produced prototypes that have improved on this substantially16, but pricing

21

information and longer term performance require further testing. In order to accommodate a

reasonable error in tracking systems, the light guide concentrators are designed to have an

acceptance angle of ±1.0°.

The weight of HCPV systems that are currently deployed greatly exceeds that of the

proposed concentrator systems, and this is not a limiting factor for deployment within currently

available trackers. The light guide concentrator is much thinner and lighter than current HCPV

systems and therefore has the potential to be deployed with alternative tracker systems that

might substantially reduce cost.

The tracker system is currently a driving cost in HCPV systems which costs approximately

$150/m2. Current trackers are large and bulky systems relying on mechanical gears and crowns

that are expensive and difficult to maintain. Research is ongoing into simpler, cheaper, and more

reliable tracking methods, and this cost is expected to fall substantially in the near future. In order

to reduce this cost, an ideal optical system will have a reasonable acceptance angle to

accommodate small misalignments, be light enough to lower the mechanical requirements of the

tracker, and be scalable to allow the size of the tracking system to be an independently optimized

parameter.

1.3.3.3 Concentrating Optics

The concentrator will be the focus of this dissertation. The performance and design of the

concentrator directly affect the requirements of the other components of the system and the

performance of the module as a whole.

22

1.3.3.4 Photovoltaic Cell

A critical quality for the solar cells in an HCPV system is the getting the maximum

conversion efficiency. The high concentration causes the cell cost to not be a critical driver in most

cases, which enables use of the highest efficiency cells available at the time of production. Rapid

advances continue to be made in many different families of high efficiency solar cells, which

makes predicting the efficiency or cost of these cells imprecise. Records for solar cell efficiency

have been set and broken many times in recent years17. The most common cells that are designed

to be used with HCPV systems are III-V multijunction cells. These cells are significantly more

efficient under concentration, and thus HCPV systems have the highest potential efficiency of any

PV system currently known. Under high concentration, these cells have reached conversion

efficiencies of 44.0%18.

One issue that there is significant disagreement over is the cost of these high efficiency

cells. Current production methods for these cells involve growth on an extremely expensive

substrate that must be discarded after use. A relatively new method for reusing the substrate to

grow more than one cell called epitaxial lift-off has promise of reducing the cost of these cells.19

Manufacturing high efficiency cells is still a subject of extensive research, and thus approximating

a final cell cost per area is imprecise. Predictions range from approximately $5,000 to $50,000 per

square meter, which affects the optimal balance of system concentration and tolerances on the

system components.

23

Figure 1-9: The efficiency improvement of several different families of cells. Rapid growth, especially in the multijunction cells, is continuing. Image reproduced with permission of copyright holder National Renewable Energy

Laboratories(NREL). Image available at http://www.nrel.gov

Multijunction cells are stacks of multiple p-n junctions with different materials designed to

convert different bands of the solar spectrum. These junctions convert a portion of the solar

spectrum efficiently into electricity while being transparent to the rest of the spectrum, which

passes through to the junction where it is most efficiently be converted. This allows a broad

spectrum to be converted more efficiently than for any single junction device, which yields the

high efficiency of these cells. One potential drawback for these cells is the added design

requirement that the cells be optimized to convert the actual spectrum delivered by the

concentrator. Vertical junction stacks with no internal contacts require the current at each

junction be matched, or the junction producing the least current limit the cell as a whole.

24

1.3.3.5 Back End Electronics and Storage

Photovoltaics produce a direct current and only do so when exposed to sunlight. In order

to be used by the end consumer, this must be converted into an alternating current of the proper

frequency, which requires the use of an inverter. A larger challenge for solar energy remains the

intermittency of energy generation. Solar energy must be stored for use on demand in order to be

a viable alternative to fossil fuels which can be burned to meet demand. This system must also be

incorporated into the grid, which represents an additional cost, though this is consistent for all

power generation methods. The approximate component cost breakdown of a solar installation is

shown in Table 1-2.

Table 1-2: Standard cost breakdown of a solar installation.

Photovoltaics produce a direct current while the electrical grid and most power

applications require an alternating current. To convert a direct current into an alternating current

of the appropriate frequency requires the use of a solar inverter, also referred to as an electric

drive. These come primarily in two forms: a micro-inverter and a string/central inverter. Micro-

inverters convert power from an individual panel and made up over 98% of inverter revenues in

201020. These systems dominate the current market because they can avoid high voltage wiring,

reducing line losses. Micro-inverters are much more expensive than string inverters,21 and also

have multiple points of failure whereas a string inverter is consolidated into a single system. String

Component Cost %

Module 40-60

Inverter 10-18

Battery 15

Charge Controller 10

25

inverters are much more cost effective for a utility scale system, and thus continuing development

of these systems is critical for utility scale solar power production.

Solar panels only produce power when the sun is out, and therefore this power must be

stored for use on demand in order to be a commercially viable replacement for fossil fuels. There

are a variety of potential storage mechanisms for PV systems, but one of the most rapidly

emerging and promising technologies is Lithium ion batteries. Extensive research and

development is being done on this technology for use in consumer electronics, as these batteries

have an extremely high energy density and can be recharged many times without being depleted.

These systems face substantial competition from more mature technologies such as Pb batteries,

but market penetration is expected to improve rapidly over the next few years as Lithium ion

technology becomes more readily available in utility scale capacities.22

While rapid advances in battery technology provide opportunities for less expensive storage

for solar power generation, this makes cost projections quite variable. Currently, no high capacity

(>1MW) Lithium ion battery system is available, yet projections of these systems have the cost

ranging from $350 to $600 per kW for utility scale systems23, which increases the cost of an

intermittent solar plant providing consistent power.

1.3.4 Current HCPV concentrators

HCPV systems currently make up a very small portion of solar power technologies. Flat

plate silicon or other thin film technologies are much more mature and have reached a stage

where large deployments are being made. Some HCPV systems have gone through construction of

either functional single units or small pilot plants, with a few utility scale projects under

construction that are set to come online in the next decade.24

26

The optical designs for these systems are dominated by Fresnel lens based concentrators.

These systems employ a large Fresnel lens as a primary element, which then focuses incident

sunlight onto a secondary optical element, which increases the concentration slightly and

homogenizes the light over the PV cell. Despite a relatively simple optical design, these systems

can reach geometric concentration ratios of nearly 1,000x while maintaining optical efficiencies of

greater than 70%. The relatively simple optical design allows manufacturers to take advantage of

previous experience fabricating Fresnel lenses, which has accelerated this design to a later stage of

deployment than potentially competitive systems.

The design of the Fresnel lens primary element and the secondary optical element vary

from system to system, but there are several factors common to these Fresnel systems that limit

potential performance. The optical efficiency of these systems is limited by two primary loss

mechanisms inherent to the design, which are Fresnel losses and “tooth” losses caused by

manufacturing limitations related to the Fresnel lens primary. The Fresnel losses resulting from

light entering and then exiting the lens are added to the Fresnel loss entering the secondary

concentrator for a combined loss of approximately 15%. Antireflection coatings can reduce this,

but broad band coatings provide a substantial extra expense to the system and are potentially

damaged by environmental factors.

The other limiting factor of Fresnel system’s optical efficiency arises from manufacturing

tolerances. Fresnel lenses are made by attaching a structured polymer (either thermoplastic or

silicone) to a glass substrate. Two imperfections are inherent in such a system: a rounding of

sharp corners and a draft angle on surfaces that are ideally vertical, as shown in Figure 1-10. Light

that hits a rounded feature or a draft wall is not coupled to the secondary concentrator and thus is

27

lost. The magnitude of these losses is be dependent on the designed tooth geometry and

manufacturing process, but is typically between 7% and 12%.

Figure 1-10: The ideal Fresnel lens (left) will suffer from a minimum draft angle (center) and rounding of the ideally sharp corners (right) which will substantially reduce optical efficiency.

While the Fresnel lens based concentrators account for the majority of currently installed

HCPV systems, other designs rely on an obscured reflector to focus incident light onto the receiver.

These can take the form of a large dish or more complicated designs involving multiple reflective

surfaces. An example design for high concentration reflective systems is shown in Figure 1-11.

These systems can achieve high geometric concentrations well over 1000x. In addition to the

obscuration caused by the receiver, most of these systems put a tremendous strain on the tracking

system, as the heavy receiver presents a heavy load that is difficult to balance. These systems are

also frequently too large to hermetically seal, and thus maintenance costs are higher than for

alternative systems.

28

Figure 1-11: A large dish concentrator. This was a test module in Phoenix, AZ that is approximately 75 feet in diameter. Image reproduced with permission of copyright holder Southwest Solar Technologies

25

1.4 Light Guide Concentrators

Light guide concentrators are designed to trap light within a solid medium where it is

coupled to the output of the system. These systems usually trap light within a relatively thin layer

using total internal reflection at the top and bottom boundaries to contain light within the guide.

There are two critical qualities that differentiate the various families of light guide concentrator.

First, the injection method is how the specific concentrator traps the light within the guide layer.

The second critical characteristic is how the light trapped within the guide is coupled to the

desired output.

1.4.1 Alternative Light Guide Concentrators

While there are many alternative light guide concepts such as fluorescent26 and dye

sensitized concentrators, microoptic concentrators use precisely engineered optical features to

deflect light into the guide substrate. These systems typically take advantage of an array of

29

primary microoptics to focus incident light onto a small injection feature, which then couples the

light into the guide material where it is trapped.

An example of such a microoptic concentrator with a dramatically different design than

the systems detailed in this research is Morgan Solar’s Sun Sumba27 concentrator. This light guide

is rotationally symmetric and is designed to couple light to the center of the part where a

secondary concentrator further concentrates the light onto the solar cell. The thickness of the

light guide increases near the center, which allows light to more efficiently couple towards the

center without interacting with injection faces closer to the center. Figure 1-12 shows a schematic

for the Sun Simba concentrator.

30

Figure 1-12: A schematic for the Morgan Solar rotationally symmetric concentrator system.

A light guide system closely related to the systems developed at University of Rochester

has been investigated at the University of California, San Diego28. This system uses a lenslet array

to focus incident light into small injection patches. These patches have small extruded triangular

prisms which then deflect light toward two edges of the guide layer as shown in Figure 1-13.

These systems have been successfully prototyped and have achieved a geometric concentration of

40x with an optical efficiency of 32.4%. These systems rely on the injection elements being small

and having a small vertical extent, which allows them to shadow less of the light injected from

31

facets upstream. Light contained within the guide that interacts with another injection feature

downstream with be coupled out of the guide.

Figure 1-13: A schematic of the UCSD light guide concentrator. Light is focused onto coupling prisms that redirect light to either side of the light guide. Image reproduced with permission of copyright holder The Optical Society.

1.4.2 Dimpled Light Guide Concentrators

The dimple light guide concept was originated at University of Rochester. Initial designing,

modeling, and prototyping were done previously, and were detailed in the PhD thesis of Blair

Unger. These were layered systems, with a lenslet layer that focused incident light onto a set of

injection prisms on the other side of the concentrator. The lenslet layer was made up of either

refractive or reflective elements. These injection prisms redirected light approximately 90° into

the guiding layer. A low index layer separated the lenslet layer from the guide layer, which

allowed light that had been injected to avoid successive interactions with the lenslet array. A

schematic of the dimpled light guide concentrator is shown in Figure 1-14.

32

Figure 1-14: Schematics for a refractive and reflective dimpled light guide system.

The injection element in this system is an air prism that reflects incident light via total

internal reflection. As light propagated down the guide layer, further interactions with the

injection prisms would cause light to couple out of the guide layer and be lost. To prevent this, a

bypass prism is combined with the injection prism to redirect light away from the facet. Light

hitting the bypass prism will continue propagating in the guide, though at a slightly increased angle

relative to the guide axis. A schematic of an injection-bypass prism combination (referred to as a

dimple) is shown in Figure 1-15.

33

Figure 1-15: A schematic of a dimple for use in a dimpled light guide. The injection prism is shielded from light injected upstream by a bypass prism.

The first dimpled light guide prototypes used employed a conic lens array with hexagonal

aperture and the “knife edge” dimple design shown below in Figure 1-16. The manufacturing

process used was not able to accurately recreate this geometry, as both the vertical side walls of

the bypass prism and the sharp tail were not fabricated accurately. These defects were modeled

to determine the relative sensitivity of each manufacturing defect, and it was found that the

rounding of the bypass prism tip and rough vertical side walls had the greatest detrimental effect

of the dimple defects.

34

Figure 1-16: When fabricated, the knife edge prototype had a rounded tail, substantial drafts on the side walls, which were also rough. This substantially degraded performance.

The second generation of dimpled light guide prototypes was designed to avoid the

defects that most dramatically reduced the efficiency of the first generation prototypes. The

steep side walls were removed, and the whole bypass prism was replaced by a rounded structure

that smoothly blended all sharp corners. The second generation prototype, along with the

designed dimples and the dimple structures that were actually fabricated are shown in Figure 1-17.

35

Figure 1-17: The second generation light guide prototype (top), the designed dimple geometry (bottom left), and an SEM image of the fabricated second generation dimple structure (bottom right).

The second generation of light guide prototypes was designed to be 50mm x 60mm with a

1mm thick glass guide layer and a 100µm dimple layer. The optical efficiency of the prototype was

measured to be 72% at a geometric concentration of 55x. The acceptance angle of the

concentrator prototype was measured to be approximately ±1.0°. This system provided a baseline

for the dimpled light guide concentrators described in the remainder of this thesis.

This first generation of light guide concentrators was intended to provide a proof of

concept. These systems validated the design methods and demonstrated the capability of the

36

modeling software for assessing performance errors. While the cost of high efficiency cells used

with CPV systems is expected to decline, these cells currently cost approximately $50,000/m2.

These concentrators were only designed to be approximately 55x geometric concentration, and

with current cell costs, this low a concentration would prevent these systems from ever being

commercially viable. The focus of this thesis is to redesign the dimpled light guide concept into a

system with concentrations of several hundred, which would allow these concentrators to

compete economically.

37

2 Modeling and Design

2.1 Overview

Efficient development of new concentrator systems requires accurate models to guide

fabrication efforts. Dimpled light guide concentrators have complex microstructured features and

complicated light paths through multiple layers of material. Modeling these complicated

structures requires the use of multiple software packages and the use of key simplifications to

make optimization feasible. In addition to predicting the optical performance of concentrators,

the lifetime of these devices and performance degradation when deployed in the field are

investigated. These devices are designed for deployment outside in a desert setting, and they

must be able to survive thermal cycling, high solar flux, and environmental conditions associated

with decades of deployment in such a setting.

The design process was used determine which concentrators were most viable to fabricate,

but the models were also used to improve manufacturing processes. Initial prototypes were

fabricated, and then characterized as discussed in Chapter 3. Prototype features were measured

and characterized, and then they used to update the model parameters. When the concentrator

prototype was sufficiently characterized, the measured optical performance and the modeled

performance mirrored each other. The model could then be used to determine which errors or

effects were the driving the performance and guide future manufacturing improvements.

2.1.1 Modeling Software

Design of the next generation of light guide concentrators relied heavily on computer

simulations to guide the development from concept through prototype fabrication. The primary

38

software packages used in the design and performance modeling of these light guide

concentrators were SolidWorks® (Dassault Systèmes SolidWorks Corp.) and LightTools® (Synposys

Inc.). These two programs were dynamically linked, which allowed for optical simulations of

systems involving complicated feature geometries. These simulations were able to model the

effects of a wide variety of design options, manufacturing limitations, and system conditions to

refine system concepts toward fabrication.

SolidWorks® is a 3D CAD design and analysis software package that was used to model the

complicated dimple and lenslet geometries required by the light guide systems. Solidworks®

enables the modeling of the complicated designed features and the inclusion of expected

manufacturing defects resulting from the high volume production processes these systems are

designed to cater to. This provides critical information about the sensitivity of the various designs

to manufacturing defects or errors. SolidWorks® also has a Finite Element Analysis (FEA)

simulation package that allows for analysis of both mechanical and thermal strains on the system.

The FEA capability is used to predict thermal and mechanical stability of light guide concentrator

systems when deployed in the field.

LightTools® is a non-sequential ray tracing program that is used to simulate the optical

performance of the light guide concentrators. The dimple and lenslet features are linked from

SolidWorks®, which allowed for optimization of these features within LightTools®. LightTools®

provides an efficient means to trace a large number of rays through complicated systems, and this

allows precise optimization of many parameters that have a complex interdependence. In

addition to accounting for the complicated geometries demanded by these systems, LightTools®

39

can model a wide variety of materials, optical coatings, and provide an approximation of the yearly

energy output of a solar system.

2.1.2 Modeling Methods

These systems were generally modeled by patterning features designed in Solidworks®

using LightTools’® 3D texturing feature. This allowed any feature that was modeled in

SolidWorks® to be patterned in an appropriate geometry, as shown in Figure 2-1. The array of

microfeatures could then be used in ray tracing simulations, and the optical performance could be

modeled. Several of the systems involved dimple features that blended together, and these could

be designed in the same fashion, though extra care must be taken to ensure that the region

joining neighboring features had an appropriate boundary.

Figure 2-1: A lenslet feature is created in Solidworks and then patterned appropriately using LightTools.

Another common modeling practice for these light guide concentrators is to use a thin

section, such that the dimension perpendicular to both the guiding axis and the incident light is

much smaller than would be practical for an actual system. This is simply to reduce the

computation time required for the ray trace, and has been observed to have no noticeable effect

40

on the performance as long as an entire repeating section is used. Rays propagating down the

guide that are incident upon these edges are reflected back into the guide as long as they are

below the critical angle. While rays incident with an angle greater than the critical angle are

unduly ejected from the system, these rays generally do not propagate far enough in the actual

guiding system to account for a significant discrepancy.

2.1.3 General System Parameters

The light guide systems are designed for deployment, and thus several common parameters

are assumed throughout the design process. All high concentration systems require the use of a

solar tracker, and the pointing accuracy of these devices determines the acceptance angle that is

required for the mounted concentrator. There are a variety of precision solar trackers available,

and more advanced systems are being developed. The maximum pointing error can be as small as

half a degree, but in most systems that consider wind loading it is substantially larger than that.

Increasing the acceptance angle decreases the concentration that the system can achieve, so a

tradeoff must be made between concentration and acceptance angle. The dimpled light guide

concentrators are designed to have acceptance angles of ±1.0°, which is achieved by a range of

tracker systems and designed to tolerate some manufacturing error in the concentrator as well as

in the deployed system. In a 2008 study of tracker accuracies, Green Mountain Engineering

measured the fraction of captured energy as a function of acceptance angle. The dependence of

tracker pointing on wind speed can be seen in Figure 2-2.29

41

Figure 2-2: Tracker Accuracy is dependent on wind loading (left) and the acceptance angle determines the fraction of energy available (right). Image reproduced with permission of copyright holder Green Mountain Engineering.

The source used in the ray tracing simulations is designed to mimic the sun both in angular

extend and spectral composition. The sun has an angular extent of ±0.26° as measured from the

surface of the earth. While the systems are designed to optimize performance over the range of

±1.0° to account for manufacturing defects and tracker pointing errors, the optical efficiencies

reported correspond to a ±0.26° source. The spectral power density of the source is critical to the

performance of the PV material the concentrator is coupling the light onto. The intensity and

spectral composition of the sunlight striking the surface of the earth varies according to a wide

array of factors including location, time of day, season, atmospheric conditions, and solar activity

variations. ASTM G173-0330 consists of two standard spectra. The first spectrum shows the direct

incident solar radiation at the average latitude of the contiguous United States at peak irradiance

under normal atmospheric conditions, and the second spectrum shows the radiation adds in the

diffuse radiation contribution to provide the total spectrum incident under optimal conditions at

37° latitude. The ASTM G173-03 spectra are shown in Figure 2-3 The direct spectrum is used as

42

the incident spectrum for design and modeling, as CPV systems cannot capture the diffuse

component.

Figure 2-3: ASTM G173-03 Direct Component. This is a standard spectrum representative of peak irradiance in the United States

The solar spectrum spans a broad band of wavelengths, but not all of the energy that

reaches the earth can be converted into electricity by photovoltaic materials. For characterizing

the optical efficiency, the spectrum is usually truncated at an energy corresponding to the lowest

bandgap material used in the solar cell. For simple silicon cells, this corresponds to a wavelength

of approximately 1100 nm, while for multijunction cells that commonly use germanium as bottom

cell, this can extend to 1770 nm. During the design and characterization of the light guide

concentrators, for this thesis the spectrum is truncated at 1856 nm, which is in the center of an

atmospheric absorption band. The spectrum is truncated on the low wavelength end at 280 nm,

43

as there is a negligible amount of solar radiation incident at wavelengths shorter than this, and

this high energy radiation is frequently damaging to system components.

2.2 Concentrator Optical Design and Performance Modeling

The previous generation of light guide concentrators was used as an initial starting point

for judging performance, and provided a substantial amount of information from which the

system design were altered to improve optical performance. Three novel families of light guide

concentrator were investigated using the knowledge gained from previous generations. The

design of each system used a set of materials and manufacturing limitations that were expected to

be compatible with high volume processes. In addition to the designed optical performance, the

sensitivity to various manufacturing and deployment defects was presented. The presented cases

did not cover all the potential variations of these concentrator families, but were designed to

demonstrate an ideal performance target while maintaining realistic manufacturing cost goals.

2.2.1 Phase Space Performance metric

The primary goal of modeling and design work is to achieve as high a geometric

concentration and optical efficiency while maintaining the ability to manufacture these systems in

a cost effective manner. One of the most useful tools for judging the performance of a

concentrator during the design process is to gauge the performance of a concentrator using

étendue, specifically the simplified phase space. The phase space volume is defined in section

1.3.1. The input to an optical system gives a volume in phase space, and in a lossless system, this

cannot be compressed. This can be expanded or diluted, but cannot be reduced without losing

light. A 4 dimensional space is difficult to use as a design tool, and thus some simplifications and

approximations are used.

44

For light guide systems, the cross-sectional area of the guide is approximately constant as

light travels down the guide. While the tail features of the guide shrink the guiding area slightly in

order to shield a downstream injection facet, this is taken to be a small effect. The angular

spectrum of the guide is also taken to be approximately independent of cross sectional position.

This does not take into account the sections close to an injection facet where a cone of injected

light has not dispersed throughout the cross sectional area. This injected light forms a small

portion of the flux through any surface except the facets farthest from the chip. The phase space

is thus reduced to the two angular components.

The angular spectrum propagating in a light guide system provides a substantial amount of

information on how effectively the system is concentrating light from an étendue standpoint.

How the system is filling the target angular space provides insight on how to improve concentrator

performance and how much further concentration can be done. The extent of the angular

spectrum dictates what loss is necessary for a certain increase in geometric concentration. The

goal for a light guide concentrator is to couple the input angular spectrum (the effective injection

angular spectrum) and couple it to the angular spectrum that can be contained within the guide at

the output face of the concentrator.

The target angular spectrum that can be contained by the guide is determined mostly by the

materials chosen, though the dimple geometry has a small effect. The light is contained by the

interface with the low index layer on one or potentially 2 sides and an air interface on the

remaining sides. The target angular spectrum is thus rectangular with a larger containment angle

in the plane of the guide. The use of the angular spectrum as a diagnostic tool is shown by looking

at the angular spectrum propagating through a dimpled light guide assembled previously and

45

described in detail elsewhere31. The angular spectrum is shown at several different distances from

the injection element in Figure 2-4.

The angular spectrum provides a useful tool for assessing the performance of a light guide

concentrator. The asymmetry of the target angular area can be seen in Figure 2-4, as the vertical

containment comes from the interface with the low index layer. Whether the bottom of the

dimple structure is an air interface or another low index interface, repeated reflections from the

top and bottom surface quickly mirror incident light, and thus the boundary is effectively

symmetric about the guide plane. The asymmetry of containment shows that it is more effective

to spread light in the guide plane (laterally) than vertically if the two can be isolated.

46

Figure 2-4: The angular spectrum a) 1mm, b) 18mm, c) 36mm, and d) 52mm from the injection element. The angular spectrum 1mm from the guide is that injected by the lenslet. The angular spectrum expands as light travels further down the guide, and any light travelling with too large an angle (outside the blue rectangle) is lost from the system.

47

Close to the injection element, the angular spectrum almost exactly mirrors the spectrum

input by the lenslets (only adding facet scattering and defects). In Figure 2-4a, the hexagonal

lenslet aperture is clearly visible. The injection element was not designed to rotate the light 90°,

which can be seen by the angular spectrum being asymmetric about the guide plane before it has

reflected off the top surface. There is also substantial spatial dependence before the injected light

has uniformly spread throughout the guide. In Figure 2-4b, the injected light has spread to fill the

light guide fairly uniformly. The angular spectrum is symmetric about the origin, and several

distinct patches can be seen. Every interaction with the tail of a dimple feature spreads the

angular spectrum by a discreet amount, which leads to these distinct regions. As light travels

down, more of the light is spread into these discreet regions as successive dimples are

encountered. The injected light does not evenly fill the space, as light traveling with a higher

lateral angle will be exposed to a larger cross section of the tail, increasing interaction probability.

It can be seen in Figure 2-4c and d that the angular spectrum has expanded to fill the entire target

area. This is the limit of the concentration that can be achieved without loss, and at these

distances, substantial guiding loss has already occurred.

The next generation of concentrators was designed to improve on some of these

deficiencies. It was critical to evenly fill the target angular area, and to minimize the dilution of

high angles. The dilution of angular space at higher angles was inherent to the dimpled light guide

concept. Higher vertical angles yielded more frequent interactions with the dimple layer and thus

faster increase in angle. Propagating with a high lateral angle increased the effective cross section

of dimples, making interaction with a dimple more likely when light traveled through the dimple

layer.

48

2.2.2 Lenslet Design

First generation light guide prototypes used conic lenslet arrays with flush hexagonal

apertures.32 This aperture shape was used because a hexagon produced the most nearly circular

angular spread while still meeting the requirement that the aperture shape tessellate. The lens

array had no designed discontinuities to make fabrication less challenging and reduce cost. The

next generation of light guide concentrators made use of offset lens arrays which had designed

discontinuities at the edge of the apertures. Offsetting the lenslet aperture substantially

decreased the effective injection numerical aperture, and thus allowed superior guiding while

maintaining high injection efficiency. Optimizing the aperture shape of the lenslets also allowed

manufacturing limitations to be considered and further optimized performance.

The ideal injection system produces an injected ray bundle that centered around the guiding

axis, which requires a 90° deviation of the input light. The exact shape of the ray bundle depends

on the dimple geometry and other system parameters. In light guide systems, light reflects many

times off the top of the guide layer and bottom of the dimple layer. These frequent reflections

cause the angular spectrum to be vertically symmetric, and thus effective vertical angular extent

injected into the guide is determined by the largest angular deviation from the guiding axis.

Having the injected ray bundle centered around a vertical angle of 0° thus produces the minimum

effective injected angular extent, and thus allows the greatest concentration.

While 90° rotation of incident sunlight is optimal for guiding efficiency, this rotation is

dependent on total internal reflection at the facet. The critical angle of a material with n=1.5 at an

air interface is approximately 42°. If the center of the ray bundle is incident at 45° in order to

reflect along the guiding axis, the incident ray bundle can only span 3° without injection losses,

49

which corresponds to an NA of .079. This small lenslet aperture makes a 45° injection facet

impractical. Offsetting the lenslet so that the center of the aperture does not correspond to the

optical axis allows the center of the ray bundle to not be normal to the guide plane. This offset

allows a significant injection numerical aperture while still maintaining TIR for the limiting rays and

injecting the center of the ray bundle in the plane of the guide. Figure 2-5 shows the light incident

on the offset lens array (red rays) and highlights the ray at the center of the aperture (cyan ray)

and the ray incident on the injection facet with the greatest angle which limits TIR (green ray).

Figure 2-5: Offsetting the lenslet aperture causes the central ray to be deviated from normal to the plane (Left). If the central ray is not deflected to travel in the plane of the guide the effective injection angular spread will be much

larger (Upper Right) than if it is deflected directly parallel to the plane of the guide (Lower Right)

50

In addition to offsetting the aperture to minimize the effective injected angular spread,

the shape of the aperture can be altered to further optimize concentrator performance.

Customizing the aperture shape is especially useful for accounting for manufacturing limitations.

The shape of the lenslet aperture determines the shape of the injected ray bundle in angular space.

The various dimple geometries all transform the injected ray bundle differently as it propagates

down the guide, so the optimal shape of the lenslet varies based on the dimple geometry.

Customized aperture shapes also allow manufacturing limitations to be taken into account. As an

example, the offset lenses tend to have large surface sag, which is the displacement along the

optical axis of the surface away from the apex. Several processes are limited in the depth they can

accurately produce optical quality surfaces. This restriction combined with the requirement that

the aperture be able to tessellate leads to an unusual optimal lenslet geometry shown in Figure

2-6.

Figure 2-6: A lenslet geometry designed to cater to a manufacturing process where the sag depth is restricted. Allowing customized aperture shapes allows improved injection and guiding efficiencies.

51

While the aperture geometry varies based on a large set of parameters, the lenslet surface

shape only depends on the guide thickness, material choice, and manufacturing capabilities. In

general, the systems performs best when the lenslet focuses to the smallest possible spot on the

injection facet. The ideal surface shape is a conic focusing to a small spot on the injection facet, as

seen in Figure 2-7. A spherical lenslet produces a large amount of spherical aberration which

results rays from the edge of the aperture having up to 250um error in the focal plane. This

causes both lost light on axis and reduced acceptance angle. Spherical lenslets cause an especially

large performance drop when combined with offset lens apertures due to spherical aberration.

Figure 2-7: Optimal optical performance requires a conic surface shape for the lenslets to achieve a tight focal spot (left). A spherical lenslet surface will leave a large amount of spherical aberration and reduce performance (right).

2.2.3 Dimple Tree Performance and Sensitivity

The “dimple tree” concentrator family is the most directly related to the earlier generation

of concentrators. One performance limitation of the “knife edge” dimple that the first dimpled

light guide concentrators employed is the rounding of the tail that is designed to be a sharp edge. .

This is overcome by blending the tails together so that there is no such sharp angle. Each row of

52

dimples is combined into a set of long strips as shown Figure 2-8: The first generation "knife edge"

dimple has been fused into a long strip to avoid the problems associated with manufacturing the

knife edge geometry.Figure 2-8.

Figure 2-8: The first generation "knife edge" dimple has been fused into a long strip to avoid the problems associated with manufacturing the knife edge geometry.

Like the first generation dimples, the system was designed to increase the angular extent

only within the plane of the guide. This system was designed to increase the vertical angular

extent as little as possible, and thus sidewall drafts were avoided if possible. To avoid the extra

draft face that arises from the side with no injection facets shown in Figure 2-8, the strip is made

wider, and the adjacent row of injection facets is attached to the side of the strip opposite the first

set of facets. The injection facets were also rotated about an axis normal to the guide to ensure a

minimum lateral angular spread was injected. The amount of rotation was determined by the

lenslet geometry to compensate for the initial interaction with the wedged side wall that

approximately half of the injected light interacted with almost immediately. These alterations

yielded the tree like shape shown in Figure 2-9.

53

Figure 2-9: The dimple geometry of the "dimple tree" family of light guide concentrators. The injection facets are highlighted in teal.

This dimple geometry is particularly well suited to a reflective design, as the mostly flat

geometry causes relatively little shadowing. In a reflective design, light going through the flat

region of the dimple structure is still focused onto the injection prism face. The only components

that cause shadowing losses are the actual injection faces, draft regions, and fillets. The

shadowing losses are given by

where X, Y, and Z represent the corresponding dimensions of either the injection facet or lenslet,

θd is the draft angle on the side walls, and rF is the fillet radius. For a system with draft angles of 2°,

a fillet radius of 2μm, 100μm injection facets, and 1 mm lenslets, this corresponds to a shadowing

loss of approximately 2.5%. This is substantially less shadowing than for other dimple geometries,

and therefore this system is a much better candidate for a reflective system.

Z

Y X

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The model of the reflective system used a basic silver coating for the mirrors. This was

primarily for cost reasons, as this was a readily available coating that is common for high volume

manufacturing purposes and still had high reflectivity. This coating had a reflection loss of

approximately 5%, and when combined with the Fresnel losses entering the guide and the

shadowing loss, the reflective systems had relatively low injection efficiency. The injection

efficiency of these systems was expected to be lower than 90%. This could be improved through

adding an anti-reflection coating to the front surface or using a more reflective coating, such as

enhanced silver. These would improve performance, and their use was strictly a cost tradeoff. An

uncoated front surface and normal silver coating were projected to be the most viable in terms of

cost effectiveness and formed the baseline for the reflective models. The basic design form of the

dimple tree geometry is consistent, but the specific parameters will vary based on the

manufacturing process, materials used, and the concentration required by the system. For each

set of materials and manufacturing limitations, the specific design parameters are reoptimized to

maximize performance. The optimal design assumes a manufacturing process capable of writing

features with 1 µm fillet radii and 1° draft angles. These are characteristic of high end

manufacturing capabilities. For a material choice, the guide layer and the dimple layer are

assumed to be made of a high refractive index, ultra-transmissive glass, NBAK-1. This is a

commercially available glass, but is dense, expensive, and likely not compatible with most

manufacturing processes capable of achieving the previously mentioned feature sizes. A reflector

array with offset rectangular apertures is assumed.

The ideal design is capable of achieving geometric concentrations well over 1000x with

optical efficiencies of above 70%. This design may not be viable for manufacturing, and is

55

extremely unlikely to be commercially viable due to the high cost and density of the glass.

Relaxing some of the design parameters to use less expensive materials and easing the

manufacturing tolerances reduces the concentration that can be achieved (while maintaining a

reasonable optical efficiency, in this case 70%). The number of possible permutations is too large

to model each individually. A sample of the range of performances that can be expected is given

below in Table 2-1, showing the range between the optimal design discussed above and a less

expensive design catering to a much less precise manufacturing process.

Table 2-1: Development of reflective dimple tree light guide variants showing an optimal design and then tracking various concessions for manufacturing purposes. The results of the earlier Generation 2.5 light guide prototypes are

also shown for comparison purposes.33

This represents a small subset of light guide designs, all of which were designed to

maintain optical efficiency of at least 70%. The field of view, defined as the angle where the

optical efficiency reaches 90% of the peak value, was kept to be ±1.0°. There is a tradeoff

56

between the geometric concentration and the optical efficiency determined by the length of the

guide. The geometric concentration increases as the guide gets longer, yet guiding losses and

absorption losses increase and reduce the optical efficiency. For a few of the dimple tree light

guide structures, the tradeoff between optical efficiency and geometric concentration is shown in

Figure 2-10. Changing the material to a lower index glass for the guide layer primarily causes an

injection efficiency decrease, while relaxing the manufacturing tolerances primarily affects the

guiding efficiency.

Figure 2-10: The efficiency fall off for various dimple tree light guide concentrators as the geometric concentration increases.

This family of dimple geometry is designed to spread light laterally in the plane of the

guide. In a system without drafts and fillets, the angular extent in the vertical direction does not

increase as light propagates down the guide. The angular spectrum that light guide concentrators

can contain is approximately rectangular with lateral containment being larger. The air-guide layer

interface has a higher index contrast than the guide layer-low index layer. The angular expansion

57

is still exponential, as the rays propagating with higher lateral angles interact more frequently with

the wedged dimple side walls. Having a small spread in vertical angle ensures fewer interactions

with the dimple layer and improves the concentration that a secondary concentrator at the output

can achieve.

58

Figure 2-11: The angular spread of a reflective dimple tree light guide with nearly ideal manufacturing parameters (1µm fillet radii, 1° draft angle). The angular spectrum expands almost entirely laterally, with the vertical expansion being due to the draft angles and fillets. The red rectangle shows the boundaries for TIR containment in the light guide structure.

59

2.2.4 Two Stepped Guide Performance and Sensitivity

The stepped light guide provides a different means of concentrating light while employing

similar manufacturing technologies. The other dimpled light guide concentrators that have been

previously investigated and the other families of light guides presented in this thesis concentrate

incident light by expanding the angular spectrum with a relatively consistent spatial extent. The

stepped light guide is not designed to expand the angular spectrum as light propagates, but

instead the guide expands in the spatial dimension. The most important consequence of this

difference is that the concentration at the output face of the guide does not increase as the guide

increases in length. The two stepped guide system has a concentration determined by the relative

size of the injection facet and lenslet aperture, not the guide dimensions. This system allows a

feasible chip size and a larger collection aperture while maintaining the approximately flat system

geometry.

The two-stepped light guide design makes use of two different means of patterning the

injection facets. The first of these is horizontal stepping, in which each facet is slightly offset

laterally from the upstream facet. This allows collection of the light from a series of lenslets into

the same guide. The concentration of this system is equal to the lenslet area divided by the

projected injection facet area. A limited number of these horizontal steps can be taken before the

facet would interfere with an injection facet directly upstream. The number of horizontal steps

that can be taken without interfering with a downstream facet is equal to the width of lenslet

aperture divided by the width of the injection facet. A schematic of horizontal stepping illustrating

the maximum number of steps for a few relative lenslet and facet geometries is shown in Figure

2-12.

60

Figure 2-12: A Schematic of horizontal stepping. This represents a top view with the light purple squares representing the lenslet apertures, the dark purple squares representing the injection facets, and the red rectangles representing

the chips. The relative size of the lenslets and injection facets determines both concentration and how many horizontal steps can be taken. Shown are a 36x concentrator with 6 steps (left), a 9x concentrator with 3 steps

(center) and a 4x concentrator with 2 steps (right)

The other important design geometry for this family of light guides is vertical stepping.

This employs the same concept, but instead of the facets being laterally offset from each other (X

offset), the facets are vertically offset (Y offset). This causes the guide to get thicker at each step,

and thus concentration does not increase with the length of the guide. The expanding guide layer

demands an alteration in the lenslet layer to compensate for the increased focal distance. The

lenslet layer can either become thinner by an amount corresponding to the increase thickness in

the guide layer, or the surface shape of the lenslets can change to have a longer focal length as the

guide gets thicker. These two geometries impose different limits on the number of vertical steps

that can be accommodated in a light guide, as if the lenslet layer is getting thinner, eventually the

curved surface of the lenslets intersects the low index layer. If the focal length is changing, it will

become long enough that the acceptance angle becomes inadequate. A schematic of vertical

Z

X

61

stepping in which the lenslet layer is decreasing in thickness to compensate for the thickening

guide is shown in Figure 2-13.

Figure 2-13: A schematic of vertical stepping. The guide layer increases in thickness so that each injection facet will not interfere with light injected upstream. In this schematic, the thickness of the lenslet layer is decreasing to

compensate for the increased guide layer thickness.

These two stepping geometries can be combined to form a two stepped guide that can

achieve the concentrations required for HCPV while maintaining reasonable chip geometries.

These guides employ horizontal stepping (along the X axis) to the maximum number allowed by

the lenslet and injection facet geometry. Upon reaching the maximum number of horizontal steps,

a vertical step is taken (along the Z axis). Combining these two concepts allows a concentration

equal to the area of the lenslet divided by the projected area of the injection facet. For a

reasonable set of parameters, this can be between 100x and 400x at the output face while still

maintaining the required acceptance angle and manufacturing tolerances. The angular spectrum

Z Y

62

at the end of the guide should be similar to that at the lenslet focus, and thus these systems are

ideal for use with secondary concentrators to bring the concentration to HCPV levels of 500x to

1000x. A schematic of a two stepped guide combining vertical and horizontal stepping is shown in

Figure 2-14.

Figure 2-14: A schematic of a two stepped guide. When a horizontal step would interfere with an upstream injection facet, a vertical step is taken.

The stepped light guide has the advantage of high optical efficiency. Because the angular

spectrum is not expanded as light travels down the guide, the only loss mechanisms in the guide

are the initial Fresnel losses during injection and losses inherent to propagating in the guide

material. These material losses are dominated by absorption, but may also include scattering and

inhomogeneity. The downside of this design is that the concentration is not increased as the guide

is made longer, and therefore it is limited by the relative sizes of the lenslets and injection facets.

Without a secondary concentrator, this geometry is typically limited to below 500x. To achieve a

higher concentration while maintaining the acceptance angle of the system, the numerical

aperture of the lenslet must increase, which will increase the surface sag and make fabrication

more difficult.

63

The angular spectrum of a perfect two stepped light guide is the injection spectrum from

the facet made symmetric about the guide plane. If the device has no manufacturing defects, the

angular spectrum at the output resembles the angular spectrum input into the guide. If the guide

layer has drafts on the side walls and/or filleted corners these does not expand the angular

spectrum, but will circularize it, making it more rotationally symmetric about the guiding axis. This

can lead to performance degradation, as the containment of a light guide concentrator is

rectangular in angle space. For an ideal system, a rectangular lenslet aperture is used to inject a

rectangular angular spectrum with the lateral angle having a substantially greater range than the

vertical angle. Significant draft angles or fillets prevent this angular discrimination and reduce

both the potential injection aperture and the concentration achievable by a secondary

concentrator at the output face of the guide.

While this angular circularization from fillets and draft angles is present in all systems, it is

most readily isolated in the two stepped geometry, as ideally there are no other effects on the

angular spectrum. Shallower drafts and larger fillet radii both increase the degree of

circularization for an angular spectrum, and thus the degree of angular discrimination must

consider the magnitude of these manufacturing defects. An example of an input angular spectrum

designed to have a much greater angular extent in the lateral direction than the vertical extent is

shown for an ideal two stepped guide system. Three different levels of manufacturing precision

are compared in Figure 2-15, which highlights the effect of manufacturing imperfections on the

circularization of the angular spectrum.

64

2.2.5 Axial Index Variation Performance and Sensitivity

The last family of concentrators utilizes an index variation along the axis normal to the

guide plane to improve guiding efficiency and concentration potential. The injection region is

Figure 2-15: The effect on the angular spectrum of a two stepped light guide for various levels of manufacturing defects. More precise manufacturing tolerances allow isolation of vertical and horizontal angles.

65

made to be a higher refractive index than the bulk guide layer, which causes rays travelling up

from the injection layer to be redirected more directly down the guide. This can result in some

rays injected with shallow vertical angle to be trapped within the injection layer, but with the

appropriate dimple geometry this does not result in rapid ejection.

The primary loss mechanism for an ideal dimpled light guide concentrator is through

repeated interactions with the dimpled structure. These interactions increase the propagation

angle of the light travelling down the guide, and if the propagation angle falls outside of the

containment region for the light guide, the light will be lost. In most light guides, the ray angle will

increase exponentially, as rays with larger angles interact more frequently with the dimple layer

and are closest to the angular containment boundary. Light injected from the edge of the lenslet

aperture has the greatest propagation angle and is lost from the system after a relatively short

propagation distance down the guide. This is the performance limitation on most light guide

concentrators. Systems with axial index variation along the y-axis are designed to cater to these

rays from the edge of the lenslet aperture by redirecting them more directly down the guiding axis.

This allows these rays to experience fewer dimple interactions as they propagate down the guide,

and thus increases the achievable concentration. Two configurations for achieving this redirection

are to have a mismatched dimple layer with a higher refractive index than the bulk guide and to

have a gradient index (GRIN) region with the highest index edge smoothly varying to the central

portion of the guide. A schematic for this bending is shown in Figure 2-16.

66

Figure 2-16: An axial index variation will reroute a ray injected with a steep angle to travel more directly down the guide. This can be done with a mismatched guide layer or a GRIN in the guide layer.

Ideally, the index change would be a smooth gradient with the higher index at the edge of

the system. Gradient index parts are more difficult and expensive to fabricate, and the same

principle can apply to a system that has a higher index injection layer with a Fresnel interface

between the guide layer and the dimple layer. The GRIN system avoids Fresnel reflections, which

can cause a portion of light to be trapped despite hitting the interface at an angle greater than the

critical angle. This reduces the performance, as a longer distance trapped in the dimple layer

opens a more direct loss mechanism. Repeated Fresnel reflections of rays incident at an angle

greater than the critical angle, the mismatched concentrators show guiding losses at shorter

propagation distances than GRIN concentrators.

67

Axial index variation does not represent an improvement for all design geometries. While

the rays with the steepest vertical injection angle are bent to travel more directly along the

guiding axis, rays with shallow vertical angles cannot escape the higher index injection region and

repeatedly interact with the dimple region. The axial index variation proves advantageous if these

dimple interactions impart some small added vertical angle. This causes the light trapped in the

higher index injection region to gradually increase in vertical angle until it is able to escape the

higher index containment region and propagate down the guide at a shallow angle. This occurs

over a relatively short distance, and thus the input light homogenizes in vertical angle relatively

quickly. If the bypass prisms impart a primarily horizontal angle, the trapped light quickly reaches

the horizontal containment edge. If the vertical angle imparted is too severe, the light is not

necessarily redirected at a shallow angle by the index contrast.

2.2.6 Wedged Stepped Concentrator

One system that has been modeled that works well with axial index variation is the

wedged step dimple geometry. This system uses the concept of horizontal stepping, as described

in the previous section. Instead of vertical steps making the guide thicker when the limit of

horizontal steps is reached, the facets that are directly along the guiding axis from each other are

connected by a small wedge. This system does not change thickness over its length like the two

stepped guide, and thus the concentration will increase with guide length as for other dimpled

light guide concentrators. Every time a ray hits the bottom surface, it is reflected with a small

increase in vertical angle proportional to the wedge in the bottom surface. Repeated interactions

with this wedged surface cause trapped light to slowly approach the critical angle needed to

escape the higher index region. This light eventually exceeds the critical angle by a small amount

68

and propagates down the guide at a shallow vertical angle. This occurs over a much shorter

distance than the angular accumulation of the initial high angle rays, and thus the vertical angular

spectrum isrelatively homogenous after a certain propagation distance. Each successive

interaction with the bottom surface only increases this propagation angle by a small amount,

which allows the light to travel down the guide a relatively long distance before it begins to

experience guiding losses. A model of the wedged stepped concentrator is shown below in Figure

2-17.

Figure 2-17: A model of a wedged stepped concentrator. The injection facets are joined to the facet directly downstream by a slight wedge. This concentrator geometry uses horizontal stepping.

This concentrator design allows for minimal guiding for a substantial propagation distance.

For the gradient system, an ideal concentrator (no draft angles or fillets impost by manufacturing

limitations) does not experience guiding losses until the rays injected at the edge of the aperture

reach the critical angle for containment. The angular spectrum spans only a small extent in the

69

vertical direction after a given propagation distance. All the rays that propagate a given distance

are ejected from the guide over a relatively short range. These guides thus have a fairly sharp

cutoff from having no guiding losses to complete loss over a fairly narrow propagation length

range.

The ideal GRIN concentrator system can contain the entirety of injected light for a distance

of half a meter or more. At propagation lengths this long, absorption in the guide layer becomes a

critical performance driver. For a concentrator that is 600mm long, absorption of 0.2% for 10mm

of travel causes an absorption loss of greater than 6%. This corresponds to a commercially

available “ultratransmissive” glass, and thus the materials available for such a long concentrator

are limited.

The index variation between the injection facet and the bulk guiding layers should be

strong enough to contain almost the entirety of the injected vertical spectrum. If the index

difference is too small, light propagates into the guide layer with vertical angles higher than ideal,

and the light guide loses the uniform vertical angular spectrum for a given propagation distance.

An index difference that is too high does not diminish performance for a GRIN light guide, but

increases the Fresnel reflections of a mismatched design, which degrades performance. If the

index difference is high enough, performance can be improved by increasing the injected vertical

aperture, though this may cause difficulties in the lenslet manufacturing. The index difference for

a given vertical angular extent θV should be approximately ninj[1-cos (θV)], where ninj is the index of

the injection layer. The index change that is required for a lenslet with an injected vertical NA of

0.3 is approximately 0.03. Many gradient index plastics have Δn on the order of 0.1, but is difficult,

though possible, to fabricate glass gradients with Δn of 0.03 using common methods .

70

These index varied designs rely heavily on isolating the vertical and angular components of

the contained light. Manufacturing defects such as drafts and fillets allow light to transfer some

horizontal angle into a vertical angle, and thus possibly avoid the range of vertical angles close to

the critical angle for the injection region. This guide design relies on all of the light that is injected

increasing in vertical angle slowly through interactions with the wedged bottom surface. Near the

critical angle of the high index injection region, the light picks up vertical angle slowly over a

relatively long propagation distance. These manufacturing errors provide an alternate means of

increasing in vertical angle through this crucial range. These defects prevent the containment of

all of the input light, and cause guiding loss to begin after a much shorter propagation distance.

The effects on the ideal GRIN design from both absorption and small manufacturing defects are

highlighted in Figure 2-18. This assumes a homogenous glass with a base refractive index of 1.536

with a gradient index of .03 over the outer 200µm of both the top and bottom of the guide layer (Y

extremes of guide layer).

71

Figure 2-18: The modeled optical efficiency for light injected into the guide at given distances. Overall the system was designed to be 600mm long with a geometric concentration of 750x. Absorption and manufacturing

imperfections both reduce performance.

The index variation causes light that has traveled a certain distance down the guide to

have a narrow vertical angular extent. This is mirrored about the guide plane, and thus the

angular spectrum comprises two symmetric bands with vertical angle proportional to the distance

travelled down the guide. This effect allows a more uniform filling of the angle space of the guide,

and thus a higher concentration without guiding losses. The ideal wedged stepped geometry

should not affect the lateral angular spectrum, but manufacturing defects will prevent perfect

angular isolation. This creates a loss mechanism by which light can gain vertical angle other than

repeated interaction with the wedged bottom surface, and thus the bands from the ideal design

will become more diffuse.

72

Figure 2-19: The angular spectrum for a gradient index light guide. Manufacturing errors will circularize the spectrum and reduce guiding efficiency of the device.

73

The system described above assumes a shallow axial gradient of 0.03 with the refractive

index at the edge of the guide layer then in the central region. This poses fabrication challenges,

as producing this gradient may be difficult or too costly. Both the GRIN light guide and the

mismatched index light guide perform favorably to a light guide with the entire guide layer and

dimple layer being a high index homogenous material. The performance of these three systems is

shown in Figure 2-20 with no absorption to highlight the difference between these three

configurations.

Figure 2-20: The modeled effects of both a mismatched guide layer and gradient index guide layer compared to the homogenous design

2.3 Material Durability and Lifetime Modeling

One of the most important challenges facing HCPV systems is finding materials capable of

withstanding many years of deployment in high solar resource areas. Typical areas for initial

74

deployment are in sunny areas with inexpensive land such as the desert in the southwestern

United States. The temperature in these areas can vary 25° C or more over the course of a day. In

addition to the daily thermal cycling that these systems must endure, HCPV concentrates sunlight

several hundred times. If the chip is encapsulated, which most HCPV systems are, the

encapsulating material must be able to endure several hundred suns of radiation flux. This

drastically reduces the number of materials available and will also prohibit materials with a

substantial amount of defects that lead to absorption centers that can damage the surrounding

material. Fresnel systems commonly use plastic-on-glass components in low flux regions (the

Fresnel lens), but high flux areas (the secondary concentrator) must be made of glass.

Concentrations of several hundred suns place strict requirements on any materials that

used in HCPV systems, yet the ultimate viability still requires considerations based on cost. In

addition to the material costs, the weight of the modules that are put onto the trackers affects the

cost of the installation. Glass is commonly used for regions of high flux due to excellent

transmission and durability, yet the cost and weight of glass materials are much higher than

polymer equivalents. Most HCPV systems to date employ a mixture of glass and plastic, which is

less expensive, lighter, and easier to manufacture to precise geometries. Material resistance to

environmental exposure is also critical, as air gaps must be hermetically sealed to prevent

moisture or particulate build-up degrading performance.

Light guide concentrators pose a different set of challenges for material selection. One of

the key advantages of light guide concentrators compared to Fresnel lens systems is the thin

geometry. Light guide concentrators are typically be 3-5 mm thick, while most Fresnel systems are

200mm thick or more. Light guide concentrators do not have a substantial air space, and thus do

75

not require hermetic sealing, and significantly reduce the load requirements on the tracker.

However, due to the long path length in the guiding layer, high transmission is even more of a

performance driver for light guide concentrators. The layered structure also poses potential issues

for delamination under temperature variation. The photostability and temperature stability of

light guide concentrators is modeled to provide a potential life cycle analysis and inform cost

modeling.

2.3.1 Ultraviolet and Infrared Absorption Models

Photostability is critical to the performance of HCPV systems, which must deliver as much

of the useful light to the cell as possible while not being damaged. Any material used for the

guiding layer of light guide systems must be extremely transparent in the visible, which contains

the majority of the sun’s energy. Both ultraviolet and infrared light are potential sources of

failure for long term HCPV deployments. While the near infrared can be used by many potential

cells, IR light from the sun with too long a wavelength is not useful for producing electricity. This

unwanted light can still damage a concentrating module if not adequately accounted for. Both

these spectral bands must be considered in the long term photostability of an HCPV system,

though they will have varying effects and solutions.

The models presented here can be easily adapted for a large range of desired materials,

whether glass or plastic. Most glasses have excellent photostability and are insensitive to both UV

and even moderate IR concentrations, and thus the examples are shown for poly(methyl

methacralate). This is a common optical plastic that is readily available in large quantities and

easily machined. PMMA is representative of many available optical plastics; UV can damage the

polymer chain and the material has substantial absorption in the IR, which can cause thermal

76

damage with sufficient power densities. PMMA has excellent transmission in the visible, which is

one of the reasons it is used so commonly as an optical material. The same modeling techniques

can be applied to glass, which usually is much less susceptible to either UV or IR, and applies for

other plastics, which have different susceptibilities that can be modeled readily.

UV light from the sun makes up only a small fraction of the energy hitting the Earth’s

surface, but the high energy photons are capable of causing damage on the molecular level. Solar

UV poses a risk to the long term durability of many optical materials even without concentration,

and thus must be considered. Plastic materials are made of long chains of individual monomers,

and these chains can be broken by photons with sufficient energy. This chain scission causes the

material chain to break down, and pushes the UV absorption edge farther into the visible. The

material begins to absorb blue photons and thus appears yellow. This reduces the concentrator

optical efficiency and can cause thermal runaway if enough light is absorbed. For PMMA, the

Figure 2-21: The UV transmission characteristics of PMMA compared with the solar spectrum incident on the surface. The chain scission peak will cause damage to the material, but a radical scavenger can be

added to absorb this UV.

77

absorption maximum that causes chain scission is at approximately 300 nm. Light with a

wavelength shorter than approximately 330nm must be removed even for applications with no

concentration. Figure 2-21 shows the UV overlap of the solar spectrum and PMMA absorption.

The chain scission absorption is also shown, and a doped PMMA material that is designed to resist

UV damage are also shown.

There are several possible methods for preventing UV damage from light guide systems.

The cost of implementing these methods determines the practicality to a large extent. The UV is

ideally removed before entering the active regions of the light guide. The cover layer can be made

of a material designed to absorb UV without suffering damage, or it can have a coating applied to

this outer surface to reflect or absorb the UV. Another means of removing UV is to employ a

reflective design. Most metal reflector coatings absorb UV, and thus prevent injection into the

guide. This does require the material endure an unconcentrated level of solar radiation before

reaching the reflectors. Many guide materials can also be treated with dopants that preferentially

absorb the damaging UV and prevent damage to the host material.

Excess heat generation from infrared absorption is another material challenge facing HCPV

systems. While many materials and applications must consider UV exposure as a failure

mechanism, the high concentrations of sunlight make overheating from absorption an additional

problem for HCPV systems. IR photons are too low energy to break most chemical bonds, and

thus small amounts is not hazardous to most materials. A large portion of solar radiation incident

on the Earth is infrared (as much as 50%), and when concentrated several hundred times, this can

lead to thermal runaways. Many PV materials can efficiently convert the near IR into electricity,

and thus materials used in concentrators should not absorb this energy before reaching the chip.

78

For most HCPV applications, IR absorption restricts the use of most materials, notably

plastics, anywhere in the concentrator system that carries concentrated flux. For common Fresnel

concentrator designs, this dictates that the secondary concentrator and any encapsulating

material be made of glass, as a plastic material in that position absorbs enough IR radiation to

deform or even melt. The absorption spectrum of most plastics has a significant overlap with the

solar spectrum in the infrared, and thus these materials cannot be used where there is sufficient IR

flux to deform or damage them. The overlap between the solar spectrum and PMMA absorption

is shown in Figure 2-22.

Figure 2-22: The spectral overlap between solar radiation hitting the Earth's surface and PMMA. PMMA shows excellent transmission in the visible, but significant absorption in the infrared at wavelengths longer than 1100 nm.

In light guide concentrators, there are two key regions where light may be concentrated

enough to result in thermal damage to the materials. The first is the foci of the lenslets, which

have concentrations of several hundred times. The concentrators are designed to have a small

0 500 1000 1500 2000 25000

0.2

0.4

0.6

0.8

1Overlap of Solar Spectrum and PMMA Absorption

Norm

aliz

ed F

raction

Wavelength (nm)

Solar Irradiance

Pmma Absorption

Solar Energy Absorption in PMMA

79

spot that can move some on the injection face to provide a more substantial field of view with a

sharper roll off. The size of the focal spot will depend on the lenslet, but is not diffraction limited,

as there is only one optically active surface. Each individual lenslet collects approximately 1mW of

incident radiation and focuses to a spot of approximately 10 µm diameter. This region of high flux

is ideally on the injection face, and therefore this material must be both able to endure this focal

spot and machinable to the precise forms required for the injection prism geometries. The effect

of this focal region depends on the absorption and thermal properties of the material. For many

materials, the actual power dissipated is low enough that the material does not heat up to a

problematic temperature. In order to model this, the absorption information from LightTools was

used in an FEA thermal simulation in Solidworks. The power absorbed throughout the focus cone

was dissipated into the surrounding air, and the final stable temperature profile was modeled. For

PMMA, this model show the focus of the lenslet heating less than a degree. The simulated

thermal effects of a PMMA guide layer absorbing the focused cone of light is shown in Figure 2-23.

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Figure 2-23: The thermal effects of a cone of light focusing onto an injection facet in PMMA. The temperature differential is not projected to be more than a degree, even at the focal spot.

In addition to the lenslet focus, light guide concentrators face thermal challenges from IR

absorption in the guide layer close to the chip where the concentration is several hundred times.

The flux through this region must be high, and covers the entire cross section of the guide as

opposed to a small spot at the lenslet focus. This region can see a flux of several hundred suns

before the secondary concentrator. The high concentration region near the chip is problematic for

most HCPV systems, and thus the material options are extremely limited and usually require high

quality glass. The nature of light guide concentrators allows materials to be used that cannot be

employed in other systems.

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Light guide concentrators allow the use of some materials that are not typically available

for HCPV applications due to the self-filtering of the spectrum that travels down the guide. Any

injected light with a wavelength that is strongly absorbed by the guiding material is quickly

removed from the system and does not propagate farther down the guide. Light that is absorbed

by the material cannot build up to levels that damage the material. This is illustrated by a

simplified model which considers a light guide to be a two dimensional system of arbitrary length

laterally. Light is assumed to be injected evenly along the guide’s length and to travel directly

along the axis of the guide. This ignores the discreet injection facets and the increasing angular

spread but illustrates the effect.

If the flux incident on and injected into the guide is given by Φ a d the ab orpt o of

the mater al g ve by α , the the power ab orbed a d ta ce X from the e d of the gu de

given by

As can be seen from this equation, the power absorbed at any given distance cannot exceed the

incident flux for that wavelength. The power dissipated by the guide cannot exceed one sun

worth of intensity. For spectral components where the guide material has high absorption, the

Figure 2-24: Simplified model of light guide IR absorption. Light is assumed to be injected evenly traveling towards the chip at the left.

82

light injected upstream is removed by the material quickly, and this prevents the buildup of this

energy. This self filtering in light guide concentrators may allow materials such as plastics that

absorb in the IR to be used even in the regions of high flux encapsulating the chip, as the light

guide filters out the regions of the solar spectrum that damage these materials. Alternative

concentration systems do not have this linear property, and thus the infrared that is strongly

absorbed by the guide reaches concentrations similar to the useful light, and damages any plastic

parts carrying high flux.

The light guide concentrator geometry enables the use of a PMMA guide layer for carrying

a high flux and not being damaged. PMMA absorbs fairly strongly in the IR at wavelengths longer

than approximately 1200 nm. Wavelengths longer than this are useful for some cells, especially

triple junction cells, but PMMA cannot efficiently be used to couple these wavelengths in a light

guide concentrator. This highlights the need to optimize the cells and concentrator materials in

parallel, as the spectrum delivered to the cell is dependent on the materials used in the

concentrator, especially in a light guide system where the light is filtered strongly.

For a guide layer of PMMA, infrared light with a wavelength of longer than 1600nm does

not propagate more than a few centimeters before being absorbed almost entirely. Light with

wavelengths between 1200 and 1600 nm travels for a significant distance within the guide, but

this energy is dissipated at approximately the same rate as it is introduced near the end of the

guide. PMMA has excellent transition in the visible, so a minimal amount of this light is absorbed,

even at hundreds of suns worth of concentration. While the optical efficiency for the entire solar

spectrum is not particularly high, most of the light that is lost in a long light guide will be the

infrared, which is less useful to many designs of PV chip. The approximate absorption at the end

83

of the concentrator is compared with the solar spectrum in Figure 2-25 for several different

lengths of concentrator.

Figure 2-25: Heat dissipation by various lengths of PMMA light guide concentrators. Most of the absorption is in the infrared. The absorption approaches the solar spectrum with a characteristic length determined by the material

absorption of the guide layer.

Light guide concentrators have the advantage of limiting the amount of heat that is

created by removing problematic light upstream in the guide. For absorption profiles that are

highly spectrally dependent, such as PMMA, the heat that must be dissipated at the end of the

guide can be fairly similar the heat that is dissipated at regions of much lower concentration. This

enables high flux regions to endure a relatively moderate temperature rise compared to

alternative concentration systems. This screening of absorbed radiation can allow many more

materials to be used as guide layer materials while still undergoing only modest temperature rises

200 400 600 800 1000 1200 1400 1600 1800 2000 22000

0.5

1

1.5Heat Dissipation from Absorption in PMMA Light Guide Concentrator

Spectr

al P

ow

er

Density (

W/m

2*n

m)

Wavelength (nm)

Solar Irradiance

Pmma Absorption

Absorbed at 200mm

Absorbed at 500mm

Absorbed at 800mm

84

despite transmitting hundreds of suns worth of flux. To determine the mechanical effects of this

absorption across the length of a guide, a thermal model of a PMMA guide layer was made to

dissipate the heat predicted through absorption through air convection through the bottom

surface. The temperature increase in this system is shown in Figure 2-26. In this example, the end

of a 600mm long guide increases in temperature by approximately 16 °C above ambient

temperature. This is not near the softening point of PMMA which is 105°C. While this

temperature change may cause some warping, the ambient temperature variation is likely to be

greater than the temperature change due to IR absorption.

Figure 2-26: Thermal model of temperature increase due to infrared absorption of a PMMA two stepped light guide. In this model, the only means of dissipating heat is convection from the bottom surface interacting with 300K air.

85

2.4 Integrated Module Performance Modeling

HCPV systems are comprised of many components, and a critical factor for assessing a

concentrator is how it is expected to perform when assembled into a full HCPV module. Extensive

research and development work is being done on several other components of the HCPV systems

such as high efficiency solar cells, high precision solar trackers, and improved electronics and

storage. While it is expected that these components will improve during any further development

of this concentrator family, currently available technologies are modeled to provide a baseline for

potential yearly energy generation.

For the module output simulations, the silicone on glass design of the ideal modeled

reflective dimple tree system was used operating at 500x concentration. The system was designed

to be 500mm long with a 2mm thick guide layer with a 2x secondary concentrator to achieve the

desired concentration. This design was used due to the faster ray tracing than either of the

stepped systems, as the yearly output requires a substantial amount of computation time. The

concentrator system was assumed to be mounted on a tracker with a tracking accuracy of ±1.0°. A

simple inverter with 95% conversion efficiency was assumed, and no storage was used. This is

consistent with a small pilot plant supplementing the grid, but storage is a critical component if

grid support is not available.

The system is assumed to be installed in Phoenix, Arizona, which is an ideal location for

concentrating photovoltaics. CPV systems require a large amount of direct sunlight and can utilize

very little of the available diffuse light. Locations with frequent cloud cover provide much less

energy for all solar projects, and concentrating systems have performance reduced much more

than flat plate designs where the increased diffuse radiation on cloudy days can slightly offset the

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loss of direct radiation. A comparison between direct/diffuse breakdown of a characteristic

summer day and a characteristic winter day in Phoenix Arizona and Chicago Illinois is shown in

Figure 2-27.

Figure 2-27: Characteristic summer and winter days in Phoenix (top) and Chicago (bottom). Phoenix has much less cloud cover, and thus much more direct sunlight. High concentration systems are primarily only able to collect direct

sunlight.

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2.4.1 Cell Models

HCPV systems are designed for use with ultra high efficiency cells that would be cost

prohibitive without the high concentration reducing the cell area required. These are typically

multijunction cells, which have stacked several different semiconductor materials with each

junction efficiently converting a portion of the solar spectrum. Development of these cells has

yielded consistent progress in efficiency and cost, with the efficiency record being broken many

times in recent years. For these models, a cell similar to the triple junction cell produced by Solar

Junction is used. This cell held the efficiency record when it was first produced, and with 41%

conversion efficiency at 500x concentration, represents an extremely efficient cell.

This cell is a stacked triple junction cell with an Indium Gallium Phosphide top cell (InGaP)

for converting the high energy visible light, an indium gallium arsenide (InGaAs) middle cell for

converting the low energy visible and near IR, and a germanium bottom cell (Ge) for converting

the lower energy IR radiation. Light incident on the top cell with energy below the bandgap of the

top cell travels through the top cell to be absorbed by the other junctions, while light that is

sufficiently high energy is converted more efficiently. A schematic of this cell is shown in Figure

2-28, with the spectral regions converted by each layer highlighted in the appropriate colors.

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Figure 2-28: Schematic for a triple junction solar cell. Each successive layer efficiently absorbs and converts the appropriate spectral region while allowing lower energy light to pass through to the cells underneath. Image courtesy

of Solar Junction

An important consideration for any multijunction solar cell is how the system is wired.

Each junction can be wired separately (parallel) or having only the electrodes at the top and

bottom of the stack (series). Wiring in series increases the output voltage and does not require

the additional complexity introduced by adding electrodes between the various layers. However,

wiring the cell in series requires that the cells be current matched, or the cell producing the least

current limits the other cells. While careful tuning of junction bandgaps can match the solar

spectrum, the incident spectrum varies substantially over the course of the day. When the sun is

lower in the sky near sunrise or sunset, there is substantially more effective atmospheric

insulation, and thus more high energy light is scattered, and the sky appears to have a redder color.

This can cause the top cell to be current limiting, and reduce system performance over the course

of the day.

The cell is modeled in LightTools using a User Defined Merit Function (UDMF) developed

by the University of Purdue34 to model multijunction solar cells. This function takes into account

parameters such as the power and spectrum of light incident on the cells and other parameters

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such as junction temperature to model the performance of each junction individually. This UDMF

calculates the efficiency of each junction and the efficiency if the cells were all wired in series. The

values reported here are for a system where each junction is wired individually and the efficiencies

are added together, as the series values require careful optimization of the band gaps.

2.4.2 Yearly Energy Output Simulations

The output of a full concentrator module was modeled using the LightTools Solar

Simulator utility. This had information about the insulation at various locations every day in 2005.

This utility separated the diffuse and direct radiation into two separate sources, the direct having a

±0.26° angular spread while the diffuse radiation was assumed to come from a hemisphere with

uniform intensity. The electrical output resulting from both diffuse and direct illumination was

Figure 2-29: Averaged monthly output from the system with insulation data taken in Phoenix in 2005. There is substantial variability between the months, as this particular year had a unique distribution of

weather in addition to the annual seasonal variability.

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calculated. As expected, the concentrating system had an efficiency of less than 2% for diffuse

light. The averaged output for several months of the year is shown in Figure 2-29. This was

particular to the year 2005, but provided a representative example of the electrical power

produced by this system.

The yearly performance of the system was summed over the entire year to show the

power this system would optimally produce annually. The total incident power on the 1m2 input

aperture of the system was 3004 kWh, of which 2466kWh was direct sunlight. The system

converted 711kWh of this into electricity, which is a conversion efficiency of 28.8%. The efficiency

varied by less than 0.3% month to month, which is expected for a tracked system with

independently wired junctions. To compare to flat panel systems, the total incident light must be

accounted for, and in this case the efficiency dropped to 23.6%, which was still higher conversion

efficiency than available flat panel systems.

Three new types of concentrator have been designed and the performance for a variety of

fabrication parameters has been modeled. In addition to the optical performance of these

systems, thermal models provide critical information for determining the lifetime of these

concentrators when deployed. Finally, an approximation of the performance of these

concentrators when assembled into full modules has been made, which provides information

about potential system output when deployed.

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3 Fabrication and Testing

The first dimpled light guide prototypes produced at University of Rochester were part of

a joint development effort that ended in 2009. Using the information gained from constructing

these prototypes35, design work continued with the aim of increasing optical performance and

manufacturability. The initial concepts and modeling work described in the previous chapter

represented the potential new generation of light guide concentrators, but a new manufacturing

partner would require a whole new process development.

The University of Rochester entered into a sponsored research agreement with Rambus to

produce the next generation of concentrator prototypes. The goal of the project was to produce

functional concentrators with three different structures: wedged stepped, two stepped, and

reflective tree. While Rambus had substantial expertise in manufacturing custom micro-optic

systems, these structures would require substantial process development.

3.1 Overview

At the outset of the project, the relative difficulty of producing each of the three systems

was unclear, so work was done in parallel on all three designs to maximize the chance of

producing a successful system. One critical challenge was determining how accurately the dimple

and lenslet structures could be produced. In addition to the microstructure geometries, the

component materials required some development work, which would also occur largely in parallel.

For all the designs, a low index adhesive capable of curing the acrylic lenslets to the glass or acrylic

guide layer was necessary. The system with a glass guide layer required an index matched

material that could be cast onto the glass to form the dimple layer. The models of these systems

are shown below in Figure 3-1.

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Figure 3-1: The wedged stepped concentrator model and illustrative schematic of the wedged stepped concentrator (a), the two-stepped concentrator model and schematic (b), and the reflective concentrator model and dimple

schematic (c).

For the first set of prototypes produced, the size of the entrance aperture must trade off

demonstrating scale and manufacturing plausibility. While the systems were designed to be

approximately half a meter along the guiding direction, this was impractical for a proof of concept

system. The size of the guide plane perpendicular to the guiding direction was inconsequential if

the side walls were polished and at least one full repeat unit was formed, as these could be tiled

indefinitely. This project was designed to demonstrate the ability to manufacture these new

geometries, and thus the final concentration was not as critical. The system was thus designed to

maintain approximately the same geometric concentration as the original prototypes (~60x) and

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the goal for the guide plane was set to be 120mm by 21mm for an approximately 2mm thick

guiding layer.

It was anticipated that the two most challenging parts of this system were to be accurately

producing the lenslet and dimple microstructures. The University of Rochester was responsible for

most of the metrology of these components and to incorporate the results into modeling software

to guide further development work. This chapter details the results of prototyping the lenslet

arrays, the dimple arrays, and then the efforts to combine these two critical components with the

rest of the system components into functional concentrator modules.

3.2 Lenslet Arrays

Manufacturing of conic microlens arrays with an offset rectangular aperture was believed

to be a new technology as of the writing of this thesis. In order to yield an offset aperture with a

high surface quality and shape, each transverse row of lenslets (perpendicular to guiding direction)

was cut as an individual blade as shown in Figure 3-2. This allowed for a steep discontinuity at the

edge of each aperture. An entire repeat unit of the wedged system (15 blades with 15 lenses

each) was produced by this method and eventually had the potential for tiling into a larger pattern.

Due to financial and time constraints, the larger pattern was not pursued. Each prototype instead

had several repeat units of lens arrays individually aligned.

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Figure 3-2: Definition of angles and transverse direction. The blades of lenslets were combined together to form a master.

In order to function properly in the concentrator system, these components had to meet a

number of critical specifications. This required measurement of the lenslet surface shape, the

lenslet surface microroughness, the thickness of the lenslet layer, and the exact spacing between

the focus of each lenslet. Testing these properties required a variety of techniques and equipment.

The surface quality was tested over a small region near the apex of each lens using a ZYGO Nuview

white light interferometer. The thickness of each lens array was checked both using a visual

microscope and calipers. To test the surface shape and focal spacing of the lenslet array, a

customized Twyman-Green interferometer was built.

3.2.1 Lenslet Interferometer

One of the most important qualities in a lenslet array was the precise location of the focal

spots. Matching the spacing of the lenslet focal spots to the injection facets of the dimple array

was critical to optical performance. It was important to know precisely the location of the focal

spots for a lenslet array, both to determine any systematic spacing error and the random variance

of the focus location for each lenslet. If the spacing between the foci and injection facets was not

consistent, the field of view would depend on the injection location. A field of view that varied

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over the input aperture would cause the integrated guide field of view to lose its sharp cutoff. A

mismatch of greater than 75µm over the input aperture would reduce maximum on-axis

performance.

Another critical parameter for diagnosing lenslet performance was measuring the surface

error of the lenslets. This provided information of the blurring of the focal spot which would

reduce the field of view of the system, or, if there was a sufficient error, degrade the on-axis

performance. This was also useful for diagnosing manufacturing errors such as scratches that

would either scatter incident light or fail to couple a certain area of the input aperture to the

injection facet.

In order to get precise measurements of both the focus location and the surface profile of

each lenslet, a unique Twyman-Green interferometer has been built. The schematic for the

system is shown below in Figure 3-3, and is designed to measure a single lenslet at a time. The

mirror in the reference arm is mounted on a PZT to enable phase shifting. The system uses N+1

bucket phase stepping algorithm to recover the phase difference between the two arms36. The

PUMA algorithm37 is used to unwrap the phase profile. If the back surface of the lens array is

considered to have negligible error, this gives an accurate surface map of the system.

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Figure 3-3: Schematic of custom Twyman-Green interferometer used to characterize lenslet arrays.

A Graphic User Interface (GUI) was created to allow the automated inspection of a full

array of microlenses. The lenslet array was mounted on a set of precision motorized stages to

allow full control of motion in all three dimensions. The program was designed to go to the

approximate coordinates of each successive lenslet in an array, find the location of the optimal

focus, and then take an interferogram to determine the surface profile of the lenslet at the

optimum focus. This allowed the precise determination of the focal point lattice of the lenslet

array and the shape error of each lenslet.

The CCD was manually focused into a lenslet in one corner of the array, and this stage

position provided a reference coordinate. The zero coordinate was found by moving the stage to

reduce the fringe density. An error in any of the three coordinates produced a characteristic

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effect on the phase pattern. An error in the x or y coordinate caused a linear tilt in the phase over

the lenslet aperture, while an error in the z position gave a parabolic error around the apex of the

lenslet. The coefficients of both of these errors were proportional the position error in the

appropriate coordinate, with the conversion factor dependent on the specific lenslet geometry.

In order to calibrate the error induced by a position shift for a specific lens array, the

system was moved a controlled distance in each direction. After moving a controlled distance

from the approximate zero, the phase error was calculated and fit to the appropriate function (a

line or parabola). The system was then moved the same distance from approximate zero in the

opposite direction to compensate for any error in the initial reference coordinate. By fitting this

difference with a known position change, the ratio between position movement and the

magnitude of the induced phase error could be determined for all three directions.

Once the relation between the induced phase error and position error was calibrated for the

specific lenslet, the system began measurement of any number of desired lenslets in the array.

Either a list of approximate lenslet coordinates could be entered or was generated from the ideal

lenslet spacing and pattern. The system travelled to the approximate coordinate of each target

lenslet and took a measurement of the phase error. This information was then converted into a

position error, and the system calculated and travelled to the position of the optimum focus for

that lenslet. In addition to taking the interferogram at the optimum focus, the precise coordinates

of the stages were then recorded.

The recorded coordinates of optimal focus were then mathematically rotated about the

initial reference point in order to remove as much tilt as possible from the system. The set of

coordinates was first rotated about the Z axis so that the best fit of the first row of lenslets was the

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X-Z plane. The coordinates were then rotated about the Y axis so that the first row of lenslets was

best fit by the X-Y plane, and then rotated about the X axis so that the first column of lenslets were

best fit by the X-Y plane. These rotations removed any residual tilt or clocking introduced by the

mounting of the lenslet array. These processed coordinates were then compared to the optimum

lenslet positions. Each coordinate error was recorded, and the total spatial error of the optimum

focus was calculated and displayed graphically.

In addition to calculating the error in the optimum focus for any given pattern of lenslets,

this system was designed to measure the surface error at the optimum focus of each lenslet. By

measuring the phase error at each position in the lenslet aperture, an optical path difference could

be determined. The laser used in the interferometer was a HeNe laser(MFC), and the refractive

index of PMMA was well known at the HeNe wavelength of 632.8nm. The optical path difference

could be converted into a sag difference (departure from the apex along optical axis), which

provided a surface figure error. A customizable aperture of each surface profile was then set, and

the RMS surface error of each lenslet within this aperture was calculated.

In order to ensure that the lenslet interferometer was running properly, a previously

characterized lens array was measured. The reference array was a set of conic lenses with

hexagonal apertures that was used for a previous dimpled light guide design. The system was

known to have a slight pitch mismatch in one direction, determined by an alignment variation

across the aperture when used with a prior dimple array having known spacing. Figure 3-4 shows

the output of the GUI measuring the Y error, perpendicular to the direction of the pitch mismatch.

There is no discernible trend, and the RMS surface error of the first lenslet is under ±2µm.

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Figure 3-4: The output of a sample patch of the reference lenslet array. The Y Error is selected and shows no notable systematic errors and a fairly small random variation. The phase profile is presented on the right, from which an RMS

error can be calculated.

The lenslet array under test was known to have a systematic spacing error in one direction.

This was originally found by measuring the variation of the field of view of an assembled light

guide constructed using a lens array made from the same process38. This was confirmed and

quantified more precisely using the lenslet interferometer. The systematic error in the X direction

can be seen in Figure 3-5. In order to verify that the systematic spacing error was actually in the

lens array and not an artifact of the interferometer, the lens array was rotated 90° and measured

again to make sure that the error then showed as a Y spacing mismatch. The results of the original

measurement of the spacing mismatch in X and the subsequent spacing mismatch of the rotated

sample confirmed this, as shown in Figure 3-5.

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Figure 3-5: The systematic spacing error can be seen in the reference lenslet array. The original measurement showing an X spacing mismatch is shown on the right, and the left shows a consistent spacing mismatch when the

sample was rotated 90° and remeasured.

The lenslet interferometer verified the spacing mismatch of the reference lens array, and

this capability could easily be extended to any desired lenslet shape and position distribution. This

system was only set up for use with refractive lenslet arrays. The reflective design was tested by

using a part that was uncoated. This reflective system did not have the ideal surface shape for

creating a point focus when used as a refractive system, but the expected error was subtracted

from the final profile to determine the optimum focus and record the corrected surface profile.

3.2.2 Refractive Lenslet Arrays for Stepped Systems

Both the two stepped design and the wedged stepped light guide design were designed

to make use of the same lenslet array in order to save time and cost. The final component

specification was to use a 1mm by 1.5mm rectangular aperture (1mm along the guiding axis)

with a 100µm step offsetting each successive row of lenslets. The optical axis of each lenslet

was offset along the guiding axis by 0.35mm. The radius of curvature was designed to be

Error (mm) Error (μm)

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1.11mm with a conic constant of -0.45. This produced a lenslet with maximum sag of 0.80 mm.

The semi- aperture of this lenslet is larger than the radius, and therefore a spherical surface

cannot be used with this curvature. The system was designed to be made of PMMA and have a

thickness of 1.35mm from the apex of the lenslets to the back surface. A model showing a

small section of the designed lens array is shown below in Figure 3-6.

Figure 3-6: A small patch of the refractive stepped lens array. The lenses have a rectangular aperture and the optical axis is offset from the center of the lens aperture. In this picture, the light will be guided toward the left.

For the optimal two stepped design, the lenslet focus was stepped vertically to make sure

the focus of the lenslet was coupled to the injection facets of the thickening guide. These lenslet

arrays presented a large manufacturing challenge, and it was decided to use the same lens array

for both stepped prototypes. The lens array for the two stepped prototype would be cast on a

wedged piece of acrylic, and thus the height of the focal spots would vary smoothly over the

prototype. This would result in the lenslets for the two stepped system focusing slightly off the

dimple facet. This defocus would be greatest near the vertical steps in the guide and would be at

most half of a vertical step (50µm for this prototype). While this was not expected to decrease on

axis performance (barring other errors or misalignments), this would reduce the expected field of

view substantially.

Light Guiding Direction

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Fabricating these lenslets required a substantial amount of manufacturing development,

and several new approaches were tried in order to achieve the desired surface shape and finish

necessary. In order to verify that the surface quality was adequate, the master of these lenslets

was measured in a Zygo white light interferometer. The lenslet has a relatively large curvature,

and thus the system was only able to measure a small region near the apex. The interferometer

was able to measure approximately 200 µm from the apex, which covered about 14% of the

entrance aperture of each lenslet. This showed an excellent surface with the exception of a small

region at the apex of the lenslet. This was an unavoidable defect given the manufacturing process

used. A vertical slice slightly off center (to avoid fitting errors caused by the imperfection at the

apex) was fitted to provide an approximate curvature and information about the surface quality,

as shown in Figure 3-7.

Figure 3-7: White light interferometer measurement of the refractive stepped master. The red vertical line on the surface map is fitted to both a variable radius and to the designed radius. While there is a slight discrepancy, this only

represents the 15% of the lenslet aperture near the apex. The microroughness of these surfaces is approximately 10nm.

The lenslets were produced in small repeat units (15x15 lenslets) which were intended to

be copied and patterned into a larger part. Due to time and financial constraints, it was decided to

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individually align a series of smaller repeat units that had one row of lenses removed in order to

enable manual alignment. Each of these repeat units covered approximately 12% of the input

aperture of the prototype. While this would substantially reduce full aperture efficiency, these

concentrators would still be able to prove out the experimental manufacturing process and design.

When these repeat units were made, they were inspected under a visual microscope which

showed substantial damage to the outermost rows of lenslets. This was an expected result the

method employed to remove these lenslet arrays from the mold. In addition to damage localized

to the lenslets on the perimeter, the parts showed a bow which was visible.

The bowed lenslet arrays posed a potential problem, as the lens array in the designed

system had a flat back surface, and the apices were designed to be a constant height. A variation

in height across the lenslet array would cause a subset of the lenslets to be defocused. Though

this bow posed a problem if the part were used in a concentrator, the bow could be removed by

using a strong low index adhesive to keep the bottom of the lenslet layer securely attached to the

guide layer. Despite the visible bowing in the fabricated lenslets, the thickness between the

bottom surface and the apex was consistent. The parts produced were found to be thicker than

they were designed. It proved extremely difficult to control the thickness of the part without

damaging the lenslet surface, and thus the guide layers were made to be thinner to compensate

for this error.

When measured on the lenslet interferometer, the bow in the part was expected to

dominate the focal spot distribution. Assuming the part was all of equal thickness but bowed, the

focal spots would be shifted slightly in Z position and slightly shifted along the plane of optimal

focus, as shown in the exaggerated schematic in Figure 3-8. The visible bow of the parts was

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consistent with the bow direction shown in Figure 3-8. In addition to moving the focal spot, the

bow would cause some lenslets to operate off-axis, which would induce aberrations, most notably

a substantial amount of coma. This would increase the spot size and cause the RMS to suffer

based on the magnitude of the induced aberrations.

Figure 3-8: An exaggerated schematic of the bowing of the lenslet array. This is the direction of bow as can be seen visually. This will cause a focal shift in the Z direction as seen by the green arrow and will reduce the X spacing shown

by the black arrows.

A lenslet array from the same batch as those integrated into the concentrator prototypes

was measured in the lenslet interferometer. The perimeter of the lenslet array was not usable,

and thus the inner region of the part was measured. The central 8x7 group of lenslets was

measured, as this was the portion that was used for characterization of the prototype. The RMS of

the measured lenslets showed an RMS of less than 1µm. The one systematic error that was visible

was a consistent defect in one bottom corner of each lenslet. This defect was consistent with a

stress induced by the removal from the mold. While this defect was consistent, it was small

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enough that was is not expected to cause a focus issue. The surface profile of a representative

lenslet and the calculated RMS surface value at the best focus was measured and shown in Figure

3-9.

Figure 3-9: The surface profile of a representative refractive lenslet and the calculated RMS surface error of each measured lenslet at the best focus. Both color scales are in mm.

Error (μm)

Error (mmx10-4)

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The RMS for the refractive lenslet array was good for an experimental manufacturing

process. The focal spot distribution was expected to be dominated by the bow in the lenslets. As

expected, both the X error and the Z error were dominated by this defect as shown below in

Figure 3-10. The bow was clearly visible, and each row was fit to a parabolic shape to quantify the

distortion of the lenslet array.

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Figure 3-10: The focus error in both Z (top) and X (bottom) directions. The Z error shows a low central region consistent with a bowed array, while the X error shows a consistent spacing mismatch being too close together. Both

of these profiles are dominated by the bow in the lenslet array as expected.

While these two profiles were dominated by the warping of the part, the Y coordinate

error was dominated by a misalignment between two rows. This imperfection could also be seen

visually, as there was some form of defect between two of the lenslet rows, as shown in Figure

Error (mm)

Error (mm)

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3-11. This was consistent with the manufacturing process and may have been caused by an

imperfection on one of the blades corresponding to a row of lenslets that had some defect. This

error manifested in the other error coordinates, as the discontinuity between the third and fourth

rows was apparent.

Figure 3-11: The Y coordinate error was dominated by an imperfection between the third and fourth row. This is indicative of an imperfection preventing the two rows during assembly.

The Z error was used to approximate the magnitude of the bow by fitting the X coordinate

to the measured Z error. The measured depth of the focal spots and their approximate X

coordinate was fitted as shown in Figure 3-12. A parabola was determined to be an accurate fit

for the warping of the parts. This provided an approximation for quantitatively modeling the

bowing of the lenslets. In addition to this method, the corners were measured with a visual

Error (μm)

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microscope with a precise adjustable focus. Both these methods provided an approximate bow of

240um at the corners of the lenslet array.

Figure 3-12: The fitting of the bow of the refractive lenslet. This fit should yield a Z error of approximately 240µm at the corners of the lenslet array.

While the warping dominated the lenslet interferometer measurements, it could be

negated by using a strong adhesive for the low index layer. Further work was not done to remove

the bow, as this should only have been present in the small units used in the system. For a much

larger system in which these units would be patterned, the surface was expected to be much

flatter. The primary goal of this development work was to demonstrate capability of producing a

high quality conic lenslet with an offset rectangular aperture, and this was accomplished. These

systems were adequate for characterization in an assembled prototype for demonstration

purposes.

3.2.3 Reflective Lenslet Arrays for Dimple Tree Systems

The reflective lenslet array provided a different set of challenges than the refractive

system. The sag of the surface was substantially less than for the refractive system, but the

aperture was designed to be offset in both directions, and the acrylic surface required a reflective

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coating. While offsetting the lenslet aperture in the transverse direction provided slight

performance improvement in simulations, this would have required an entirely new

manufacturing process. The offset of the lenslet array in the transverse dimension was thus taken

out so that a similar method could be used to manufacture these lenslet arrays as was used to

fabricate the refractive lenslet arrays. This reduced the performance of the 600mm modeled

system by approximately 3%, but for the current prototype size was not expected to have any

effect on the optical efficiency.

The final designed system also had a rectangular aperture with an aperture of

1.35 mm in the transverse direction and 0.90 mm in the guiding direction. The reflectors had a

parabolic shape and a radius of curvature of 5mm. This resulted in a surface sag of 0.16mm

and a 3um maximum departure from a spherical surface. The final designed thickness of the

reflector arrays was designed to be 0.45mm from apex to the top of the reflector layer. The

alternating transverse shift between two rows of lenslets was designed to be 0.26mm. For

similar reasons to the refractive lens arrays, the reflector arrays were produced as small

patches measuring 14x21 mm which would be attached to the guide layer individually. The

system was originally designed to have a simple silver coating, but this was later changed to an

aluminum coating for cost reasons. This does did affect the optical design, though the

reflectivity and optical efficiency were reduced by approximately 3%.

These lens arrays were produced in a similar manner to the refractive systems, with each

row of lenses being cut individually and then manually aligned to form a master. Before using the

master to produce daughter copies, the surface roughness was checked using the white light

interferometer. The curvature of these parts was substantially lower than for the refractive

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system, so the data were limited by the field of view of the interferometer. The system was

designed to measure the surface profile of each lenslet with a sample shown below in Figure 3-13.

There was still a small defect at the apex of the lens, but this was less pronounced than for the

refractive lenslets.

Figure 3-13: The surface map near the apex of a reflective lenslet master (right) and the profile of a slice through the apex. The surface roughness is quite low, and the fitting of the curvature shows a slightly weaker curve than

designed.

Daughter copies were pulled from the master and then an aluminum reflective coating

was applied. The lenslet interferometer was not set up to measure reflective microlens arrays,

and thus one of the parts was tested before coating on the lenslet interferometer. The surface

was designed to produce a tight focus when used as a reflector, and thus significant aberrations

were expected when this system was used as a refractive lenslet array, specifically approximately

3 waves of spherical aberration. The expected performance for a perfect system was no longer a

flat phase map when measured through the lenslet interferometer, but the expected phase profile

of a perfectly manufactured system was subtracted in order to determine the optimal focus and in

the resultant phase map that was used to calculate a surface map of each lenslet. The RMS

X (μm)

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surface profile of the reflective lenslet array was measured, and the surface map of each lenslet

was calculated as seen below in Figure 3-14.

Figure 3-14: The RMS of the reflective lenslet array when used as a refractive system. The error is dominated by the fourth row. It is believed that a scratch along the lenslet array caused a failure of the phase unwrapping algorithm.

The RMS profile of the lenslet array was dominated by the fourth row. The RMS profile of

this row was dominated by what appeared to be a discontinuity along the X-direction. Further

inspection of this row of lenslets showed a scratch or other horizontal defect. This caused a failure

in the phase unwrapping algorithm, which then yielded a discontinuity between the two sections

of the phase profile. The “optimal” focus was then shifted in Y, which produced this RMS profile.

Ignoring the fourth row of lenslets, the RMS profile of the reflective lenslet arrays showed surface

error of less than 100nm RMS, as shown in Figure 3-15.

Error (μmx10) Error (μmx10)

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Figure 3-15: The RMS profile of a lenslet not in the fourth row. Substantial tooling marks can be seen in the bottom section of this figure, but the profile is very good. There are highly visible tooling marks on the bottom section of the

lenslet, which is consistent with the two regions separated by the discontinuity in the fourth row.

The Y-error measurement from the lenslet interferometer was also dominated by the

scratch on the fourth row, as this caused the phase unwrapping algorithm to yield two distinct

sections with different surface heights. This was fitted as a substantial tilt error, and the optimal

focus was calculated to be substantially off in Y position, as seen in Figure 3-16. While the Y error

was dominated by this scratch, the X error was again dominated by a bow in the system, though

this time in the other direction. This was likely due to the way the part was mounted in the

interferometer, as it was held by tension on the outside perimeter. These parts were thin and

flexible, so a distortion from mounting was plausible.

Error (μmx10-1)

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Figure 3-16: X (top) and Y (bottom) position errors of the focal spot for the reflective lenslet array. The Y error is dominated by a scratch on the fourth row, while the X error is dominated by a bowing in the system.

The reflective system used in transmission had a much longer focal length than the parts

for the stepped systems. This caused substantial problems with the ability to measure the Z

coordinate of the optimal focus, as this parameter was not as sensitive as for the system designed

as a refractor. The error in the Z coordinate shift was often larger than the calculated shift, and

Error (mm)

Error (mm)

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thus this measurement was not useful. The Z coordinate shift was thus substantial enough that

the depth of focus of the imaging system began to become a substantial source of error. The Z

position of the optimal focus was thus not able to be reliably obtained using the lenslet

interferometer.

3.3 Dimple Arrays

The dimple geometries presented in this thesis had never been fabricated before, and thus

the prototyping of these microstructures required extensive manufacturing development work. In

order to refine the manufacturing process, small patterns (approximately 10cm2) of the

appropriate geometry were cut into a nickel coated master, and acrylic copies were then made

from these master tools. This work was done by Rambus based on the designs from this thesis.

These copies were characterized in order to refine the machining parameters. Once the small

patch cuts were satisfactory, a longer master cut of the full proposed area was done. This

required a longer cut time (up to 8 days) than had been previously machined, and thus further

development work was required in order to speed up the pattern cutting.

For each dimple geometry, the initial goal was to yield copies of the dimple array in a

variety of different materials in order to test the effect of varying guide materials. Each system

was to be prototyped as a monolithic acrylic piece, with an acrylic guide layer and dimple layer,

and also a polymer dimple layer cast onto a glass guide layer. Light guide systems had not been

produced with an entirely acrylic guide layer, and it was unknown how well the material would

withstand the high concentration light. The glass guide system required development of an

appropriate polymer that had the correct index of refraction and was still compatible with the

processes used to machine the microstructures and adhere to the glass. Both of these approaches

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were pursued in parallel in order to minimize risks, and both material choices could use the same

dimple geometry master and the appropriate lenslet arrays.

3.3.1 Wedged Stepped Dimple Arrays

The wedged stepped dimple geometry required a surface that was fully covered by the

dimple features. The channels required a sharp transition, as either a large fillet or substantial

draft angle would ruin the angular isolation of this system. The fabrication method used to create

the previous generation of prototypes yielded a fillet radius on corners of approximately 10µm

and a minimum draft angle of approximately 10°. The side wall between adjacent channels in the

designed system approximately 8µm, and thus this would be completely rounded if fabricated by

the same process used for the previous generation. The first cuts of a small patch pattern showed

that the process used was capable of much steeper and sharper side walls. The cutting

parameters clearly still required tuning, especially on the actual injection facet, but the machining

method showed promise for producing the dimple geometry much more faithfully to the design

than for previous fabrication methods. SEM images of these early cuts showed substantial error in

the injection facets, as seen in Figure 3-17.

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Figure 3-17: The first attempt at an injection facet (left) showed an obvious ripple. After refining manufacturing parameters, the injection features were improved significantly (right).

While the SEM images provided an accurate measurement of the dimple geometry, the

surface roughness was also important to system performance. This was measured using a Zygo

NewView white light interferometer. The system was limited to a field of view of a few hundred

microns, and thus measuring the entire part was impractical. Scans were done of several regions

of the system to measure the surface quality of both the bypass elements and the injection facet.

Surface measurements of the final patch cut were taken with the white light interferometer, as

seen below. The actual measurements required a schematic to show which region of the dimple

structure was shown in the accompanying measurement. The orientation of the schematics was

given a color coded schematic to show consistent height differences (high regions and low regions),

as shown in Figure 3-18.

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Figure 3-18: Schematic showing dimple layer for the purposes of orienting white light interferometer measurements. The colors of the channel are consistent with respect to height differences.

The surface map is measured for an acrylic dimple layer pulled from the master to

determine measure the surface quality at several regions around the part. A sample of a white

light interferometer measurement of an acrylic part in a region where there is no facet proximate

is shown below in Figure 3-19. In addition to the surface map, one dimensional slices of the data

are presented to highlight the microroughness of the system. The red and blue lines on the

surface map correspond to the vertical and horizontal 1-D scans respectively and are shown in the

corresponding colors.

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Figure 3-19: White light interferometer measurements of a central region of an acrylic wedged stepped dimple layer. The surface roughness of each channel in this region is approximately ±5nm.

Once the patch cut was satisfactory, the next step was to master an entire repeat unit of

the system. The goal of the system was to be 120mm long and 21mm wide. Even with machining

parameters optimized for speed, cutting a part of this size required enough time that tool wear

and machine failure posed a substantial risk. In order to minimize tool wear and reduce cutting

time, the first full master was cut into aluminum. The softer material produced less tool wear, and

this was expected to increase the chances of the part cutting successfully. However, the softer

material did not produce the geometry faithfully, and this substrate change resulted in a

substantial reduction in the part quality.

X(μm)

120

Due to the extensive degradation caused by cutting the master out of aluminum, another

master was cut out of a nickel substrate. This was more demanding on the tool due to the

increased material hardness and also caused the cut to take approximately 3 days longer. The full

part was successfully cut as shown in the SEM image of the final part in Figure 3-20.

Figure 3-20: An SEM image of the final wedged stepped dimple geometry. The feature replication is quite good, though there is a considerable amount of debris that can be seen on the part.

The geometry of the final replicated wedged stepped part matched the modeled geometry. The

fillet radii were less than 2µm and there were no noticeable draft angles (<1°) from the replication

process. There was a substantial amount of debris on these parts, though some of this debris

resulted from handling after production and was not actually a result of the master cutting process.

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The image shown in Figure 3-20 was from an acrylic copy pulled from the final wedged stepped

master.

Once the master had been made, two different processes were used to produce the two

different dimple and guide layer combinations. The polymer on glass system required a fairly

expensive glass substrate for this prototype, and thus a destructive SEM test was not performed

on this part. Both the polymer on glass and the monolithic acrylic system were tested on the

white light interferometer to characterize surface quality. Surface quality measurements of the

bypass prisms of the acrylic dimple system were taken as shown in Figure 3-21.

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Figure 3-21: White Light Interferometer measurements of polymer on glass wedged stepped dimple geometry. Both the middle region and the high region are very smooth surfaces. The casting on glass process introduces some roll off

near steam height transitions, as can be seen in the bottom figure near the abrupt height transition.

While the primary defect in the bypass prism appeared to be debris that was either

collected on the master or after the copies were produced, there was substantial variation in the

X(μm)

X(μm)

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surface quality of the injection facets. Over 20 injection facets were measured using the white

light interferometer, and every facet observed had obvious defects. Many regions of the

measured facets were high quality surfaces that would produce relatively little scattering. The

facets in the polymer on glass sample were highly variable, shown below in Figure 3-22. One

presented facet showed a substantial amount of debris (Figure 3-22a) on the facet, while the other

had a large smooth region but a missing corner (Figure 3-22b). Variations in the injection facets

caused substantial variations in the injection efficiency and prevented uniform device

performance.

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Figure 3-22: White light measurement of facets of wedged stepped dimple array cast onto glass. Substantial variations are observed from facet to facet, but there are several regions that will have a small amount of scattering.

The roughness on the injection facet caused some of the light to be scattered from the

surface. Most of the light that was scattered from the injection surface was ejected almost

immediately. If injected with a substantial angle relative to the guiding axis, light initially contained

a)

b)

X(μm)

X(μm)

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within the guide was coupled out of the light guide after a relatively short propagation distance.

The relationship between the RMS surface roughness and the scattering from that surface was

given approximately by39

This equation showed that light was scattered more strongly at lower wavelengths, higher

angles of incidence, and for rougher surfaces. Light incident on the injection facets hit the surface

at a relatively shallow angle of approximately 41° at the center of the ray bundle. Light incident at

500nm was scattered from the injection facet as shown in Figure 3-23. While the light scattered

was not all lost immediately, most of the scattered light was coupled directly out of the guide or

after a short propagation distance.

Figure 3-23: Scattering fraction from injection facet surface is a function of RMS surface roughness.

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The injection facets shown in Figure 3-22 did not have a uniform roughness, and thus it

was difficult to make simple predictions for the effect of scattering. There were regions of these

facets that have roughness of hundreds of nanometers, while other small regions had RMS errors

of less than 10nm. For this level of facet variability, the location of the lenslet focus on the facet

largely determined the scattering loss, which ranged between a few percent up to approximately

50 percent.

While the RMS roughness provides a common standard for most surfaces, the injection

facets will be most dramatically affect the optical efficiency for high spatial frequencies. These will

scatter light more than the slower rippling that results from the replication process or other non-

uniformities of the dimple arrays. The spatial frequency components of the injection facets are

best characterized by a 2D power spectral density (PSD), which separates the low frequency

variations due to imperfect replication from the high frequency roughness that will strongly

scatter light. The angular spread of the scattered light will depend on the PSD of the facet, as

higher spatial frequencies will cause more of the light to be scattered into angles that the guide

cannot contain.

3.3.2 Two Stepped Dimple Arrays

The two stepped dimple arrays were made using a similar process to the wedged stepped

dimple array. Instead of offsetting the channels in height, the system was designed to cut each

channel to the same height. This yielded the large flat regions between the vertical steps. As with

the wedged stepped design, the initial cutting parameters were refined by cutting small patches

before cutting a full sized master. The small patch cut was characterized using the SEM, with the

results shown in Figure 3-24. The system had the desired large flat regions, though small channels

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were still visible. There was a substantial amount of debris on the part, but the geometry was

consistent the design.

Figure 3-24: A small patch cut of the two stepped dimple geometry. Channels are still visible, but the flat regions are relatively consistent.

The two stepped design was different from the other geometries designed in that the

guide layer changed thickness along the guiding axis of the part. This was expected to be a

substantial obstacle to fabricating this design. In order to use the machining methods developed

for the other designs, the two stepped dimple geometry would be cut into a flat part at a slight

angle, and then the dimples would be cast onto a wedged guide substrate, either acrylic or glass.

This required a deeper cut than for the other dimple geometries, as the cut depth had to account

for both the facet height and the height of a vertical step.

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The white light interferometer images of this system showed well defined channels with

small height variations. This was expected, as a similar method was used as was used in the

wedged stepped geometry. The channels did not line up perfectly, but the small sharp boundary

was not expected to substantially degrade performance. Other than these small steps between

channels, the flat regions were smooth, having less than 20nm peak to valley roughness. In

addition to measuring the surface roughness of the flat region, several of the facets were also

measured, a sample of which are shown in Figure 3-25.

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Figure 3-25: White light interferometer measurements of the two stepped patch cut. The flat region has clearly defined channels separated by a fraction of a micron while the injection facet cut shows signs of tool wear.

X(μm)

X(μm)

130

After cutting the small patch of the two stepped guide, a full size master was cut. This

system was cut into a nickel coated piece of aluminum. Upon inspection of the final master, it was

obvious that the system had substantial defects. The increased depth of cut caused the cutting

tool to penetrate the nickel coating and rip the aluminum underneath. This caused substantial

gouges in the dimple layer, with an extremely rough surface underneath covering a substantial

portion of the guide layer, as shown in Figure 3-26.

Figure 3-26: The master cut for the two stepped dimple geometry showed substantial damage. The deeper cut appears to have ripped away the base substrate through the nickel coating, and caused deep gouges over a

substantial portion of the dimple layer.

This master cut unfortunately would provide little information if assembled into a full light

guide concentrator. A large percentage of the bottom surface would scatter almost all of the light

that hits it, and thus injected light was expected to be coupled out of the system after a

propagation distance of only a few millimeters. The reason this cut failed was known, and it was

expected that a second cut would be able to fix this problem. However, due to time and cost

constraints, this dimple geometry was abandoned due to the failure of this master cut.

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3.3.3 Dimple Tree Arrays

The dimple tree array for the reflective system could not be fabricated by the same

method as the stepped dimple arrays and required more development work to accurately produce.

As with the other dimple geometries, the first step was to produce a small patch cut in order to

refine the machining parameters. These initial cuts produced the correct geometry with sharp

side walls, which allowed the angular isolation critical to the system. The small patch cut was

measured using the SEM, as shown below in Figure 3-27.

Figure 3-27: An SEM image of the dimple tree patch cut. While there is substantial debris and visible marks ear the facets, the geometry is roughly correct.

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The white light interferometer measurements showed substantial surface character up to

500nm peak to valley variance, especially near the facets. Due to the cutting design, the flat

region near the dimple exhibited a substantial amount of tool ringing along the guiding axis. This

could be seen from the white light interferometer measurements shown below in Figure 3-28. In

a small section of the cut, the scattering from this ringing was easily visible with the naked eye.

When measured, the magnitude of this error approximately doubled in this section. In addition to

the ringing along the guiding axis, the system also had a noticeable height step along the

transverse direction when approaching the injection feature. This was not expected to cause as

much degradation in performance, as these height transitions were sharp and run parallel to the

guide axis and thus did not cause substantial deviation of the angular spectrum.

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Figure 3-28: The first cuts of the reflective tree design showed substantial ringing along the guiding axis and a sharp height transition along the transverse axis. There was a substantial portion of the cut in which these errors were

much more pronounced and scattering from this section of the part was easily visible with the naked eye (bottom).

X(μm)

X(μm)

134

After some refinement of the machining parameters based on these parts, a full size

master was cut of the dimple tree system. In this system, the ringing of the dimple layer near the

injection facets was substantially dampened as shown in Figure 3-29. The magnitude was not

substantially lower than for previous cuts. The reduced frequency and distance covered by the

ringing reduced the effect of this error on system performance. In addition to minimizing the

ringing near the injection facets, the height transition near the facets was significantly reduced by

an order of magnitude.

Figure 3-29: The final dimple tree cut showed substantial dampening of the ringing near the facets. While the magnitude is not substantially lower for the master, the distance covered by the ringing will be substantially reduced.

The low frequency also will reduce the scattering effect.

The injection facets of the final dimple tree parts were measured on an acrylic copy pulled

from the master. The roughness of these facets was measured using the white light

X(μm)

135

interferometer, as presented in Figure 3-30. The injection facets showed substantial roughness up

to 400nm peak to valley, especially along the guiding dimension. This was thought to be due to

tool wear. This scattered a substantial portion of the light from the lenslets. These defects on the

injection facets were much more consistent from facet to facet than for the wedged stepped

prototypes, and thus the injection efficiency of the reflective tree guide was expected to be

reduced by up to 40%.

Figure 3-30: The injection facet of the reflective tree guide system showed substantial roughness, mostly along the guiding direction (right to left in this figure). The marks were consistent from facet to facet.

The acrylic dimple tree guide was successfully reproduced from the master, but casting

the tree design on the glass substrate proved difficult. The polymer on glass guide layer showed

substantial damage to the dimple structure. Accurately reproducing the polymer on glass dimple

layer would require substantially more process development of the casting process. Due to time

X(μm)

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and financial constraints, the polymer on glass prototype of the reflective tree design was

abandoned.

3.4 Assembled Concentrators

The lenslet layers, guide layers, and dimple layers described above were assembled into

full concentrator prototypes and attached to solar cells in order to characterize the final

concentrator performance. The initial goal was to produce six functional concentrators: a polymer

on glass and monolithic acrylic version of all three dimple geometries. Three concentrator

modules were assembled. The final three modules that were assembled were both guide

substrates of the wedged stepped concentrator and the monolithic acrylic reflective dimple tree

concentrator.

Each of these three concentrators was mounted in a custom plastic housing and the

output face of the concentrator was coupled to a silicon solar cell to test optical performance. The

three modules were measured using a variety of techniques in order to ensure that modeled

performance adequately matched the measured performance of the final system. The three

concentrator modules are shown in Figure 3-31.

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Figure 3-31: The three final concentrator modules that were fabricated and characterized for this thesis. The acrylic wedged stepped guide (left), acrylic reflective tree guide (center), and polymer on glass wedged stepped guide (right).

3.4.1 Concentrator Module Testing Methods

The final modules were tested using the University of Rochester Solar simulator. This

system was designed to match both the angular extent of the sun and the spectral content at

Earth’s surface. The system was made up of a 1kW Xenon lamp which was aimed at a collector

lens that focused the energy onto a hexagonal mixing rod. This homogenized the angular

spectrum of at the output face of the rod. The output face of the mixing rod was placed at the

focus of a large off axis parabola, which then produced a collimated beam approximately 20cm in

diameter. Spectral filters or neutral density filters could be placed between the output face of the

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mixing rod and the off axis parabola in order to better match the solar spectrum. A schematic of

the simulator used is shown in Figure 3-32.

Figure 3-32: A schematic of the University of Rochester Solar Simulator. This produces an approximately uniform 20cm diameter beam that matches both the spectral content and angular extent of the sun.

Each concentrator module was attached to a 3mm x 50mm silicon solar cell, which

allowed measurement of the optical efficiency of the concentrator. Before mounting to the

concentrator, each solar cell was characterized so the output could be interpreted when a

concentrator was attached to the cell. The cells were characterized by comparison of the IV

curves to the dual diode model40 . This model considers imperfections in the solar cell as ideal

electronic components, which allows a relative quality of the various solar cells to be determined.

The simplified circuit diagram for this model of solar cell is shown in Figure 3-33. The short circuit

current of the three best cells available was measured when illuminated by the slit aperture to

provide a reference point, and then these cells were mounted in the concentrator modules.

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Figure 3-33: The dual diode model of a solar cell. Image from pveducation.org41

The IV curve of a solar cell measures the current flowing across the cell as a function of an

externally applied voltage. When no light is applied to the solar cell, the solar cell produces no

current unless there is an external voltage applied. When exposed to light, the solar cell should

produce a current in the absence of an external voltage. This is called the short circuit current and

should be directly proportional to the amount of light incident on the solar cell. The external

voltage that must be applied in order to prevent all current flow is referred to as the open circuit

voltage. The maximum power point is the largest product of the current and the voltage along the

IV curve. The fill factor is a measure of this maximum power point divided by the product of the

open circuit voltage and the short circuit current. A fill factor approaching 1 is a quantitative

method of determining the quality of a solar cell. The measured dark IV curves for the solar cells

mounted to the concentrators are shown in Figure 3-34.

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Figure 3-34: Dark IV curves for the three silicon solar cells mounted to the three light guide concentrators. The cells were chosen as the closest to ideal fits from an available batch of silicon cells.

The current-voltage relationship for a silicon solar cell with no light incident on it is given

by

where RSe is the parasitic series resistance, RSh is the shunt resistance, I0R is the recombination

saturation current, and I0D is the diffusion saturation current.42 The series and shunt resistances

of the solar cells were approximated from the high voltage current profile (>5V) and the low

voltage profile (<1.5V) respectively, as these two effects were dominant in these regions, with the

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results shown in Table 3-1. The concentrator LG003 had the best performance, and thus was

paired with the wedged stepped on glass concentrator. This was expected to be the best

performing concentrator, and thus pairing it with the best performing cell would provide the

highest efficiency system. The other two concentrators were mounted to the second and third

best performing cells, which exhibited similar performance to each other.

Table 3-1: The shunt and parasitic series resistances were calculated for the three solar cells integrated into the concentrator modules. Ideally a solar cell will have a high shunt and low series resistance value, so LG003 was the

best of this cell batch.

The full concentrator assemblies were then mounted in a setup designed to allow precise

automated control of the angular pointing and one degree of translational motion. This stage

setup is shown in Figure 3-36. A small aperture was placed in the beam to illuminate a small and

controlled section of the concentrator. Moving the concentrator so that a different portion of the

entrance aperture was illuminated allowed the performance of the guide to be measured as a

function of the distance the light had to propagate from injection before reaching the solar cell, as

seen in Figure 3-35.

Figure 3-35: Scanning the illuminated slit allows determination of how far injected light has propagated within the concentrator before reaching the solar cell at the output face.

43

LG002 LG003 LG005

Series Resistance (Ω) 0.0249 0.0165 0.02

Shunt Resistance (Ω) 388 813 446

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Figure 3-36: The apparatus for measuring optical efficiency at different sections of the concentrator input aperture. Two rotation axes and a translation axes are automated.

The solar simulator was designed to match the spectral content and angular extent of the

sun. While this allowed for the most accurate approximation of concentrator performance when

used as a solar collector, some additional information could be gained by using a source with a

smaller angular extent. A removable mirror was put into the system to allow the use of a HeNe

laser which was collimated by the off axis parabola. This produced a narrow angular spectrum,

allowing tighter focal spots, and the single wavelength simplified absorption calculations.

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3.4.2 Acrylic Wedged Stepped Concentrator

After a substantial amount of process development, it was determined that the most

practical way to produce the repeat unit of wedged stepped lenslets was to cast the shapes onto

an available acrylic substrate. This produced a back surface that was of sufficient quality and a

consistent thickness of the lenslet parts, though these parts had a noticeable bow as described in

section 3.2.2. This limited the potential thicknesses of the lenslet arrays depending on the

availability of certain thicknesses of acrylic substrate. The lenslet arrays used in this prototype

were thus approximately 1.6 mm thick (compared to the design thickness of 1.35mm), and thus to

keep the focus of the lenslet arrays on the injection facets, the guide layer had to be reduced in

thickness to approximately 1.80 mm (from a design thickness of 2.1mm.

The monolithic acrylic guide layers could be produced at a controllable thickness, though

the final part thickness was not precise. The parts produced in this way also had a substantial

amount of wedge, which was believed to be due to a mechanical misalignment. Parts were

measured to have up to 200µm in thickness variation along the guiding direction and up to 60µm

variation along the transverse axis. This thickness variation caused the lenslet focal point to vary

over the extent of the guide.

The guide was assembled by hand using an LED light board. An LED bar was placed near

the output face of the guide layer, and each lens array was aligned manually to maximize the light

coming directly up out of the lenslet array. Once aligned, the low index adhesive was cured using

a UV source, fixing the lenslet array in place so the next lenslet array could be aligned. The

completed guide was then mounted in the plastic holder and attached to a solar cell. The optical

efficiency of the guide was measured using a slit aperture at each lenslet array along the guide.

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Each point was scanned in both rotation angles in order to determine the optical efficiency at the

optimum pointing for each lens array. These results give the optical efficiency falloff for

illumination at increasing distance from the cell, as shown in Figure 3-37.

Figure 3-37: The optical efficiency falloff of the acrylic wedged stepped prototype. A small slit aperture illuminated a small portion of each lenslet array and found the optimum pointing to determine the efficiency falloff.

The optical efficiency was strongly dependent on several parameters, and several

fabrication errors prevented this system from performing as designed. The field of view of the

designed system was approximately ±1.0° square with little variation within the acceptance angle

and a sharp transition as the tight focal spot no longer hits the injection facet. The field of view

measured at the lenslet array closest to the solar cell and lenslet array farthest from the solar cell

were substantially different, as shown in Figure 3-38.

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Figure 3-38: The field of view of the acrylic wedged stepped concentrator at the front lenslet array (15 mm from cell) and at the rear lenslet array (90mm from cell). The profile is fairly broad and the center moves substantially from

lenslet to lenslet.

The field of view was substantially wider than the designed system and had a shape that

resembles a Gaussian more than a square. This was due to a focal length error. These parts were

of approximately matched thicknesses, but the lenslets varied substantially in thickness and the

guide layer was not exactly matched to compensate. In an otherwise perfect system, this amount

of broadening in the field of view would correspond to a defocus of approximately 190 µm. This

reduced the on-axis efficiency by approximately 11% and caused the field of view to be broadened

into a Gaussian shape of approximately this shape. The broadening of the field of view may also

have been due to a misalignment of the lenslet array such that different lenses had different

optimal pointing angles.

Another error that was known to be reducing the injection efficiency of the guide was the

injection facet roughness. The final master for the wedged stepped concentrator was cut with a

significantly worn tool, and thus there was substantial roughness on the injection facets. There

was variability between a few nanometers of RMS roughness and up to 50nm RMS roughness with

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no discernible pattern. In addition, each facet had substantial regions that were much better than

other regions on the same facet. Some of this was due to dust or debris, which prevented light

from being injected into the guide, and some of this variation was due to uneven roughness

patches.

The acrylic guide had numerous loss mechanisms which caused it to operate below the

ideal modeled performance. The different loss mechanisms are summarized in Table 3-2. The

modeled results agreed with the concentrator measurements. The facet scattering varied

substantially from facet to facet, and thus an approximate average of the measured facet

roughness was modeled. Some of the scattered light was contained within the concentrator for a

short distance. A substantial portion of this light was propagating at larger angles than from the

designed injection, and thus coupled out after a short propagation distance before reaching the

cell.

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Table 3-2: The various sources of loss for the acrylic wedged stepped concentrator. The facet scattering was the

dominant loss mechanism, though the defocus caused substantial losses.

From Table 3-2, the dominant loss mechanisms are from the focal effort and the injection

facet scattering. These are targets for improvement of any future iterations of this system. The

injection facet roughness is thought to be largely due to tool wear, and if remastered with an

undamaged tool, it is expected that future iterations of the dimple layer would have much

smoother injection facets. The losses due to the lenslets covering only a portion of the input

aperture are thought to be remedied using known manufacturing processes, and thus of relatively

little concern, despite causing the concentrator to perform poorly as a whole unit.

3.4.3 Polymer on Glass Wedged Stepped Concentrator

The polymer on glass system was expected to have the best optical performance of any

concentrator produced. The glass substrate provided a higher guide index for containing light, a

Loss Mechanism Optical Loss Variance Modelled Efficiency Note

Injection Loss

-Entrance to Guide Layer 6% ±.5% (96±0.5)%Dominant injection loss source in

designed system

-Focal Error 11% ±3% (85±3)%Combination of thickness mismatch

and alignment error

-Facet Scattering 20% -15% to +40% (62 +9/-24)%Symmetric roughness variation

produces asymmetric scattering

Guiding Loss

-Defect Scattering 4% -1% to +5% (59 +9/-23)%Density of debris and scratches on

concentrator

-Scatterd Light Loss 3% ±1% (57 +8/-21)%Light scattered from facet will be

contained for a short distance, then

-Absorption Loss 5% ±1% (54 +8/-20)% Modeled light absorption

Concentrator System

-Sparse Lenslet Aperture 30% -0% to 20% (37 +6/-16)%The lenslets did not cover the whole

guide, and perimiter lenslets low

quality -Field of View Misalignment 52% ±5% (19 +3/-9)%

The lenslet arrays were aligned to

slightly different optimal pointing

Total 81% 3/-9% (19 +3/-9)%

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lower absorption and scattering, and a flat, high quality surface to attach the other layers to and

provide mechanical stability. As with the acrylic wedged stepped guide, the lenslets could only be

fabricated with thicknesses determined by the available sizes of acrylic sheet to cast them on.

Thus the lenslets that were produced were approximately 1.70 mm thick, which was

approximately 0.35 mm thicker than the design. The glass guide substrate was cut to be 1.70mm

thick to compensate (designed to be 2.0mm), as the dimple layer of initial cast parts was

measured to have 0.05 mm thicker base than in the design specification.

The concentrator was assembled by hand using an LED light board. Light going back

through the concentrator was coupled out the lenslets, and if the system was well aligned, should

be roughly collimated normal to the guide plane. A fused silica plate was used as a weight to hold

down the lenslet array and minimize the bow in the system during alignment. When each lenslet

array was aligned, a UV lamp was focused onto the lenslet array in order to cure the low index

adhesive and securely attach the lenslet to the guide substrate. Once all the lenslet arrays were

attached, the concentrator was secured in a plastic housing, and a silicon solar cell was attached to

the output face.

The concentrator module was mounted in the testing apparatus, and the field of view

taken for a slit aperture at each of the attached lenslet arrays. The optical efficiency at the

optimum pointing angle for varying distances from the solar cell is shown in Figure 3-39.

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Figure 3-39: The optical efficiency falloff for the polymer on glass wedged stepped guide.

While this was slightly more efficient than the monolithic acrylic version, the efficiency

was much lower than the designed system. The relation between efficiency and distance from the

cell varied with little visible trend over the 6 measured lenslet arrays, and was dominated by a

random fluctuation. From the earlier component inspection, it was determined that this was

consistent with variations in the injection efficiency.

The field of view was taken at each lenslet in order to diagnose errors such as focal length

or misalignments. The field of view resembled the designed system much more closely than for

the monolithic acrylic prototype, as seen in Figure 3-40. The field of view moved substantially

between the various lenslet arrays due to slight misalignments, but consistently appeared to be

approximately ±1°. The field of view had a square shape with sharp transitions and substantial

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uniformity in the middle region. This eliminated a thickness mismatch and clocking mismatch as

performance drivers.

Figure 3-40: The normalized field of view from a slit aperture of the polymer on glass wedged stepped guide. The field of view much more closely resembled the design specifications than for the other prototypes.

The low index adhesive used to secure the lenslet arrays was designed to adhere to acrylic

materials. A quick test showed that it also adhered strongly to the glass substrate. While this

bond was initially quite strong, it proved to be temporary. After the polymer on glass prototype

was assembled, the bond strength between the low index adhesive and the glass substrate

weakened. After a few weeks, the low index layer with the attached lenslets fell off the glass

substrate in a ribbon. The concentrator was reassembled, but it was noticed that within an hour

or so of assembly, the stress that caused the lenslet arrays to bow had overcome the adhesive

strength. The lenslets were thus bowed, and the edges of the lenslet array had delaminated

completely.

The bow of the lenslet had been measured and fitted as described in section 3.2.2. The

effects of a bowed lenslet array were modeled in LightTools in order to approximate the effect this

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defect would have on system performance. The model used is shown in Figure 3-41. The system

was modeled as though the lenslet had fully returned to its original shape, and the low index

adhesive was not distorting the bow at all. By varying the thickness of the low index layer, the

approximate amount of delamination could be modeled to determine the effect on the optical

efficiency.

Figure 3-41: The model of the bowed lenslet array. The bowing of the lenslet array was approximated from the unattached lenslet array measured in the lenslet interferometer. The amount of delamination was controlled by

changing the thickness of the low index layer.

The edge of the lenslet array was observed to have delaminated, which would add two

significant Fresnel losses and cause the bow in the system to have substantially more optical

power than if immersed. The design specification for the low index layer thickness was 25µm, but

this would have only immersed a small fraction of the bowed lenslet array. The size of the

observed immersed region was consistent with a low index layer reaching up to 100µm. This

bowing defect caused dramatic losses outside of the immersed region (>30%), but within the

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observed immersed region, only minor losses were predicted (<10%). The modeled loss at each

lenslet in the array is shown in Figure 3-42 for both the modeled 25µm thickness and the observed

100µm thick low index layers.

Figure 3-42: The optical efficiency of each lenslet in the array for a system with the observed bowing defect and no others. The observed immersed region covers slightly more than half the aperture.

The modeling of the bowed lenslet array suggested that there was a substantial region

near the apex of the bow that should be minimally affected by this error. With the thicknesses of

the lenslet layer and guide layer approximately correct and relatively little clocking observed in the

parts, it was expected that the low injection efficiency was primarily due to facet scattering. The

observed facets were rough enough to account for such a low measured efficiency, but were

largely random and highly variable in roughness. If random facet scattering was indeed the

primary loss driver in the immersed regions, using a much smaller aperture was expected to be

able to find one of the smoother facets in the immersed region of the lenslet layer that had high

injection efficiency.

The slit aperture was reduced to be 3mm x 1mm, which spanned two adjacent lenslets.

The front lenslet was scanned in order to find a “sweet spot” with smooth facets. Such an area

was located near the center of the lenslet array closest to the chip. This spot had an injection

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efficiency of 89.6% at optimal pointing. The efficiency 2 mm to either side of this spot were found

to be much lower than for this “sweet spot” as shown in Figure 3-43. This indicated a large

efficiency variation within one lenslet array, which would indicate a fairly random process was

driving performance. This was consistent with the observed facet roughness variability.

Figure 3-43: The optical efficiency of the glass wedged stepped design near the sweet spot. The variation in efficiency within the immersed region of a lens array is caused by a substantial randomness in the injection facet roughness.

This sweet spot was further investigated using a collimated HeNe laser instead of the

Xenon source. This allowed a more precise measure of the acceptance angle, and also allowed a

more thorough mapping of the efficiency variation over the two facets of this region. The field of

view was taken for with much smaller steps. The HeNe laser had a much smaller angular spread,

and thus formed a much smaller spot on the injection facet which allowed for much more precise

characterization of the facet variability, as seen in Figure 3-44. The field of view had sharp

transitions and clearly resembles the ±1.0° square. Both images in Figure 3-44 were produced

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from the same data but with different color scales to highlight the variance on the facet.. There

was still variation of approximately ±5% even within this region, which highlighted facet roughness

as a critical performance driver in these concentrator systems.

Figure 3-44: Detailed field of view of sweet spot measured with collumated HeNe beam. The field of view very closely resembled the designed system, and there is relatively little variation within the injection facet.

The above methods accurately explained the discrepancy between the injection efficiency

of the designed system and the measured system. The large variability of the injection efficiency

obscured the guiding efficiency. This made it difficult to evaluate the performance of the system,

specifically the bypass features. In order to characterize the guiding efficiency of the system, the

injection losses were mitigated as much as possible. The regions of the guide covered by the

lenslet arrays provided many other sources of error, and the best way to roughly characterize the

guiding efficiency was to focus the HeNe beam using an external lens through the regions of the

guide layer that did not have lenslets attached at the front and back of the guide. The

performance of this system gave information about the guiding efficiency of the concentrator.

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A large number of injection facets were scanned at both the front and back of the guide,

as it was determined that injection efficiency would vary substantially from facet to facet. By

comparing the best facet measured at the back of the guide (farthest from the cell) to the best

facet measured at the front of the guide (closest to the cell), a rough approximation of the guiding

efficiency was established. The measurements shown in Figure 3-45 were normalized to the peak

reading for the facet close to the chip that produced the highest reading. This facet was only 2

mm from the chip, and thus there are not expected to be any guiding losses. The best measured

facet near the back of the guide was 116 mm away from the cell, and thus experienced the guiding

loss from travelling approximately the whole length of the system. Adjacent facets to each

showed the injection efficiency variation, and the substantial uncertainty on what portion of this

was actually guiding loss.

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Figure 3-45: Laser Scans at the front and back of the glass wedged stepped system. The guiding loss from the best facet near the back of the guide to the best facet found near the front of the guide was 22.7%.

This measurement gave an approximate guiding loss for light injected at the back of the

concentrator of 22.7%. This was approximate, as the best facet was chosen from a set of 12

measured facets near the rear of the guide and 8 facets near the front of the guide. With the

known variation of injection facet roughness, the injection efficiency variation gives this an

uncertainty of approximately ±3%. This measurement was taken after the third reconstruction of

this concentrator, and thus was expected to show substantial wear and dust collection despite

being cleaned during each reconstruction. The adhesion between the dimple layer and the glass

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substrate was also discovered to be temporary, as substantial portions of the dimple layer had

begun to delaminate. Due to these defects at the time the measurement was made, this

measurement was not expected to show the optimal guiding efficiency for a clean and undamaged

system, but provided an approximation.

Table 3-3: Summary of loss mechanisms for glass wedged stepped concentrator.

The loss mechanisms for the glass wedged stepped concentrator are presented in Table

3-3. The injection loss due to facet roughness is still the primary performance driver for this

system. The guiding efficiency is consistent with the experiments, and should improve for a

cleaner system that has not required repeated reassembly. A “sweet spot” corresponding to a

facet with low surface roughness was found, and measured to have excellent injection efficiency

and a field of view that very closely resembled the designed system.

Loss Mechanism Optical Loss Variance Modeled Efficiency Notes

Injection Loss

-Entrance to Guide Layer 4% ±0.5% (96±0.05)% Fresnel Losses

-Focal Length Error 0% 0% (96±0.05)%The thickness stack in this system we

well matched

-Facet Scattering 20% -15% to +40% (77 +12/-31)%

Random variation in roughness.

Symmetric roughness tolerance yield

asymmetric scattering tolerance.

Guiding Loss

-Defect Scattering 4% -1% to +5% (74 +11/-30)%Density of debris and scratches on

concentrator

-Scattered Light Loss 3% ±1% (72 +11/-29)%Light scattered from facet and

contained will be lost quickly

-Absorption Loss 5% ±1% (68 +11/-28)% Modeled light absorption

Concentrator System

-Sparce Lenslet Aperture 30% -0% to 20% (47 +7/-24)%The lenslets did not cover the whole

face of the guide

-Lenslet Bow 9% ±3% (43+7/-22)%The low index adhesive did not

prevent the lenslet from bowing

-Field of View Misalignment 36% ±5% (28+4/-14)%

The lenslets were aligned by hand,

and thus had different optimum

pointing angles.

Total 72% (14/-4)% (28+4/-14)%

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3.4.4 Reflective Dimple Tree Concentrator

The reflective tree concentrator was very different from the other two concentrators

fabricated, as this system had a different dimple geometry, lenslet geometry, and a reflective

coating on the lenslets. This system was assembled from the small reflector arrays and monolithic

acrylic guide layer by hand using a method similar to how the other concentrators were assembled.

Due to the reflective coating, the system had to be assembled upside-down with respect to the

other systems. The thinner lenslet array and large flat guide layer allowed lenslet arrays to be

pressed flat when cured.

As with the other concentrators, the efficiency at each lenslet array was measured, and a

field of view was taken to find the optimum pointing angle. These data for the reflective tree

concentrator are shown in Figure 3-46.

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Figure 3-46: Efficiency falloff for reflective tree concentrator system, taken at optimum pointing angle.

The efficiency for the reflective tree concentrator was much lower than the design

specification, which predicted optical efficiencies above 85%. The field of view of the system at

the front lenslet array and the back lenslet array were measured and presented inFigure 3-47.

This field of view was extremely broad, which was indicative of a large focal error or clocking

misalignment. In order to yield a field of view this broad, the thickness mismatch would have to

be approximately 400um, which was inconsistent with caliper thickness measurements.

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Figure 3-47: Normalized field of view of acrylic reflective tree concentrator for the lenslet array closest to the cell (left)

and farthest from the cell (right).

In order to determine what was attributable to a focal length mismatch and what was due

to a clocking misalignment, a much smaller aperture was used. This aperture would ensure that

only a few lenslets were illuminated at once, and thus if the field of view was still broad, a focal

length problem was causing the blurred field of view. If the field of view moved systematically as

the illuminated spot moved across the aperture, this was indicative of a clocking misalignment.

The results of this small slit scan showed a substantial defocus problem, but also some clocking

misalignment.

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Figure 3-48: The small slit scan of the field of view for the front lenslet of the reflective tree concentrator. The field of view is substantially blurred, indicating a focal length error, but the center moves almost a full degree and

systematically, indicating a clocking error.

In order to produce a this variation in the field of view, the lenslet array must be clocked

relative to the concentrator by approximately 0.7°, which was well within the range of a manual

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alignment. This clocking error was more difficult to eliminate than in the refractive systems due to

the focal length error. During assembly, the LEDs at the output face caused the lenslets to light up

when properly aligned, but with this focal length error, it was more difficult to determine precisely

when the lenslets were aligned. The field of view for this small spot was still blurred enough that a

focal error of approximately 170 µm was estimated. In addition to the issues with focal length and

misalignments, the reflective tree concentrator had the roughest injection facets, which caused

further injection loss. The nature of the reflective system also decreased potential injection

efficiency, as shadowing loss and reflection loss must also be included.

Table 3-4: Summary of loss mechanisms for the reflective tree concentrator prototype.

Loss Mechanism Optical Loss Variance Modeled Efficiency Notes

Injection Loss

-Entrance to Guide Layer 11% ±2% (89±2)%Fresnel losses, shadowing losses, and

reflection loss

-Focal Length Error 15% 3% (76±3)%The thickness stack in this system we

well matched

-Clocking Misalignment 5% 3% (72±4)%System misalignment due to manual

assembly

-Facet Scattering 31% -15% to +40% (48 +11/-29)%

Random variation in roughness.

Symmetric roughness tolerance yield

asymmetric scattering tolerance.

Guiding Loss

-Defect Scattering 4% -1% to +5% (46 +11/-28)%Density of debris and scratches on

concentrator

-Scattered Light Loss 3% ±1% (45 +10/-27)%Light scattered from facet and

contained will be lost quickly

-Absorption Loss 5% ±1% (43 +10/-26)% Modeled light absorption

Concentrator System

-Sparce Lenslet Aperture 30% -0% to 20% (30 +7/-23)%The lenslets did not cover the whole

face of the guide

-Field of View Misalignment 39% ±5% (18+4/-14)%

The lenslets were aligned by hand,

and thus had different optimum

pointing angles.

Total 88% (14/-4)% (18+4/-14)%

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A summary of the modeled defects and resulting efficiency losses for the reflective tree

concentrator is presented in Table 3-4. While the scattering from the injection facet was still the

dominant loss mechanism, other injection losses such as the focal length error and the clocking

misalignment caused substantially reduced performance.

Three concentrator prototypes were fabricated and characterized. While none of the

concentrators performed as well as the ideal modeled system, the driving errors for each system

were determined, and the relative effect of these imperfections was determined. It was

determined that many of these defects could be substantially reduced in future prototyping

generations. The most important fabrication errors were highlighted, and the potential for

improvements by fixing these errors was shown.

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4 Conclusion and Future Work

The three concentrator prototypes produced in this project all performed substantially

below the modeled efficiency of each design. The discrepancies between the laboratory

measurements and the modeled performance were determined such that the updated models

matched the performance of the prototypes. This modeling work allowed determination of the

relative importance of the various manufacturing errors and how the concentrator system could

be most effectively improved for future generations of prototypes.

4.1 Improving Concentrator Prototypes

The prototypes described in Chapter 3 were designed as a proof of process for the new

manufacturing methods used throughout this project. These processes produced both dimple and

lenslet geometries that had never been fabricated before. The tolerances and error drivers of

these processes was unknown. Testing of the components and final prototypes showed the

limitations of the manufacturing processes used. The error drivers of the concentrator designs

made using these new processes provided a pathway to produce a concentrator having

dramatically improved optical performance.

In this project, there were several errors that were accepted due to the exploratory nature

of this process that are projected to be corrected in future generations of light guide prototype.

The original goal of the project was to produce six functional prototypes, yet only three were

successfully fabricated. Both two stepped prototypes were abandoned due to a failure while

producing the dimple master. The cause of this cut failure was believed to be known, and thus a

second cut would be expected to produce a master of comparable quality to the other designs.

The polymer on glass tree design was abandoned due to difficulty casting the dimple features onto

165

the glass substrate, but this was again thought to be a matter of refining the process over a period

of time.

For the concentrators that were produced, the two driving errors were related to the

fragmenting of the lenslet array and the roughness of the dimple array. The lenslet array was

produced in small repeating units with the intention of tiling them into a larger unit spanning the

whole prototype. Tiling these repeat units to form a much larger lenslet array required a process

that was known but time consuming and fairly expensive. The demand for alignment of the

lenslet pieces placed a tight tolerance on the tiling process, yet it was expected that future

generations of lenslet parts would be able to span the entire prototype using methods that had

already been developed. This would almost certainly improve the bowing of the lenslet parts, as

the ratio of thickness to area would be greatly reduced. Producing a lenslet array with an

acceptable back surface quality and a precise thickness proved difficult, and future development

work would likely be needed to produce copies of these tiled lenslet arrays with acceptable back

surface quality and a precisely controlled thickness.

The dimple layer masters were produced using experimental machining processes. It was

determined that parts could be made with extremely small fillets (<2µm) and steep draft walls

(<2°). While the process showed the capability of producing surfaces with microroughness of less

than 5nm, many faces showed substantial scratches or other machining artifacts. A substantial

portion of this could be attributed to tool wear. The tools used to cut these masters were used for

several iterations of process development, and many of the parts produced near the end of this

project showed consistent character due to tool wear, as seen in Figure 4-1. This was especially

prevalent on the cuts of the injection facets, where the roughness was measured to be the largest

166

in these parts, and where roughness had the largest scattering effect. It was expected that a new

cutting tool combined with further iterations of machining parameters could dramatically reduce

the scattering of the part both from the injection facet and bypass prisms.

Figure 4-1: A representative injection facet of the two stepped light guide system. The pattern of scratches was

consistent over all facets measured on this part and is thought to be due to tool wear.

The prototypes described in Chapter 3 demonstrate the fabrication process and provide a

path towards a full scale prototype. In addition to the expected improvements described above, it

is important that future work be done to scale the prototypes to a size where they may be cost

effective at concentrations of several hundred times. These systems are designed to tile in order

to form larger concentrators, and thus this work is expected to use better known manufacturing

techniques and require less experimental process development. This work should yield full size

concentrator panels, which must then be integrated into HCPV modules, which requires additional

process development work.

167

4.2 Material Research

The primary goal of this project was to demonstrate the process for producing the

complicated geometries demanded by both the dimple and lenslet layers. The optimization of the

materials these systems were fabricated out of required future development work. Both the

dimple layer of the polymer on glass prototypes and the low index adhesive used for all the

fabricate prototypes were experimental materials. The dimple layer was designed to have to have

the correct refractive index and allow for accurate replication of the dimple geometries, but the

absorption of this layer was not expected to survive highly concentrated radiation. Finding a

material that could accurately reproduce the mastered geometries, possess the correct index of

refraction, bind to the glass substrate, and capable of withstanding high concentrations of solar

radiation required substantial future development work.

The low index adhesive was another experimental material, and while it created a strong

bond to both acrylic and glass parts, it was determined that this bond was only temporary. This

bond must last for many years in harsh environmental conditions, and finding a material that can

survive the expected module life time deployment that still has a low refractive index and strong

adhesion to both lenslet and guide substrates is critical. This requires further materials research,

and the characterization of the lifetime of the bond between guide layer and lenslet layer.

4.2.1 Gradient Index Material Research

Fabricating a gradient index guide layer that can be produced economically in high volumes

is difficult. Conventional ion diffusion processes that raise the index of refraction tend to use

prohibitively expensive reagents such as silver. This added cost has prevented these diffusions

from being commercialized in significant capacity. The most common exchanges involving alkaline

168

ion substitutions lower the index by diffusing sodium ions into glass and replacing lithium ions.

While the Na+ for Li+ exchange is well understood and has been commercialized, the reverse

exchange (replacing Na+ with Li+) has been shown to cause extensive devitrification and cracking.

Gradient Lens Corporation has explored a solution to this problem. The new process

allowed the index to be raised while maintaining a high quality optical surface. The clarity of the

diffused GRIN part with and without this new process is compared to the undiffused part in Figure

4-2.

Figure 4-2: A comparison of the clarity of the undiffused glass (right), the diffused GRIN sample pretreated with K+

ions(center), and the diffused GRIN sample without pretreatment (left). Photo by G. Schmidt

169

The process is designed to balance the stress on the glass during diffusion. This can be

seen through the edge effects where the surface is distorted. A white light interferometer is used

to measure the surface profile at the edge of a 2mm thick slab of glass before and after addition of

the gradient. The undiffused piece shows an edge roll off of approximately 500 nm over a distance

of approximately 100µm. When the gradient is introduced, the surface height profile undergoes a

substantial change but does not deviate more than a micron from the central flat region. The

edge profiles of these three samples are shown in Figure 4-3.

Figure 4-3: Surface heights at the edge of 2mm thick slab of glass that has not been diffused (left), pretreated for 6

hours (center), and pretreated for 16 hours (right). The 2D plots show the vertical and horizontal slices of the data

represented by the corresponding line color.

170

The refractive index profile of the diffused glass sample can be measured by slicing a

section and using an interference microscope to determine the gradient profile. By measuring the

phase difference in the interferometer, the profile can be reconstructed. The index change is

roughly 0.07, which is lower than the optimal Δn of 0.1 or greater. The fringe pattern observed on

the microscope interferometer and the derived index profile are shown in Figure 4-4.

Figure 4-4: Fringe pattern and calculated refractive index profile for diffused GRIN sample.

Producing a glass sample with a stronger gradient economically while keeping the optical

quality is another challenge. The absorption and scattering that result from this gradient must

also be investigated. The GRIN light guide has the highest potential for optical performance, but

requires a substantial amount more development work in order to fabricate.

4.3 Lifetime Durability and Performance Degradation

The lifetime of the concentrator system and the performance degradation when deployed

are critical parameters for determining the viability of a CPV system. There are several critical

failure mechanisms that must be address. The most critical factors for the concentrator of a CPV

171

system are photostability, temperature stability, and mechanical stability. In addition, the optical

performance degradation that results from deployment must be characterized to inform the cost

modeling.

While models have been developed to provide information about the long term

photostability of these concentrator systems, these were not able to be tested in conditions that

mimicked actual deployment. The materials used to fabricate the dimple layer of the polymer on

glass design and the two monolithic acrylic guide layers both were designed to test the machining

capabilities, and the materials were not designed to withstand actual deployment. The

simulations presented in Chapter 2 were for pure PMMA. Neither the experimental polymer used

in the polymer on glass nor the acrylic used for the monolithic parts had an absorption profile that

was expected to withstand high solar flux. The acrylic system showed non-negligible absorption in

the visible due to impurities (the acrylic used was not pure PMMA) and due to incomplete

polymerization.

CPV systems are most likely to be deployed in a desert environment due the large amount

of direct solar radiation these areas receive and the low cost of land. These areas experience large

temperature fluctuations which can be more than 20°C between day and night. The system must

be able to survive the thermal stresses resulting from the different materials of the layers without

delaminating or becoming internally misaligned. In addition, mechanical factors must be

considered such as wind loading and abrasion. These properties require further modeling work

and experimental investigation.

I

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Appendix A: Microstructure Dimensions

Reflective Dimple Tree Geometry

A

Fillets were set to be 2μm andsidewall drafts were set at 2°. Theseare consistent with measurements

made on fabricated parts.

Reflective Tree Mirror Pair

Reflective surface is parabolic withradius of curvature of 5.0 mm.

Wedged Stepped Dimple Geometry

Fillets were set to be 2μm and sidewall drafts were setat 2°. These are consistent with measurements made

on fabricated parts.

Stepped System Refractive Lenslet Geometry

Lenslet has conic surface with a radius of curvature of 1.11mmand a conic constant of -0.45 for PMMA lenslet in air.

Stepped System Refractive Lenslet Geometry

Fillets were set to be 2μm and sidewall drafts were set at 2°.These are consistent with measurements made on fabricated

parts.

Appendix B: Layer Dimensions and Materials

Reflective Tree System

Wedged Stepped System

Two-Stepped System

Material Index of Refraction

n vPMMA 1.491 53

GLC Glass 1.536 59

Material Transmission