I OPTIMIZATION of ORGANIC SOLAR CELLS a DISSERTATION

OPTIMIZATION OF ORGANIC SOLAR CELLS

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF ELECTRICAL ENGINEERING

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Seung Bum Rim March 2010

This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/yx656fs6181

ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Peter Peumans, Primary Adviser

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Michael McGehee

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Philip Wong

Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives.

iii Abstract

Organic solar cell is a promising technology because the versatility of organic materials in terms of the tunability of their electrical and optical properties and because of their relative insensitivity to film imperfections which potentially allows for very low-cost high-throughput roll-to-roll processing. However, the power conversion efficiency of organic solar cell is still limited and needs to be improved to be competitive with grid parity. In this thesis, I'll discuss major factors to limit efficiencies of bilayer organic solar cells such as light absorption, exciton diffusion and open circuit voltage.

Light trapping enhances light absorption and increases efficiencies with thinner devices structure. The technique is particularly important in organic solar cells because internal quantum efficiency of organic solar cells is low with thick films while absorption is weak with thin films. V-trap configuration is a simple and effective light trapping scheme for organic solar cells since there is no need to modify active layers, thinner films achieve high efficiencies and no tracking system is necessary.

The effects of total internal reflection in shaped substrates and the comparison with shapes other than V-shape will be also provided in Chapter 2.

Exciton diffusion is a main bottleneck in bilayer organic solar cells and thus the exciton diffusion length (L D) is an important parameter that determines efficiency.

However, different groups report different L Ds because there are many factors that affect the diffusion length or because there is a systematic error in the measurement

iv Abstract

method. The photocurrent spectroscopy method to estimate L D in Chapter 3 and the effect of molecular packing on L D will be discussed in Chapter 4.

Even when light absorption and exciton diffusion are optimized, the efficiency of a single junction organic solar cell is too low for commercial applications. Multi- junction cells are a way to achieve the efficiencies needed. I'll discuss the practical efficiencies of tandem organic solar cells in the case of a series-connected tandem cell and an unconstrained (multi-terminal) tandem cell. In practical cases, unconstrained tandem cells result in higher efficiencies because of the increased freedom in choosing materials and device structures without requiring current matching. Semitransparent solid state dye sensitized cells are demonstrated as a route to realize three terminal tandem cells in Chapter 5.

Curved focal plane arrays on stretchable silicon mesh networks can lead to realize high performance optical system with simple design. In Chapter 6, I show that curved focal plane arrays have optical advantages such as small number of elements, bright and accurate imaging for off-axis locations. Fabrication method is briefly introduced.

Acknowledgement

I would like to gratefully thank to my advisor, Professor Peter Peumans, for his encouragement and guidance. I appreciate all his contributions of time, ideas and funding to make my Ph.D. program motivated and productive. It has been really my pleasure to learn from him to solve challenging problems with deep understanding and creativity. His guidance with deep knowledge on broad spectrum of science and bright intuition keeps me motivated and going forward. I am also thankful to my reading committees; Professor Michael D. McGehee and Professor Philip Wong. It would not be possible to complete my projects without Prof. McGehee’s and his students’ help. I have shared ideas and have done many experiments with his students in his lab. I also appreciate Prof. Wong for his great teaching about nanoelectronics and advanced silicon devices. I appreciate BASF, Samsung scholarship foundation and center for advanced molecular photonics and KAUST for sponsoring my Ph.D. program.

I also thank my co-workers; Peter Erk, Jan Schoneboom, Felix Eickemeyer in

BASF for perylene project, Shanbin Zhao and Shawn R. Scully for V-trap project,

Rostam Dinyari and Kevin Huang for curved focal plane array project, Brian E.

Hardin for multi-junction dye sensitized cell project and Jung-Yong Lee and Whitney

Gaynor for multi-terminal multi-junction cell project. I thank Junbo Wu, Albert Liu,

Nicholas Sergeant and all members in Peumans’ group for fruitful discussions on various topics. I acknowledge Taeksoo Kim, Sungwoo Kim, Daeho Lee, Sangwook

Lee and Intaik Park for their advices and consulting throughout Ph.D. program.

vi Table of Contents

I greatly appreciate my wife, Hye Jung Lee, for endless support and my kids,

Aiden and Katie, for their being.

Seung Rim

vii

Table of Contents

Abstract ...... iv

Acknowledgement ...... vi

List of Tables ...... xi

List of Figures ...... xii

List of Equations ...... xviii

List of Symbols ...... xix

List of Abbreviations ...... xx

List of Chemicals ...... xxi

List of Publications, Conference Contributions ...... xxii

Chapter 1 Introduction ...... 25 1.1 Thin film photovoltaic cells...... 25 1.2 Cost analysis of organic solar cells ...... 26 1.2.1 Introduction ...... 26 1.2.2 Levelized cost of energy ...... 27 1.2.3 Efficiency goal for organic solar cells...... 30 1.3 Current status of organic solar cells ...... 31 1.4 Physics of organic solar cells ...... 32 1.4.1 Introduction ...... 33 1.4.2 Light absorption ...... 36 1.4.3 Exciton diffusion ...... 40 1.4.4 Charge transfer and separation ...... 46 1.4.5 Charge collection ...... 49 1.5 Dye sensitized solar cells ...... 49 1.6 Multi-junction cells ...... 50 1.7 Conclusion and outlook ...... 51 Bibliography ...... 52

viii Table of Contents

Chapter 2 V-shaped light trapping in organic solar cells ...... 63 2.1 Introduction ...... 63 2.2 Light trapping in thin film solar cells ...... 64 2.3 Principles of V-shaped light trap ...... 66 2.3.1 Structure ...... 66 2.3.2 Optical pathlength enhancement ...... 67 2.4 Modeling methods ...... 69 2.5 V-shaped light trap ...... 71 2.5.1 Effects of V-trap on efficiency ...... 71 2.5.2 Performance estimation ...... 73 2.5.3 Experiments ...... 75 2.6 Effects of geometrical shapes...... 77 2.6.1 Short circuit current density ...... 80 2.6.2 Open circuit voltage and power conversion efficiency ...... 83 2.6.3 Angular response ...... 85 2.6.4 Parasitic absorption ...... 88 2.6.5 Thin film Si solar cells in traps ...... 90 2.7 Conclusion ...... 91 Bibliography ...... 92

Chapter 3 The effects of optical interference on exciton diffusion length measurements using photocurrent spectroscopy ...... 97 3.1 Introduction ...... 97 3.2 Simulation method ...... 98 3.3 Feng-Ghosh model ...... 101 3.4 Correct estimation of exciton diffusion length ...... 104 3.4.1 Transmittance correction ...... 104 3.4.2 Thickness consideration ...... 106 3.4.3 Multiple exciton diffusion lengths ...... 107 3.5 Conclusion ...... 109 Bibliography ...... 110

Chapter 4 Effect of molecular packing on exciton diffusion length 113 4.1 Introduction ...... 113 4.2 Exciton diffusion length ...... 115 4.2.1 Experimental measurement ...... 115 4.2.2 Theoretical estimation...... 120 4.2.3 Molecular packing ...... 121 4.3 Conclusion ...... 123 Bibliography ...... 125

Chapter 5 Multi-junction organic solar cells ...... 128

ix Table of Contents

5.1 Introduction ...... 128 5.2 single junction organic solar cells ...... 129 5.2.1 Open circuit voltage of organic solar cells...... 129 5.2.2 Maximum efficiency of single junction organic solar cells ...... 130 5.3 Efficiency of multi-junction organic solar cells ...... 132 5.3.1 Box EQE model ...... 132 5.3.2 Gaussian absorption model ...... 135 5.3.3 Real materials ...... 137 5.3.4 Efficiencies of the optimized multi-junction cells ...... 140 5.4 Multi-terminal multi-junction organic solar cells ...... 140 5.4.1 Three-terminal double-junction organic solar cells ...... 141 5.4.2 Spectrum shifts and angular light incidence ...... 142 5.5 Semitransparent solid state dye sensitized cells ...... 144 5.6 Three terminal thin film silicon solar cell ...... 148 5.7 Conclusions ...... 149 Bibliography ...... 151

Chapter 6 The optical advantages of curved focal plane arrays ..... 154 6.1 Curved focal plane arrays ...... 154 6.2 Advantages of curved focal plane arrays ...... 155 6.2.1 Modulation transfer functions ...... 156 6.2.2 Point spread function ...... 157 6.2.3 Ray curves ...... 158 6.2.4 Distortion ...... 159 6.2.5 Relative illumination ...... 160 6.3 Image projection...... 161 6.4 Fabrication of curved FPA...... 162 6.5 Conclusion ...... 164 Bibliography ...... 165

Chapter 7 Conclusion and future work ...... 168

List of Tables

Table 5.1 HOMO, LUMO and bandgap (E G) of materials selected for the optimized 3- junction cell...... 138 Table 5.2 The comparison of performance of the series connected triple-junction cells in three models...... 140 Table 5.3 Performance of the 3-terminal 2-junction cell...... 142

List of Figures

Fig. 1.1 Levelized cost of energy as a function of module cost when the system scales are 1GWp with different PCE of 5%(black solid line), 10%(red dashed line) and 15%(blue dotted line). The current price of grid electricity, 9.3¢/kWh, is shown as blue dashed dot lines. Lifetime of OPV cells are assumed to be 10 years. For comparison, a-Si and CdTe thin film PV are shown in case of 25MWp and 1GWp scale as black dots. CdTe and a-Si are assumed to have 25 years of lifetime...... 28 Fig. 1.2 LCOE vs. module PCE with lifetime of 5years, 10years and 20years. When lifetime is 10 years, LCOE can reach grid price (red dash dot line) at 13% of PCE. .. 30 Fig. 1.3 The basic operation of a bilayer OPV cell. After a photon is absorbed in organic layers (1), an electron-hole pair is generated and relaxed to form an exciton (2). Then, the exction diffuse to DA interface (3) to be dissociated into charge carriers (4) and they are collected to metal electrodes (5) to generate photocurrent...... 33 Fig. 1.4 Summary of absorption coefficients ( α) of small molecular weight organic materials. α of ClAlPc is estimated from absorbance...... 38 Fig. 1.5 (a) Energy diagram of a donor-acceptor pair in flat band condition. Solid lines show HOMO and LUMO and dashed lines show Fermi levels. (b) Dissociation probability as a function of electric field intensity assuming that the mobility ratio of a donor and an acceptor is 10 2. Electric Field intensities and estimated dissociation probabilities of 35nm CuPc/35nm PTCBI bilayer cells are shown as solid circles (0V bias) and open circles (0.2V bias). Upper two circles and lower circles are obtained based on the assumption that the layers doped with the doping density of 10 18 cm -3 or the layers are intrinsic, respectively. Insets: energy diagrams of the bilayer structure. Field intensities are calculated at DA interfaces in the diagrams. Dashed lines are quasi Fermi levels...... 47 Fig. 2.1 Light trapping configurations using (a) randomized scattering surfaces when W>d, (b) regularized periodic structures when W>d~λ and (c) large-scale texturing when Welectrode are deposited under V-shaped substrate with opening angle of 2 α...... 67 Fig. 2.3 (a) Optical path length enhancement in a V-shaped light trap for an active layer with refractive index n=1.1 (filled squares). The thermodynamic limit to optical path length enhancement with full Ω=2 π acceptance cone (4 n2) is shown as a dotted line. Inset: the V-shaped light trap with the tip angle of 2 α. (b) Maximum optical path length enhancement in a V-shaped light trap as a function of refractive index n (solid line). The thermodynamic limit to optical path length enhancement with full Ω=2 π acceptance cone (4 n2) is shown as a dotted line. The two curves intersect when n=1.16...... 69

xii List of Figures

Fig. 2.6 The JSC of the ITO/390Å CuPc/420Å PTCBI/150Å BCP/1000Å Ag bilayer device (cell A) measured in the V-shaped configuration near the tip (open circles) and near the edge (open squares). The solid lines are model calculations. The JSC of a thinner cell with device structure ITO/300Å CuPc/400Å PTCBI/150Å BCP/1000Å Ag (cell B) near the tip of the V-shape (filled circles) is also shown together with a model calculation (dashed line)...... 75

Fig. 2.7 (a) JSC of ITO/500Å PEDOT-PSS/ P3HT:PCBM/1000Å Al cells as a function of the V-shape opening angle 2 α. The active layer thicknesses are 70nm (square), 110nm (circle) and 170nm (square). (b) The Voc (filled symbols) and ηP (open symbols) of the same cells. Solid lines are provided as guides to the eye...... 77 Fig. 2.8 Geometries and rays (gray lines) traced in ray-tracing simulations of six light trapping configurations. Cells are embedded on the four sides of an inverted pyramid light trap. The solar cells are indicated by a solid black line in the other five geometries. The organic solar cell layer structure used for the model calculations is also shown...... 79 Fig. 2.9 Comparison of the performance of the V-shaped (open squares), parabolic (solid circles), elliptical (open triangles), inverted parabolic (solid stars), inverted elliptical (open right triangle) and inverted pyramid (solid inverted triangles) light traps with an organic solar cell with layer structure ITO/10nm CuPc/3nm PTCBI/15nm BCP/100nm Ag, at normal incidence. (a) The calculated short circuit current density, JSC , as a function of the ratio of the device area to the light incidence area (RA). Inset: Magnified plot for 1.5

xiii List of Figures

Fig. 2.11 Comparison of the six considered light traps in (a) V OC and (b) PCE...... 84 Fig. 2.12 The device performance of the light traps as a function of angle of incidence of the illumination. (a) Short circuit current density, JSC , averaged over 0 to 90 degrees of incidence angles. (b) JSC as a function of angle of incidence for RA=4.0...... 85 Fig. 2.13 Map of absorbed optical power as a function of angle of incidence and distance from the center of the light trap calculated for λ=600nm and RA=4.0, for a (a) V-shaped, (b) inverted pyramid, (c) parabolic, (d) inverted parabolic, (e) ellipse and (f) inverted ellipse light trap. Darker regions indicate stronger absorption. Inset: Ray diagrams of the traps for a 30 °angle of incidence...... 87

Fig. 2.14 (a) Short circuit current density, JSC , at normal incidence (squares) and averaged over 0 to 90 degrees of incidence angles (triangles) including the effect of metal absorption (closed symbols) and without absorption in the metal (open symbols). (b) External quantum efficiency for RA=4.0 when metal absorption is included (solid line) and not included (dashed line). For comparison, the external quantum efficiency of a planar cell (gray line) is also shown...... 88 Fig. 2.15 Comparison of the performance of the V-shaped (squares), parabolic (circles), elliptical (inverted triangles), inverted parabolic (triangles), inverted elliptical (left triangle) and inverted pyramid (right triangles) light traps with (a) an amorphous silicon solar cell with layer structure Glass/150nm ZnO/300nm a-Si/100nm Ag, at normal incidence. (b) an microcrystalline silicon solar cell with layer structure Glass/150nm ZnO/1200nm c-Si/100nm Ag, at normal incidence. For comparison, the best textured devices are shown (dashed lines). Inset: device structures used in calculations...... 90 Fig. 3.1 Modeled photocurrent yield (quantum efficiency) at the front and back contact for a 400nm-thick DIP film sandwiched between ITO and Ag (solid lines), assuming LD=10nm. The absorption coefficient of DIP is also shown (dashed line). The separate extraction of the photocurrent from the front and back contact requires appropriate electrical bias...... 100 Fig. 3.2 (a) Plot of the inverse of modeled photocurrent yield at the front contact vs. 1/α and the FG model fits. (b). Plot of the inverse of modeled photocurrent yield at the back contact vs. 1/ α and the FG model fits...... 102 Fig. 3.3 Modeled optical electric field intensity and exciton concentration profiles in a 400nm-thick DIP layer. In the presence of optical interference effects, the optical field intensity and exciton concentration are strongly modulated (solid curves) in strong contrast to the assumptions made by FG (dashed curves). (a) When 1/α =150nm, the optical electric field intensity and exciton concentration are close to those obtained ignoring interference effects. (b) For 1/α =830nm, the actual optical field intensity and exciton concentration differ strongly from the FG assumptions...... 104 η λ η η Fig. 3.4 (a) Plots of 1/ FRONT (circles), T()/ FRONT (squares) and 1/ FRONT calculated without optical interference (crosses) vs. 1/α and their FG model fits. (b) η− α λ η− α Plots of 1/BACK exp(l ) (circles), T( ) /BACK exp( l ) (squares) and

xiv List of Figures

η− α α 1/BACK exp(l ) calculated without optical interference (crosses) vs. 1/ and their FG model fits...... 106

est Fig. 3.5 LD estimated by applying FG fits over the spectral range for which η λ η η (1/ α)max =500nm to FRONT /T ( ) (black), FRONT (light gray) and BACK (dark gray) vs. est η λ the thickness of the DIP layer. The errors in LD based on FG fits to FRONT /T ( ) are <10%, when the thickness of the DIP film >4.2(1/ α)max . Inset: The same plot with a full view...... 107 Fig. 3.6 FG fits of the inverse of modeled photocurrent yield (front contact) vs. 1/α of a single layer merocyanine device (20nm Al/260nm Merocyanine/20nm Ag) assuming that LD=6.0nm...... 108 Fig. 4.1 Molecular structure of isomer pure PTCBI...... 116 η Fig. 4.2 The external quantum efficiency ( EQE ) of devices with layer structure ITO/350Å CuPc/300Å PTCBI/150Å BCP/1000Å Ag (cis-PTCBI: filled squares, trans-PTCBI: filled triangles, mixture: filled circles), measured using monochromatic η light chopped at 30Hz. Model calculations of EQE (gray solid lines) and absorption coefficients (dashed lines) are also shown...... 117 Fig. 4.3 Current density vs. voltage characteristics of devices with ITO/150Å CuPc/300Å PTCBI/150Å BCP/1000Å Ag under 94mW/cm2 AM1.5G simulated solar illumination (cis-PTCBI: filled squares, trans-PTCBI: filled triangles, mixture: filled circles)...... 118 Fig. 4.4 Photoluminescence (PL) intensity ratio of cis (open circles) and trans (open triangles) PTCBI vs. film thickness for films grown on 50Å of CuPc on glass. The lines are fits yielding LD=28±2.0Å for cis-PTCBI (solid line) and LD=43±3.0Å for trans-PTCBI (dashed line). The excitation wavelength was λ=540nm...... 119 Fig. 4.5 Crystal structures of cis-PTCBI and trans-PTCBI. Crystal planes parallel to the substrate are indicated (gray planes). LD show exciton diffusion lengths estimated by theoretical calculations described in Error! Reference source not found. assuming perfect crystal. Estimated LD are 20 times longer than LD in experiments. 121 Fig. 4.6 (a) X-ray diffraction (XRD) patterns for 2400Å-thick films of PTCBI isomers and mixture of isomers PTCBI on glass taken in the θ− 2 θ geometry using the Cu Kα line. The XRD pattern of the glass substrate is also shown. Simulated XRD patterns (gray lines) of a trans-PTCBI film assuming that the (011) planes are parallel to the substrate and trans-PTCBI powder are shown. (b) Scanning electron micrographs of 400Å-thick trans-PTCBI, cis-trans mixture, and trans-PTCBI films on top of ITO/320Å PEDOT:PSS/200Å CuPc on glass substrates. The width of the images is 576nm...... 123

Fig. 5.1 (a) Relationship between V OC and interface gap ( EDA ) [Courtesy by Junbo Wu] (b) Schematic of a donor and acceptor pair that shows linear relationship between VOC and EDA ...... 129

xv List of Figures

Fig. 5.2 (a) Maximum power conversion efficiency of single junction organic solar cells calculated along with bandgaps of the donor-acceptor pairs (Inset) band diagram of a donor-acceptor pair used in this calculation. The highest efficiency is 11.3% at EG=1.63eV. (b) J SC and V OC of a single junction organic solar cells at given bandgap...... 131

Fig. 5.3 (a) PCE( ηP),J SC and V OC estimated by box EQE model. (b) The optimized bandgap at each number of subcells in multi-junction cells. (c) Constant EQE within band from E G,n-1 to E G,n in box EQE model...... 133 Fig. 5.4 Thermalization ratio of multi-junction cells (open squares). Energy of photons absorbed (solid circles) and not absorbed (solid squares) in the cells are shown...... 134

Fig. 5.5 (a) absorption ( ηA, dashed) and external ( ηEQE , solid) quantum efficiency of the optimized triple-junction cell. Quantum efficiency contributions of subcells are represented as dotted lines. (b) Angular response of the optimized triple-junction cell. The J SC of the cell (solid curve) is close to ones of subcells and also cosine curve (gray) is shown for comparison. (Inset) Inset in bottom left corner shows the structure of the tandem cell that consists of antireflective coating (ARC), transparent conductive oxide electrode (TCO), buffer layers, intermediate electrodes (dashed lines) and donor- acceptor (D:A) subcells. Inset in top right corner shows absorption coefficients, α, of active layers assumed in the model...... 136 Fig. 5.6 (a) absorption coefficients of subcells in the optimized triple-junction cell with real materials. Each subcell is assumed to have mixed donor-acceptor layers with 1:1 ratio. HOMO-LUMO level and material names are shown as inset. Gray dashed lines show EG used in this model. (b) The ηA (dashed), ηEQE (solid) and contributions of each stack (dotted, color) are shown. The blue, green and red dotted curves show the contributions of SubPc:PTCBI, ClAlPc:C 60 and SnPc:C 60 , respectively...... 139 Fig. 5.7 (a) Structure of the three terminal triple-junction cell. (b) absorption (dashed) and external (solid) quantum efficiencies of the three terminal cell. Contributions of subcells (dotted) are also shown...... 141 Fig. 5.8 (a) Simulated solar spectrum at 6am (red) and 12pm (black) at 7/15/1999 (b) Time series power conversion efficiencies of the optimized 3-terminal 2-cell device (black circles) and the optimized 2-terminal 3-cell device (black squares) and the ratio of the efficiencies (red squares) along 6am to 6pm...... 143 Fig. 5.9 (a) Power conversion efficiency of the series-connected optimized 3-junction cell (circle) and the optimized 3-terminal 2-junction cell (square) plot along angle of light incidence. (b) Ratio of PCE of two optimized cells versus angle of light incidence...... 144 Fig. 5.10 Structure of multi-terminal multi-junction ss-DSC and semitransparent cell as a bottom layer...... 145 Fig. 5.11 Processing steps of semitransparent ss-DSC. [Courtesy by J.-Y. Lee] (Center) SEM picture of Ag NW mesh network on semitransparent ss-DSC device...... 146

xvi List of Figures

Fig. 5.12 (a) I-V of semitransparent ss-DSC and Ag capped device. (Inset) Device structure of the ss-DSCs. (b) Transmission of Ag NW ss-DSC and ss-DSC without top electrodes...... 147 Fig. 5.13 Power conversion efficiencies of 2-junction a-Si(1 st layer)/µc-Si(2 nd layer) solar cells. (a) 2-terminal with maximum PCE=10.8% (b) 3-terminal with maximum PCE=11.6%...... 149 Fig. 6.1 Modulation transfer functions (MTFs) of (a) a simple plano convex lens with a planar image plane (System I), (b) Cooke triplet camera system lenses with a planar image plane (System II) and (c) a simple ball lens with a spherical curved image plane (System III). (a-c) MTFs of diffraction limited systems (black dotted lines), image points on axis (red), tangential image points (solid) at 0.4 field (green) and 0.7 field (blue) and sagittal image points (dashed dots) at both fields are shown. Inset: schematics of the three systems...... 156 Fig. 6.2 Point spread functions for (a-c,g-i,m-o) on-axis and (d-f,j-l,p-r) off-axis (2mm image height) points. (a-f) show PSFs for System I, (g-l) for System II and (m-r) for System III...... 158 Fig. 6.3 Ray curves of astigmatism field curvature of (a) System I, (b) System II and (c) System III. Tangential field curvature (dotted lines) and sagittal field curvature (solid lines) are shown together...... 159 Fig. 6.4 (a) Mapping of image points on a curved image plane to points on a 2-D image plane in System III. (b-d) Image height distortion of (b) System I (c) System II and (d) System III...... 160 Fig. 6.5 Relative illumination fall-off of (a) System I, (b) System II and (c) System III...... 161 Fig. 6.6 (a) Object image and simulated radiometric images by (b) System I (c) System II and (d) System III...... 162 Fig. 6.7 (a,b) Optical micrographs of a fabricated curved silicon die. (a) Curved die on a spherical surface with radius of cuvature of 1cm. (b) Detail of the curved die at an off-axis location. (c) Scanning electron microscopy (SEM) picture of an undeformed die. [By courtesy of Rostam Dinyari] ...... 163

xvii List of Equations

List of Equations

(1.1) ...... 28 (1.2) ...... 29 (1.3) ...... 36 (1.4) ...... 41 (1.5) ...... 41 (1.6) ...... 42 (1.7) ...... 43 (1.8) ...... 48 (2.1) ...... 68 (2.2) ...... 69 (2.3) ...... 69 (2.4) ...... 69 (2.5) ...... 73 (2.6) ...... 84 (3.1) ...... 100 (3.2) ...... 101 (3.3) ...... 105 (4.1) ...... 120 (4.2) ...... 120 (5.1) ...... 130 (5.2) ...... 130 (5.3) ...... 131 (5.4) ...... 133 (5.5) ...... 133 (5.6) ...... 135

xviii

List of Symbols

λ wavelength

T temperature n refractive index

κ extinction coefficient

α absorption coefficient

ηP power conversion efficiency

ηA absorption efficiency

ηED exciton diffusion efficiency

ηCT charge transfer efficiency

ηCC charge collection efficiency

ηIQE internal quantum efficiency

ηEQE external quantum efficiency

JSC short circuit current density

VOC open circuit voltage

LD exciton diffusion length

E electric field magnitude k Boltzmann constant (1.38×10 -23 J/K)

S(λ) solar spectrum in photons per unit area per unit time per unit wavelength a-Si amorphous silicon

xix

List of Abbreviations

AM Air mass

BHJ Bulk heterojunction

DA Donor acceptor

DSC (DSSC) Dye sensitized solar cell

EBL Exciton blocking layer

EQE External quantum efficiency

FF Fill factor

IR Infrared

IQE Internal quantum efficiency

HOMO Highest occupied molecular orbital

LUMO Lowest unoccupied molecular orbital

MJ Multi-junction

MT Multi-terminal

NW Nanowire

OPV Organic photovoltaic

PCE Power conversion efficiency

PV Photovoltaic

UV Ultraviolet

List of Chemicals

Alq 3 tris-(8-hydroxyquinoline) aluminum

BCP 2,9-dimethy-4,7-diphenyl-1,10-phenanthroline

CuPc copper phthalocyanine

DIW deionized water

IPA isopropanol

ITO indium tin oxide

PEDOT:PSS poly(3,4,-ethylene dioxythiophene):poly(styrenesulfonate)

PTCBI 3,4,9,10-perylene tetracarboxylic bis-benzimidazole

PTCDA 3,4,9,10-perylene tetracarboxylic dianhydride

xxi

List of Publications, Conference Contributions

Publications

S.-B. Rim and P. Peumans, "An analysis of lighttrapping configurations for thin film solar cells based on shaped substrates," Journal of Applied Physics , accepted

S.-B. Rim , P. B. Catrysse, R. Dinyari, K. Huang and P. Peumans, "The optical advantages of curved focal plane arrays," Optics Express 16, 4965 (2008)

S.-B. Rim and P. Peumans, "The effects of optical interference on exciton diffusion length measurements using photocurrent spectroscopy," Journal of Applied Physics 103, 124515 (2008)

R. Dinyari, S.-B. Rim , K. Huang, P. B. Catrysse and P. Peumans, "Curving monolithic silicon for non-planar focal plane array applications," Applied Physics Letters 92, 091114 (2008)

A. Liu, S. Zhao, S.-B. Rim , J. Wu, M. Koenemann, P. Erk and P. Peumans, "Control of electric field strength and orientation at the donor-acceptor interface in organic solar cells," Advanced Materials 20, 1065 (2008)

S.-B. Rim , S. Zhao, S.R. Scully, M.D. McGehee and P. Peumans, "An effective light trapping configuration for thin-film solar cells," Applied Physics Letters 91, 243501 (2007)

S.-B. Rim , R. F. Fink, J.C. Schoeneboom, P. Erk and P. Peumans, "Effect of molecular packing on the exciton diffusion length in organic solar cells," Applied Physics Letters 91, 173504 (2007)

xxii List of Publications , Conference Contributions

Presentations & Posters

S.-B. Rim , B. E. Hardin, H.-S. Kim, Y. Cui, M. D. McGehee and P. Peumans, "Semitransparent dye sensitized solar cells," SPIE Symposium on Photonic Devices + Applications, August 2009, San Diego, CA

S.-B. Rim , J.-Y. Lee, W. Gaynor, B. E. Hardin, S. T. Connor, H.-S. Kim, Y. Cui, M. D. McGehee and P. Peumans, "Multi-junction organic solar cells," CAMP annual meeting, April 2009, Stanford, CA

S.-B. Rim and P. Peumans, "An analysis of lighttrapping configurations for thin film solar cells based on shaped substrates," MRS Fall 2008, December 2008, Boston, MA

R. Dinyari, S.-B. Rim , K. Huang and P. Peumans, "Curving monolithic silicon for nonplanar focal plane array applications," SPIE Symposium on Photonic Devices + Applications, August 2008, San Diego, CA

S. Zhao, A. Liu, S.-B. Rim and P. Peumans, "New Insight into Carrier Recombination in Organic Solar Cells," 33rd PVSC Conference, May 2008, San Diego, CA

A. Liu, S. Zhao, S.-B. Rim , M. Koenenmann, P. Erk and P. Peumans, "Control of electric field strength and orientation at the donor-acceptor interface in organic solar cells," MRS Fall 2007, November 2007, Boston, MA

S.-B. Rim , S. Zhao, S.R. Scully, M.D. McGehee and P. Peumans, "An effective light trapping configuration for thin-film solar cells," MRS Fall 2007, November 2007, Boston, MA

S.-B. Rim , J. C. schoeneboom, P. Erk and P. Peumans, "Effect of molecular packing on the exciton diffusion length in organic solar cells," MRS Fall 2007, November 2007, Boston, MA

xxiii List of Publications , Conference Contributions

J. Wu, S.-B. Rim and P. Peumans, "Study of Boron Subphthalocyanine Chloride based Photovoltaic Cells," MRS Fall 2007, November 2007, Boston, MA

S.-B. Rim , A. Liu, L. Verslegers, J. Wu, S. Zhao and P. Peumans, "Progress in Organic Solar Cells," SPRC Symposium 2007, Stanford CA

xxiv

Introduction

Chapter 1 Introduction

1.1 Thin film photovoltaic cells

Photovoltaic (PV) cells are regarded as a potentially important source of our future energy supplies [1]. However, the cost of electrical power produced using PV cells is approximately a factor of 5 times more expensive than electrical power from the grid produced using fossil fuels. In order to reach grid parity, substantial reductions need to be achieved in module and installation cost. While conventional PV technologies such as crystalline silicon and thin-film amorphous Si, CdTe and CuInGaSe 2 (CIGS) solar cells appear to be on a path to reach grid parity by 2015, there are concerns about the ability of these technologies to scale to the very large production volumes required if we were to supply a substantial fraction of our energy using PV cells. A fundamental limitation is the limited crustal abundance of Te and In, used in CdTe and CIGS solar cells, respectively, has been cited[2-4] as a potential limiter for that type of solar cell.

While the crustal abundance is not a limiter in the immediate future, it will be when

PV cells are to supply TW of electrical power[2, 5]. Another important limitation of current PV technologies is that the capital equipment required per MW of yearly

25 Cost analysis of organic solar cells production capacity is too large. Furthermore, conventional PV technologies based on inorganic semiconductors are necessarily limited to specific semiconductor energy gaps or limited ranges of energy gaps, which limits the achievable efficiencies. Their deposition requires specific substrate temperatures (e.g. close-spaced source deposition of CdTe is performed at a substrate temperature of Tsubs =500°C) which limits substrate choice and/or relatively low deposition rates which limits the ability to lower cost by increasing throughput.

1.2 Cost analysis of organic solar cells

1.2.1 Introduction

Thin-film PV technologies provide ways to reduce manufacturing cost by using high- throughput manufacturing paradigms that don’t require handling of individual silicon wafers [6, 7]. Despite the success of entrenched thin-film PV technologies such as amorphous Si, CdTe and CIGS, organic PV (OPV) cells attract attention because the electronic and optical properties of organic materials can be tuned by altering the molecular structure of the materials. This ability to tune the material properties is an important element that may eventually lead to high cell efficiencies, as discussed below. OPV cells also have the oft-cited potential of being manufactured at very low cost. This is potentially true for solution [8] as well as for vacuum-deposited OPV cells [9] provided that high throughputs are achieved. Closed coupled showerhead with OVPD[10] was tested for large area deposition, because high throughput

Introduction processing is an important issue to reduce cost[11] such as in-line vacuum deposition system[12, 13] or roll-to-roll processing[14].

1.2.2 Levelized cost of energy

To reduce the cost of electrical power produced by solar cells, one can either lower the manufacturing costs per unit area, or improve the power conversion efficiency (PCE).

The cost of an installed PV system consists of the cost of the PV modules and other items (installation, inverter, taxes, engineering, etc.) called the balance of system

(BOS) cost. In practice, since a large fraction of the BOS cost of a PV system scales linearly with area of the installation and is hence inversely proportional to the PCE,

PCE is a powerful lever on the cost of electrical power from a PV technology and vey- low-cost low-efficiency PV modules are of limited value. This is illustrated in Fig. 1.1, where the cost per kWh produced, C, is plotted as a function of the manufacturing cost per square meter, M, for a PCE of ηP=5%, 10% and 15%. These calculations were performed for system sizes of 1GWp (PV systems are sized based on their peak power output expressed in peak Watts or Wp). The largest PV systems in use today are

26MWp [15] and systems up to 800MWp have been planned [16]. 1GWp corresponds roughly to the steady-state power output of both nuclear and conventional power plants. No PV systems of that size exist or have been planned.

27 Cost analysis of organic solar cells

 M + BOS  C =  A + BOS ()1 + f C + C  η P  i 0 OM (1.1)  I 0 P 

2 ,where I0 (=1000W/m ) is the peak intensity of Sun, fi is the fraction of indirect cost such as marketing profit and marketing and COM is cost per kWh for operation and maintenance (O&M). COM and fi are assumed to be 0.05¢/kWh and 10% for the 1GWp system. The BOS cost that scales linearly with installed Wp (e .g. the inverter), BOS P, was assumed to be $0.27/Wp, for 1GWp systems, and the BOS cost that scales

2 linearly with total installed module area, BOS A, is $40/m . These BOS costs are

Introduction estimates based on large ground mounted systems such as the system in Springerville,

Arizona, managed by Tucson Electric Power [5]. C0 is LEC of a $1/Wp system without O&M and is obtained by

I r(r + )1 n C = 0 (1.2) 0 η + n − DA qins (r )1 1

2 ,where qins is insolation (=1700kWh/m yr in average in United States), ηDA is conversion efficiency from DC to AC, r is interest rate and n is lifetime of system and

ηDA =0.8, r=7% and n=10 years are assumed in this calculation. The point at which grid parity is achieved depends on the location of the system which determines capacity factor (through the insolation and hours of clear sky) and local cost of grid power. C0 in United States is 10.47¢/kWh in average, while the current retail price of electricity

(blue dash dot line) is 9.26¢/kWh[17].

29 Cost analysis of organic solar cells

1.2.3 Efficiency goal for organic solar cells

Fig. 1.2 LCOE vs. module PCE with lifetime of 5years, 10years and 20years. When lifetime is 10 years, LCOE can reach grid price (red dash dot line) at 13% of PCE. At a PCE of 5%, it is impossible to reach grid parity, even for a very large installation. At a modul e cost of $30/m 2, grid parity would be reached for a 1GWp system for module efficiency of 13% ( Fig. 1.2). Given that even in today’s CdTe modules, with a module cost of approximately $100/m 2, the active materials cost

(source materials cost and capital cost required for their deposition) accounts for only

15% of the module cost, with the remaining cost attributed to packaging, substrate, etc.[5] , simply reducing the cost of the active layers by the use of organic materials only leads to marginal cost reductions. It is clear that achieving a high PCE (>13%)

Introduction will be paramount if organic PV cells are to supply us with a large fraction of our energy.

1.3 Current status of organic solar cells

Regarding small molecular weight materials [18], the reported PCE of such PV cells has improved steadily since Tang’s [19] demonstration of a heterojunction bilayer cell with a PCE of ηP=0.95% using the small molecular weight materials copper phthalocyanine (CuPc) and 3,4,9,10-perylene tetracarboxylic benzimidazole (PTCBI).

The highest PCEs reported for small molecular weight organic PV cells reach 4.4% in a single heterojunctionn device [20] and 5.7% in a tandem structure[21]. For polymer devices, 6.5% in a tandem structure[22] and 6.1% in a single junction[23] device are reported. These PCEs are far lower than those of record inorganic thin film PV cells, which are 13%, 16.5% and 19.5% for amorphous silicon, CdTe and CuInGaSe 2 cells, respectively[11, 24] and the best laboratory silicon solar cells that reach efficiencies of up to 24.4%[25]. As explained above, it is imperative that the module efficiencies of organic PV cells are increased to 13% or better, which corresponds to 15% in cell efficiencies.

There are many aspects of organic PV cells that can be further improved to increase the PCE. Doing so hinges upon an understanding of the device physics and the development of novel device architectures that overcome the shortcomings inherent to organic devices. In the following sections, I describe the physics underlying the operation of single heterojunction devices. The physical processes of

31 Physics of organic solar cells photon absorption, exciton diffusion, charge transfer, charge pair separation and charge collection are covered. Approaches to overcome the shortcomings of organic materials are then discussed. Light trapping techniques[26-33] can be used to improve device efficiencies.by enhancing optical absorption in very thin active layers with high internal efficiencies, nanostructured junctions (also known as bulk heterojunctions)

[34] can be used to achieve efficient exciton harvesting, and nanocrystalline networks[35] can be used to broaden the spectral sensitivity. I then describe the multi- junction cells that can realistically achieve high PCEs by stacking multiple heterojunctions.

1.4 Physics of organic solar cells

In this section, we will briefly review physics behind organic solar cells, focusing on planar junction bilayer cells.

Introduction

1.4.1 Introduction

Fig. 1.3 The basic operation of a bilayer OPV cell. After a photon is absorbed in organic layers (1), an electron -hole pair is generated and relaxed to form an exciton (2). Then, the exction diffuse to DA interface (3) to be dissociated into charge carriers (4) and they are collected to metal electrodes (5) to gene rate photocurrent. The basic operation of a single junction device is described as a 5 -step process in Fig. 1.3. The active layers of the device consis t of a material with a low ionization potential, called the donor, and a material with a large electron affinity, called the acceptor. The total device active layer thickness is of the order of 100nm. The conversion steps are: (1) the active layers absorb incident photons leading to the promotion of a molecule into an excited state. This is equivalent to the creation of an electron-hole pair in conventional semiconductor parlance. A major distinction with inorganic PV cells is that the excited state quickly (within ~10ps) [36] relaxes to a

33 Physics of organic solar cells bound state, called an exciton, that cannot be dissociated into a free electron and hole using electric fields typically present in devices [37]. (2) A fraction of the photogenerated excitons diffuse to the donor/acceptor (DA) interface before they decay radiatively or, more commonly, non-radiatively. (3) Excitons residing on a donor (acceptor) molecule at the DA interface transfer an electron (hole) to an adjacent acceptor (donor) molecule. This charge-transfer step is usually exothermic, although it doesn’t strictly need to be so (see below), and very fast (~100fs)[38, 39].

The result is an electron polaron in the lowest unoccupied molecular orbital (LUMO) of an acceptor molecule and a hole polaron in the highest occupied molecular orbital

(HOMO) of a donor molecule. The electron-hole pair spans the DA interface and is referred to as a geminate electron-hole pair (GEHP). The spatial separation between the electron and hole immediately preceding the charge-transfer process is an important parameter that influences the next step. (4) The GEHP is bound by a strong

Coulomb attraction. Because of the presence of a barrier for both the electron and hole

(they are each confined to a half space), diffusion of the electron and hole favors their separation. This is a driving force that is entirely statistical in nature. At the same time, an electric field may be present that aids or prevents GEHP dissociation [37, 40]. The loss of electron-hole pairs due to recombination of GEHPs is called geminate recombination. (5) In a final step, the charge carriers, now separated from their geminate partner, travel through the device structure and are collected at the electrodes if they don’t recombine with an opposite carrier type en route. This type of recombination is called non-geminate since it involved electrons and holes that do not originate from the same exciton.

Introduction

Each of the above steps has a yield or quantum efficiency associated with it.

The ratio of the number of electrons that contribute to photocurrent over the number of incoming photons is the external quantum efficiency, ηEQE , and it can be expressed as the product of the quantum efficiencies of each of the 5 steps: ηEQE =ηA.ηED .ηCT .ηCS .ηCC

=ηAηIQE , where ηA is optical absorption efficiency, ηED is the exciton diffusion efficiency, ηCT is the charge-transfer quantum efficiency, ηCS is the GEHP separation probability, ηCC is the carrier collection efficiency, and ηIQE is the internal quantum efficiency. Efficient optical absorption ( ηA~100%) can be achieved when active layer thicknesses larger than the optical pathlength, LA=1/ α, where α is an absorption coefficient, are used. In practice, since the film thicknesses are of the order of a wavelength, optical interference effects have to be taken into account [41]. However, films thick enough to achieve ηA~100% across most of the spectral range of an organic absorber result in sub-optimal cell performance since exciton diffusion and carrier collection/transport cannot both be made efficient for such thick films. In thin films that absorb incompletely, both exciton diffusion and carrier collection/transport can be efficient.

The photocurrent under short-circuit conditions, JSC , is:

= η λ λ J SC q∫ EQE S( )d , where S(λ) is the AM1.5 solar spectrum expressed in number of photons per unit area per unit time per unit wavelength. We note that this is valid only if carrier recombination is not intensity dependent as is often the case[42-44].

η = The PCE is obtained using P J SC VOC FF / Pin , where Pin is the power of incoming light and VOC is the open-circuit voltage. FF is the fill factor defined by

35 Physics of organic solar cells

FF =JmVm/JSC VOC , where Jm and Vm are the current density and voltage at the point of maximum electrical power output. We now discuss the current understanding of and recent findings in the areas of light absorption, exciton diffusion, exciton dissociation and charge separation.

1.4.2 Light absorption

Since active layers thick enough to absorb all the incident photons have limited IQEs, techniques that increase the amount of light absorbed for a given film thickness can be used to increase the PCE. Because of the absence of extended electronic states, organic materials have absorption spectra that are narrow compared to the broad absorption bands of inorganic crystals. Another distinction with most inorganic thin film PV cells is that optical interference effects have to be considered to calculate ηA since OPV cells have film thickness comparable to the wavelengths present in sunlight, leading to standing wave effects that can alter the optical absorption likelihood. The absorbed optical power density at position x in the active layer can be expressed as[41]

= 1 ε αη 2 Q(x) c 0 E(x) 2 (1.3) where c is the speed of light, ε0 is permittivity in vacuum, η is the real part of refractive index, and E(x) is electric field at position x. The field, E(x), can be calculated using the transfer matrix formalism. Total absorption in film can be measured by transmittance and reflectance measurement using UV-Vis spectroscopy or ellipsometer. To maximize optical absorption, the film thicknesses of the various

Introduction layers in the stack should be tuned to spatially concentrate light in layers where it is strongly absorbed [18, 41].

1.4.2.1 Theoretical estimation techniques

Light absorption can be accurately estimated by solving Maxwell equations in arbitrary solar cell structures in theory. Accurate and fast theoretical estimation of absorption can expedite the design of new device structures. However, proper techniques need to be applied depending on dimensions and device structures.

Geometrical ray tracing[31, 45] is used for devices with feature size that is larger than wavelength, for example, thick crystalline silicon solar cells, crystalline

III-V solar cells and large scale concentrator solar cells. Fresnel reflection and refraction laws are applied to surfaces or interfaces. When multilayer thin film structures are incorporated such as antireflective coating [45] or active layers[31], proper handling of them with transfer matrix calculation or other wave optics calculation methods need to be addressed.

When feature sizes are comparable or smaller than wavelength, various wave optics calculation techniques can be used such as transfer matrix method in one dimension and finite difference time domain (FDTD)[46], finite element method

(FEM)[47] and rigorous coupled wave analysis (RCWA)[48] in 2- or 3-dimensions.

FDTD method has been widely used in photonics area and well developed, giving accurate results. However, it needs appropriate model of optical constants in time domain, which is sometimes hard for organic materials. FEM gives a way to calculate

Maxwell equations in frequency domain but it usually takes long when mesh is big.

37 Physics of organic solar cells

RCWA shows faster calculation time compared to other methods when num ber of modes are limited. However, in cases where number of modes is not well defined such as randomized surfaces, calculation time of RCWA approaches to other methods.

1.4.2.2 Absorption of organic materials

Fig. 1.4 Summary of absorption coefficients ( α) of small molecular weight organic materials. α of ClAlPc is estimated from absorbance. To make use of a large fraction of the solar spectrum, the active materials need to cover a wide spectral range. Many small molecular weight materials typically used, such as CuPc, PTCBI and C 60 , have optical gaps EG>1.7eV, corresponding to a band edge of λ=730nm. Since 49% of the AM1.5 solar spectral energy occurs for λ>730nm, lower optical gap absorbers are required. In Fig. 1.3, the absorption constant, α, of a few typical small molecular weght materials including a few near -infrared-absorbing

Introduction materials used in organic PV cells. A tin(II) phthalocyanine (SnPc)-based solar cell absorbs up to λ~1000nm, as shown by Rand et al.[49], and a nanostructured

CuPc/SnPc/C 60 with a PCE of ηP=2.9% was demonstrated [35]. Chloroaluminum phthalocyanine (ClAlPc)[50] with an absorption peak at λ=755nm and lead phthalocyanine (PbPc)[51] with an absorption peak at λ=739nm, were also investigated as low optical gap material. These materials are particularly useful for multi-junction tandem cells discussed in Chapter 5.

1.4.2.3 Light trapping in organic solar cells

The thickness of the active layers in organic PV cells is normally of the order of 50-

250nm. This is comparable to or shorter than their LA, especially near the edge of the optical absorption spectrum, where the devices are able to conserve more of the absorbed photon energy, and light absorption is therefore suboptimal. Light trapping techniques that enhance light absorption in the thin active layers can be used to improve the PCE. Light trapping is also important in order to increase performance of

OPV cells thickness because IQE typically decreases with active layer so that active layers are preferred to be thin to achieve high IQE. For absorption enhancement, we need anti-reflective coating[52] to reduce reflections at air/substrate interfaces and light confinement scheme[26] to trap photons in active layers are required to harvest more incoming photons. For the light confinement scheme, randomized scattering surfaces[26, 53], which have been used for silicon solar cells, are challenging to be applied to OPV because films in OPV are thin compared to the wavelength of light and refractive index of organic materials is low compared to inorganic materials[54,

39 Physics of organic solar cells

55]. Light trapping schemes that do not require etching or patterning and are compatible with organic processing are keys in realizing practical light traps in OPV.

Agrawal et al.[30] showed that photocurrent can be increased up to 40% in

PCE of a CuPc/PTCBI BHJ cell by inserting multilayer dielectric stacks between substrate and anode. The dielectric stacks act as anti-relfective coating layer as well as mirrors to incorporate resonant cavity effects[56]. From the benefit of aperiodic design, only 4 layers using TiO 2 and SiO 2 provide the optimal design for a CuPc/PTCBI BHJ cell. This scheme uses one-dimensional planar dielectric stacks without incorporating patterning or etching that could not be used with thin film organic processing.

Shaped substrates in scale larger than film thickness are also proposed as effective light traps for OPV. Rim et al.[31] showed that V-shaped substrates (Fig.A1a) improve absorption via multiple reflections between reflective electrodes and could lead to 3.6-fold increase at normal incidence (Fig.A1b) and 3.7-fold in a day response

(Fig.A1c) in a small molecule solar cell. This is also effective in polymer[31, 57] and thin film silicon solar cells[58]. The V-shape light trap provides optical pathlength enhancement per unit cell area that exceeds theoretical limit[59] at normal incidence for low refractive index materials. So this scheme is particularly useful for low index material such as OPV. We will cover details of the V-trap technique further in Chapter

1.4.3 Exciton diffusion

Upon absorbing a photon, a neutral excited state of a molecule that polarizes the surrounding lattice, called an exciton, is generated in organic molecules. Excitons hop

Introduction or diffuse in organic solid and a fraction of excitons which reach DA junction have high probability to be dissociated into charge carriers [37]. Exciton diffusion is therefore the main efficiency bottleneck in planar bilayer organic PV cells. In bulk heterojunctions, DA junctions throughout active layers provide efficient exciton dissociation removing the LD bottleneck. However, the short LD constrains the morphologies that can be used to build efficient cells. An improved understanding of the physics underlying LD and the development of molecular materials with longer LD are required.

1.4.3.1 Theoretical estimation

One-dimensional exciton diffusion

Exciton diffusion in a planar DA junction can be modeled using the one-dimensional diffusion equation:

∂ 2 2 p − + τ = LD 2 p G 0 ∂x (1.4) where p is the exciton concentration, τ is the exciton lifetime and

G(x) = (λ / hc )Q(x) is the generation rate of excitons[41] and Q(x) is obtained from

Eq.(1.3 Eq.(1.4 is subject to boundary conditions on either side of the film of the form:

∂p D = sp )0( ∂x (1.5) x = 0

Here, D is exciton diffusivity and s is surface recombination velocity. At interfaces where excitons are removed very quickly (quenching) by fast recombination or charge-transfer, s can be approximated as infinity resulting in the boundary condition

41 Physics of organic solar cells p=0. The other extreme is an interface where s=0, resulting in the simplified boundary condition ∂p / ∂x = 0 . Incomplete quenching is modeled using a finite s.

Eq. (1.4) can be solved analytically or using discretization. The analytical solution can be expressed as[41]

αN / / x Ae Be e Ce D α (1.6) 4πRe Ccos δ λ where N is incident photon flux, n is complex refractive index, d is layer thickness, λ is wavelength, ρ and δ are the magnitude and argument of the complex reflection coefficient at x=d and

and C ρ e C 2ρe

A and B are coefficients determined by boundary conditions of s 0=s|x=0 and s d=s|x=d .

Their analytical forms are expressed as

and A B A D B D

1 4πRe A s α se Cα se C scosδ sinδ λ

/ 1 e s α s Cα s

4πRe 4πRe 4πRe C scos δ sin δ λ λ λ

Introduction

1 4πRe B s α se Cα se C scosδ sinδ λ

/ 1 e s α s Cα s

4πRe 4πRe 4πRe C scos δ sin δ λ λ λ and

1 1 / 1 1 / D s s e s s e L L L L Diffusion in molecular crystal

The fundamental physics of exciton transport in organic molecules in isotropic configurations are recognized [60, 61]. The theories extend to the closely packed molecules[62] and conjugated polymers[63]. In the weak-coupling regime, where vibrational relaxation energy of a donor molecule is stronger than electron coupling energy, the energy transfer rate between an excited donor molecule and ground state acceptor molecule is expressed as

π = 2 2 k DA J (FCWD ) h (1.7) where J is the electronic part of energy transfer and FCWD is frank-condon weighted density of states factor that includes vibrational density of states[62]. As a rough approximation, the diffusion length for a 1D diffusion process is LD=

τ = τ D kDA rDA , where rDA is the distance between the exciton donor and acceptor.

In order to evaluate LD more accurately, the crystal structure needs to be taken into account when evaluating kDA for all molecular pairs in a molecular lattice using Eq.

43 Physics of organic solar cells

(1.7. The Pauli master equation [63] or Monte Carlo simulations [64] can then be used to calculate LD in all crystal directions.

Although these approaches model exciton transport accurately in principle, in practice, it is difficult to estimate LD because exciton transport is affected by molecular packing, disorder, presence of impurities and film morphologies.

Theoretical estimates of LD are usually an order of magnitude larger than experimentally [65]. X-ray diffraction studies suggest that structural disorder plays an important role [65]. Terao et al.[66] reported that the charge-carrier mobility of metal- phthalocyanines correlates with their LD. Madigan et al.[67, 68] simulated the time- resolved evolution of the photoluminescence (PL) of aluminum tris-(8- hydroxyquinoline) (AlQ 3) by Monte Carlo methods and found that spatial disorder and energetic disorder significantly affect exciton diffusion in disordered organic molecules.

1.4.3.2 Measurement

The exciton diffusion length, LD, is experimentally determined by steady-state[69] or time-resolved[70] photoluminescence (PL) quenching, bimolecular PL quenching[71], photocurrent spectroscopy[72], or by fitting a model for the spectral shape of the EQE to experimental data [41]. Since experiments to determine LD usually make use of Eq.

(1.4, and since the generation term, G, is influenced strongly by optical interference effects, these effects need to be considered in order to accurately determine LD[73, 74].

With a few exceptions, the experimentally measured LD [18] is usually <50nm. Long

LD=225nm for perylene 3,4,9,10-tetracarboxylic dianhydride (PTCDA)[75] and

LD=2.5 m for perylenes bis(phenethylimide) (PPEI)[69] were observed but more

Introduction careful interpretation of the experiments are needed[74] or the reason of long LD is unexplained.

1.4.3.3 Bulkheterojunction organic solar cells

Bulkheterojunction (BHJ) OPV cells[34, 76] overcome LD bottleneck by incorporating large donor-acceptor (DA) interface area but they need to be ordered to have pathways where charge carriers efficiently conduct to electrodes obtaining high ηCT and ηCC .

Excitons are dissociated efficiently in fine-grained structure but GEHP recombination and resistive pathways make cells inefficient. On the other hand, in coarse-grained structure, charge transfer and charge transport are efficient but excitons are dissociated only around DA interface. Thus, grains need to be optimized to maximize ηED , ηCT and

ηCC simultaneously and they are on the order of 2 LD. Thermal annealing, which induces phase separation improving charge transport, was applied to a CuPc/PTCBI bilayer cell, showing ηP=1.4% [34]. A hybrid planar mixed heterojunctions (PM-HJ), which have mixed layer between planar donor and acceptor layers with thickness ~ LD, show low resistivity due to better charge transport than that in mixed layer only[76].

In order to obtain optimal grain size in mixed layers, cells were fabricated using organic vapor phase deposition (OVPD). In OVPD, crystalline organic films can be grown vertically and DA interfaces are made in and interdigitated structure[77, 78].

The controlled growth of a CuPc/PTCBI BHJ cell in OVPD exhibited ηP=2.7% over

ηP=1.1% of the planar junction cell[77]. OVPD grown BHJ cells, however, did not improve PCE of CuPc/C 60 OPV cells because the region of interdigitated DA interfaces is not thick enough to obtain the enhancement for C 60 that has long

45 Physics of organic solar cells

LD~40nm[20, 78]. Thus, the concept is developed further to alternate DA layers to have thicker DA interfaces while maintaining crystalline regions, where excitons are well dissociated as well as charge carriers are efficiently collected via low resistive pathways[20]. Using this alternating growth technique, a cell with 6 alternating

CuPc/C 60 layers shows ηP=4.4% while a bilayer cell without alternating layers exhibits

ηP=1.4%[20]. The work demonstrated that a BHJ cell is fabricated with interconnected nanocrystalline networks, which provides good charge transfer and charge collection and it is realized via controlled growth of organic molecules using OVPD techniques.

This growth technique of alternating layers can be used to fabricate three component cells in one stack. OPV cells with multiple DA interfaces were manufactured with pentacene/CuPc/C 60 in a BHJ cell previously[79] but this technique has advantages because crystalline regions can be maintained due to the controlled growth[35]. SnPc absorbs lights in NIR region but it forms islands when the layer is thin and thick SnPc film has protrusions which prevent the layer from being covered by an acceptor layer C 60 . However, thick SnPc/C 60 can be deposited on CuPc using the nanocrystalline network deposition technique using controlled OVPD. A

CuPc/SnPc/C 60 cell was fabricated and showed the enhancement in ηEQE over

600nm< λ<1000nm compared to the planar junction three layer devices.

1.4.4 Charge transfer and separation

Excitons generated upon absorbing photons need to be dissociated into charge carriers.

While exciton dissociation in bulk organic materials is not an efficient process without large external field (>10 6V/cm)[18], efficient dissociation occurs at DA

Introduction heterojunctions. Exciton dissociation is energetically favorable when E ex,D >IP D-EA A for excitons in donors and E ex,A > IP D-EA A. Here, Eex =E G-EB is energy of exciton and

EB is exciton binding energy typically 0 -1.4eV[80, 81] . IP and EA are the ionization potential and electron affinity, respectively. These conditions correspond t o

EB,D

Fig. 1.5 (a) Energy diagram of a donor -acceptor pair in flat band condition. Solid lines show HOMO and LUMO and dashed lines show Fermi levels. (b) Dissociation probability as a function of electric field intensity assuming that the mobility ratio of a donor and a n acceptor is 10 2. Electric Field intensities and estimated dissociation probabilities of 35nm CuPc/35nm PTCBI bilayer cells are shown as solid circles (0V bias) and open circles (0.2V bias). Upper two circles and lower circles are obtained based on the as sumption that the layers doped with the doping density of 10 18 cm -3 or the layers are intrinsic, respectively. Insets: energy diagrams of the bilayer structure. Field intensities are calculated at DA interfaces in the diagrams. Dashed lines are quasi Fermi levels. Immediately following exciton dissociation, the GEHP is still bound by a strong Coulomb force and in the absence of a strong driving force for carrier

47 Physics of organic solar cells separation, recombination of the geminate pair is likely[36]. The primary driving force that separates GEHPs is the electric field, F, obtained by solving Poisson’s equation:

∂ 2V ρ − = subject to V=V(d)-V(0)= HOMO − LUMO − ∆ϕ ∂x 2 ε D A (1.8) where V is the electrostatic potential, ρ is the charge density, ε is dielectric constant and d is film thickness. HOMO D is the HOMO of the donor material, LUMO A is the

LUMO of the acceptor material and φ stands for the sum of the difference between cathode Fermi level ( EFn ) and LUMO A and anode Fermi level ( EFp ) and HOMO D in

Fig. 1.5a. When the organic layers are intrinsic, the electric field is constant and equal

5 to F=V/qd =( HOMO D-LUMO A-φ)/ qd < 10 V/cm. This field is insufficient to dissociate GEHPs with a high likelihood in a planar bilayer cell, as shown in Fig. 1.5b

[37, 40]. It appears that in efficient bilayer solar cells, GEHP dissociation occurs with a high likelihood because the donor and acceptor materials are doped p- and n-type doped, respectively, resulting in a high electric field at the DA interface[40]. This conclusion was drawn from capacitance-voltage (CV) measurements that provide an estimate of the electrically active doping density profile. This type of doping was found in CuPc/PTCBI[18] and CuPc/C 60 . The p-type doping in CuPc is known to be due to oxygen-doping. The origin of the n-type doping in the acceptor materials is unknown and appears to be intrinsic to the material since it cannot be removed by repeated thermal gradient sublimation. In other cells, such as CuPc/ N,N’-bis(2- phynelethyl)-perylene-3,4,9,10-tetracarbonicacid-diimide (BPE-PTCDI) and

CuPc/N,N’-diphenyl-perylene-3,4,9,10-tetracarbonicacid-diimide (DP-PTCDI) the

Introduction acceptor materials are intrinsic and need to be intentionally n-type doped [83] to obtain efficient GEHP separation under short-circuit conditions [40].

1.4.5 Charge collection

Seperated charges are collected to metal electrodes to contribute photocurrents. In a thin film planar junction cell, ηCT ≈1 at DA interface and ηCC ≈1[18]. For BHJ structure, chance of GEHP recombination makes ηCT <1 and charge trapping and incomplete pathways lower ηCC <1. Drift-diffusion equation can be used to model incomplete

η = [ − − ] charge collection as CC (LC / d) 1 exp( d / LC ) , where LC is charge collection length determined expreimentally and d is active layer thickness [76]. LC is a parameter that includes many physical orientations such as morphologies and traps.

ηCC depends on the morphologies of DA interfaces and morphologies needs to be optimized to provide high probability of charge separation and collection[78]. We will discuss more about BHJ structure in Nanostructured OPV cells.

1.5 Dye sensitized solar cells

Dye sensitized solar cells (DSSCs) demonstrated power conversion efficiencies over

11.1%[84] which are promising for DSSCs to be commercially available. However, the DSSCs are fabricated using liquid electrolyte based on iodide and triiodide redox system and include solvents that evaporate and can cause leakage and corrosion. In order to avoid these problems, solid state dye sensitized cells (ss-DSCs) were

49 Multi-junction cells investigated by replacing liquid electrolyte with solid state hole transport materials such as spiro-OMeTAD[85]. Ss-DSCs showed efficiencies up to 5%[86].

While small molecular weight and polymer organic solar cells have donor acceptor pair as active layers, DSSCs are composed of dyes, electron semiconductor

(usually TiO 2), either liquid electrolyte or hole conducting polymer and electrodes.

After light is absorbed by dyes, excited holes are injected to hole conducting layer and excited electrons are transferred to electron semiconductor. Then, those charge carriers are collected at electrodes to generate photocurrent.

1.6 Multi-junction cells

The efficiency of single junction cells is limited because only higher energy photons than bandgap of active material are absorbed[87]. Multi-junction cells incorporate multiple sub-cells that have various bandgaps so that photons in broad spectrum are absorbed and the efficiency can increase as more sub-cells are used[88]. In order to realize efficient multi-junction organic solar cells, careful optimization of device structure to account for optical interference effects and development of effective intermediate electrodes between sub-cells are required[18]. Silver nanoparticles{{65

Peumans, P. 2003}} wa proposed for intermediate electrodes in series-connected multi-junction cells. Recently, Lee et al. proposed that multi-terminal multi-junction can be realized using silver nanowire mesh network. We will discuss more on the practical efficiency limit of multi-junction organic solar cells and multi-terminal multi-junction organic solar cells in chapter 5.

Introduction

1.7 Conclusion and outlook

Organic solar cells attract attention as promising techniques to realize low cost energy source. However, in order for them to be commercially available, efficiency increase is essential to reduce cost to compete with current price of electricity. Efficiency of organic solar cells has improved up to 6.5% in tandem structure[22]. In this thesis, we will cover light trapping techniques (Chapter 2), understanding exciton diffusion length (Chapter 3 and 4) and multi-junction approach (Chapter 5) as a way to increase efficiency.

51 Conclusion and outlook

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55 Conclusion and outlook

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57 Conclusion and outlook

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61 Conclusion and outlook

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V-shaped light trapping in organic solar cells

Chapter 2 V-shaped light trapping in organic solar cells

2.1 Introduction

In crystalline silicon solar cells, surface texturing is used to trap light, leading to an enhancement in optical path length by up to 4 n2, where n is the refractive index of the active layer[1, 2]. The increase in effective absorption allows one to reduce the volume of the active layer, leading to lower recombination currents, a higher operating voltage and higher conversion efficiencies. However, this approach becomes increasingly challenging as the film thicknesses become comparable or smaller than the wavelength of light[3] and alternative light trapping schemes are needed for thin- film solar cells.

In many thin-film solar cells, the probability that an absorbed photon contributes to photocurrent, known as the internal quantum efficiency (IQE), decreases as a function of film thickness over distances shorter than the optical absorption length[4].

This is especially the case for organic photovoltaic (OPV) cells where either exciton diffusion[5] or carrier-collection in a donor-acceptor blend[6] limits the IQE for active layers thick enough to absorb most photons. In this case, it is important to achieve

63 Light trapping in thin film solar cells complete optical absorption for active layers much thinner than an optical absorption length to maximize the photocurrent and minimizing the active layer volume is less important than minimizing its thickness.

2.2 Light trapping in thin film solar cells

Various light trapping techniques have been investigated and demonstrated such as geometrical surface texturing[7], concentrators using mirrors[5] or lenses[5, 8], dielectric stacks[9], photonic crystals[10-12] and plasmonic light trapping[13].

Surface texturing is the most commonly used technique used to trap light in wafer- based silicon solar cells. In the geometric optics regime, i.e. when the film thickness,

W, is larger than the size of the texture, d, and when both W and d are much larger than the wavelength, λ, as shown in Fig. 2.1a, random scattering surfaces[1] or regular pyramidal textures[2, 14] are effective. This approach leads to an enhancement in optical absorption of up to 4 n2 compared to a single pass through a film of the same thickness for a weakly absorbing material[1], where n is the refractive index of active material. However, this approach is much less effective for thin film solar cells because scattering surfaces with roughness larger than film thickness are required for sufficiently strong scattering and such surface texturing typically degrades electrical performance[15]. In addition, for the specific case of organic photovoltaic (OPV) cells, the achievable enhancement in optical absorption of 4 n2 is >4 times smaller than that achievable in inorganic materials because the index of refraction of most organic materials is >2 smaller than that of a typical inorganic absorber.

V-shaped light trapping in organic solar cells

Fig. 2.1 Light trapping configurations using (a) randomized scattering surfaces when W>d, (b) regularized periodic structures when W>d~λ and (c) large -scale texturing when W

In this chapter , we explore light -trapping approaches for which d>W, p >W and

W~λ, as shown in Fig. 2.1c. Such light traps are particularly effective for thin film solar cells [21-24], as will be discussed in later sections for amorphous silicon and organic solar cells. [21 -23, 25] In this approach, which can be used for many t ypes of thin-film solar cells, the substrate of the thin -film cell is structured in such a way that incident light undergoes multiple bounces off the reflective solar cell structure. This

65 Principles of V-shaped light trap type of light trap is readily implemented using structured substrates or by folding of a cell on a planar, flexible substrate[24].

2.3 Principles of V-shaped light trap

2.3.1 Structure

The geometry of the proposed light trapping scheme is shown in Fig. 2.2. The active layer and reflective metal electrode are deposited on a V-shaped transparent substrate coated with a transparent electrode such as indium-tin-oxide (ITO). Incident optical rays bounce off the solar cell structure multiple times. The maximum number of bounces a ray undergoes as a function of the V-fold opening angle, 2 α, without considering total internal reflections between the air/substrate interface is N

, where θi is the angle of incidence with respect to the substrate π θ α/2α normal (Fig. 2.2). The enhancement in number of ray bounces per unit cell area over that in a planar structure at each point in the V-fold structure was calculated as a function of 2 α. The V-fold acts as an optical funnel, resulting in a high density of ray reflections near the tip of the V-fold structure, also seen in Fig. 2.2. Moreover, the density of reflections increases rapidly as the V-fold opening angle 2 α decreases.

V-shaped light trapping in organic solar cells

Fig. 2.2 Structur e of V -shaped light trap. Active layers and metal electrode are deposited under V -shaped substrate with opening angle of 2 α.

2.3.2 Optical pathlength enhancement

The V-shaped trap is particularly useful for low index materials, as shown in Fig. 2.3a, where the enhancement in optical path length (in units of the thickness of the active layer) is shown as a function of the opening angle (2 α) of a V-shaped light trap. For this calculation, interference effects were ignored and the active layer volume was held constant by scaling the film thickness by the inverse of the increase in area when the cell is deposited over the V -shaped light trap. T his calculation further assumes that solar cells have a reflective coating on their backside and are not supported by a substrate for simplicity (see Fig. 2.3a inset). The optical path length enhancement can be written as

67 Principles of V-shaped light trap

2 sin α ∑ −1 −1 ≤ − α <π {}− α (2.1) 0 2( k )1 cos sin (n cos( 2k )1 )

The enhancement surpasses the 4 n2 limit[1] for sufficiently small n. Because rays in the active layer propagate closer to the surface normal for high -n materials

(nsin θact =sin θair ) and the number of bounces of each ray in the light trap is independent of n, the optical path length enhancement (2sin α/cos θact ) decreases as n increases. This is also shown in Fig. 2.3b, where the maximum enhancement is plotted as a function of n showing that a V -shaped trap provides more enhancement than the theoretical limit of 4 n2 when n<1.16 and under normal incidence. Note that no theoretical limits[1] are violated because an optical path length enhancement >4 n2 only occurs near normal incidence. Also note that no practically useful solar cell materials with n<1.16 exist.

V-shaped light trapping in organic solar cells Fig. 2.3 (a) Optical path length enhancement in a V-shaped light trap for an active layer with refractive index n=1.1 (filled squares). The thermodynamic limit to optical path length enhancement with full Ω=2 π acceptance cone (4 n2) is shown as a dotted line. Inset: the V-shaped light trap with the tip angle of 2 α. (b) Maximum optical path length enhancement in a V-shaped light trap as a function of refractive index n (solid line). The thermodynamic limit to opt ical path length enhancement with full Ω=2 π acceptance cone (4 n2) is shown as a dotted line. The two curves intersect when n=1.16.

2.4 Modeling methods

The light trapping performance was analyzed using geometrical raytracing to keep track of light propagation from surface to surface. The transfer matrix formalism was used to calculate reflection and transmission coefficients at each surface. Rays with s

(TE) and p-polarization (TM) are calculated separately. The reflection coefficient, rjk , at the interface between layer j and k, is

n~ cos φ − n~ cos φ r = j j k k for s-polarized light (TE) jk ~ φ + ~ φ n j cos j nk cos k (2.2)

n~ 2 n~ cos φ − n~ 2 n~ cos φ r = k j j j k k for p-polarized light (TM) jk ~ 2 ~ φ + ~ 2 ~ φ (2.3) nk n j cos j n j nk cos k

S 2 S 2 r = r and t = 1 − r for both polarizations jk jk (2.4) Si Si

~ ~ φ φ where, n j and nk are the complex refractive indices, j and k are the angles of the light rays inside layers j and k, and Si, Sr and St are the Poynting vectors for incident, reflected and transmitted light. Reflected rays and transmitted rays are traced recursively at every bounce. When rays hit a thin-film structure such as the thin-film solar cell, reflection, transmission and absorption coefficients of the multilayer stack

69 Modeling methods are calculated for both the s and p-polarization using the transfer matrix approach using the incidence angle determined by the raytracing model. The EQE is calculated by evaluating the spatially-resolved exciton generation rate in the thin-film structure and solving the one-dimensional exciton diffusion equation[26] and using the drift- diffusion model[27] for the bulk-heterojunction polymer cell. Complete carrier collection is assumed for the a-Si and c-Si cells[28] since we are interested in evaluating the increase in optical absorption for a typical film thickness. The angular dependence of light intensity is assumed to follow the cosine law[29]and the absorption of the cells was calculated using the transfer matrix formalism. All layers are assumed to have flat and smooth interfaces.

V-shaped light trappin g in organic solar cells 2.5 V-shaped light trap

2.5.1 Effects of V -trap on efficiency

Fig. 2.4 (a) Absorption efficiencies, internal (IQE) and external (EQE) quantum efficiencies of the organic solar cell in a V -shaped light trap with a 2α=29° opening angle and of a planar cell with the same structure (inset), as a fun ction of the thickness of the active layers. The solid lines show the efficiencies of the V -shaped cell while the dashed lines show those of the planar cell. (b) Structure of the V-shaped light trap with a 2 α=29° opening angle. Many types of thin -film sola r cells exhibit a decrease in internal quantum efficiency (IQE) as the active layer thickness is increased. This is due to an increase in carrier recombination probability as the carrier residence time increases. In the bilayer

OPV cell used for the analys is here, the IQE decreases with active layer thickness for active regions thicker than 5nm because the exciton diffusion length is only 3nm (for

PTCBI)[30] to 10nm (for CuPc) [5] . Other effects that decrease the IQE are a reduced

71 V-shaped light trap geminate carrier separation probability[31]or charge carrier collection

27,28 efficiency .[32, 33]The absorption efficiency, ηA, increases with active layer thickness, albeit not necessarily monotonically due to optical interference effects. As a result of a decreasing IQE and increasing ηA, the external quantum efficiency (EQE), i.e. the product of the IQE and ηA, reaches a maximum for a certain film thickness that optimally trades off absorption losses and recombination losses. This is shown for the specific case of a planar CuPc/PTCBI bilayer OPV cell at =600nm (planar configuration, dotted lines) in Fig. 2.4. Since the IQE peaks well before ηA saturates, the EQE has a low optimal value. The effect of a light trap is to increase ηA without affecting the IQE. This is shown for a planar bilayer OPV cell in the V-shaped light trap with an opening angle of 29° in Fig. 2.4 (V-shape, solid lines) at λ=600nm, where the cell absorbs strongly. The two bilayer cells (planar and V-shape) have the same structure (glass/150nm ITO/ x nm CuPc/ x nm PTCBI/100nm Ag, also see inset to Fig.

2.4). For the planar cell, ηA increases as x increases while its IQE reduces for x>5nm, limiting the EQE to a maximum of 22% for x=11nm. For the V-shaped light trap, however, ηA is up to 3.8 times larger for the same thickness while the IQE is similar for both cells, leading to a higher peak EQE of 44% for x=6nm. The IQE curves of the planar and V-shaped cells are slightly different because averaging over all angles of incidence in the V-shaped cells leads to slightly different optical interference effects.

The enhancement in optical absorption is larger for wavelengths where the cell absorbs weakly. For example, at λ=800nm, the cell in the V-shaped light trap is predicted to achieve a 3.3-fold higher EQE for x=9nm compared the planar cell which is predicted to have a maximum in EQE for x=58nm. We note that while we analyzed

V-shaped light trapping in organic solar cells the benefits of the V-shaped light trap for a thin-film OPV cell, this approach is also effective for more conventional thin-film PV cells.

2.5.2 Performance estimation

To analyze the achievable performance gains using a V-shaped light trap, we modeled the spectral response of small molecular weight organic solar cells with CuPc and

PTCBI[34]. The device structure optimized in V-trap is Glass/150nm ITO/10nm

CuPc/3nm PTCBI/15nm BCP/100nm Ag and one in planar configuration is

Glass/150nm ITO/15nm CuPc/10nm PTCBI/15nm BCP/100nm Ag. Short circuit current density ( JSC ) is estimated by geometrical raytracing and multilayer calculations as described in section 2.4. Since the number of ray bounces increases as 2 α decreases

(Fig. 2.5, inset), absorption increases per unit cell area and JSC increases from

JSC=3.6mA/cm 2 in planar configuration to JSC=8.6mA/cm 2 at 2 α=30° as shown in

Fig. 2.5a. In Fig. 2.5a, discrete jumps in J SC are observed because the number of bounces increases at where N is a positive integer in quantized manner. 2π/2N 1

Open circuit voltage (V OC ) can be estimated by

nkT  J  nkT  J  V = log  SC + 1 ≈ V planar + log  SC sin α  OC   OC  planar  (2.5) q  J 0  q  J SC  where n=2.0 is the ideality factor[35], k is the Boltzmann constant, T is room

planar temperature and q is the charge of a single electron. VOC and fill factor (FF) are assumed to be 0.5V and 0.6, respectively[5]. VOC (Fig. 2.5b) is reduced at small 2 α due to the increased volume of active layers, while PCE (Fig. 2.5b) improves from

ηP=1.1% in planar configuration to ηP=2.5% at 2 α=30° because increase in JSC is

73 V-shaped light trap

larger than decrease in V OC . Note that the optimized cell in planar configuration gives

ηP=1.3%.

Fig. 2.5 (a) Calculated short circuit current density ( JSC ) versus opening angle. (b) Calculated open circuit voltage (V OC ) and power conversion efficiency (PCE) of V-trap cells. Note that the device optimized in V-trap (closed squares) has thinner active layers compared to the device optimized in planar configuration (open square) in J SC and PCE. Inset: ray bouncing diagrams to show that the small opening angle of V -trap increase the number of bounces as well as a bsorption. Whether the use of the V -shaped light trap is viable for a particular solar cell depends on the balance of the added cost of the shaped substrate and increase in active material use, with the reduction in installation cost for modules with highe r efficiencies. For example, for the CuPc/PTCBI cell (100Å CuPc/30Å PTCBI) in the

V-fold with 2 α=30°, the amount of active material required is (130Å/sin α)/250Å=2.0 times that used in the corresponding optimized planar cell (150Å CuPc/100Å PTCBI), while JSC increases 1.9 -fold. Adopting the V-shaped light trap is in fact more attractive than this analysis suggests since the active layers are responsible for only about 1/9 th of the overall thin-film PV manufacturing cost [36].

V-shaped light trapping in organic solar cells 2.5.3 Experiments

To verify our models, bilayer CuPc/PTCBI solar cell structures were fabricated on glass substrates coated with a 1300 -Å-thick ITO anode . The organic materials were purified using thermal gradient sublimation. 21 The organic layers and metal c athode were deposited via thermal evaporation in high -vacuum (base pressure ~1×10 -7 Torr).

P3HT:PCBM solar cells were fabricated by spin -coating a blend of P3HT/PCBM in

1:1 weight ratio in dichlorobenzene on glass substrates coated with a 1500 -Å-thick

ITO anode modified by a spin -coated 500-Å-thick PEDOT-PSS layer. A 1000 -Å-thick

Al cathode was deposited by thermal evaporation. The V -shaped light trap was configured using two planar cells held in place via optical mounts.

Fig. 2.6 The JSC of the ITO/390Å CuPc/420Å PTCBI/150Å BCP/1000Å Ag bilayer device (cell A) measured in the V -shaped configuration near the tip (open circles) and near the edge (open squares). The solid lines are model calculations. Th e JSC of a thinner cell with device structure ITO/300Å CuPc/400Å PTCBI/150Å BCP/1000Å Ag (cell B) near the tip of the V -shape (filled circles) is also shown together with a model calculation (dashed line).

75 V-shaped light trap

The CuPc/PTCBI cells were structured as an arra y of small devices (cell area =

0.81mm 2) to verify the spatial dependence of the light intensity in the light trap. The

JSC of cells with structure ITO/390Å CuPc/420Å PTCBI/150Å BCP/1000Å Ag (cell A)

2 under 32mW/cm AM1.5G illumination is shown in Fig. 2.6. JSC was measured at two locations (see Fig. 2.6, inset): 7% from the tip (open circles) and 14% from the edge

(open squares). Modeling results are shown for comparison (solid lines). JSC for a thinner structure ITO/300Å CuPc/400Å PTCBI/150Å BCP (cell B) located 7% from the tip (filled circles ) and the corresponding modeling results (dashed line) are also shown. As predicted by our models, JSC for cell A near the tip increases 3 -fold from

0.8mA/cm 2 for the planar configuration to 2.5mA/cm 2 for 2 α=14° since the V -shape funnels light towards the tip. Near the edge of the light -trap, JSC decreases from

0.9mA/cm 2 for the planar configuration to 0.75mA/cm 2 for 2 α=21°, in agreement with our model. A 26% increase in overall JSC would have been obtained f or a cell that occupies the full substrate area. Larger increases in JSC would be obtained with thinner cells as discussed above.

V-shaped light trapping in organic solar cells

2 shaped area. JSC vs. 2 α measured under 32mW/cm AM1.5G illumination is shown in

Fig. 2.7a. Compared to the planar configuration, JSC increases by 68%, 57% and 43% for the 170nm, 110nm and 70nm-thick cells, respectively, for 2 α=35°. The decrease in

JSC for 2 α<35° is attributed to anisotropy of the optical constants of the P3HT:PCBM films. 22 The polymer chain alignment is likely stronger for the thinner devices and may also explain the reduced benefit of the V-shaped light trap for the thinner

P3HT:PCBM cells. The power conversion efficiency ( ηP) and open circuit voltage

(VOC ) are plotted in Fig. 2.7b. The 170nm-thick cell achieves ηP=3.5% at 2 α=35°, a 52% increase over ηP=2.2% for the planar configuration. VOC systematically decreases as 2 α decreases due to an increase in dark current proportional with the area of the cell.

2.6 Effects of geometrical shapes

The above analysis and prior experimental results show that the V-shaped light trap is effective for thin film solar cells[15, 23, 25]. This raises the question whether geometries other than the V-shape are equally or more effective in improving optical absorption. To understand the effect of the light trap geometry on the light trapping effectiveness, we analyze and compare six different light trap shapes: the V-shape, parabola, ellipse, inverted parabola, inverted ellipse and inverted pyramid (Fig. 2.8).

77 Effects of geometrical shapes

For each light trap, the substrates are structured and an OPV cell (black solid lines in

Fig. 2.8) is assumed to be coated onto the shaped side of the substrate. The area of the device active layers is larger than the area on which light is incident. This leads to a decrease in average optical power received per unit cell area and hence to a decrease in open circuit voltage if the loss in power received is not compensated by trapping of the incident light. In order to compare the different light trap geometries, we use the relative device area (RA), i.e. the ratio of the device active layer area over the area obtained by projecting the cell on a plane parallel to the top surface of the substrate, as a reference to compare the different light traps. The RA is obtained by calculating the arc length of the two-dimensional geometries (V-shape, parabola, ellipse, inverted parabola and inverted ellipse) and surface area of the three-dimensional pyramid geometry. A high RA corresponds to high aspect ratio structures. For example,

RA=1.0 refers to the planar configuration while RA=4.0 corresponds to an opening angle of 29° for the V-shaped trap.

V-shaped light trapping in organic solar cells

Fig. 2.8 Geometries and rays (gray lines) traced in ray -tracing simulations of six light trapping configurations. Cells are embedded on the four sides of an inverted pyramid light trap. The solar cells are indicated by a solid black line in the other five geometri es. The organic solar cell layer structure used for the model calculations is also shown. In our analysis, we assume a thin -film organic solar cell with layer structure glass/indium tin oxide (ITO)/10nm copper phthalocyanine (CuPc)/3nm 3,4,9,10 - perylene te tracarboxylic bisbenzimidazole (PTCBI)/15nm bathocuproine

(BCP)/100nm Ag unless noted otherwise. This type of cell is useful in our analysis since it benefits greatly from light trapping because of the large mismatch between the exciton diffusion length (3 -10nm) and optical absorption length (~100nm) [5].

However, the analysis is general and can be applied to other thin -film solar cells. We note that the BCP layer helps maximize the optical absorption in the active laye rs by separating the active layers from the reflective cathode [5] . The film thicknesses are measured in the direction normal to the local surface of the substrate. The overall

79 Effects of geometrical shapes efficiencies of the various light trappin g configurations were evaluated by averaging

100 to 1,000 rays for two -dimensional configurations (V-shape, elliptical, parabolic, inverted elliptical and inverted parabolic) and 10,000 rays for the three -dimensional configuration of inverted pyramids.

2.6.1 Sh ort circuit current density

Fig. 2.9 Comparison of the performance of the V -shaped (open squares), parabolic (solid circles), elliptical (open triangles), inverted parabolic (solid stars), inverted elliptica l (open right triangle) and inverted pyramid (solid inverted triangles) light traps with an organic solar cell with layer structure ITO/10nm CuPc/3nm PTCBI/15nm BCP/100nm Ag, at normal incidence. (a) The calculated short circuit current density, JSC , as a function of the ratio of the device area to the light incidence area (RA). Inset: Magnified plot for 1.5

V-shaped light trapping in organic solar cells parabola-shaped (solid stars), inverted ellipse-shaped (open right triangles), ellipse- shaped (open triangles) and parabola-shaped (solid circles) traps, as shown in Fig. 2.9a.

The JSC of the inverted pyramid trap is slightly higher than that of the V-shape and the inverted parabola for RA<4.0. This difference disappears for RA>4.0. All traps apart from the V-shaped and inverted pyramid trap exhibit JSC that increase monotonically as RA increases. The ellipse-shaped trap exhibits fewer bounces than the V-shape or inverted pyramid and hence results in lower absorption and JSC . The parabolic trap has only two bounces at normal incidence regardless of RA unless the air/glass interface is considered, resulting in a JSC that is nearly independent of RA. For RA=6.0, the JSC of the inverted pyramid, V-shape, inverted parabolic, inverted ellipse-shaped, parabolic and ellipse-shaped traps are 2.8, 2.8, 2.8, 2.6, 1.5, and 1.9-fold higher than that of a planar cell, respectively. For RA=4.0, the peak EQE (at λ=600nm) of the V-shaped trap and the inverted parabolic trap differ only by ±1.2% from that of the inverted pyramid trap, as shown in Fig. 2.9b. The ellipse-shaped (open triangles) and parabolic

(solid circles) traps show a 49% and 63% enhancement in EQE over the planar (gray line) cell at λ=600nm while the V-shaped (open squares), inverted parabolic (solid stars), inverted ellipse-shaped (open right triangles) and the inverted pyramidal trap

(solid inverted triangles) result in a 124%, 119%, 100% and 122% improvement, respectively. From the JSC and EQE analysis, the inverted pyramidal trap provides the best performance as a light trap. However, the V-shaped and inverted parabolic traps exhibit similar performance for RA>4.0 and the V-shaped trap is likely simpler to fabricate.

81 Effects of geometrical shapes

Fig. 2.10 (a) Rays traced in V -shaped light traps for RA=1.2, 1.4, 1.8 and 2.0. (b) Short circuit cu rrent density, JSC , as a function of the angle of incidence of illumination. JSC decreases steeply with angle when total internal reflection plays a role as in the case of the V -shape trap at RA=1.2 (solid circles) and RA=1.8 (solid squares). The angular response decreases more gradually for RA=1.4 (open circles) and RA=1.9 (open squa res). Inset: The angular response of the V-shape trap for RA=1.8 when the refractive index of the substrates is n=1.5, 1.9 and 2.3.

The shape of the JSC vs. RA characteristics of the V -shaped and inverted pyramid traps, shown in Fig. 4a, exhibit sharp features that are caused by total internal reflection. The first peak in JSC is observed around RA=1.2 for the V -shape and inverted pyramid traps because light rays start to undergo multiple bounces starting from RA=1.15 and an enhanced response is obtained du e to total internal reflection

(TIR) at the air/glass interface (RA=1.2, Fig. 2.10 a). RA=1.15 corresponds to a 120° angle of V-shape trap and this con figuration yields a maximum optical path length enhancement as observed in Fig. 2.3a. The enhancement in JSC in the V-shaped trap decreases from RA=1.2 to RA=1.4 because TIR disappears and oblique rays reduce optical absorption (RA=1.4, Fig. 2.10a). JSC of the inverted pyramid light trap exhibits

V-shaped light trapping in organic solar cells the second peak near RA=1.9 because TIR occurs once again, leading to additional light trapping and a JSC that is 2.6 times higher than that of a planar cell (inset, Fig.

2.9a). This effect disappears for RA>2.2. The effects of TIR are also observed in the

V-shaped trap for 1.8

TIR, an incident ray bounces up to 9 times off an active layer for RA=1.8 while for

RA=2.0, there are only 3 bounces. The gains in light trapping performance due to TIR can be exploited to make better light traps[37]but this happens only near normal incidence and is not beneficial at oblique incidence. Higher index substrates could potentially be used to further amplify these effects (inset, Fig. 2.10b). When TIR occurs in the V-shape trap at RA=1.2 (solid circles) and RA=1.8 (solid squares), JSC decrease more rapidly with angle of incidence compared to the traps with larger RA

(open symbols) in Fig. 2.10b. Because TIR effects depend strongly on angle of incidence, an enhancement due to TIR is not observed when JSC is averaged over 0 to

90 degrees of incidence angles (see below and Fig. 2.12a).

2.6.2 Open circuit voltage and power conversion efficiency

In order to estimate the power conversion efficiency (PCE) accurately, the open circuit voltage ( VOC ) of the cells in the various light traps has to be considered since VOC decreases as the RA increases. The reason for the decreasing VOC is a decrease in optical flux received per unit active device area. We note that the assumption that dark current increases with device area is the worst case scenario that is accurate for bilayer

OPV cells. In many cases, the dark current is linear with active layer volume as is the

83 Effects of geometrical shapes case in many bulk heterojunction OPV cells [38] and most inorganic thin -film PV cells[39][40] . In that case, since the active layer thickness of the device in a light trap wil l be smaller than that of a planar cell, dark current will scale slower than linear with device area. The assumptions used here are therefore a worst -case analysis.

Fig. 2.11 Comparison of the six considere d light traps in (a) V OC and (b) PCE.

Assuming that JSC in the traps is much larger than the saturation current density J0,

From Eq. (2.5, VOC can be expressed as

nkT  J  nkT  J  V = log  SC +1 ≈ V planar + log  SC  OC   OC  planar ⋅  (2.6) q  J 0  q  J SC RA 

The calculated VOC and PCE are shown in Fig. 2.11. VOC of the V -shaped, inverted parabolic, inverted ellipse -shaped, parabolic, ellipse-shaped and inverted pyramidal traps at RA=6.0 are 7.9%, 8.0%, 8.8%,14%, 12% and 7.9% smaller th an that of the planar cell, respectively ( Fig. 2.11a). The resulting PCE of the cells in these light traps

(Fig. 2.11b) are 2.5%, 2.5%, 2.3%, 1.3%, 1.7% and 2.5%, respectively, substantially larger than that the PCE of this particular planar cell (1.0%). The PCE increase

V-sh aped light trapping in organic solar cells because of the enhancement in JSC due to the light-trapping effects is much higher than the fall-off in VOC . The PCE at normal incidence of the V-shaped trap for RA=1.8 and that of the inverted pyramidal trap for RA=1.9 are 2.5% and 2.6%, respectively.

This substantial enhancement for moderate RA stems largely from TIR at air/substrate interfaces. Because these RAs are moderate and the corresponding substrates may be relatively easily fabricated, these geometries are likely preferred.

2.6.3 Angular response

Fig. 2.12 The device performance of the light traps as a function of angle of incidence of the illumination. (a) Short circuit current density, JSC , averaged over 0 to 90 degrees of incidence angles. (b) JSC as a function of angle of incidence for RA=4.0. The angular response of the light traps is an important issue when designing light traps. A higher optical concentration can always be obtained at the expense of a limited angular acceptance cone but such an approach is not desirable for many thin- film solar cells because of the added cost of the tracking system that would be required for a solar cell with a limited acceptance cone. Here, we are interested in light traps

85 Effects of geometrical shapes that concentrate without sacrificing angular response, as is the case for Lambertian textures. To quantify the angular response of the light traps, the angle-dependent short

θ = η θ θ λ circuit current, J SC ( ) q∫ EQE ( )S λ cos d , and JSC averaged over 0 to 90

π < > = π / 2 θ θ degrees of incidence angles, J SC θ 2( / ) J SC ( )d , were calculated, ∫0 where θ is the angle of incidence, Sλ is the solar spectrum expressed in number of photons per unit area per unit time per unit wavelength and ηEQE (θ) is the EQE as a function of angle of incidence θ[41]. < JSC >θ is obtained by averaging JSC (θ) for θ=0 to

90 degrees with a 10 degree interval. JSC averaged over incidence angles (Fig. 2.12a) for the V-shaped (open squares), inverted parabolic (solid stars), inverted elliptical

(open right triangles), parabolic (solid circles), elliptical (open triangles) and inverted pyramid (solid inverted triangles) traps show 2.8, 2.7, 2.4, 2.5, 2.4 and 2.8-fold higher values than that of a planar cell, respectively. The V-shaped and inverted pyramid

2 traps result in the highest average JSC =5.9mA/cm at RA=6.0 compared to

2 JSC =2.1mA/cm for the planar configuration. The angular response of the traps at

RA=4.0 are shown in Fig. 2.12b, showing that all the light traps considered exhibit an improvement in JSC over a planar cell for all angles of incidence. The responses of the

V-shaped and inverted pyramid light traps approach each other. We note that the parabolic trap performs better off-normal because incident rays undergo more than two bounces. This analysis of angular response shows that the V-shaped and inverted pyramid traps perform significantly better than the planar cell even when averaged over incidence angles.

V-shaped light trapping in organic solar cells

Fig. 2.13 Map of absorbed optical power as a function of angle of incidence and distance from the center of the light trap calculated for λ=600nm and RA=4.0, for a (a) V -shaped, (b) inverted pyramid, (c) parabolic, (d) inverted parabolic, (e) ellipse and (f) invert ed ellipse light trap. Darker regions indicate stronger absorption. Inset: Ray diagrams of the traps for a 30 °angle of incidence. In Fig. 2.13 , the distribution of absorbed optical power is shown as a function of the angle of incidence of the light for the various trap geometries considered for

λ=600nm and RA=4.0. Ray diagrams for t he particular case of an angle of incidence of 30 degrees are shown as insets. The left sides and valleys of the traps are shadowed and only reached by reflections. Absorption in the V -shape and the inverted pyramid traps show that absorption is distribute d over a large area (Fig. 2.13a and b) because multiple reflections distribute light over most of the surface of the light traps. The inverted parabola ( Fig. 2.13d) and inverted ellipse (Fig. 2.13 f) traps have stronger absorption near the bottom of the traps but light is still absorbed over most of the surface of the traps. In the parabola and ellipse -shaped traps, absorption is locally

87 Effects of geometrical shapes concentrated on the left side of the traps, as shown in Fig. 2.13 c and e. The locally high light intensities may lead to local heating and fast degradation of the solar cells. It is no surprise that the best per forming light traps (inverted pyramid and V -shape) are able to spread the light intensity more uniformly.

2.6.4 Parasitic absorption

V-shaped light trapping in organic solar cells calculated when optical absorption in the metal is “turned off” by replacing the metal with a virtual material whose real part of the refractive index is that of Ag while the complex part is set to zero (open symbols), and compared to the case where optical absorption in the metal is taken into account (solid symbols) for a V-shaped light trap.

2 For light incident from the normal direction, JSC increases 2.8-fold from 3.27mA/cm to 9.21mA/cm 2 for RA=6.0 when optical absorption in the metal is taken into account

(solid squares). When non-absorbing metal is used instead, JSC increases to

13.64mA/cm 2, a 4.2-fold increase over the planar cell (open squares). Note that a slight peak at RA=1.5 appears not because of TIR but because of small increase in angle of incidences on active layers and optical path lengths. When averaged over 0 to

90 degrees of incidence angles, the PV cells with an ideal back reflector (open triangles) show a 43% higher JSC compared to cells with a regular Ag reflector (solid triangles). The EQE plotted for RA=4.0 in Fig. 2.14b also shows that the maximum

EQE including metal absorption (solid line) is 0.50 while one without metal absorption (dashed line) is 0.63. In planar configuration, JSC and EQE are the same regardless of metal absorption since planar cells do not rely on multiple bounces of the incident light. Suppressing parasitic absorption is clearly very important in light trapping cells to achieve high efficiency.

89 Effects of geometrical shapes

2.6.5 Thin film Si solar cells in traps

Fig. 2.15 Comparison of the performance of the V -shaped (squares), parabolic (circles), elliptical (inverted triangles), inverted parabolic (triangles), inverted elliptical (left triangle) and inverted pyramid (right triangles) light traps with (a) an amorphous sil icon solar cell with layer structure Glass/150nm ZnO /300nm a-Si/100nm Ag, at normal incidence. (b) an microcrystalline silicon solar cell with layer structure Glass/150nm ZnO/1200nm c-Si/100nm Ag, at normal incidence. For comparison, the best textured dev ices are shown (dashed lines). Inset: device structures used in calculations. The V-trap light trap can be applied to thin film silicon solar cells including amorphous silicon or microcrystalline silicon layer. Complete carrier collection is assumed for the a-Si and c-Si cells[28] since we are interested in evaluating the increase in optical absorption for a typical film thickness. The cosine law is used to calculate the angular response of these cells [29] . All layers are assumed to have flat and smooth interfaces. For the a -Si and c-Si cells, active layer thicknesses for the a -

Si and c-Si cell of 300nm and 1.2 m, respectively [43] . A 1000Å -thick-Ag top electrode was assumed for these cells. V -trap and inverted pyramidal trap give 2x and

1.5x increase in J SC of the a -Si and c-Si cell, respectively, as shown in Fig. 2.15. For comparison, the best thin film silicon solar cells demonstrated in experiments ( Fig.

V-shaped light trapping in organic solar cells 2 2 2.15, dashed lines) are JSC =17.5mA/cm and JSC=22.9mA/cm for a-Si and c-Si cells in the degraded states, respectively[44].

2.7 Conclusion

The V-shaped light-trap is an alternative to surface texturing that can be used for solar cell structures with active layer thicknesses of the order of the wavelength of light or less. The scheme is particularly effective for solar cells whose IQE drops quickly as a function of film thickness. A 52% increase in power conversion efficiency was demonstrated using P3HT:PCBM polymer blend cells. We anticipate that applying the

V-fold light trap to the most efficient organic solar cells[] will lead to further improvements in their efficiency.

We have shown that light traps based on shaped substrates in conjunction with reflective solar cells can result in light traps that are effective for thin-film solar cells in cases where texturing of the active region is not. Light is efficiently trapped by reflections between two reflective electrodes and TIR at the air/substrate interface.

The light traps studied rely on structuring of the transparent substrate on a length scale that is much larger than the active layer thickness and wavelength. The inverted pyramid and V-shaped trap exhibit the best performance, with the V-shape being likely easier to implement. It was also shown that parasitic absorption due to incomplete reflection from the metal electrode limiting the performance of the light traps. Techniques that increase metal electrode reflectivity[11, 12, 45]will significantly impact overall system efficiency.

91 Conclusion

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[16] P. Sheng, A. N. Bloch and R. S. Stepleman, "Wavelength-selective absorption enhancement in thin-film solar cells," Appl. Phys. Lett. 43, 579-581 (1983)

[17] C. Haase and H. Stiebig, "Thin-film silicon solar cells with efficient periodic light trapping texture," Appl. Phys. Lett. 91, 061116-3 (2007)

[18] J. M. Gee, "Optically enhanced absorption in thin silicon layers using photonic crystals," in Conference Record of the Twenty-Ninth IEEE Photovoltaic Specialists Conference, 2002, pp. 150-153.

93 Conclusion

[19] M. Niggemann, M. Glatthaar, M. Gombert, A. Hinsch and V. Wittwer, "Diffraction gratings and buried nano-electrodes - architectures for organic solar cells," Thin Solid Films 451-452, 619 (2004)

[20] L. S. Roman, O. Inganäs, T. Granlund, T. Nyberg, M. Svensson, M. R. Andersson and J. C. Hummelen, "Trapping light in polymer photodiodes with soft embossed gratings," Adv Mater 12, 189-195 (2000)

[21] D. Thorp, P. Campbell and S. R. Wenham, "Absorption enhancement in conformally textured thin-film silicon solar cells," in Conference Record of the Twenty Fifth IEEE Photovoltaic Specialists Conference, 1996, pp. 705-708.

[22] K. Tvingstedt, V. Andersson, F. Zhang and O. Inganas, "Folded reflective tandem polymer solar cell doubles efficiency," Appl. Phys. Lett. 91, 123514 (2007)

[23] S. Rim, S. Zhao, S. R. Scully, M. D. McGehee and P. Peumans, "An effective light trapping configuration for thin-film solar cells," Appl. Phys. Lett. 91, 243501 (2007)

[24] Y. Zhou, F. Zhang, K. Tvingstedt, S. Barrau, F. Li, W. Tian and O. Inganas, "Investigation on polymer anode design for flexible polymer solar cells," Appl. Phys. Lett. 92, 233308 (2008)

[25] Y. Zhou, F. Zhang, K. Tvingstedt, W. Tian and O. Inganas, "Multifolded polymer solar cells on flexible substrates," Appl. Phys. Lett. 93, 033302 (2008)

[26] L. A. A. Pettersson, L. S. Roman and O. Inganas, "Modeling photocurrent action spectra of photovoltaic devices based on organic thin films," J. Appl. Phys. 86, 487- 496 (1999)

V-shaped light trapping in organic solar cells [27] R. S. Crandall, "Modeling of thin film solar cells: Uniform field approximation," J. Appl. Phys. 54, 7176-7186 (1983)

[28] E. A. Schiff, "Low-mobility solar cells: a device physics primer with application to amorphous silicon." Solar Energy Materials and Solar Cells, vol. 78, pp. 567, 2003.

[29] J. K. Balenzategui and F. Chenlo, "Measurement and analysis of angular response of bare and encapsulated silicon solar cells," Sol. Energy Mater. Sol. Cells 86, 53-83 (2005)

[30] S. Rim, R. F. Fink, J. C. Schoneboom, P. Erk and P. Peumans, "Effect of molecular packing on the exciton diffusion length in organic solar cells," Appl. Phys. Lett. 91, 173504 (2007)

[31] P. Peumans and S. Forrest, "Separation of geminate charge-pairs at donor- acceptor interfaces in disordered solids," Chemical Physics Letters 398, 27 (2004)

[32] M. Hiramoto, H. Fujiwara and M. Yokoyama, "Three-layered organic solar cell with a photoactive interlayer of codeposited pigments," Appl. Phys. Lett. 58, 1062- 1064 (1991)

[33] J. Xue, B. P. Rand, S. Uchida and S. R. Forrest, "A hybrid planar-mixed molecular heterojunction photovoltaic cell," Adv Mater 17, 66-71 (2005)

[34] C. W. Tang, "Two-layer organic photovoltaic cell," Appl. Phys. Lett. 48, 183-185 (1986)

[35] J. Xue, S. Uchida, B. P. Rand and S. R. Forrest, "4.2% efficient organic photovoltaic cells with low series resistances," Appl. Phys. Lett. 84, 3013-3015 (2004)

[36] Zweibel, "Issues in thin film PV manufacturing cost reduction," Solar Energy Mater. Solar Cells 59, 1 (1999)

95 Conclusion

[37] D. Redfield, "Multiple-pass thin-film silicon solar cell," Appl. Phys. Lett. 25, 647-648 (1974)

[38] D. W. Sievers, V. Shrotriya and Y. Yang, "Modeling optical effects and thickness dependent current in polymer bulk-heterojunction solar cells," J. Appl. Phys. 100, 114509 (2006)

[39] M. A. Green, "Limits on the open-circuit voltage and efficiency of silicon solar cells imposed by intrinsic auger processes," Electron Devices, IEEE Transactions on 31, 671-678 (1984)

[40] M. A. Green, "Limiting efficiency of bulk and thin-film silicon solar cells in the presence of surface recombination," Prog Photovoltaics Res Appl 7, 327-330 (1999)

[41] D. Cheyns, B. P. Rand, B. Verreet, J. Genoe, J. Poortmans and P. Heremans, "The angular response of ultrathin film organic solar cells," Appl. Phys. Lett. 92, 243310 (2008)

[42] V. Andersson, K. Tvingstedt and O. Inganas, "Optical modeling of a folded organic solar cell," J. Appl. Phys. 103, 094520 (2008)

[43] J. Müller, B. Rech, J. Springer and M. Vanecek, "TCO and light trapping in silicon thin film solar cells," Solar Energy, 77, 917-930 (2004)

[44] A. V. Shah, H. Schade, M. Vanecek, J. Meier, E. Vallat-Sauvain, N. Wyrsch, U. Kroll, C. Droz and J. Bailat, "Thin-film silicon solar cell technology," Prog Photovoltaics Res Appl 12, 113-142 (2004)

[45] L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling and B. A. Alamariu, "Efficiency enhancement in si solar cells by textured photonic crystal back reflector," Appl. Phys. Lett. 89, 111111-3 (2006)

The effects of optical interference on exciton diffusion length measurements using photocurrent spectroscopy Chapter 3 The effects of optical interference on exciton diffusion length measurements using photocurrent spectroscopy

3.1 Introduction

The exciton diffusion length, LD, is an important parameter in many types of organic solar cells. This is especially the case for bilayer organic solar cells, where it directly determines the external quantum efficiency[1]. However, accurately measuring and understanding exciton diffusion has proven challenging. LD can be measured by photoluminescence (PL) quenching in layered structures[2], bimolecular PL quenching[3], and spectrally resolved photocurrent measurements[4]. Fitting the wavelength dependence of the external quantum efficiency (EQE) of solar cells to a model that takes into account optical interference and exciton diffusion[5] is a more accurate version of the spectrally resolved photocurrent method. However, each method has its limitations and idiosyncrasies.

Photocurrent spectra provide a simple way to estimate the exciton diffusion length by comparing the measured photocurrent yield as a function of wavelength to a model based on optical absorption data as initially reported by Feng and Ghosh (FG)

97 Simulation method

[4]. The FG model assumes an exponentially decaying optical intensity and ignores optical interference effects. Often, both the back and front contact are probed by applying various bias conditions. However, interference effects are important in thin- film structures that contain highly reflecting interface[5] as is the case for organic cells with a metallic cathode, and its effects must be taken into account for accurate estimates of LD. An analysis of the effect of optical interference on LD measurements using PL quenching was recently reported[6]. Using a concrete example, we show that for measurements of LD using the photocurrent spectrum method, it is essential that optical interference effects are considered. We evaluate the dependence of LD

est estimated by photocurrent spectroscopy, LD , on film thickness, the spectral range used and the actual LD. These considerations are known by researchers in the organic

PV field, but no analysis is available in the literature and the FG model continues to be used inappropriately. In this manuscript, we show that LD can be substantially over- or underestimated using the FG model. We outline the conditions under which the FG model can be used.

3.2 Simulation method

We focus our analysis on systems consisting of 10-800nm-thick layers of diindenoperylene (DIP) sandwiched between an 150nm-thick indium-tin oxide (ITO) electrode on glass and a 100nm-thick Ag electrode, as shown in the inset of Fig. 1a. All photocurrent spectra shown here were obtained by modeling as detailed below. All layers are assumed to be optically flat. The samples are assumed to be illuminated

The effects of optical interference on exciton diffusion length measurements using photocurrent spectroscopy from the glass substrate side. The optical constants of DIP film were obtained from

Oss ό[7]. The photocurrent yield was modeled as described in Pettersson, et al[5]. The optical field in the device structures under monochromatic illumination at a specific wavelength is obtained using the transfer matrix method. Normal incidence is assumed throughout this treatment although angular incidence does not significantly affect the

= ε αη2 ν results. The exciton generation rate is G c0 E/ 2 h , where c is the speed of light, ε0 is the permittivity in vacuum, α is the absorption coefficient of active layers, η is the real part of refractive index, h is Planck’s constant, ν is the frequency of light and E is the electric field calculated by the transfer matrix method. The photogenerated excitons are then allowed diffuse to both the ITO/DIP and the DIP/Ag interfaces. The stead-state exciton concentration profile, n, is obtained by solving the exciton diffusion equation, 0=D d2 n dx 2 − n /τ + G , where D is the exciton diffusivity and τ is the exciton lifetime. The interfaces are assumed to behave as perfect exciton sinks. The photocurrent yields of the front and back contact are

η = η = − calculated as FRONT Ddn/ dx at the ITO/DIP interface and BACK Ddn/ dx at the

DIP/Ag interface. The photocurrent yields that would be measured are a fraction of the values calculated here since only a fraction of the excitons that reach the interface dissociate into electron-hole pairs that can be collected. For the purpose of this analysis, only the shape of the photocurrent spectra is important. The photocurrent yields at the ITO/DIP interface and the DIP/Ag interface are predicted assuming that an external bias is provided and excitons dissociated at only one interface contribute to the photocurrent (Fig. 3.1a, inset)[8]. This condition is required to apply the FG model

99 Simulation method

although it might not be satisfied in some cases [9] . We investigate the esimation of LD

η η based on both the photocurrent yield from the front ( FRONT ) and back ( BACK ) contact using the FG model.

Fig. 3.1 Modeled photocurrent yield (quantum efficiency) at the front and back contact for a 400nm -thick DIP film sandwiched between ITO and Ag (solid lines), assuming LD=10nm. The absorption coefficient of DIP is also shown (dashed line). The separate extraction o f the photocurrent from the front and back contact requires appropriate electrical bias . η According to the FG model, the photocurrent yield at the ITO/DIP interface, FRONT , can be approximated as

−  1 1  − η 1 = 1+ η 1 (3.1) FRONT L est α 0  D  where α is the absorption coefficient of the film and η0 is the quantum efficiency of

η charge carrier collection and exciton dissociation at the interface. Plotting 1/ FRONT vs.

α est 1/ should result in a linear curve that intersects the abscissa at - LD . The

η photocurrent yield at the DIP/Ag interface, BACK , can be approximated as

100

The effects of optical interference on exciton diffusion length measurements using photocurrent spectroscopy

−1 1 1  − ()ηexp( αl )= − 1 +  η 1 (3.2) BACK L est α 0 D  where l is the thickness of the film. A linear curve should be obtained when

(η α ) α est 1/BACK exp(l ) is plotted vs. 1/ that intersects the abscissa at LD . The main assumption of the model is that the optical field decays exponentially without reflections or optical interference effects and therefore the model describes the photocurrent accurately only if the layer is much thicker than the optical penetration depth, 1/α . It also assumes that all excitons at the same position diffuse to the same

electrode and therefore the model holds only when LD is far shorter than the film thickness.

3.3 Feng-Ghosh model

To test the validity of the FG approach, we modeled ηFRONT and ηBACK including optical interference effects assuming that LD=10nm for a 400nm-thick film of DIP sandiwched between ITO and Ag, as shown in Fig. 3.1a (solid lines). The optical absorption of DIP is also shown for comparison (dashed line). In Fig. 3.2a and Fig.

η (η α ) α η 3.2b, 1/ FRONT and 1/BACK exp(l ) are plotted vs. 1/ . We reiterate that FRONT

and ηBACK were obtained using an accurate model that includes optical interference

η effects, as outlined above. It is imediately clear that linear fits to 1/ FRONT will necessarily be poor fits. Linear fits for (1/ α)max <1.5 m were performed to evaluate the

est LD that would be extracted using the FG method, resulting in LD =630nm based on

101 Feng-Ghosh model

η est η est FRONT , and LD =23nm, based on BACK . The large discrepancy between LD and the true LD is a result of strong optical interference effects in the 400nm -thick DIP film.

When the range of 1/ α is limited to 1/ α<0.5 m and 1/ α<1.0 m to suppress interference effects by consi dering only wavelengths for which optical absorption is strong, one

est η est obtains LD =-0.4nm and 500nm, respectively, using FRONT and LD =24nm and 12nm,

η est respectively, using BACK . Although LD becomes closer to LD when smaller ranges of

1/ α are used, especially using ηBACK , limiting 1/ α to <0.5 m is still not sufficient to completely suppress interference effects and further limiting 1/ α to a smaller range is not practical because insufficient data would be available for fitting.

Fig. 3.2 (a) Plot of the inverse of modeled photocurrent yield at the front contact vs. 1/α and the FG model fits. (b). Plot of the inverse of modeled photocurrent yield at the back contact vs. 1/ α and the FG model fits.

est To better understand the effect of optical interference on LD , we compare the optical field intensity and the exciton concentration profiles for the FG assumptions

(dashed lines) with the case where optical interference effects are considered (solid lines) in Fig. 3.3 at λ=490nm and λ=600nm. At λ=490nm, the optical absorption

102

The effects of optical interference on exciton diffusion length measurements using photocurrent spectroscopy length 1/α =150nm is smaller than the film thickness such that the optical field profile approaches an exponen tially decaying profile with a superimposed oscillatory component due to optical interference. The exciton concentration profile shows a

η η α similar trend. Using the FG assumptions , 1/ FRONT =23.7 and 1/( BACK exp(l )) =163.4, while the model that accounts for optical interferenceinterference effects yields 26.7 and 12.4,

est η respectively. A large discrepancy in LD would be obtained using BACK despite the film thickness (400nm) being significantly larger thanthan 1/α . This is due to reflections at the DIP/Ag interface ignored in the FG model.

103 Correct estimation of exciton diffusion length

Fig. 3.3 Modeled optical electric field intensity and exciton concentration profiles in a 400nm -thick DIP layer. In the presence of optical interference effects, the optical field intensity and exciton concentration are strongly modulated (solid curves) in strong contrast to the assumptions made by FG (dashed curves). (a) When 1/α =150nm, the optical electric field intensity and exciton concentration are close to those obtained ignoring interference effects. (b) For 1/α =830nm, the actual optical field intensity and exciton concentration differ strongly from the FG assumptions.

At λ=600nm, the optical absorption length 1/α =830nm exceeds the film thickness resulting in strong interference effects and large differences between the FG model and the model that takes into account optical interference, as shown in Fig. 3.3b.

η η α The FG model results in 1/ FRONT =104.9 and 1/(BACK exp(l )) =100.8, while the model that accounts for optical interference yields 1/ ηFRONT =42.9 and

η α 1/(BACK exp(l )) =9.2.

3.4 Correct estimation of exciton diffusion length

3.4.1 Transmittance correction

est It is clear that to prevent large errors in LD , the film under study needs to be substantially thicker than the optical absorption length. In order to examine whether

est the FG model yields an accurate LD using thick films, FG fits were performed on a modeled photocurrent spectrum for a 5000nm-thick DIP film. The thickness of this film is 10x larger than spectral range 1/α <500nm used for the FG fits. The DIP layer is sandwiched between ITO on glass substrate and Ag and we used LD=10nm. As

η est shown in Fig. 3.4a, an FG fit (dashed line) of 1/ FRONT (circles) yields LD =17nm

104

The effects of optical interference on exciton diffusion length measurements using photocurrent spectroscopy η which is 70% longer than the true LD. This error occurs because FRONT is proportional to T (λ) , the wavelength -dependent transmittance[5] of the ITO/DIP -interface, which is ignored in the FG model. T (λ) will exhibit especially strong wavelength dependence at the onset of optical absorption, exactly where FG f its are performed. To correct for this wavelength -dependent transmission, Eq. (1.3) needs to be modified to

T(λ)  1 1  − = 1 + η 1 (3.3) η  Lest α  0 FRONT  D  λ η A FG fit (Fig. 3.4a, solid line) of T ( /) FRONT (squares) using Eq. (3.3), yields an

est accurate estimate LD =10nm. Hence, even in cases where the FG model appeappeararss appropriate, a modification to the or iginal equation needs to be used to obtain accurate estimates of LD.

105 Correct estimation of exciton diffusion length

η λ η η Fig. 3.4 (a) Plots of 1/ FRONT (circles), T ( ) / FRONT (squares) and 1/ FRONT calculated without optical interference (crosses) vs. 1/α and their FG model η− α λ η− α fits. (b) Plots of 1/BACK exp(l ) (circles), T ( ) /BACK exp( l ) (squares) η− α and 1/BACK exp(l ) calculated without optical interference (crosses) vs. 1/α and their FG model fits.

η α est In Fig. 3.4b, an FG fit (dashed line) of 1/(BACK exp(l )) (circles) yields LD

λ η α =14nm, which is off by 40%. Fitting (solid line) T ( /() BACK exp( l )) (squares)

est λ results in LD =19nm. This error is not due to the wavelength-dependence of T ( ) .

Instead, it is attributed to reflections at the DIP/Ag interface that cannot be avoided.

We conclude that FG fits using the back contact cannot result in accurate estimates of

LD because Eq. (3.2) is not valid due to reflections.

3.4.2 Thickness consideration

est Fig. 3.5 shows the dependence of LD extracted using the FG procedure using modeled

photocurrent spectra, on the thickness of the DIP layer assuming that LD =10nm. The

est linear fits used to obtain LD using Eqs. (1.3), (3.2) and (3.3) were limited to the spectral range for which 1/ α<500nm. For film thicknesses thicker than 4 times than

est the maximum optical absorption length, (1/ α)max =500nm, used for fitting, LD using

λ η T (/) FRONT converges to LD within a 10% error. In the case of DIP, substantial errors in LD are obtained even for a film thickness of 800nm because the absorption coefficient of DIP is relatively small, which might be attributed to the out-of-plane orientation of the long-axis of stacked molecules in crystalline DIP films[10]. Fits of

η η α 1/ FRONT and 1/(BACK exp(l )) cannot be used for any film thickness.

106

The effects of optical interference on exciton diffusion length measurements using photocurrent spectroscopy

est Fig. 3.5 LD estimated by applying FG fits over the spectral rangerange for which η λ η η (1/ α)max =500nm to FRONT /T ( ) (black), FRONT (light gray ) and BACK (dark est gray ) vs. the thickness of the DIP layer. The errors in LD based on FG fits to η λ FRONT /()T are <10% , when the thickness of the DIP film >4.2(1/ α)max . Inset: The same plot with a full view.

3.4.3 Multiple exciton diffusion lengths

Another illustration of how FG fits may lead to wrowrongng conclusconclusionsions is shown in Fig.

3.6. Here, a FG analysis of LD is performed on a modeled ηFRONT spectrum for a

260nm-thick film of merocyanine [4, 11] sandwiched between a semitransparent

20nm-thick Al electrode and 20nm -thick Ag electrode. The model assumes LD=6.0nm.

Plotting 1/ ηFRONT vs. 1/ α results in two approximatly linear datasets due to the opticaloptical

est interference effects . Fitting the FG model results in LD =17.5nm for the wavelength

est range λ=480nm~520nm, and LD =3.6nm for the range λ=580 nm~700nm. Based on

107 Correct estimation of exciton diffusion length the FG model, one might erroneously conclude that two types of excitons are present in merocyanine with different diffusion lengths. Since the model for the ηFRONT spectrum used only one value for LD, this conclusion is in fact only an artifact of the

FG model.

Fig. 3.6 FG fits of the inverse of modeled photocurrent yield (front contact) vs. 1/α of a single layer merocyanine device (20nm Al/260nm Merocyanine/20nm Ag) assuming that LD=6.0nm. Because of its simplicity, the photocurrent method and FG model have been widely used to measure LD of organic compounds[4, 8, 12-18] . Bulovic and Forrest [8] reported a charge-transfer exciton with LD=225nm in 3,4,9,10-perylenetetr acarboxylic dianhydride (PTCDA) in addition to a Frenkel exciton with LD=88nm. However, the

500nm-thick PTCDA film was not thick enough to suppress optical interference effects for the range of 1/ α used (up to 1000nm) in the FG fits. As disscussed for the

108

The effects of optical interference on exciton diffusion length measurements using photocurrent spectroscopy merocyanine case, interference effects may solely be responsible for the appearance of

est a feature with LD =225nm alongside the main feature that resulted in LD=88nm.

η α Moreover, FG fits of 1/(BACK exp(l )) do not lead to accurate estimates of LD, as discussed above, and should be avoided. The conclusions of Ref. 8 and that of other work that uses FG fits should therefore be reconsidered.

3.5 Conclusion

In conclusion, the FG method for estimating the exciton diffusion length needs to be used with considerable care. The method can be used to extract LD based on ηFRONT for films that are thicker than ~4 times the maximum absorption length encountered in the spectral range considered for the fits, provided that the model is modified to include the transmittance of the transparent electrode/active layer interface. FG fits for ηBACK always lead to inaccurate estimates due to reflections of the back electrode. These requirements limit the practical use of the FG method for several reasons. In most cases, the required film thicknesses will be much larger than those typically used in organic solar cells and might therefore exhibit different morphologies and molecular packing. Moreover, for the thick films needed for reliable LD measurements using the

FG method, charge collection can be problematic. This is especially the case because small electric fields need to be used to prevent exciton dissociation in the bulk. One therefore needs to exercise caution when using LD data obtained using the FG method to explain device performance.

109 Conclusion

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110

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[14] T. Skotheim, J. -. Yang, J. Otvos and M. P. Klein, "Photovoltaic properties of au-- merocyanine--TiO[sub 2] sandwich cells. II. properties of illuminated cells and effects of doping with electron acceptors," J. Chem. Phys. 77, 6151-6161 (1982)

[15] C. Nasr, T. Taleb, R. M. Leblanc and S. Hotchandani, "Exciton diffusion length in microcrystalline chlorophyll a," Appl. Phys. Lett. 69, 1823-1825 (1996)

[16] N. Matsusue, S. Ikame, Y. Suzuki and H. Naito, "Charge-carrier transport and triplet exciton diffusion in a blue electrophosphorescent emitting layer," J. Appl. Phys. 97, 123512-5 (2005)

111 Conclusion

[17] J. Kalinowski, W. Stampor, J. Szmytkowski, M. Cocchi, D. Virgili, V. Fattori and P. Di Marco, "Photophysics of an electrophosphorescent platinum (II) porphyrin in solid films," J. Chem. Phys. 122, 154710 (2005)

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112

Effect of molecular packing on exciton diffusion length

Chapter 4 Effect of molecular packing on exciton diffusion length

4.1 Introduction

In this chapter, we investigate what factors affect exciton diffusion lengths in organic solar cells. we focus on archetypal small molecular weight bilayer organic solar cells built from the electron donor copper phthalocyanine (CuPc) and electron acceptor

3,4,9,10-perylene tetracarboxylic bisbenzimidazole (PTCBI)[1]. The broader classes of phthalocyanines and perylenes are known to be among the organic materials most stable against photooxidation[2]. The efficiency of bilayer devices based on these materials is only of the order of 1%[1, 3]. Nanostructuring the donor-acceptor (DA) interface leads to improved efficiencies of up to 2.7%[4, 5], still falling short of today’s best organic solar cells that reach 6%[6] and falling far short of the best laboratory thin-film amorphous Si[7], CdTe and CuInGaSe 2 cells[8] that reach 13%,

16.5%, and 19.5%, respectively. One reason for the low efficiencies is the trade-off that is made between exciton transport and carrier transport. In fine-grained nanostructured devices, excitons diffuse efficiently as evidenced by the nearly

113 Introduction complete photoluminescence quenching, but the resulting electron-hole pairs are dissociated inefficiently[9] or carrier transport to the electrodes is inhibited[10]. In coarse-grained nanostructured devices, carrier separation is more efficient, but exciton diffusion becomes less efficient. In bilayer devices, carrier separation is typically

>80% efficient and exciton diffusion is the main bottleneck. Improved exciton diffusion would lead to increased efficiencies for both planar and nanostructured cells.

Exciton diffusion is characterized by an exciton diffusion length, LD. The fundamental concepts of exciton transport were recognized long ago[11-13] but the accurate calculations of LD in molecular solids are complicated because the reliable prediction of exciton electronic coupling integrals, vibrational relaxation and lifetime is challenging[14, 15]. Moreover, the influence of packing geometry, disorder, impurities or grain boundaries on LD is not fully understood. Measurements of LD on nominally identical materials by different groups and methods often yield different results[16], because the material is in a different state of purity, the molecular packing and morphology are different, or the measurement method results in a systematic error[17, 18]. Terao, et al.[19] recently reported the effect of the phthalocyanine central metal atom on LD and showed that LD and charge carrier mobility are correlated. In this chapter, we report on a study of the effect of molecular packing on

LD in PTCBI.

114

Effect of molecular packing on exciton diffusion length 4.2 Exciton diffusion length

4.2.1 Experimental measurement

Bilayer CuPc/PTCBI solar cell structures were fabricated on glass substrates coated with a 1300-Å-thick transparent conducting indium-tin-oxide (ITO) anode with a sheet resistance of 15 /sq. Prior to the deposition, the substrates were solvent cleaned, followed by a UV-ozone treatment for 15 minutes. PTCBI is usually obtained from the synthesis as a mixture of the cis- and trans-isomer (See Fig. 4.1). Isomerically pure

PTCBI was prepared by repeated fractionation in sulfuric acid. All other organic materials were obtained commercially. All organic materials were purified using two thermal gradient sublimation runs[20]. The organic layers and metal cathode were deposited via thermal evaporation in a high-vacuum chamber (base pressure ~1 × 10 -7

Torr). The devices consist of a 50-500Å-thick film of CuPc on ITO, a 50-500Å-thick film of PTCBI, and a 100-200Å-thick bathocuproine (BCP) exciton-blocking layer. A

1000Å-thick Ag electrode was deposited through shadow masks with 0.81 mm 2 and

0.073mm 2 openings. X-ray-diffraction (XRD) measurements were performed using a

2400Å-thick layer deposited on a glass substrate in the θ− 2 θ geometry using a 40kV

Cu Kα radiation source. For exciton diffusion length measurements by photoluminescence (PL) quenching, a series of films of PTCBI with thickness varying from 10Å to 120Å PTCBI film was deposited on a glass slide half covered with a

50Å-thick layer of CuPc.

115 Exciton diffusion length

Fig. 4.1 Molecular structure of isomer pure PTCBI. η In Fig. 4.2, we compare the external quantum efficiencies ( EQE ) of cells with an identical layer structure (ITO/350Å CuPc/300Å PTCBI/150Å BCP/1000Å Ag) where the PTCBI film consisted either of the pure cis - (squares) and trans -isomers

(triangles), or a mixture (circles). The cells based on trans -PTCBI show the highes t

η λ EQE over a broad spectral range. At =480nm, CuPc does not contribute appreciably

η to the photocurrent. At this wavelength, EQE is 14.5%, 6.9% and 8.9%, for the devices using trans-PTCBI, cis -PTCBI and cis-tra ns mixture, respectively. Although trans-PTCBI shows a 30% higher absorption coefficient compared to the cis -trans

λ η mixture at =480nm, this alone does not explain the 2 -fold increase in EQE of trans-

PTCBI over cis-PTCBI. In addition, even at λ =700nm, where the difference in absorption coefficient is minimal, a cell based on trans -PTCBI still exhibits a higher

η EQE .

116

Effect of molecular packing on exciton diffusion length

cis mix 6 0.2 trans model

4 /cm) 5 EQE

η 0.1 (10 α

0.0 0 400 600 800 λ (nm)

η Fig. 4.2 The external quantum efficiency ( EQE ) of devices with layer structure ITO/350Å CuPc/300Å PTCBI/150Å BCP/1000Å Ag (cis-PTCBI: filled squares, trans-PTCBI: filled triangles, mixture: filled circles), m easured using η monochromatic light chopped at 30Hz. Model calculations of EQE (gray solid lines) and absorption coefficients (dashed lines) are also shown. The current-voltage (I-V) characteristics of cells with structure ITO/150Å

CuPc/300Å PTCBI/150Å BCP/1000Å Ag are plotted under AM1.5G simulated solar illumination with a power intensity of 94mW/cm 2 in Fig. 4.3. After correcting for the

1 2 spectral mismatch factor , the short circuit current density ( JSC ) is 4.18mA/cm ,

3.66mA/cm 2, and 3.68mA/cm 2, for the trans-, cis- and mixed-PTCBI cell, respectively.

η The trans-PTCBI cell exhibits the highest performance in agreement with the EQE

η measurements. The power conversion efficiency ( P ) of the trans-, cis- and the mixed-PTCBI cell is 1.1%, 0.93% and 0.99%, respectively. The relative increase in

1The spectral mismatch factor is 71% for these devices and our light source, i.e. the measured photocurrent is 71% of the value obtained by integrating the external quantum efficiency with the AM1.5G solar spectrum.

117 Exciton diffusion length

η η JSC and P for trans-PTCBI is smaller than that the increase in EQE because the

CuPc layer contributes a large fraction of the photocurrent.

1 ) 2 0 cis mixture -1 trans

-2

-3 CurrentDensity (mA/cm -0.4 0.0 0.4 Voltage (V)

Fig. 4.3 Current density vs. voltage characteristics of devices with ITO/150Å CuPc/300Å PTCBI/150Å BCP/1000Å Ag under 94mW/cm2 AM1.5G simulated solar illumination (cis-PTCBI: filled squares, trans-PTCBI: filled triangles, mixture: filled circles). η The EQE and JSC data suggest that LD of trans-PTCBI exceeds that of cis-

PTCBI and the cis-trans mixture. To confirm this hypothesis, we measured LD in films of trans- and cis-PTCBI using the PL-quenching technique using CuPc as the exciton quencher. The ratio χ of the PL signal of the PTCBI films on CuPc ( PL 1) divided by that on glass ( PL 2) is shown as functions of the thickness of the PTCBI films in Fig.

4.4. No PL from CuPc was observed, and the PL intensity of the PTCBI films on glass exhibits a linear dependence on PTCBI thickness such that optical interference effects can be ignored. Fitting of χ [21] yields LD=43±3.0Å and LD=28±2.0Å, for trans- and cis-PTCBI, respectively. Compared to LD=30±3.0Å for the cis-trans mixture[16], the

118

Effect of molecular packing on exciton diffusion length trans-PTCBI films exhibit a 43% longer LD while the LD of cis-PTCBI is 7% shorter.

η This corroborates the EQE and JSC data.

1.0 trans-PTCBI (exp.) trans-PTCBI(theory L =43 ±3.0Å) D 0.8 cis-PTCBI (exp.) cis-PTCBI(theory L =28 ±2.0Å) D

2 0.6 /PL 1

PL 0.4 χ= 0.2

0.0 0 20 40 60 80 100 120

PTCBI Film Thickness (Å)

Fig. 4.4 Photoluminescence (PL) intensity ratio of cis (open circles) and trans (open triangles) PTCBI vs. film thickness for films grown on 50Å of CuPc on glass. The lines are fits yielding LD=28±2.0Å for cis-PTCBI (solid line) and LD=43±3.0Å for trans-PTCBI (dash ed line). The excitation wavelength was λ=540nm.

An additional estimate of LD was made by fitting the experimentally obtained

η EQE to a model that assumes planar interfaces[22]. This results in LD=50Å, 26Å and

34Å for the trans-PTCBI, cis-PTCBI and mixture, respectively. The model fits are shown in Fig. 4.2(gray solid lines). The discrepancy between LD measured using PL

η quenching and fitting of EQE is attributed to differences in interface roughness between device structures and samples used for PL quenching[20].

119 Exciton diffusion length

4.2.2 Theoretical estimation

To obtain deeper insight into the factors that determine exciton diffusion in PTCBI, we calculated the theoretical LD assuming perfect crystals. Diffusion theory in 1- dimension gives and where D is the diffusivity, k is the transfer √2 rate of an exciton and τ=1.8ns [16] is the diffusion time. The Golden Rule gives

(4.1) | |H | | , where ħ is Planck’s constant, f and i are wavefunctions of final and initial states, H’ is Hamiltonian, ρ is density of states, F is the Franck-Condon weighted density of states factor estimated to be 0.1/eV [14]. The electron coupling integral J can be expressed as [15]

D* )1( D )1( A* )2( A )2( J =< D* A | H | DA * >≈ dr dr (4.2) DA ∫∫ r 1 2 12

,where D and A are wavefunctions of a donor and an acceptor, D* and A* are excited state wavefunctions, H DA is Hamiltonian between the donor and the acceptor, r12 is distance between site 1 and 2. The electronic coupling integral J=74meV and 55meV are obtained for trans- and cis-PTCBI in the direction normal to the substrate by ab- initio computations at the CASSCF/cc-pVDZ level with the recently proposed monomer transition density approach[15]. This results in theoretical LD of 990Å and

730Å, for trans- and cis-PTCBI, respectively, normal to the substrate plane, and

LD=1300Å and 1173Å, respectively, in the stacking direction. These LD may be overestimated up to ~3x due to the neglect of the polarizability of the surrounding medium and other errors[15]. These estimates of LD are >20x longer than the

120

Effect of molecular packing on exciton diffusion length experimental values, which suggests that intrinsic effects like vibrational relaxation and the formation of excit on pairs, or extrinsic causes such as chemical impurities and structural disorder play dominant roles in determining LD. Based on the evidence presented here, we conclude that structural disorder plays a dominant role in determining LD.

Fig. 4.5 Crystal structures of cis -PTCBI and trans-PTCBI. Crystal planes parallel to the substrate are indicated (gray planes). LD show exciton diffusion lengths estimated by theoretical calculations described in Error! Reference source not found. assuming perfect crystal. Estimated LD are 20 times longer than LD in experiments.

4.2.3 Molecular packing

The XRD patterns of the isomerically pure and mixed PTCBI films are shown in Fig.

4.6a, along with that of an uncoated glass substrate for reference. T he trans-PTCBI film has a prominent peak at 2 θ =12.4º while the cis-PTCBI and the mixed film have lower intensity peaks at 2 θ =12.0º and 2 θ =12.1º, respectively. The interplanar stacking distance for trans -PTCBI is d=7.1Å, corresponding to the (011) reflection, and for cis-PTCBI, d=7.4Å, corresponding to the (021) reflection [23]. The structure

121 Exciton diffusion length factor of the cis-PTCBI (021) reflection is 1.9 times that of the trans-PTCBI (011) reflection and does not explain the difference in peak intensity. Scanning electron micrographs of cis- and trans-PTCBI films (Fig. 4.6b) show that the grain size of both films are similar (25nm, determined using blob analysis), while that of the mixed film is smaller (22nm). The similar grain size observed for cis- and trans-PTCBI indicates that the molecular ordering within crystalline grains is substantially better in trans-

PTCBI films. The closer packing and concomitantly higher packing energy of trans-

PTCBI is likely responsible for the improved packing. The difference in sublimation temperatures (470°C for trans- and 450°C for cis-PTCBI) required during thermal gradient purification is in agreement with this hypothesis. The dominant molecular packing for cis- and trans-PTCBI is shown in Fig. 4.5. The molecular π-π stacking direction is the (100) direction which lies in the substrate plane for both cis- and trans-

PTCBI films. We note that the LD value of PTCBI is relatively short compared to other materials with π-π stacking such as 3,4,9,10 perylene tetracarboxylic dianhydride ( LD=880Å)[24] and CuPc ( LD=100Å)[16].

122

Effect of molecular packing on exciton diffusion length

Fig. 4.6 (a) X-ray diffraction (XRD) patterns for 2400Å -thick films of PTCBI isomers and mixture of isomers PTCBI on glass taken in the θ− 2 θ geometry using the Cu Kα line. The XRD pattern of the glass substrate is also shown. Simulated XRD patterns (gray lines) of a trans -PTCBI film assuming that the (011) planes are parallel to the substrate and trans -PTCBI powder are shown. (b) Scanning elec tron micrographs of 400Å-thick trans-PTCBI, cis -trans mixture, and trans -PTCBI films on top of ITO/320Å PEDOT:PSS/200Å CuPc on glass substrates. The width of the images is 576nm.

4.3 Conclusion

In conclusion, understanding the factors that limit LD is important since exciton diffusion is an efficiency bottleneck in many organic solar cells. Theoretical estimates of LD in PTCBI are about one order of magnitude larger than measured values. This study shows that improved molecular ordering in thin -films of small molecular weight

123 Conclusion

materials leads to a longer LD, suggesting that structural disorder is a main contributor to the discrepancy between theoretical estimates and experimentally measured values of LD.

124

Effect of molecular packing on exciton diffusion length Bibliography

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[3] P. Peumans, V. Bulovic and S. R. Forrest, "Efficient photon harvesting at high optical intensities in ultrathin organic double-heterostructure photovoltaic diodes," Appl. Phys. Lett. 76, 2650-2652 (2000)

[4] F. Yang, M. Shtein and S. R. Forrest, "Controlled growth of a molecular bulk heterojunction photovoltaic cell," Nat. Mater. 4, 37-41 (2005)

[5] P. Peumans, S. Uchida and S. R. Forrest, "Efficient bulk heterojunction photovoltaic cells using small-molecular-weight organic thin films," Nature 425, 158- 162 (2003)

[6] J. Y. Kim, K. Lee, N. E. Coates, D. Moses, T. Nguyen, M. Dante and A. J. Heeger, "Efficient tandem polymer solar cells fabricated by all-solution processing," Science 317, 222-225 (2007)

[7] J. Yang, A. Banerjee and S. Guha, "Triple-junction amorphous silicon alloy solar cell with 14.6% initial and 13.0% stable conversion efficiencies," Appl. Phys. Lett. 70, 2975-2977 (1997)

[8] R. Noufi and K. Zweibel, "High-efficiency CdTe and CIGS thin-film solar cells: Highlights and challenges," in 2006, pp. 317.

125 Conclusion

[9] P. Peumans and S. Forrest, "Separation of geminate charge-pairs at donor-acceptor interfaces in disordered solids," Chemical Physics Letters 398, 27 (2004)

[10] G. A. Buxton and N. Clarke, "Predicting structure and property relations in polymeric photovoltaic devices," Phys. Rev. B 74, 085207-5 (2006)

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[12] D. L. Dexter, "A theory of sensitized luminescence in solids," J. Chem. Phys. 21, 836-850 (1953)

[13] V. May and O. Kuhn, Charge and Energy Transfer Dynamics in Molecular Systems. Berlin: Wiley, 2000,

[14] E. Hennebicq, G. Pourtois, G. D. Scholes, L. M. Herz, D. M. Russell, C. Silva, S. Setayesh, A. C. Grimsdale, K. Mullen, J. -. Bredas and D. Beljonne, "Exciton migration in rigid-rod conjugated polymers: An improved förster model," J. Am. Chem. Soc. 127, 4744-4762 (2005)

[15] R. F. Fink, J. Pfister, A. Schneider, H. Zhao and B. Engels, "Ab initio configuration interaction description of excitation energy transfer between closely packed molecules," Chemical Physics 343, 353-361 (2008)

[16] P. Peumans, A. Yakimov and S. R. Forrest, "Small molecular weight organic thin-film photodetectors and solar cells," J. Appl. Phys. 93, 3693 (2003)

[17] S. R. Scully and M. D. McGehee, "Effects of optical interference and energy transfer on exciton diffusion length measurements in organic semiconductors," J. Appl. Phys. 100, (2006)

126

Effect of molecular packing on exciton diffusion length [18] S. Rim and P. Peumans, "The effects of optical interference on exciton diffusion length measurements using photocurrent spectroscopy," J. Appl. Phys. 103, 124515 (2008)

[19] Y. Terao, H. Sasabe and C. Adachi, "Correlation of hole mobility, exciton diffusion length, and solar cell characteristics in phthalocyanine/fullerene organic solar cells," Appl. Phys. Lett. 90, 103515-3 (2007)

[20] S. R. Forrest, "Ultrathin organic films grown by organic molecular beam deposition and related techniques," Chem. Rev. 97, 1793 (1997)

[21] B. A. Gregg, J. Sprague and M. W. Peterson, "Long-range singlet energy transfer in perylene bis(phenethylimide) films," J Phys Chem B 101, 5362-5369

[22] L. A. A. Pettersson, L. S. Roman and O. Inganas, "Modeling photocurrent action spectra of photovoltaic devices based on organic thin films," J. Appl. Phys. 86, 487- 496 (1999)

[23] S. Mizuguchi , "Electronic structure of the cis and trans isomers of benzimidazo perylene derivatives and their use as black pigments," The Journal of Imaging Science and Technology, vol. 50, pp. 115, 2006.

[24] V. Bulovic and S. R. Forrest, "Study of localized and extended excitons in 3,4,9,10-perylenetetracarboxylic dianhydride (PTCDA) II. photocurrent response at low electric fields," Chem. Phys. 210, 13-25 (1996)

127 Introduction

Chapter 5 Multi-junction organic solar cells

5.1 Introduction

In single junction solar cells, photons with energy ( hν) higher than bandgap (E G) lose energy hν-EG due to thermalization and photons with energy hν

5].

Even when light absorption and exciton diffusion are optimized, the efficiency of a single junction organic solar cell is too low for commercial applications. Multi- junction cells are a way to achieve the efficiencies needed. In this Chapter, I’ll show the practical efficiencies of tandem organic solar cells in the case of a series-connected tandem cell and an unconstrained (multi-terminal) tandem cell. In practical cases, unconstrained tandem cells result in higher efficiencies because of the increased freedom in choosing materials and device structures without requiring current matching. Ag NW mesh networks are a good candidate for an intermediate electrode

128

Multi-junction organic solar cells to realize unconstrained multi -junction cell because they are cheap, and their properties are comparable with ITO and can be deposited without damage on organic films. Semitransparent small mo lecule, polymer, solid state dye sensitized cells are demonstrated as a route to realize three terminal tandem cells.

5.2 single junction organic solar cells

5.2.1 Open circuit voltage of organic solar cells

Fig. 5.1 (a) Relationship between V OC and interface gap ( EDA ) [Courtesy by Junbo Wu] (b) Schematic of a donor and acceptor pair that shows linear relationship between V OC and EDA

Open circuit voltage (V OC ) of organic solar cells is a major factor to determine po wer conversion efficiency (PCE) because the energy of photons are larger than bandgap (E G) but only the amount of energy less than V OC can be obtained when

129 single junction organic solar cells

charge carriers are collected. V OC is equal or less than built-in voltage (V bi ), which is the difference between Fermi level of the donor (E Fp ) and the acceptor (E Fn ) in Fig.

5.1b. It can be expressed as

(5.1) qV E E ∆E log where EDA is the interface gap that is the difference of HOMO of the donor and

LUMO of the acceptor, N C and N V are effective density of states in LUMO of the acceptor and HOMO of the donor, N D and N A are doping density in LUMO of the acceptor and HOMO of the donor. Fig. 5.1a shows that linear relationship

(5.2) qV ∆E 0.3eV between V OC and EDA out of 11 different donor acceptor pairs in small molecular weight organic solar cells. The same results are observed in polymer solar cells[6].

5.2.2 Maximum efficiency of single junction organic solar cells

In order to estimate the maximum efficiency that single junction organic solar cell can achieve, we build the simplified model of a donor-acceptor organic solar cells as shown in inset in Fig. 5.2a. The donor and acceptor assumed to have bandgap E G and band offset between LUMOs of the donor and acceptor is E, which is assumed to be

0.5eV to have complete exciton dissociation[Wu, unpublished]. Then, from Eq. (5.2),

VOC of the single junction solar cells can be expressed as

130

Multi-junction organic solar cells

(5.3) qV E ∆E 0.3eV E 0.8eV

Maximum J SC can be obtained assuming that the cell absorbs photons with energy >

EG and gives IQE=85%, which is observed in case of efficient organic solar cells [4].

FF is assumed to be 0.65.

Fig. 5.2 (a) Maximum power conversion efficiency of single junction organic solar cells calculated along with bandgaps of the donor -acceptor pairs (Inset) band diagram of a donor -acceptor pair used in this cal culation. The highest efficiency is 11.3% at E G=1.63eV. (b) J SC and V OC of a single junction organic solar cells at given bandgap.

Fig. 5.2a shows PCEs of single junction solar cells calculated along with E G and

Fig. 5.2b provides J SC and V OC estimated by the model. As E G increases, J SC decreases due to loss of photons with energy < E G and V OC increases due to high EDA . It results in the maximum PCE=11.3% at E G=1.63eV, which is 13.3% even when

IQE=100%[7] . Note that E=0.5eV reduces V OC more than expected in homo junction solar cells so that the optimal E G=1.63eV in organic solar cells is larger than the optimal E G=1.34eV in inorganic homo junction solar cells [8]. The maximum

131 Efficiency of multi-junction organic solar cells

PCE=11.3% is smaller than our target PCE=15%. Therefore, multi-junction is a way to achieve our efficiency target.

5.3 Efficiency of multi-junction organic solar cells

While single junction cells cannot achieve higher than 11.3% as we see in the previous section, efficiency limit of multi-junction organic solar cells remains as a question. In this section, we will investigate practical efficiency limits of series-connected multi- junction organic solar cells based on the simple V OC model in Eq. (5.3. In order to compute realistic efficiency limits, we investigate three models step by step. The first model, called box EQE model, assumes constant EQE=0.85 to estimate the optimized

EG roughly. The optimized E G obtained in the box EQE model is put into the second model, called Gaussian absorption model. The model is used to optimize E G and structure of multi-junction cells with virtual materials whose absorption profiles are

Gaussian. The third model uses real materials whose properties are close to virtual materials obtained in the Gaussian absorption model and its structure is optimized further to obtain maximum PCE. For these calculations, series-connected tandem cells are used.

5.3.1 Box EQE model

Box EQE model provides approximate estimate to PCE of multi-junction organic solar cells. The simple donor-acceptor model that we used in section 5.2 is used as basic building blocks to describe subcells. In this model, EQE is assumed to be constant

132

Multi-junction organic solar cells when the energy of photon lies in between the bandgap of n

th (n+1) subcell, E G,n+1

0.85 when EQE E 0 otherwise Then, J SC can be expressed as

J min qS E where S(E) is AM1.5 solar spectrum in photons per unit area per second between E and E+dE and E G,j is the bandgap of the donor and acceptor of the j calculated as sum of V optimized E G,j (Fig. 5

FF=0.65 and P in =100mW/cm

Efficiency of multi-junction organic solar cells

PCE (red circles, Fig. 5.3a) increases from 11.3% in the single junction cell to

22.3% in the 10-junction cell. As the number of subcells increases, JSC decreases to

2 share energy with other subcells and VOC increases. In Fig. 5.3a, JSC =16.8mA/cm ,

2 2 14.2mA/cm and 4.88mA/cm and VOC =1.69V, 2.30V and 8.52V for two, three and ten subcells, respectively. PCE of the cells with 2, 3 and 10 junction cells are 15.7%,

18.0% and 23.0%, respectively. If IQE is 100% [7], 2-junction cell gives PCE=18.5% and 3-junction cell can achieve PCE=21.1%.

Fig. 5.4 Thermalization ratio of multi -junction cells (open squares). Energy of photons absorbed (solid circles) and not absorbed (solid squares) in the cells are shown. Multi-junction cells absorb photons in different subcells to reduce loss by thermalization, i.e. the difference between energy of ph otons and bandgap (E ph -EG,j ).

In Fig. 5.4, the loss can be quantified by using the thermalization ratio (open squares), which is the ratio between ener gy absorbed by multi-junction cells (solid circles) to energy loss by thermalization (solid squares) expressed as

134

Multi-junction organic solar cells

η λ λ  hc −  λ ∑ A,i ( )S( ) EG,i d ∫  λ  ρ = i (5.6) th hc η (λ)S(λ) dλ ∑ ∫ A, i λ i

th ,where ηA,j is the absorption quantum efficiency at the j stack and c is the speed of light. The loss for the optimized tandem cell structures is shown in Fig. 5.4. The thermalization ratio will be used in the following sections as a measure of loss in multi-junction cells. While ρth =26.5% for the single junction cell, ρth =16.2% and

6.33% for the 3- and 10-junction cell, respectively. This shows that loss reduces and

PCE increases with incorporating more subcells while more subcell need more cost in materials and processing.

5.3.2 Gaussian absorption model

In order to make our multi-junction model more realistic, we assumed virtual materials with Gaussian absorption profiles and optimize bandgaps and device structure in this section. Typically organic crystal show Gaussian absorption profiles with single or multiple peaks because electronic states exist discretely than continuously like in inorganic crystal. Virtual organic crystal (Inset, Fig. 5.5b) is assumed to have

Gaussian absorption profile with a single peak of at wavelength α 1.5 10 /cm

, where is wavelength corresponding to band edge, E G, and λ λ FWHM/2 λ FWHM is full width half maximum that is set to 200nm. For example, CuPc has absorption profile with a peak of and FWHM is 200nm. 1.5 10 /cm

135 Efficiency of multi-junction organic solar cells

(TCO)/115nm D1:A1/buffer/0.5nm Ag/50nm D2:A2/buffer/0.5nm Ag/230nm

D3:A3/buffer /100nm Ag, where ARC, glass, TCO and buffer layers are assumed to be non-absorbing and ARC provides no reflect ion with the cell. Thin Ag layers serve as intermediate electrodes to connect subcells [9] . Bandgaps (dashed lines, Fig. 5.5a) are optimized to E G=2.28eV for D3:A3, 1.49eV for D2:A2 and 1.09eV for D1:A1 starting from the optimized E G obtained in Box EQE model.

2 The optimized cell gives J SC =13.36mA/cm , V OC =2.37V an d PCE=18.30%.

Current density is slightly higher than the optimized cell in Box EQE model because

136

Multi-junction organic solar cells long tail of Gaussian absorption profile allows the cell to absorb low energy photons with E ph <1.09eV. V OC is also higher because increased J SC gives more freedom to optimize bandgaps. Fig. 5.5b shows the angular response of the optimized cell. Series- connected multi-junction cells are prone to have weak responsivity at oblique incidence due to current matching requirement. However, the cell provides angular response comparable to the cosine curve (gray). This model tells us that series connected 3-junction cells can achieve PCE=18.30% if we have proper materials.

5.3.3 Real materials

Models in section 5.3.1 and 5.3.2 are investigated based on ideal materials. Now we will show what the efficiency limit of multi-junction cells with real materials is. We choose materials whose properties are close to the virtual materials shown in section

5.3.2 out of materials available in literature. The relevant organic materials are shown in

137 Efficiency of multi-junction organic solar cells

Table 5.1. Bandgaps need to be close to E G=1.09eV for D1:A1, E G=1.49eV for D2:A2 and E G=2.28eV for D3:A3 and appropriate donor-acceptor pairs have to be found with band offset E≥0.5eV. Based on these two requirements, SnPc:C 60 , ClAlPc:C 60 and

SubPc:PTCBI are chosen for D1:A1, D2:A2 and D3:A3.

138

Multi-junction organic solar cells

Table 5.1 HOMO, LUMO and bandgap (E G) of materials selected for the optimized 3-junction cell.

Material HOMO(eV) LUMO(eV) EG(eV) Ref.

CuPc 5.2 3.5 1.7 [9]

SubPc 5.6 3.6 2.0 [10, 11]

Pentacene 4.9 3.0 1.9 [12]

ClAlPc 5.4 3.9 1.5 [13]

PTCBI 6.1 4.4 1.7 [9]

PTCDA 6.8 4.6 2.2 [14]

C60 6.2 4.5 1.7 [9]

SnPc 5.2 4.0 1.2 [15]

CuPc: copperphthalocyanine

SubPc:subphthalocyanine

ClAlPc: chloroaluminumphthalocyanine

PTCBI: 3,4,9,10-perylene tetracarboxylic bisbenzimidazole

PTCDA: perylene-3,4,9,10-tetracarboxylic -3,4,9,10-dianhydride

SnPc: tinphthalocyanine

139 Efficiency of multi-junction organic solar cells

Fig. 5.6 (a) absorption coefficients of subcells in the optimized triple -junction cell with real materials. Each subcell is assumed to have mixed donor -acceptor layers with 1:1 ratio. HOMO -LUMO level and material names are shown as inset. Gray dashed lines show EG used in this model. (b) The ηA (dashed), ηEQE (solid) and contributions of each stack (dotted, color) are shown. The blue, green and red dotted curves show the contributions of SubPc:PTCBI, ClAlPc:C 60 and SnPc:C 60 , respectively. Fig. 5.6 shows the optimized 3 -junction cell with real materials. The optimized

2 cell gives J SC =9.1mA/cm , V OC =1.9V and PCE=11.24%. J SC is 47% lower than the optimized cell in section 5.3.2 because SnPc:C 60 layer absorbs weakly at wavelengths

λ>930nm while D1:A1 layer with ideal materials absorb well even around λ=1135nm.

VOC is also smaller than V OC of the cell with ideal materials because ELUMO =0.8eV and 0.6eV for SubPc:PTCBI and ClAlPc:C 60 are larger than 0.5eV that we assumed in the Gaussian absorption model. Overlaps of absorption between subcells are more significant with real materials than with ideal materials because real materials have more than single peak or large shoulders. For example, SnPc:C 60 absorbs photons at

λ<400nm (Fig. 5.6b), which means that high energy photons are absorbed by a low bandgap subcell, SnPc:C 60 , and energy of photons are lost. The thermalization loss

140

Multi-junction organic solar cells ratio ρth =10.4% in Gaussian absorption case while ρth =21.4% with real materials. In order to obtain the efficiency estimated in Gaussian abosprtion model, we put more efforts on developing low bandgap materials spanned to 1eV, finding D-A pairs with low E to have high V OC and reducing overlaps between subcells.

5.3.4 Efficiencies of the optimized multi-junction cells

Table 5.2 summarizes performance of optimized series-connected multi-junction cells in three models we covered in previous sections. All optimized cells have 3-junction connected in series. Provided virtual materials, the optimized cell provides

PCE=18.30% which is higher than our efficiency target 15% obtained in Chapter 1.

However, PCE goes down to only 11.24% with materials available.

Table 5.2 The comparison of performance of the series connected triple - junction cells in three models.

2 Model EG(eV) ρth (%) JSC (mA/cm ) VOC (V) ηP(%)

Box EQE 1.15/1.52/2.02 16.2 12.03 2.30 17.96

Gaussian 1.09/1.49/2.28 10.4 13.36 2.37 18.30

Real 1.2/1.5/2.0 21.4 9.1 1.9 11.24

5.4 Multi-terminal multi-junction organic solar cells

The optimized device in the previous section shows only 11.24% with real materials, which is less than 15% target. One major reason of this low efficiency is that the freedom of design materials is limited by current matching requirements in series- connected multi-junction cells. In practical cases, multi-terminal multi-junction cells

141 Multi-terminal multi -junction organic solar cells result in higher efficiencies because of the increased freedom in choosing materials and device structures without requiring current matching. In this section, we will show that efficiency and benefits of multi -terminal multi-junction cells.

5.4.1 Three-terminal double -junction organic solar cells

Fig. 5.7 (a) Structure of the three terminal triple -junction cell. (b) absorption (dashed) and external (solid) quantum efficiencies of the three terminal cell. Contributions of subcells (dotted) are also shown. In order to investigate the advantages of multi -term inal multi -junction cells, absorption and external quantum efficiencies of an optimized 2 -terminal 3-junction cell and an optimized 3 -terminal 2-junction cell are shown in Fig. 5.7. The optimization performed to maximize PCE by optimizing device structure and bandgaps. Absorption is calculated based on transfer matrix method and internal quantum efficiency is assumed to be 0.85 [4] . Open circuit voltage, V OC , are obtained in literature [10, 13, 16, 17] or calculated as the difference between HOMO of donor

142

Multi-junction organic so lar cells and LUMO of acceptor subtracted by 0.3eV [6] . Short circuit current density, J SC , are

9.1mA/cm 2 for the 2 -terminal cell while the 3-terminal device gives 8.45mA/c m2 for

2 ClAlPc:C 60 and 15.41mA/cm for SubPc: PTCBI. Assuming FF=0.65, PCE of the 3 - terminal 2-junction cell is 12.31%, which is higher than PCE=11.24% of the 2 - terminal 3-junction cell ( Table 5.3). Note that PCE of the multi-terminal device is sum of PCE of the top and the bottom cell in the device. The multi -terminal cell gives higher efficiency because the device can be optimized without current matchi ng requirement. It gives more freedom to optimize device structure and materials.

Therefore, multi-terminal multi -junction structure gives higher PCE in practical cases than series-connected structure.

Table 5.3 Performance of the 3-terminal 2-junction cell.

2 EG(eV) ρth (%) JSC (mA/cm ) VOC (V) ηP(%)

1.5/2.0 12.3 8.45/15.41 0.6/0.9 12.31

5.4.2 Spectrum shifts and angular light incidence

143 Multi-terminal multi -junction organic solar cells

Fig. 5.8 (a) Simulated solar spectrum at 6am (red) and 12pm (black) at 7/15/1999 (b) Time series power conversion efficiencies of the optimized 3 - terminal 2-cell device (black circles) and the optimized 2 -terminal 3-cell device (black squares) and the ratio of the efficiencies (red squares) along 6am to 6pm. Multi-terminal structure has another advantage of robustness in spectrum shifts and angular incidence due to the freedom from current matching requirement. Solar spectrum shifts to red around sunrise and sunse t because blue photons are scattered by atmosphere due to long pathlength of sunlight. Fig. 5.8a shows simulated solar spectrum at Phoenix, Arizona at 7/15/1999 [18] . The spectrum at 6am (red) is redder than at 12pm (black) in a sunny day and the s ituation also happens in cloudy days.

When we simulated the efficiency versus time using the simulated spectrum, the 3 - terminal cell performs better than the 2 -terminal cell especially around sunrise and sunset. The multi-terminal structure gives more robu stness to spectrum shifts because of freedom from the current matching requirement. This robustness can be more significant in rainy or cloudy days.

144

Multi-junction organic solar cells Fig. 5.9 (a) Power conversion efficiency of the series-connected optimized 3 - junction cell (circle) and the optimized 3 -terminal 2-junction cell (square) plot along angle of light incidence. (b) Ratio of PCE of two optimized cells versus angle of light incidence. Multi-terminal cells show better performance at angular light incidence as shown in Fig. 5.9. The 3-terminal cell provides 14% higher PCE at 85° of incidence while 9% is obtained at normal incidence (Fig. 5.9b). This suggests that multi- terminal multi-junction cells give more benefits when they are used without tracking system.

5.5 Semitransparent solid state dye sensitized cells

Transparent and highly conductive intermediate electrodes are a major issue in realizing multi-terminal multi-junction solar cells. Indium tin-oxide (ITO) was proposed for thin film silicon solar cells [19] but ITO is expensive and brittle and it can damage organic films[20]. To realize low-cost multi-terminal multi-junction cells, cheap, conductive and non-damaging transparent conductor is required. Ag nanowire

(NW) mesh network is a good candidate because it is solution processible, it is cheaper than ITO, it has low sheet resistance and high transparency comparable to

ITO and it does not introduce damages on organic layers[20].

145 Semitransparent solid state dye sensitized cells

Fig. 5.10 Structure of multi -terminal multi-junction ss -DSC and semitransparent cell as a bottom layer. While the highest efficient small molecule and polymer devices are in multi-junction structures[4, 5] , multi -junction ss-DSC has not been reported up to the author’s knowledge. Incorporating AgNW intermediate electrodes, we could build multi - junction ss-DSC . The structure of 3 -terminal 2-junction ss-DSCs is proposed in Fig.

5.10 . Ag NW layer is sandwiched between two ss -DSC cells while the bottom cell is supposed to be semitransparent. Thus, the fabrication of the semitransparent ss -DSC is a step towards 3-terminal 2 -junction ss-DSC.

146

Multi-junction organic solar cells

Fig. 5.11 Processing steps of semitransparent ss -DSC. [Courtesy by J. -Y. L ee] (Center) SEM picture of Ag NW mesh network on semitransparent ss -DSC device. Ss-DSC cells were fabricated on glass substrates coated with fluorine -doped tin oxide (FTO). A compact TiO 2 layer was deposited by spray pyrolysis to prevent recombination between hole conductor layer and FTO. On the compact TiO 2 layer, a mesoporous TiO 2 layer was deposited by doctor blading and sintered at 450°C.

Subsequently, samples were soaked in a solution of amphiphilic polypyridyl ruthernium complex, Z907 to be adsorbed on TiO 2 surface. A hole conducting layer,

2,2’,7,7’-tetrakis-(N,N-di-p-methoxyphenylamin)9,9’-spirobifluorene(spiro -OMeTAD) with additives Li[CF 3SO 2]2N and tert.-butylpyridine in chloroben zene, was applied and allow it permeate TiO 2 pores for 1 minute prior to spin-coating [21]. Devices were completed by depositing Ag or Au electrodes by thermal evaporation or semitransparent devices were capp ed by laminating Ag NW.

147 Semitransparent solid state dye sensitized cells

Ag NW mesh network was prepared separately and laminated on top of spiro -

OMeTAD layer as shown in Fig. 5.11. Ag NW solution in ethanol was drop casted on glass substrates and NWs dispersed on substrates on a shaker operated at 350rpm for

3-5 minutes. After drying ethanol in air, Ag NW mesh network was annealed at 180°C for one hour in order to remove surfactants, polyvinylpyrrolid one (PVP), which wrapped around nanowires to prevent from conducting electrical currents. Patterns were made by scribing Ag NW layer if necessary. Then, Ag NW network was transferred to the top surface of spiro -OMeTAD layer by pressing with ~(1.4±0.6)×10 4 psi uni-axial pressure using a hydraulic press for 30 seconds. Ag NWs laminated on spiro-OMeTAD layer were randomly connected as shown in inset in Fig. 5.11.

Fig. 5.12 (a) I-V of semitransparent ss -DSC and Ag capped device. (Inset) Device structure of the ss -DSCs. (b) Transmission of Ag NW ss -DSC and ss - DSC without top electrodes. Current-Voltage (I -V) characteristi cs were measured using a parametric analyzer under AM1.5 solar simulator with power of 70mW/cm 2. The semi -transparent ss-

2 DSCs with Ag NW network shows J SC =3.42mA/cm , V OC =0.78V, FF=0.50 and

148

Multi-junction organic solar cells 2 PCE=1.91%, while a control device with Ag cap shows J SC =3.84mA/cm , V OC =0.81V,

FF=0.64 and PCE=2.83%. J SC of the semitransparent device is lower than the control device because a fraction of photons are lost by transparent Ag NW electrode ( Error! eference source not found. b). Lower FF of the semitransparent device could be explained by high resistance between Ag NW and spiro-OMeTAD layer. Fig. 5.12b shows specular transmission of the semitransparent device (solid curve) and the device without a reflective electrode (dotted curve) measured by UV-Vis spectroscopy. The semitransparent device and the device without a reflective electrode show up to 42% and 58% of transmission, respectively.

5.6 Three terminal thin film silicon solar cell

To see if multi-terminal structure can apply for thin film inorganic solar cells, 3- terminal 2-junction a-Si/µc-Si is simulated using AMPS-1D[22]. Intermediate layer is assumed to be transparent and highly conductive and parameters for a-Si and µc-Si are provided from AMPS-1D reference[22]. In order to simulate 3-terminal structure, one subcell is electrically “wired” by making bandgap zero without affecting optical absorption.

149 Conclusions

Fig. 5.13 Power conversion efficiencies of 2 -junction a-Si(1 st layer)/µc-Si(2 nd layer) solar cells. (a) 2 -terminal with maximum PCE=10.8% (b) 3 -terminal with maximum PCE=11.6%. In result, maximum PCE of the optimized 3 -terminal 2-junction a -Si/µc-Si cell is 11.6% while one of 2 -terminal series-connected tandem cell gives 10.8%. Although efficiency increase is only 7.4%, the optimized thickness of a -Si layer is 1.75 times thinner in 3-terminal cell due to the freedom from current matching constraint.

Thinner a-Si layer gives advantages such as less degradation and les s recombination currents without losing absorption. Thus, multi -terminal multi -junction scheme has advantages not only in organic solar cells but also inorganic thin film solar cells.

5.7 Conclusions

In conclusion, the efficiency of organic solar cells needs to be improved to be commercially available. Multi -junction provides a way to achieve high efficiency and multi-terminal structure has advantage to reach high efficiencies due to the freedom from current matching restriction. Ag NW mesh network plays a maj or role as an intermediate electrode to realize multi -terminal devices because it gives low sheet

150

Multi-junction organic solar cells resistance (~10 Ω/sq) with high transmission (~80%) with low-cost processing. The semitransparent dye sensitized solar cells were demonstrated with Ag NW mesh network as a route to realize multi-terminal multi-junction ss-DSC.

151 Conclusions

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[2] C. H. Henry, "Limiting efficiencies of ideal single and multiple energy gap terrestrial solar cells," J. Appl. Phys. 51, 4494-4500 (1980)

[3] W. Guter, J. Schoene, S. P. Philipps, M. Steiner, G. Siefer, A. Wekkeli, E. Welser, E. Oliva, A. W. Bett and F. Dimroth, "Current-matched triple-junction solar cell reaching 41.1% conversion efficiency under concentrated sunlight," Appl. Phys. Lett. 94, 223504 (2009)

[4] J. Y. Kim, K. Lee, N. E. Coates, D. Moses, T. Nguyen, M. Dante and A. J. Heeger, "Efficient tandem polymer solar cells fabricated by all-solution processing," Science 317, 222-225 (2007)

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[6] G. Dennler, M. C. Scharber, T. Ameri, P. Denk, K. Forberich, C. Waldauf and C. J. Brabec, "Design rules for donors in bulk-heterojunction tandem solar cells?towards 15 % energy-conversion efficiency," Adv Mater 20, 579-583 (2008)

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Multi-junction organic solar cells [8] A. S. Brown and M. A. Green, "Detailed balance limit for the series constrained two terminal tandem solar cell," Physica E: Low-dimensional Systems and Nanostructures 14, 96-100 (2002)

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153 Conclusions

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154

The optical advantages of curved focal plane arrays

Chapter 6 The optical advantages of curved focal plane arrays

6.1 Curved focal plane arrays

Digital photography has advanced at a fast pace over the last two decades[1] resulting in an increasing demand for digital cameras for mobile imaging, video conferencing and biosensing[2]. Compared to the rapid progress in digital image sensors, the optical systems of digital cameras have evolved at a much slower pace. One factor that constrains the design of optical systems for digital cameras is that the image surface, i.e., the Petzval surface, must be planar such that the image can be recorded using a planar silicon focal plane array (FPA). This constraint leads to off-axis aberrations that include astigmatism, field curvature and coma. These need to be corrected using additional optical elements, complicating the optical system design and resulting in a higher cost. If the requirement that the image surface be planar can be relaxed, simpler, more compact and lower-cost optics can be used.

Schmidt proposed the use of curved FPAs to remove spherical aberrations caused by a spherical mirror together with an aspheric corrector[3]. Large field-of- view (FOV) cameras[4], spherical imagers[5], artificial retina and biomimetic optical sensors[6] have been proposed or realized with curved FPAs. Because such curved

155 Advantages of curved focal plane arrays

FPAs require specialized processing[7], or can be manufactured only with a large radius of curvature ( r>75mm) using tiling, bending or selective etching of CCDs[8-

10], the scope of research on curved FPAs camera systems has been limited to large, high-end optical systems such as astronomical telescopes[8, 11]. Recently, Dinyari et al.[12] demonstrated a method to curve monolithic silicon into a hemispherical shape.

This method may be an economically viable method to manufacture curved FPAs with a radius of curvature that is useful for consumer digital cameras. In this chapter, we analyze the optical performance of hemispherically curved FPAs using a system level analysis[13, 14], and demonstrate their potential for excellent optical performance in conjunction with simple optical systems.

6.2 Advantages of curved focal plane arrays

When designing a compact camera system consisting of one to three lens elements, the designer is mainly concerned with reducing chromatic and spherical aberrations, distortion, off-axis illumination fall-off and field curvature. The latter causes astigmatism, affects the image FOV, is corrected using shaped lenses and an increased number of lens elements. A camera system with a curved image surface, on the other hand, provides more freedom in choice of lens shapes. In addition, a lower number of lens elements suffices leading to a lower cost and a more compact camera.

Furthermore, a curved image surface allows for a symmetrical arrangement where all points on the image surface are essentially on-axis points, as shown below, which also simplifies design[15]. Here, we compare a camera system with a ball lens and

156

The optical advantages of curved focal plane arrays spherical FPA to camera systems that consist of singlet and triplet lenses and a planar

FPA and illustrate the benefits of the curved FPA.

The three systems considered (Fig. 6.1a-c insets) have an identical F-number of 3.5. System I consists of a plano-convex lens with a 6.25mm-diagonal planar FPA.

System II[16] is a Cooke triplet, typical for low-end photographic cameras[17], with a

5.9mm-diagonal planar FPA. System III is based on a hemispherical FPA (radius-of- curvature r=5.87mm) and a 4mm-radius ball lens. BK-7 is used as lens material for the three systems. Unless specified, the optical design and analysis were performed using a weighted sum of the response at the wavelengths λ=656.3nm, 486.1nm and

587.6nm, with a relative weight of 1, 1, and 2, respectively.

Fig. 6.1 Modulation transfer functions (MTFs) of (a) a simple plano convex lens with a planar image plane (System I), (b) Cooke triplet camera system lenses with a planar image plane (System I I) and (c) a simple ball lens with a spherical curved image plane (System III). (a-c) MTFs of diffraction limited systems (black dotted lines), image points on axis (red), tangential image points (solid) at 0.4 field (green) and 0.7 field (blue) and sagitt al image points (dashed dots) at both fields are shown. Inset: schematics of the three systems.

6.2.1 Modulation transfer functions

The modulation transfer function (MTF) for each of the three systems is shown in

Error! Reference source not found. . It is clear that system I performs poorly

157 Advantages of curved focal plane arrays ompared to systems II and III. The MTF of system I is significantly smaller and, in particular, the off-axis response (at 0.4 of the FOV in green, and at 0.7 of the FOV in blue) is far inferior to the on-axis response (red). System III, on the other hand, is superior to system II, especially off-axis and for the radial MTF (dashed dot lines).

The on-axis response of system II is slightly better than that of system III at high sampling frequencies. We note also that the MTF of system III is nearly identical for on-axis and off-axis illumination as expected by the spherical symmetry of the system.

System III retains 60% of the on-axis modulation at 68 cycles/mm, corresponding to an optical resolution of 7.4 µm at both the center and edge of the image surface.

6.2.2 Point spread function

In Fig. 2, the on-axis (Fig. 6.2a-c,g-i,m-o) and off-axis (at 2mm image height, Fig.

6.2d-f,j-l,p-r) point spread functions (PSFs) for λ=450nm, 550nm and 650nm are shown for the three systems, using system simulations of the imaging system[18]. The advantage of a symmetric optical system with a curved FPA is clear: all image positions are on-axis and this significantly suppresses coma. The off-axis PSF of system I (Fig. 6.2d-f) shows a large degree of aberration compared to the other two systems. The off-axis PSF of system II (Fig. 6.2j) exhibits a double peak at λ=450nm and coma at all wavelengths (Fig. 6.2j-l). In contrast, the PSF of system III has a single peak (Fig. 6.2p-r). The PSF of system III is clearly more invariant with respect to wavelength and image height, which in turn leads to superior image formation.

158

The optical advantages of curved focal plane arrays

Fig. 6.2 Point spread functions for (a-c,g-i,m-o) on-axis and (d-f,j-l,p-r) off - axis (2mm image height) points. (a-f) show PSFs for System I, (g-l) for System II and (m-r) for System III.

6.2.3 Ray curves

The other fundamental monochromatic aberrations, i.e. astigmatism, field curvature and distortion are significantly reduced by use of a curved image surface. In Fig. 6.3, the astigmatism field curves of systems I and II show the presence of astigmatism and differences between the sagittal (solid lines) and tangential (dotted lines) focal planes

(Fig. 6.3a-b). In system III (Fig. 6.3c), the sagittal and tangential focal plane are

159 Advantages of curved focal plane arrays identical, such that no astigmatism is present. We note that the astigmatism ray curves are shifted because the best focal plane is shifted to minimize spherical and chromatic aberrations.

Fig. 6.3 Ray curves of astigmatism field curvature of (a) System I, (b) System II and (c) System III. Tangential field curvature (dotted lines) and sagittal field curvature (solid lines) are shown together.

6.2.4 Distortion

Due to the symmetrical design, all chief rays in System III pass through the optical center, O (see Fig. 6.4a), such that there is no distortion. The mapping of image points in three-dimensional space onto the curved FPA is done as follows. Suppose that the image point on the curved FPA, P(px,p y,p z), is transformed to the image point, P' , on the virtual planar image surface. As shown in Fig. 6.4a, when

= θ = OP ' OP / cos ( f / p z )OP and P(px,p y,p z) is mapped to ( fp x/p z,fp y/p z) on the image plane, where f is the focal length of the ball lens, the transformed image height is FP ' =ftan θ, which is the paraxial ideal image height. Hence, system III has no distortion regardless of the image heights and wavelengths, λ (Fig. 6.4d). For

160

The optical advantages of curved focal plane arrays comparison, the distortion heights of system I and II are shown as a function of image height and λ in Fig. 6.4b and c.

Fig. 6.4 (a) Mapping of image points on a curved image plane to points on a 2 - D image plane in System III. (b-d) Image height distortion of (b) System I (c) System II and (d) System III.

6.2.5 Relative illumination

Fig. 6.5a, b and c show the relative illumination intensity of systems I, II and III, respectively. In systems I and II (planar FPA), the intensity of illumination has a cos 4 θ dependence, where θ is the angle between the line from an off-axis point to the center of exit pupil with the optical axis. In system III, all pixels are at the same distance to the exit pupil removing a cos 2 θ dependence. In addition, the illumination is incident on the image surface along the normal direction which eliminates another cos θ factor, leading to an overall cos θ -dependence of illumination intensity. We

161 Image projection note that the remaining cos θ -factor is approximate and valid only when the off-axis pixels are far (i.e., many pupil diameters) from the exit pupil. Off-axis illumination intensity fall-off is an unavoidable problem in digital cameras because of reduced pixel fill factors and pixel vignetting[19], and is much more severe for a planar FPA than for a curved FPA because in a curved FPA, all chief rays are incident to the image plane at normal angle. Moreover, the illumination fall-off is more severe for complex optical systems with a multitude of reflective surfaces, again favoring curved

FPAs because their optics are simpler.

Fig. 6.5 Relative illumination fall-off of (a) System I, (b) System II and (c) System III.

6.3 Image projection

Images projected by the three optical systems were simulated in a radiometrically accurate model using lens design software[20] and imaging system engineering software[18] by taking into account object radiance and lens properties such as relative illumination, geometric distortion and spatially-variant PSFs at various wavelengths. This method enables the analysis of not only the lens systems but the entire imaging systems[13]. An object image, shown in Fig. 6.6a, is placed in the

162

The optical advantages of curved focal plane arrays object plane and projected by the three systems. The image of system I (Fig. 6.6b) exhibits barrel distortion and reduced sharpness as expected based on the MTF analysis. The images obtained for systems II (Fig. 6.6c) and III (Fig. 6.6d) are similar in image quality. However, system III provides a sharper image for off-axis locations as expected from the MTF analysis. System III also delivers a brighter image for off- axis pixels.

Fig. 6.6 (a) Object image and simulated radiometric images by (b) System I (c) System II and (d) System III.

6.4 Fabrication of curved FPA

The design of simple and compact camera systems with curved FPAs has not received much attention, partly because there are no practical, low-cost techniques to realize

163 Fabrication of curved FPA such FPAs. The two major challenges are to produce a high-quality curved semiconductor substrate suitable to build photodetector arrays and to create patterned circuits[7] on such curved substrate. We recently demonstrated a process to curve monolithic silicon substrates after standard foundry processing to address these challenges[12]. In Fig. 6.7, we show a curved monolithic silicon die produced by this method. The approach uses a deep reactive ion etch step to microstructure the silicon die into a two-dimensional (2D) network of nodes and springs. The springs allow for local deformation of the die necessary to attain a spherical shape. The resulting die can be stretched to a spherical shape on a latex membrane. The nodes can house the photodetectors and addressing circuitry while the springs serve as mechanical and electrical interconnects. The size of the array shown in Fig. 6.7 is 1.0cm and the radius of curvature of the curved die in Fig. 6.7a is 1.0cm. This process, discussed in more detail in Ref. 12, can be scaled to wafer-scale for the economical production of curved imagers.

Fig. 6.7 (a,b) Optical micrographs of a fabricated curved silicon die. (a) Curved die on a spherical surface with radius of cuvature of 1cm. (b) Detail of the curved die at an off-axis location. (c) Scanning electron microscopy (SEM) picture of an undeformed die. [By courtesy of Rostam Dinyari]

164

The optical advantages of curved focal plane arrays 6.5 Conclusion

In summary, we have shown that a curved imager provides a large degree of freedom in the design of the camera system, helps reduce fundamental aberrations and provides better resolution and brightness. This was demonstrated using designs for a simple and compact camera system by a full analysis of the characteristics of digital imaging systems with planar and curved FPAs. Using a microfabrication process that structures a silicon die into a stretchable membrane, it might be possible to produce such curved image plane cameras in a cost-effective manner using foundry-processed silicon.

165 Conclusion

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166

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[16] H. Lowenthal, "Photographic objective of the triplet type," 2645157, Jul 1953, 1953.

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167 Conclusion

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Conclusion and future work

Chapter 7 Conclusion and future work

Organic solar cell is a promising technology as a low cost renewable energy source.

However, efficiency improvement higher than 15% of power conversion efficiency is needed to be commercially available. In order to achieve this high efficiency, effective light trapping, long exciton diffusion and new device schemes such as multi-junction structure have to be investigated. In this thesis, V-trap light trapping is proposed and analyzed as a simple and effective way of improving light absorption in organic solar cells. The effect of various active layers and geometries on the efficiency of V-trap is also conducted. It is also shown that molecular packing is an important factor to affect exciton diffusion lengths. The efficiency of multi-junction organic solar cell is theoretically estimated and semi-transparent solid state dye sensitized cells are demonstrated as a first step to realize multi-terminal multi-junction organic solar cells.

The efficiency of organic solar cells has improved steadily and further research is needed to improve efficiency higher as well as reliability.

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