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
i
© 2010 by Seung Bum Rim. All Rights Reserved. Re-distributed by Stanford University under license with the author.
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.
v
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
x
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
xi
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 W
xii List of Figures
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 2 α=29° opening angle and of a planar cell with the same structure (inset), as a function 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...... 71
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 absorption...... 74
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 xx 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 26 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 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. Levelized cost of energy (LCOE) of a PV sys tem, C, is expressed as [5] 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 28 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%) 30 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. 32 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. 34 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 36 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 38 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 2. 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 40 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 C e D α (1.6) 4πRe C cos 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