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 AttributionNoncommercial 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

AbstractOrganic 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 (LD) is an important parameter that determines efficiency. However, different groups report different LDs 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 LD in Chapter 3 and the effect of molecular packing on LD 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. Multijunction 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

AcknowledgementI 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. McGehees 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 ContentsAbstract ............................................................................................... 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 11.1 1.2

Introduction ................................................................... 25

Thin film photovoltaic cells......................................................................... 25 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 22.1 2.2 2.3

V-shaped light trapping in organic solar cells .................. 63

Introduction ................................................................................................ 63 Light trapping in thin film solar cells .......................................................... 64 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 ..................... 973.1 3.2 3.3 3.4 Introduction ................................................................................................ 97 Simulation method ..................................................................................... 98 Feng-Ghosh model ................................................................................... 101 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 44.1 4.2

Effect of molecular packing on exciton diffusion length 113

Introduction .............................................................................................. 113 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 .................................. 128ix

Table of Contents 5.1 5.2 Introduction .............................................................................................. 128 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 66.1 6.2

The optical advantages of curved focal plane arrays ..... 154

Curved focal plane arrays ......................................................................... 154 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 TablesTable 5.1 HOMO, LUMO and bandgap (EG) of materials selected for the optimized 3junction 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 FiguresFig. 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 () of small molecular weight organic materials. 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 102. 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 1018cm-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~ and (c) large-scale texturing when W730nm, lower optical gap absorbers are required. In Fig. 1.3, the absorption constant, , of a few typical small molecular weght materials including a few near-infrared-absorbing near

38

Introduction materials used in organic PV cells. A tin(II) phthalocyanine (SnPc)-based solar cell absorbs up to ~1000nm, as shown by Rand et al.[49], and a nanostructured CuPc/SnPc/C60 with a PCE of P=2.9% was demonstrated [35]. Chloroaluminum phthalocyanine (ClAlPc)[50] with an absorption peak at =755nm and lead phthalocyanine (PbPc)[51] with an absorption peak at =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 50250nm. 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 TiO2 and SiO2 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 diffusionUpon 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:LD where p2

2 p p + G = 0 x 2 is the exciton concentration,

(1.4)

is

the

exciton

lifetime

and

G ( x) = ( / 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:

D

p x

= sp(0)x =0

(1.5)

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] x D

N

4Re C cos

Ae/ Be/ e C e (1.6)

where N is incident photon flux, n is complex refractive index, d is layer thickness, is wavelength, and are the magnitude and argument of the complex reflection coefficient at x=d and C e and C

2e

A and B are coefficients determined by boundary conditions of s0=s|x=0 and sd=s|x=d. Their analytical forms are expressed as A B A D and B D

1 4Re A s se C s e C s cos sin 1 e/ s s C s

4Re 4Re 4Re C s cos sin

42

Introduction 1 4Re B s s e C s e C scos sin e/ 1 s s C s

4Re 4Re 4Re C s cos sin and 1 1 1 1 D s s e/ s s e/ L L L LDiffusion 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 ask DA = 2 2 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=

D =

k DA 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 metalphthalocyanines correlates with their LD. Madigan et al.[67, 68] simulated the timeresolved evolution of the photoluminescence (PL) of aluminum tris-(8-

hydroxyquinoline) (AlQ3) 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 IPD-EAA. Here, Eex=EG-EB is energy of exciton and EB is exciton binding energy typically 0 0-1.4eV[80, 81]. . IP and EA are the ionization potential and electron affinity, respectively. These conditions correspond to t EB,Dd~ and (c) large large-scale texturing when WW and W~, as shown in Fig. 2.1c. c. 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 [21-23, 25]In In this approach, which can be used for many t types of thin-film film solar cells, the substrate of the thin-film 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 trap2.3.1 StructureThe 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, without considering total internal reflections between the air/substrate interface is N

/2, where i is the angle of incidence with respect to the substrate 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. 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 decreases.

66

V-shaped shaped light trapping in organic solar cells

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

2.3.2 Optical pathlength enhancementThe V-shaped 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) of a V-shaped 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 V-shaped light trap. This 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 a inset). The optical path length enhancement can be written as

67

Principles of V-shaped shaped light trap

0 ( 2 k 1) <

2 sin cos sin (n 1 cos(2k 1) )

{

1

}

(2.1)

The enhancement surpasses the 4n2 limit[1]for for sufficiently small n. Because rays in the active layer propagate closer to the surface normal for high high-n materials (nsinact=sinair) and the number of bounces of each ray in the light trap is independent of n, the optical path length enhancement (2sin/cosact) decreases as n increases. This is also shown in Fig. 2.3b, b, where the maximum enhancement is plotted as a function of n showing that a V-shaped V shaped trap provides more enhancement than the theoretical limit of 4n2 when n4n2 only occurs near normal incidence. Also note that no practically useful solar cell materials with n5nm, limiting the EQE to a maximum of 22% for x=11nm. For the V-shaped light trap, however, A 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 =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

72

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 estimationTo 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 decreases (Fig. 2.5, inset), absorption increases per unit cell area and JSC increases from JSC=3.6mA/cm2 in planar configuration to JSC=8.6mA/cm2 at 2=30 as shown in Fig. 2.5a. In Fig. 2.5a, discrete jumps in JSC are observed because the number of bounces increases at 2/2N 1 where N is a positive integer in quantized manner. Open circuit voltage (VOC) can be estimated by

VOC =

J SC J SC nkT nkT planar log + 1 VOC + log sin planar q q J0 J SC

(2.5)

where n=2.0 is the ideality factor[35], k is the Boltzmann constant, T is roomplanar 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 due to the increased volume of active layers, while PCE (Fig. 2.5b) improves fromP=1.1% in planar configuration to P=2.5% at 2=30 because increase in JSC is

73

V-shaped light trap larger than decrease in VOC. Note that the optimized cell in planar configuration gives P=1.3%.

Fig. 2.5 (a) Calculated short circuit current density (JSC) versus opening angle. (b) Calculated open circuit voltage (VOC) and power conversion efficiency (PCE) of V-trap 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 JSC and PCE. Inset: ray bouncing diagrams to show that the small opening angle of V-trap V trap increase the number of bounces as well as absorption. bsorption. Whether the use of the V-shaped 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 higher highe efficiencies. For example, for the CuPc/PTCBI cell (100 CuPc/30 PTCBI) in the V-fold with 2=30, the amount of active material required is (130/sin)/250=2.0 times that used in the corresponding optimized planar cell (150 CuPc/100 PTCBI), while JSC increases 1.9-fold. 1.9 Adopting the V-shaped shaped light trap is in fact more attractive than this analysis suggests since the active layers are responsible for only about 1/9th of the overall thin-film film PV manufacturing cost[36]. cost

74

V-shaped shaped light trapping in organic solar cells

2.5.3 ExperimentsTo verify our models, bilayer CuPc/PTCBI solar cell structures were fabricated on glass substrates coated with a 1300--thick 1300 ITO anode. . The organic materials were purified using thermal gradient sublimation.21 The organic layers and metal cathode c were deposited via thermal evaporation in high-vacuum high vacuum (base pressure ~110-7 Torr). P3HT:PCBM solar cells were fabricated by spin-coating spin coating a blend of P3HT/PCBM in 1:1 weight ratio in dichlorobenzene on glass substrates coated with a 1500--thick 1500 ITO anode modified by a spin spin-coated 500--thick PEDOT-PSS PSS layer. A 1000--thick 1000 Al cathode was deposited by thermal evaporation. The V-shaped V shaped light trap was configured using two planar cells held in place via optical mounts.

Fig. 2.6 The JSC of the ITO/390 CuPc/420 PTCBI/150 BCP/1000 Ag bilayer device (cell A) measured in the V-shaped V shaped configuration near the tip (open circles) and near the edge (open squares). The solid lines are model calculations. The e JSC of a thinner cell with device structure ITO/300 CuPc/400 PTCBI/150 BCP/1000 Ag (cell B) near the tip of the V-shape V (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 array y of small devices (cell area = 0.81mm2) to verify the spatial dependence of the light intensity in the light trap. The JSC of cells with structure ITO/390 CuPc/420 PTCBI/150 BCP/1000 Ag (cell A) under 32mW/cm2 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/300 CuPc/400 PTCBI/150 BCP (cell B) located 7% from the tip (filled circles 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 3 from 0.8mA/cm2 for the planar configuration to 2.5mA/cm2 for 2=14 since the V V-shape funnels light towards the tip. Near the edge of the light-trap, light trap, JSC decreases from 0.9mA/cm2 for the planar configuration to 0.75mA/cm2 for 2=21, in agreement with our model. A 26% increase in overall JSC would have been obtained for f a cell that occupies the full substrate area. Larger increases in JSC would be obtained with thinner cells as discussed above.

76

V-shaped light trapping in organic solar cells Fig. 2.7 (a) JSC of ITO/500 PEDOT-PSS/ P3HT:PCBM/1000 Al cells as a function of the V-shape opening angle 2. The active layer thicknesses are 70nm (square), 110nm (circle) and 170nm (square). (b) The Voc (filled symbols) and P (open symbols) of the same cells. Solid lines are provided as guides to the eye. P3HT:PCBM cells of different thicknesses (70nm, 110nm and 170nm) were configured as large area devices (cell area = 2.4-3.2mm2) that occupy the complete Vshaped area. JSC vs. 2 measured under 32mW/cm2 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=35. The decrease in JSC for 275mm) using tiling, bending or selective etching of CCDs[810], 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 arraysWhen 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-ofcurvature 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 =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 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.

6.2.1 Modulation transfer functionsThe 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 7.4m at both the center and edge of the image surface.

6.2.2 Point spread functionIn 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 =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 =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) offaxis (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 curvesThe 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 DistortionDue 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,py,pz), is transformed to the image point, P ' , on the virtual planar image surface. As shown in Fig. 6.4a, when

OP' = OP / cos = ( f / p z )OP and P(px,py,pz) is mapped to (fpx/pz,fpy/pz) on theimage plane, where f is the focal length of the ball lens, the transformed image height is FP ' =ftan, which is the paraxial ideal image height. Hence, system III has no distortion regardless of the image heights and wavelengths, (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 in Fig. 6.4b and c.

Fig. 6.4 (a) Mapping of image points on a curved image plane to points on a 2D 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 illuminationFig. 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 acos 4 dependence, where 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 same2 distance to the exit pupil removing a cos dependence. In addition, the illumination

is incident on the image surface along the normal direction which eliminates another

cos factor, leading to an overall cos -dependence of illumination intensity. We161

Image projection note that the remaining cos -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 projectionImages 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 offaxis 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 FPAThe 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 ConclusionIn 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

Bibliography[1] P. Gregory, "Digital photography," Optics & Laser Technology, 38, 306-314 (2006) [2] A. El Gamal and H. Eltoukhy, "CMOS image sensors," Circuits and Devices Magazine, IEEE 21, 6-20 (2005) [3] E. Hecht, Optics. San Francisco, CA, U.S.A.: Addison Wesley, 2002, pp. 226. [4] H. Jin, J. R. Abelson, M. K. Erhardt and R. G. Nuzzo, "Soft lithographic fabrication of an image sensor array on a curved substrate," J. Vac. Sci. Technol. B 22, 2548-2551 (2004) [5] P. J. Hung, K. Jeong, G. L. Liu and L. P. Lee, "Microfabricated suspensions for electrical connections on the tunable elastomer membrane," Appl. Phys. Lett. 85, 6051-6053 (2004) [6] L. Lee and R. Szema, "Inspirations from biological optics for advanced photonic systems," Science 310, 1148-1150 (2005) [7] P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe and C. G. Willson, "Patterning curved surfaces: Template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography," in 1999, pp. 2965-2969. [8] P. K. Swain, D. J. Channin, G. C. Taylor, S. A. Lipp and D. S. Mark, "Curved CCDs and their application with astronomical telescopes and stereo panoramic cameras," in 2004, pp. 109-129.

166

The optical advantages of curved focal plane arrays [9] T. J. Jones and S. Nikzad, "Curved focal plane arrays using conformed thinned detector membrane," Nanotech Brief 28, (2004) [10] M. R. Ackermann, J. T. McGraw and P. C. Zimmer, "Are curved focal planes necessary for wide-field survey telescopes?" in 2006, pp. 626740-10. [11] P. Swain and D. Mark, "Curved CCD detector devices and arrays for multispectral astrophysical applications and terrestrial stereo panoramic cameras," in 2004, pp. 281-301. [12] R. Dinyari, S. Rim, K. Huang, P. B. Catrysse and P. Peumans, "Curving monolithic silicon for nonplanar focal plane array applications," Appl. Phys. Lett. ; Appl. Phys. Lett. 92, 091114 (2008) [13] P. B. Catrysse and B. A. Wandell, "Roadmap for CMOS image sensors: Moore meets planck and sommerfeld," in 2005, pp. 1-13. [14] P. Y. Maeda, P. B. Catrysse and B. A. Wandell, "Integrating lens design with digital camera simulation," in 2005, pp. 48-58. [15] J. M. Rodgers, "Curved Focal Surfaces: Design Optimization Through Symmetry, Not Complexity," Photonics Tech Briefs Online, April 2003. 2003. [16] H. Lowenthal, "Photographic objective of the triplet type," 2645157, Jul 1953, 1953. [17] E. Hecht, Optics. San Francisco, CA, U.S.A.: Addison Wesley, 2002, pp. 219. [18] ImageEval Consulting, "ISET digital camera simulator," vol. 1.0, 2004. [19] P. B. Catrysse, X. Liu and A. El Gamal, "QE reduction due to pixel vignetting in CMOS image sensors," in 2000, pp. 420-430.

167

Conclusion [20] Optical Research Associates, "CODE V," vol. 9.5, August 2004.

168

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.

169