Nanostructured Electrodes for Organic Solar Cells: Analysis and Design Fundamentals

Transcription

1 Purdue University Purdue e-pubs Birck and NCN Publications Birck Nanotechnology Center Nanostructured Electrodes for Organic Solar Cells: Analysis and Design Fundamentals Biswajit Ray Purdue University - Main Campus, ray0@purdue.edu Mohammad R. Khan Purdue University Charles Black Brookhaven National Lab Muhammad A. Alam Purdue University, alam@purdue.edu Follow this and additional works at: Part of the Electrical and Electronics Commons, Electronic Devices and Semiconductor Manufacturing Commons, and the Power and Energy Commons Ray, Biswajit; Khan, Mohammad R.; Black, Charles; and Alam, Muhammad A., "Nanostructured Electrodes for Organic Solar Cells: Analysis and Design Fundamentals" (2012). Birck and NCN Publications. Paper This document has been made available through Purdue e-pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information.

2 This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE JOURNAL OF PHOTOVOLTAICS 1 Nanostructured Electrodes for Organic Solar Cells: Analysis and Design Fundamentals Biswajit Ray, Student Member, IEEE, Mohammad Ryyan Khan, Charles Black, Senior Member, IEEE, and Muhammad Ashraful Alam, Fellow, IEEE Abstract Nanostructured electrodes (NEs) improve optical absorption and charge collection in photovoltaic (PV) devices. Traditionally, the electrodes have been designed exclusively for higher optical absorption. Such an optical design of the electrodes does not necessarily ensure better charge collection. Since the efficiency of organic PV (OPV) devices is hindered by the low carrier mobility of the organic semiconductors, the charge collection property of the NEs provides an interesting design alternative. The goal of this paper is the formulation of the essential design rules for NEs to improve charge collection in the low-mobility organic materials. We use detailed optoelectronic device simulation to explore the physics of NEs embedded in the organic semiconductors and quantify its effect on the performance gain of organic solar cells. Our analysis suggests that an optimum codesign of electrodes and morphology is essential for significant performance improvement (mainly through fill factor) in OPV cells. Index Terms Bulk heterojunction (BHJ), fill factor (FF), morphology, nanostructured electrodes (NEs), organic photovoltaic (OPV) cell. I. INTRODUCTION ORGANIC photovoltaics (OPV) is a relatively new technology that promises low-cost solar energy conversion and the possibility of novel PV applications (e.g., portable cells, building-integrated PV). Successful commercialization of this technology, however, will require significant improvement in efficiency and lifetime. The power conversion efficiency η of any solar cell is determined by three parameters: short-circuit current J SC, open-circuit voltage V OC, and fill factor FF, i.e., η = J SC V OC FF/P in, where P in is the input power from the sun. J SC and V OC are mainly dependent on the energy band profile of the absorbing materials. FF, on the other hand, is related to the Manuscript received July 24, 2012; revised September 5, 2012; accepted September 13, This work was supported in part by the Center for Re- Defining Photovoltaic Efficiency Through Molecule Scale Control, an Energy Frontier Research Center funded by the U.S. Department of Energy Office of Science, and in part by the Office of Basic Energy Sciences under Award DE- SC The computational resources for this work were provided by the Network of Computational Nanotechnology under Award EEC from the National Science Foundation. B. Ray, M. R. Khan, and M. A. Alam are with the School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN USA ( biswajit.025@gmail.com; ryyan.khan.eee@gmail.com; alam@ purdue.edu). C. Black is with the Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY USA ( ctblack@bnl.gov). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /JPHOTOV efficiency of charge extraction from the cell and depends on the mobility of charge carriers and their recombination rates. Over the past few years [1] [8], there have been several breakthroughs in developing new absorbing polymers [also called donors (D)] with lower band gap (hence higher J SC ) and improved band alignment with acceptor (A) molecules (hence higher V OC ). These improvements in J SC and V OC have raised the cell efficiency continually, with the current record being more than 10% [48]. Despite material innovations, however, the FF of OPV cells remains stagnant at ( ) [1] [10], much lower than the inorganic counterparts ( 0.85) [6]. The OPV efficiency cannot reach its theoretical limit unless FF is improved significantly. Fill factor of a solar cell reflects the ability of the photogenerated charge carriers to be collected by the respective contacts. Thus, it is defined by the carrier mobility and the recombination properties of the active material [11], [12]. Most organic semiconductors have very low mobility (e.g., cm 2 V 1 s 1 ) [13], [14], which makes the charge extraction inefficient, especially under the operating (or maximum power point) bias condition when the internal field is low. Various approaches have been adopted to improve the carrier mobility in the OPV materials. One approach involves increasing the nanoscale crystallinity and molecular packing of the polymer film by controlling the annealing conditions [15]. Another approach involves percolation-doping [16] [18] of the polymer film by carbon nanotubes or conducting nanowires. While both approaches improve the carrier mobility in the organic films, the improvement is often marginal. Indeed, the requirement of solution processing precludes many film growth techniques that may otherwise improve the material mobility significantly. Recently [19] [21], there have been several efforts for the efficient charge collection from the low-mobility semiconducting materials by the insertion of electrodes in the active layer. Hsu et al. [19] have shown that embedding the ITO nanoelectrode inside the organic material can balance the carrier transport by increasing the effective hole mobility, which is the slower carrier in a typical OPV cell. Similarly, Allen et al. [20] demonstrated improved carrier collection by inserting the electrode in the active materials for radial charge collection. However, the performance gain in both approaches was low, because the electrode design was not optimized. Similarly, nanostructuring of the front/back contacts [22] [29] has also been used to enhance photon absorption in organic solar cells (photonic crystals [22] [25] and plasmonic structures [26], [28]). For example, Niggemann et al. [23] have shown increased absorptance by embedding comb-like array of Al electrodes in the photoactive polymer blend. Similarly, Ko et al. [24] have shown that by embedding /$ IEEE

3 This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 2 IEEE JOURNAL OF PHOTOVOLTAICS a photonic crystal geometry made of nanocrystalline ZnO (also acts as a cathode for electron collection), the band-edge absorption in OPV can be enhanced significantly. These recent studies imply that optimizing the design of nanostructured electrodes (NEs) may improve OPV efficiency by simultaneously increasing light absorption (high J SC ) and by efficient charge collection (improved FF). The optimization of NEs for the high-efficiency OPV cells is not straightforward: The inserted electrodes not only alter the optical field (hence photogeneration), but also redistribute the electrical field that affects charge collection. Most of the theoretical works [27], [30] regarding the optimized design of the electrodes have focused exclusively on the optical absorption, and hence, electrode dimensions have been tailored as a function of light wavelength. However, for low-mobility organic materials, the potential of efficient charge collection by NE offers an intriguing design possibility. Although several experimental results are available, unfortunately there is no theoretical work that explores the charge transport or recombination dynamics in the complex organic materials in the presence of inserted electrodes, and hence, NEs have never been optimized to improve charge collection in OPV cells. That is why, we believe, most of the reported works have failed to demonstrate simultaneous improvement in all the three solar cell performance matrices (J SC,V OC, and FF) after the insertion of electrodes. The objective of this paper is to explore the fundamental physics of electrode insertion in the organic semiconductors in order to formulate the general design principles for this concept. With this goal, we use a detailed and systematic optoelectronic device simulation of planar and bulk heterojunction (BHJ) OPV with NEs to arrive at the following conclusions: First, the inserted electrodes minimize the average carrier extraction length and hence do improve the FF of the OPV cell. Second, the field distribution (and carrier density) inside the cell is altered by the insertion of NEs in such a manner that it can either improve or degrade the performance based on the details of active-layer morphology. In general, performance gain is achieved if the inserted electrodes exclusively remain in a single material, typically the donor which has lower mobility. Thus, a planar heterojunction (PHJ) [see Fig. 1(a)] structure is more suited than BHJ [see Fig. 1(c)] morphology for the implementation of this concept. Third, the design criterion for absorption (mainly band-edge) enhancement not necessarily ensures better charge transport and vice versa. In other words, the transport-oriented electrode design is different from the photonic crystal design. However, we find that electrode design for the better transport also provides optical enhancement which compensates the loss of active volume due to electrode insertion. This paper is organized as follows. We first describe the basic device structure of an OPV cell and its working principle. Next, the optoelectronic modeling approach is presented. The optoelectronic simulation framework is then applied to study the effect of electrode insertion on the short-circuit current, opencircuit voltage, FF, etc., for various OPV morphologies. Finally, we discuss the essential design rules for the NEs in order to achieve higher efficiency. Fig. 1. Structure and operation of OPV cells. (a) PHJ-type OPV cell. The sequences of device operations are indicated in the figure. (b) Energy band diagram of a PHJ cell under the short-circuit condition. The various current fluxes are shown by the arrows. The current components are exciton diffusion flux J ex, generation-dependent recombination current J rec, dark or injection current J dark, and the photocurrent J ph. (c) Structure of a BHJ-based OPV cell. (d) Electron (black) and hole (red) concentration profiles in a PHJ cell for low (solid line) and high mobility (dashed line). Carriers pile up at the interface for low mobility μ, and hence, the interfacial recombination loss is higher in low-μ cells. Here we assume μ e = μ h = μ. II. DEVICE STRUCTURE AND WORKING PRINCIPLE OF ORGANIC PHOTOVOLTAIC The light-absorbing layer of an organic solar cell consists of two organic semiconductors, which are called donor (D) and acceptor (A). In the PHJ [31] type OPV cells, these two D A semiconductors are deposited (thermal evaporation) on top of each other [see Fig. 1(a)]. However, the more commonly used structure for the OPV devices is the BHJ [32] [BHJ, Fig. 1(c)], which consists of randomly intermixed donor acceptor materials that are fabricated by spin-coating. The operation of an OPV cell has four sequential steps [numbered in Fig. 1(a)]. First, when the photon transmits through the transparent glass substrate and the electrode (TCO), it is absorbed in the active layer generating a strongly bound electron hole pair called exciton. Excitons, being charge neutral, diffuse in the active material (step 2) until they encounter an interface, where they form a charge transfer (CT) state (step 3) with the electron in the acceptor material and the hole in the donor. However, if excitons cannot find the interface within the diffusion length (L ex (5 10)nm) [33], they are irreversibly lost to self-recombination. Thus, the BHJ morphology ensures that regardless of the point of photoexcitation, all the excitons are collected by the large interfacial area. Finally, the CT states dissociate into free carriers (electrons and holes) which are transported toward the respective electrodes by the built in field (step 4).

4 This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. RAY et al.: NANOSTRUCTURED ELECTRODES FOR ORGANIC SOLAR CELLS: ANALYSIS AND DESIGN FUNDAMENTALS 3 Ideally, the electron-carrying acceptor material should be contacted exclusively by the cathode (see Al in Fig. 1). Likewise, the hole-carrying donor material should be in contact only with the anode (ITO/PEDOT). If the cathode (or anode) directly contacts the donor (or acceptor), it would act as interface recombination centers. Thus, interlayer, minority-carrier blocking materials are used along with the electrodes (e.g., LiF on Al, and PEDOT: PSS on ITO) to minimize the contact recombination loss, especially in BHJ devices where both the D/A materials touch both the electrodes. The interlayer material selectively allows only the majority carrier (e or h) to escape and prevents the recombination of the minority carrier in the wrong contact by a high energy barrier. The current conduction in OPV devices is unipolar [34], with hole and electron currents exclusively confined within the donor and acceptor materials, respectively. Only at the D/A interface, electron and hole can come together and recombine. We illustrate the various current components in Fig. 1(c) using the energy band diagram of the PHJ device. Here, J ex is the exciton diffusion flux or the rate of charge generation (assuming that exciton dissociation efficiency is unity), J ph is the photocurrent or the rate of charge extraction, and J rec is the recombination rate at the interface, such that J ex J ph (V )+J rec (V ). The detailed analytical derivation of the photo-current is given in our previous publication [49]. Since J ph μ e,h,thej rec must compensate the poor J ph in a low mobility μ material. The carrier profile [see Fig. 1(d)] obtained by numerical simulation confirms this hypothesis by showing how carriers pile up at the interface in a low-μ material. This increase in carrier concentrations leads to high recombination (J rec γnp) loss. Here, n and p are the electron and hole densities, respectively, and γ is the bimolecular recombination coefficient [35]. III. MODEL SYSTEM AND MODEL EQUATIONS A. Optics Optical absorption in different layers of the OPV cell is calculated by the full-wave solution of Maxwell s equations with the input of AM1.5 illumination. The materials in different layers of the cell are characterized by the complex refractive indices η med that are obtained from measurements [36]. Transfer matrix method (TMM) [37] calculations are used for the optical studies of the planer electrode structure. In this approach, the structure is modeled using a series of interface and phase matrices. The interface matrices are defined by Fresnel complex refection and transmission coefficients. The phase matrix describes the change in phase of the electromagnetic waves as it flows through a layer. The central quantity which is calculated in this approach is the point-wise optical absorptance [A(λ,r)] inside various layers of the cell. The optical absorption for the NEs is implemented using COMSOL RF-module [38] in 2-D grid space with periodic boundary conditions. We study the results for both transverse electric (TE) and transverse magnetic (TM) waves for normal incidence. The wavelength range of nm is used for our calculations. We consider power absorption only in the polymer blend. Absorption in the top ITO, back contact (Al), and the projected electrodes (ITO) are subtracted from the total ab- TABLE I EQUATIONS FOR CARRIER TRANSPORT sorption of the system under AM1.5 illumination. The optical model is comprehensive, but the equations and approach are traditional we make no claim for novelty in this regard. B. Transport The transport of carriers (excitons, electrons, and holes) is modeled by generalized drift-diffusion formalism, which is described in detail in the previous publications [39] [42]. For completeness, we offer the following summary. Exciton generation is calculated from the optical absorption profile discussed previously. The diffusion and recombination of the net generated exciton is modeled by the finite exciton diffusion length. Dissociation of the CT excitons is assumed to be field independent, consistent with recent experiments [11], [43] [47]. The electron and hole transport inside the cell morphology is simulated by a self-consistent solution of Poisson and continuity equations. The generation term in the e h continuity equations is calculated from the solution of exciton transport. The charged carrier recombination term in the continuity equations is implemented by the bimolecular recombination [35]. Since the D A interface is the only place where free carriers can recombine as well as generate, the generation and recombination terms in the e h continuity equations are nonzero only at the D A interfacial nodes. We made no new contribution to model development; rather, we use the well-calibrated and well-tested model equations [39] [42] (see Table I) and simulation parameters (see Table II) to explore the implications of electrode insertion on the performance of organic solar cells.

5 This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 4 IEEE JOURNAL OF PHOTOVOLTAICS Fig. 3. Effect of inserted electrode height H e le c on the performance of a PHJ-based OPV cell. Various solar cell performance matrices are plotted as a function of electrode height. (a) Efficiency, (b) short-circuit current, (c) opencircuit voltage, and (d) FF. The electrode dimensions [see Fig. 2(a)] are S e le c = 100 nm and W e le c = 10 nm. The thicknesses of the donor (T D ) and acceptor (T A ) layers are 50 nm each. The JS C value reflects AM1.5 illumination and exciton diffusion length of 25 nm. However, in this plot we did not consider any effect on optical absorption profile with the electrode insertion. Fig. 2. Structure and functionality of the nano-structured electrodes (NEs). (a) Schematic of comb-like NE geometry which is assumed for simulation in this study. A blocking layer is assumed deposited on top of the inserted (ITO) electrodes. The two key functionalities of NEs are shown in (b) and (c). The arrows in (b) represent the path of electron (in acceptor) and hole (in donor) current. The potential redistribution inside the cell with the inserted electrodes is shown by color coding in (c). IV. RESULTS AND DISCUSSION We now explore the effect of nanostructured projected electrodes on the performance of organic solar cells. For this analysis, we choose typical material parameters representing P3HT:PCBM system (summarized in Table II). The results presented here are, however, applicable for any other material system. For simplicity, we choose a periodic comb-like electrode structure which is characterized by three geometric parameters: height Helec, width Welec, and spacing Selec ; see Fig. 2(a). For the systematic explanation, we first analyze the effects of electrode insertion on the carrier transport (assuming that the optical absorption is unaltered), and then, we discuss how optical absorption is affected by inserted electrodes. A. Effect of the Nanostructured Electrodes on Carrier Transport 1) Planar Heterojunction Cell: Conceptually, it is easier to explain the effect of NEs by exploring its implication for the PHJ morphology. We will later translate many of the conclusions derived from PHJ-OPV to BHJ-OPV. Fig. 2(b) shows the device structure of a PHJ-OPV with electrode inserted in the donor material. We assume that the inserted electrodes are made of optically transparent conducting oxide (e.g., ITO) with conformal coating of appropriate minority carrier blocking layers (e.g., PEDOT-PSS). Typically, holes in the donor material are the slower carrier, and hence, it is advantageous to have electrodes inserted into lower mobility material. Due to the periodicity/symmetry of the assumed electrode structure [see Fig. 2(a)], it will be sufficient to analyze only one half of the periodic structure in the 2-D geometry. From the point of charge transport, inserted electrodes have two important effects: First, they reduce the average carrier extraction time by providing low resistive pathways [illustrated in Fig. 2(b)] and, hence, enhance the FF. Second, they alter the potential and charge carrier distribution inside the cell [illustrated by color coding in Fig. 2(c)] in such a way that holes are attracted toward the electrode, and electrons are pushed away from it. The first effect (reduced carrier collection length) significantly improves the I V characteristics mainly under the maximum power point condition when the effective field in the device is low. The second effect (redistributed potential and charge carriers) affects the free carrier recombination and hence alters the I V curve primarily under the short-circuit condition, when the built in field in the device is the maximum. Taken together, the NEs make the charge extraction faster and improve the OPV performance, as shown in Fig. 3(a). In Fig. 3, we plot the efficiency and related solar cell performance matrices (JSC, VOC, and FF) as a function of the height of the inserted electrode Helec. Below, we explain the effect of the NEs on each of these performance matrices. Short-Circuit Current JSC : For the transport analysis in Fig. 3, we assume that optical absorption remains unaltered with the NEs. Thus, as shown in Fig. 3(b), JSC remains almost

6 This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. RAY et al.: NANOSTRUCTURED ELECTRODES FOR ORGANIC SOLAR CELLS: ANALYSIS AND DESIGN FUNDAMENTALS 5 Fig. 4. Carrier concentration and recombination dynamics in the PHJ-OPV cells with the NEs under the short-circuit condition. (a) (c) 2-D carrier profile within the active layer is shown for three different electrode heights (P0, P1, and P2). Note that carrier profile in the donor represents only holes, and in the acceptor, it represents electrons. The arrows represent the electric field distribution. (d) Current voltage characteristics corresponding to the three cells. (e) Electron (n) and hole (p) density at the interface of D A region is plotted for the three cell structures, and the corresponding position-dependent recombination rates are shown in (f). unchanged with electrode height. Only a small improvement in current is possible with increasing electrode height (but Helec < TD ) purely from better electrical transport. This is because the built-in electric field at the SC condition is high, and hence, the transport gain is not significant. However, once the electrode crosses the interface (Helec > TD ), it induces significant recombination loss (as explained in detail in Fig. 4) which reduces JSC. Open-Circuit Voltage VOC : In Fig. 3(c), we plot VOC against Helec which shows that VOC remains unchanged with the electrode height. This behavior of VOC can be explained as follows: Under the open-circuit condition, the net current in the cell is zero. Since transport in OPV is mostly unipolar [41], the electron current in acceptor and hole current in donor both are zero. Thus, at the VOC point, the quasi-fermi levels in the donor and acceptor are flat ( Fe/h = 0). This implies that VOC is almost independent of carrier mobility and mainly dictated by the material properties of the D A interface [41]. Since the inserted electrode effectively improves carrier mobility (or shortens the carrier path length), which has no effect on the VOC point, thus VOC remains unchanged with electrode height. However, a key assumption in this analysis is that we have assumed zero recombination at the electrode surface (or perfect minority carrier blocking). If we include electrode surface recombination, then once the electrode penetrates through the D A interface, VOC will degrade sharply. Fill Factor FF: In Fig. 3(d), we plot the variation of the FF with the electrode height. At the maximum power point (or FF point) the built-in field is low, and hence, the transport gain due to the NEs is most prominently reflected on FF. With increasing Helec, the photocarrier collection path becomes shorter, and hence, FF increases rapidly. However, beyond a certain electrode height (Helec thickness of the donor layer), FF degrades with Helec due to the significant interface recombination loss (explained in detail in Fig. 4). Since under the assumptions of this analysis JSC and VOC remain almost flat, efficiency variation [see Fig. 3(a)] mirrors the variation in FF. In the next paragraph, we explain the variation of efficiency with electrode height by exploring in detail the physics associated with three representative points (P0, P1, and P2) in Fig. 3(a). In Fig. 4(a) (c), we show electric field (arrows) and charge carrier (color coding) distribution inside the D A layers for three different electrode heights, i.e., usual planar electrode (cell P0), inserted electrode only in the donor (cell P1), and inserted electrode breaching the D A interface (cell P2). The corresponding current voltage characteristics are plotted in Fig. 4(d). The I V characteristics illustrate the improvement in FF (and slight increase in JSC ) for cell P1 but a significant degradation in performance (both JSC and FF) for cell P2. To explain these I V characteristics, we plot the charge carrier densities and the recombination rates along the D A interface in Fig. 4(e) and (f), respectively. The inserted electrodes alter the electric field in

7 This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 6 IEEE JOURNAL OF PHOTOVOLTAICS Fig. 5. Effect of the electrode spacing S e le c on the performance of a PHJbased OPV cell. Various solar cell performance metrics are plotted as a function of S e le c. (a) Efficiency, (b) short-circuit current, (c) open-circuit voltage, and (d) FF. The other electrode dimensions are H e le c = 40 nm and W e le c = 10 nm. The thicknesses of the donor and acceptor layers are 50 nm each. JS C remains flat since we have not considered any effect on the absorption profile with the NEs. such a way that holes are attracted toward the electrode, while the electrons are pushed away from it. Thus, as long as the inserted electrodes remain in the donor (e.g., cell P1), the free carrier density along the D A interface remains lower [see the red dashed line in Fig. 4(e)] than the usual PHJ cell (black solid line). The reduction of electron and hole densities at the interface reduces charge recombination at the interface [see the red dashed line in Fig. 4(f)] and improves the cell efficiency. However, once the electrode crosses the heterojunction (e.g., cell P2), the electric field forces accumulation of free holes along the interface, especially closer to the inserted electrodes [see the blue dotted line in Fig. 4(e)]. Thus, the recombination increases throughout the interface, with corresponding loss in JSC and FF [see the blue dotted line in Fig. 4(f)]. In Fig. 5, we explore the effect of electrode spacing [(Selec in Fig. 2(a)] on the device performance. The height of the electrodes is kept fixed (Helec = 40 nm). The figure clearly shows that the benefit of inserted electrode in terms of carrier transport is minimal for higher spacing (Selec > 200 nm). However, the optical absorption enhancement is possible with higher electrode spacing, as recently demonstrated with various photonic crystal structures [22] [28]. Since the goal of this study is to understand and optimize the NEs for the transport enhancement, we have assumed constant absorption in these simulations, and hence, JSC remains flat with electrode spacing in Fig. 5(b). In the later sections, we will use the closely spaced electrode structure to explore its effect on optical absorption. 2) Bulk Heterojunction Cell: BHJ-based OPV cells have complex intermixed morphology, as shown in the schematic of Fig. 6(a). However, it is easy to see (and we have confirmed it quantitatively in our previous work [41], [42]) that the key Fig. 6. Effect of the NEs on the performance of a BHJ-OPV cell. (a) NE in a typical BHJ cell, which can be divided into four simple cell structures (B0, B1, B2, and B3). Various solar cell performance matrices are plotted as a function of electrode height for B1 and B2. (b) Efficiency, (c) short-circuit current, (d) open-circuit voltage, and (e) FF. The electrode dimensions are S e le c = 100 nm and W e le c = 10 nm. The thicknesses of the active layer are 100 nm. The JS C value is higher than that in the PHJ case, because we have assumed all the photogenerated excitons are collected by the BHJ structure with average D/A domain width 50 nm (=2L e x ). solar cell parameters (such as JSC and VOC ) of the complex BHJ cells can be accurately analyzed with the equivalent regularized geometric transform. Since the goal of this study is to formulate the general design guidelines, we focus our analysis on four representative sections of the morphology [shown by the dashed lines in Fig. 6(a)]. The four representative sections are as follows: B0 is the ordered vertical junction cell with usual planar electrodes; B1 represents the circumstances when inserted electrode (ITO) remains exclusively in the donor; B2 represents the instances where the inserted electrode remains in the acceptor; and B3 indicates the situations when the inserted electrode crosses the D A interface. The instances that are represented by B3 are equivalent to the PHJ devices, and the conclusions that

8 This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. RAY et al.: NANOSTRUCTURED ELECTRODES FOR ORGANIC SOLAR CELLS: ANALYSIS AND DESIGN FUNDAMENTALS 7 Fig. 7. Carrier concentration and recombination dynamics in the ordered BHJ-OPV cells with inserted electrodes under the short-circuit condition. (a) (c) 2-D carrier profile within the active layer is shown for three different electrode heights (B0, B1, and B2). Carrier profile in the donor represents only holes, and in the acceptor, it represents only electrons. The arrows in the diagram represent the electric field distribution. (d) Current voltage characteristics corresponding to the three cells. (e) Electron (n) and hole (p) density at the interface of D A region is plotted for the three cell structures, and the corresponding position-dependent recombination rates are shown in (f). The donor/acceptor domain width is assumed to be equal to twice the exciton diffusion length ( 50 nm). are drawn in the previous section apply. For the other two cases (B1 and B2), we plot the performance matrices as a function of electrode height in Fig. 6(b) (e). The figure clearly shows that if the electrode remains in the donor (red dashed line), then there will be significant improvement in FF (and slight improvement in JSC ) and hence in performance of the BHJ cell. On the contrary, if the electrodes are in the acceptor region (blue dotted line), then JSC degrades significantly, while the other parameters (FF and VOC ) remain essentially unchanged. Let us emphasize that the electrodes are conformally coated with minority carrier blocking layer. Therefore, any performance loss should not be (mistakenly) attributed to minority carrier recombination in the electrode surface. In the next paragraph, we show that the performance loss arises from the nontrivial remote electrostatic effect by the inserted electrodes, which causes higher carrier recombination at the DA interface. In Fig. 7(a) (c), we illustrate the change in carrier distribution inside the cell depending on the position of the inserted electrodes. Fig. 7(a) represents the ordered (vertical junction) cell with planar electrode geometry, and Fig. 7(b) and (c) show the carrier redistributions in the presence of electrode representing the two cases (B1 and B2) discussed in Fig. 6(a). The corresponding I V characteristics are shown in Fig. 7(d). The I V characteristics show performance improvement for the inserted electrode in donor (red dashed line) but degradation in performance when the electrodes reside in the acceptor (blue dotted line). This efficiency variation can be interpreted by the carrier distribution plots that are shown in Fig. 7(a) (c). In the case of cell B1, inserted electrodes attract the holes from the interface [see the arrows in Fig. 7(b)] and push the electrons away from the interface. Thus, the carrier concentrations at the vertical interface are reduced [see the red dashed line in Fig. 7(e)], leading to lower recombination loss [see the red dashed line in Fig. 7(f)] and improved charge collection (high FF) and overall higher efficiency. In the case of cell B2, the direction of horizontal electric field is reversed [see the arrows in Fig. 7(c)], which pushes the electrons (in the acceptor material) toward the interface as well as attracts the holes (from the donor material) toward the interface, leading to significant enhancement of recombination at the vertical interface [see the blue dotted line in Fig. 7(f)]. This recombination loss is reflected in dramatic reduction in JSC and FF [see the blue line in Fig. 7(d)]. In a random BHJ morphology with a 1:1 D A volume ratio, the inserted electrode will be in pure donor, or in pure acceptor, or donor acceptor stack roughly in equal proportion, i.e., 1/3 of the time. Thus, this analysis of the idealized vertical junction cells indicates that in the random BHJ morphology, projected electrodes will improve the device FF if placed (statistically) in the donor region, but at the same time, there will be some degradation in the JSC value when the electrodes are in the acceptor region. As a result, we conclude that there will be no

9 This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 8 IEEE JOURNAL OF PHOTOVOLTAICS Fig. 8. Effect of the NEs on the performance of a fin morphology-based BHJ-OPV cell. (a) Fin morphology with ITO inserted in the donor phase. The carrier distribution (under the short-circuit condition) inside the cell is plotted with color coding in (b) H e le c = 0 and (c) H e le c > H D. Carrier profile in the donor represents only holes, and in the acceptor, it represents only electrons. Various solar cell performance matrices are plotted as a function of electrode height in (d) (g). (d) Efficiency, (e) short-circuit current, (f) open-circuit voltage, and (g) FF. The electrode dimensions are S e le c = 100 nm and W e le c = 10 nm. The thicknesses of the active layer are 100 nm, with H A =H D = 25 nm. significant improvement in the overall efficiency of the BHJ cells with this concept of NEs. 3) Optimum Bulk Heterojunction Morphology: In our previous publication [39], we have explored the theoretical optimum morphology, which resembles a fin-like structure, see Fig. 8(a). We found that the performance gain with such morphology is not very significant compared with the (optimized) random BHJ structure. However, the NEs offer additional transport advantage for the fin morphology which is not accessible to the random BHJ cells as discussed in the previous section. Therefore, in this section, we explore the implication of the NEs for fin morphology. In Fig. 8(d) (g), we summarize the expected performance gains with the various heights of the inserted electrodes in a finlike morphology. As expected from our previous discussion, the inserted electrode (ITO in donor) improves FF significantly. Remarkably and counterintuitively, however, Fig. 8(d) also shows a reduction of efficiency when Helec > HD (the donor offset), even though the electrode is still immersed exclusively in the donor material. The reason for such reduction in JSC is explained in Fig. 8(c), where we show pile up of holes close to the D A interface at the donor offset (HD ). This pile up of hole density causes recombination loss at JSC, which is analogous to the situation that inserted electrode crossing the D A interface discussed in the PHJ cell. Thus, even though the electrode is still in the donor material, its remote electrostatic effect in the neighboring junction leads to performance degradation. Thus, the design of fin morphology with projected electrodes should use an asymmetric morphology (HD > HA ) with the electrode height, Helec < HD. B. Effect of the Nanostructured Electrodes on the Optical Absorption The analysis of the concept of projected electrodes in the previous sections was focused on carrier transport assuming optical absorption unaltered. However, electrode insertion in the active material not only alters the electric field distribution, but also changes the optical field and, hence, photon absorption. In this section, we analyze the effect of electrode insertion on the optical absorption in the active layer of OPV cells. Organic materials have very high absorption coefficient, and hence, almost all the photons (with sufficient energy) are absorbed in a film of nm thickness. However, the bandedge absorption can still be improved with proper nanostructuring of the electrodes as reported by various groups in recent years [22] [28]. However, the electrode spacing/periodicity in such optimized photonic crystal geometry is generally large, and hence it does not impact the transport property of the cell significantly (see Fig. 5). Since the goal of this paper is to evaluate the potential improvement of the charge transport property, we utilize the closely spaced electrode structure (Selec 100 nm) to explore its effect on photon absorption instead of optimizing the photonic crystal dimensions for absorption enhancement. In Fig. 9(a), we plot the optical field distributions inside a PHJ cell under AM1.5 illumination for the P3HT:PCBM material system. In Fig. 9(b), we show the photon absorption profile along the horizontal line [shown as a dashed line in Fig. 9(a)] for two cases: without inserted electrode (solid line) and with inserted electrode (dashed line). We find that even though the optical field (hence photon absorption) enhances in the close proximity of

10 This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. RAY et al.: NANOSTRUCTURED ELECTRODES FOR ORGANIC SOLAR CELLS: ANALYSIS AND DESIGN FUNDAMENTALS 9 For more quantitative analysis of the effects of the NEs on optical performance, we express the integrated absorption in the active layer in terms of the maximum possible short-circuit current as follows: A(λ)I0 (λ) dλ. (1) JSC(m ax) = q hc/λ Fig. 9. Effect of the NEs on the absorption profile (or optical field distribution) in the OPV cells. (a) PHJ cell with inserted (ITO) electrodes. The 2-D absorption profile is shown by color coding. (b) 1-D cut of the absorption profile in the four different layers: ITO, donor, acceptor, and Al. (c) Absorption profile in D A blend with the inserted electrodes. (d) Photon absorption in the various layers of the BHJ cell. Solid lines represent the results without NEs, and dashed lines represent the results with the NEs. Fig. 10. Effect of NEs on optical absorption of 1:1 P3HT:PCBM blend. (a) Absorption spectrum in a BHJ cell for three different electrode geometries. Solid line: optimized planar electrode (PE) ((L IT O = 100 nm; L b le n d = 100 nm; L A l = 100 nm); dotted line: un-optimized PE (L IT O = 100 nm, L b le n d = 140 nm, L A l = 100 nm) and dashed line: comb-like NE (L IT O = 100 nm, L b le n d = 100 nm, L A l = 100 nm, H e le c = 50 nm, S e le c = 100 nm and W e le c = 20 nm). (b) Total photon absorption (expressed as maximum JS C )) in D-A blend as a function of active layer thickness. The solid blue line is for planner electrode (PE), the black dashed line represents NE with ITO, and the red dotted line represents NE with Al. Electrode heights are assumed half of the film thicknes. the inserted electrode, but the field remains relatively unaltered in rest of the active layer. Similar analysis for BHJ cells in Fig. 9(c) and (d) also leads to the same conclusion. Next, we explore the effect of the NEs on the absorption spectra (A(λ)) of 1:1 P3HT: PCBM blend in Fig. 10(a). Note that we first optimize various layer thicknesses for maximum absorption in the planar electrode-based typical BHJ-OPV cell [dimensions given in the caption of Fig. 10(a)] and then compare its absorption property in the presence of inserted electrodes. The figure also shows that even though the inserted electrodes reduce the active volume by 10%, the overall absorption remains relatively unaltered. If the layer thicknesses are not properly optimized, even a thicker active layer may absorb less [see the dotted line in Fig. 10(a)]. The NEs in such unoptimized cells will apparently show higher optical gain [see Fig. 10(b)]. Here, A (λ) is the absorption spectrum in the blend calculated by the procedure described in the model system, and I0 (λ) is the AM1.5 spectrum. q, h, and c are electron charge, Planck s constant, and speed of light, respectively. We calculate JSC (max) for various thicknesses of the active layer (keeping the thickness of the other layers fixed) and plot them in Fig. 10(b). In this figure, the solid line represents the results that are obtained for usual planar electrodes with different active layer thicknesses. The dashed line (or dotted line) represents the total absorption in the presence of inserted ITO (or back electrode Al) electrodes. Electrode heights are assumed to be half of the film thickness. The plot shows that the inserted electrodes can increase (slightly) or decrease (slightly) the optical absorption, depending on the thickness of the active layer. For example, in Fig. 10(b) higher absorption is observed with the NEs for 150 nm film thickness, while slightly degrading effect in absorption is observed for 100 nm film thickness. Thus, the key point here is the fact that even though the inserted electrodes displace the absorbing volume (by 10% in the simulation), the integrated optical absorption still remains almost unchanged due to the field enhancement closer to the electrodes. If one nano-structures the metallic electrode instead of the ITO, the absorption of the TE waves is diminished. Thus, nanostructured metallic electrodes will have much lower absorption for a given active layer thickness compared to that of ITO electrode [see Fig. 10(b)]. Therefore, we must design the projected electrode structure with optically transparent electrodes (ITO). V. DESIGN FUNDAMENTALS AND CONCLUSION The optoelectronic analysis of the electrode insertion concept in OPV shows that the design space for optical enhancement and transport enhancement is not necessarily the same. For the significant enhancement of the charge transport, inserted electrodes need to be very closely spaced (<100 nm), which would not represent a photonic crystal design. Moreover, the transport analysis of the effect of projected electrode shows that electrode insertion significantly enhances the interfacial recombination in the BHJ structure. Regardless, we find that for the PHJ structure, an inserted electrode significantly enhances the fill factor of the device. Thus, the ideal design with the projected electrode should involve the interdigitized fin-like morphology embedded with a projected electrode, which exploits the advantages of BHJ morphology as well as the better transport property of the inserted electrode. The essential physics of the electrode insertion (explored in the previous two sections) can be summarized as follows. 1) We find that for the efficient extraction of the charged carriers from the low-mobility organic materials, the electrode dimensions need to be designed quite differently from the

11 This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 10 IEEE JOURNAL OF PHOTOVOLTAICS TABLE II SIMULATION PARAMETERS photonic crystal design which improves optical absorption. We find that for better charge collection, the spacing between the electrodes needs to be very close ( 100 nm), and electrode heights need to be approximately half the film thickness. 2) Our analysis shows significant recombination loss whenever the projected electrode crosses the D A interface. This restricts the electrode design exclusively in a single material. Since hole mobility in the donor polymer is low, it is evident that the inserted electrode should be designed to collect the holes in a donor polymer. This design consideration can be easily implemented for PHJ cells, but in BHJ cells, additional care (such as fin morphology, etc.) needs to be taken. 3) The inserted electrodes enhance the optical absorption in the proximity of the electrode surface. However, this local enhancement is compensated by the active volume loss due to the finite volume of the electrodes. Hence, we find that the overall integrated absorption remains relatively unaltered with inserted electrodes. However, insertion of a metal electrode can degrade the absorption. Thus, nanostructuring of the electrode needs to be done for the optically transparent electrodes (e.g., ITO) as the metallic electrode degrades absorption of TE waves. REFERENCES [1] S. E. Shaheen, C. J. Brabec, N. S. Sariciftci, F. Padinger, T. Fromherz, and J. C. Hummelen, 2.5% efficient organic plastic solar cells, Appl. Phys. Lett., vol. 78, pp , Feb [2] F. Padinger, R. S. Rittberger, and N. S. Sariciftci, Effects of postproduction treatment on plastic solar cells, Adv. Funct. Mater.,vol.13,pp.85 88, [3] W. Ma, C. Yang, X. Gong, K. Lee, and A. J. Heeger, Thermally stable, efficient polymer solar cells with nanoscale control of the interpenetrating network morphology, Adv. Funct. Mater., vol. 15, pp , Oct [4] J. Peet, J. Y. Kim, N. E. Coates, W. L. Ma, D. Moses, A. J. Heeger, and G. C. Bazan, Efficiency enhancement in low-bandgap polymer solar cells by processing with alkane dithiols, Nat. Mater., vol. 6, pp , Jul [5] Y. Liang, Z. Xu, J. Xia, S.-T. Tsai, Y. Wu, G. Li, C. Ray, and L. Yu, For the bright future Bulk heterojunction polymer solar cells with power conversion efficiency of 7.4%, Adv. Mater., vol. 22, pp. E135 E138, [6] M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, Solar cell efficiency tables (version 39), Prog. Photovol.: Res. Appl., vol. 20, pp , [7] M. Reyes-Reyes, K. Kim, and D. L. Carroll, High-efficiency photovoltaic devices based on annealed poly(3-hexylthiophene) and 1-(3- methoxycarbonyl)-propyl-1-phenyl-(6,6)c[sub 61] blends, Appl. Phys. Lett., vol. 87, pp , [8] G. Li, V. Shrotriya, J. S. Huang, Y. Yao, T. Moriarty, K. Emery, and Y. Yang, High-efficiency solution processable polymer photovoltaic cells by self-organization of polymer blends, Nat. Mater., vol. 4, pp , [9] D. Gupta, S. Mukhopadhyay, and K. S. Narayan, Fill factor in organic solar cells, Sol. Energy Mater. Sol. Cells, vol. 94, pp , Aug [10] D. Gupta, M. Bag, and K. S. Narayan, Correlating reduced fill factor in polymer solar cells to contact effects, Appl. Phys. Lett., vol. 92, pp , [11] R. Mauer, I. A. Howard, and F. Laquai, Effect of nongeminate recombination on fill factor in polythiophene/methanofullerene organic solar cells, J. Phys. Chem. Lett., vol. 1, pp , Dec [12] W. Tress, A. Petrich, M. Hummert, M. Hein, K. Leo, and M. Riede, Imbalanced mobilities causing S-shaped IV curves in planar heterojunction

12 This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. RAY et al.: NANOSTRUCTURED ELECTRODES FOR ORGANIC SOLAR CELLS: ANALYSIS AND DESIGN FUNDAMENTALS 11 organic solar cells, Appl. Phys. Lett., vol. 98, pp , Feb [13] G. Garcia-Belmonte, A. Munar, E. M. Barea, J. Bisquert, I. Ugarte, and R. Pacios, Charge carrier mobility and lifetime of organic bulk heterojunctions analyzed by impedance spectroscopy, Org. Electron., vol. 9, pp , Oct [14] C. Tanase, E. J. Meijer, P. W. M. Blom, and D. M. de Leeuw, Unification of the hole transport in polymeric field-effect transistors and light-emitting diodes, Phys. Rev. Lett., vol. 91, pp , Nov [15] C.-W. Chu, H. Yang, W.-J. Hou, J. Huang, G. Li, and Y. Yang, Control of the nanoscale crystallinity and phase separation in polymer solar cells, Appl. Phys. Lett., vol. 92, pp , Mar [16] A. J. Miller, R. A. Hatton, and S. R. P. Silva, Interpenetrating multiwall carbon nanotube electrodes for organic solar cells, Appl. Phys. Lett., vol. 89, pp , [17] C. Nam, Nanostructured electrodes for organic bulk heterojunction solar cells: Model study using carbon nanotube dispersed polythiophenefullerene blend devices, J. Appl. Phys., vol. 110,pp , [18] C.-H. Kim, S.-H. Cha, S. C. Kim, M. Song, J. Lee, W. S. Shin, S.-J. Moon, J. H. Bahng, N. A. Kotov, and S.-H. Jin, Silver nanowire embedded in P3HT:PCBM for high-efficiency hybrid photovoltaic device applications, ACS Nano, vol. 5, pp , [19] M.-H. Hsu, P. Yu, J.-H. Huang, C.-H. Chang, C.-W. Wu, Y.-C. Cheng, and C.-W. Chu, Balanced carrier transport in organic solar cells employing embedded indium-tin-oxide nanoelectrodes, Appl. Phys. Lett., vol. 98, pp , Feb [20] J. E. Allen and C. T. Black, Improved power conversion efficiency in bulk heterojunction organic solar cells with radial electron contacts, ACS Nano, vol. 5, pp , [21] G. I. Koleilat, X. Wang, A. J. Labelle, A. H. Ip, G. H. Carey, A. Fischer, L. Levina, L. Brzozowski, and E. H. Sargent, A donor-supply electrode (DSE) for colloidal quantum dot photovoltaics, Nano Lett., vol. 11, pp , [22] K. S. Nalwa, J.-M. Park, K.-M. Ho, and S. Chaudhary, On realizing higher efficiency polymer solar cells using a textured substrate platform, Adv. Mater., vol. 23, pp , [23] M. Niggemann, M. Glatthaar, A. Gombert, A. Hinsch, and V. Wittwer, Diffraction gratings and buried nano-electrodes Architectures for organic solar cells, Thin Solid Films, vol , pp , Mar [24] D.-H. Ko, J. R. Tumbleston, L. Zhang, S. Williams, J. M. DeSimone, R. Lopez, and E. T. Samulski, Photonic crystal geometry for organic solar cells, Nano Lett., vol. 9, pp , [25] S.-J. Tsai, M. Ballarotto, D. B. Romero, W. N. Herman, H.-C. Kan, and R. J. Phaneuf, Effect of gold nanopillar arrays on the absorption spectrum of a bulk heterojunction organic solar cell, Opt. Express, vol. 18, pp. A528 A535, Nov [26] W. Bai, Q. Gan, G. Song, L. Chen, Z. Kafafi, and F. Bartoli, Broadband short-range surface plasmon structures for absorption enhancement in organic photovoltaics, Opt. Express, vol.18,pp.a620 A630,Nov [27] J. R. Tumbleston, D.-H. Ko, E. T. Samulski, and R. Lopez, Electrophotonic enhancement of bulk heterojunction organic solar cells through photonic crystal photoactive layer, Appl. Phys. Lett., vol. 94, pp , Jan [28] C. Min, J. Li, G. Veronis, J.-Y. Lee, S. Fan, and P. Peumans, Enhancement of optical absorption in thin-film organic solar cells through the excitation of plasmonic modes in metallic gratings, Appl. Phys. Lett., vol. 96, pp , Mar [29] Z. Fan, H. Razavi, J. Do, A. Moriwaki, O. Ergen, Y.-L. Chueh, P. W. Leu, J. C. Ho, T. Takahashi, L. A. Reichertz, S. Neale, K. Yu, M. Wu, J. W. Ager, and A. Javey, Three-dimensional nanopillar-array photovoltaics on lowcost and flexible substrates, Nat. Mater., vol. 8, pp , [30] D. Duché, L. Escoubas, J.-J. Simon, P. Torchio, W. Vervisch, and F. Flory, Slow bloch modes for enhancing the absorption of light in thin films for photovoltaic cells, Appl. Phys. Lett., vol. 92, pp , May [31] C. W. Tang, Two-layer organic photovoltaic cell, Appl. Phys. Lett., vol. 48, pp , Jan [32] G. Yu, J. Gao, J. C. Hummelen, F. Wudl, and A. J. Heeger, Polymer photovoltaic cells: Enhanced efficiencies via a network of internal donor acceptor heterojunctions, Science, vol. 270, pp , Dec [33] R. R. Lunt, N. C. Giebink, A. A. Belak, J. B. Benziger, and S. R. Forrest, Exciton diffusion lengths of organic semiconductor thin films measured by spectrally resolved photoluminescence quenching, J. Appl. Phys., vol. 105, pp , Mar [34] N. C. Giebink, G. P. Wiederrecht, M. R. Wasielewski, and S. R. Forrest, Ideal diode equation for organic heterojunctions. I. Derivation and application, Phys. Rev. B, vol. 82, pp , Oct [35] L. J. Koster, V. D. Mihailetchi, and P. W. Blom, Bimolecular recombination in polymer/fullerene bulk heterojunction solar cells, Appl. Phys. Lett., vol. 88, pp , [36] H. Hoppe, N. S. Sariciftci, and D. Meissner, Optical constants of conjugated polymer/fullerene based bulk-heterojunction organic solar cells, Mol. Cryst. Liq. Cryst., vol. 385, pp , Oct [37] L. A. A. Pettersson, L. S. Roman, and O. Inganas, Modeling photocurrent action spectra of photovoltaic devices based on organic thin films, J. Appl. Phys., pp , [38] Rf module microwave optical antenna simulation software, Available: [39] B. Ray and M. A. Alam, Random vs regularized OPV: Limits of performance gain of organic bulk heterojunction solar cells by morphology engineering, Sol. Energy Mater. Sol. Cells, vol. 99, pp , Apr [40] B. Ray, P. R. Nair, and M. A. Alam, Annealing dependent performance of organic bulk-heterojunction solar cells: A theoretical perspective, Sol. Energy Mater. Sol. Cells, vol. 95, pp , Dec [41] B. Ray, M. S. Lundstrom, and M. A. Alam, Can morphology tailoring improve the open circuit voltage of organic solar cells? Appl. Phys. Lett., vol. 100, pp , Jan [42] B. Ray and M. A. Alam, A compact physical model for morphology induced intrinsic degradation of organic bulk heterojunction solar cell, Appl. Phys. Lett., vol. 99, pp , Jul [43] R. A. Street, S. Cowan, and A. J. Heeger, Experimental test for geminate recombination applied to organic solar cells, Phys. Rev. B, vol. 82, pp , [44] R. A. Street, M. Schoendorf, A. Roy, and J. H. Lee, Interface state recombination in organic solar cells, Phys. Rev. B, vol. 81, pp , May [45] F. C. Jamieson, T. Agostinelli, H. Azimi, J. Nelson, and J. R. Durrant, Field-independent charge photogeneration in PCPDTBT/PC70BM solar cells, J. Phys. Chem. Lett., vol. 1, pp , [46] A. A. Bakulin, A. Rao, V. G. Pavelyev, P. H. M. van Loosdrecht, M. S. Pshenichnikov, D. Niedzialek, J. Cornil, D. Beljonne, and R. H. Friend, The role of driving energy and delocalized states for charge separation in organic semiconductors, Science,vol.335,pp , Mar [47] S. R. Cowan, N. Banerji, W. L. Leong, and A. J. Heeger, Charge formation, recombination, and sweep-out dynamics in organic solar cells, Adv. Funct. Mater., vol. 22, pp , Mar [48] L. J. A. Koster, S. E. Shaheen, and J. C. Hummelen, Pathways to a new efficiency regime for organic solar cells, Adv. Energy Mater., vol. 2, pp , [49] B. Ray and M. A. Alam, Achieving fill factor above 80% in organic solar cells by charged interface, IEEE J. Photovoltaics, vol. PP, 2012, to be published, DOI: /JPHOTOV [50] Y. Kim, S.A. Choulis, J. Nelson, D.D.C. Bradley, S. Cook, and J.R. Durrant, Device annealing effect in organic solar cells with blends of regioregular poly(3-hexylthiophene) and soluble fullerene, Appl. Phys. Lett.,vol. 86, pp , Biswajit Ray (S 12) received the B.Tech. degree in electrical and electronics engineering from the National Institute of Technology, Trichy, India, and the M.Sc.(Eng.) degree from the Indian Institute of Science, Bangalore, India, in 2006 and 2008, respectively. Since 2008, he has been working toward the Ph.D. degree with the School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN. His research interests include semiconductor device physics and electronic transport in organic and amorphous materials. Mr. Ray received the Technoinventor Award in 2009 from the Indian Semiconductor Association for his master s thesis. He also received the Best Poster Award in the area of Organic Photovoltaics at the 38th IEEE Photovoltaic Specialist Conference, in 2012.

13 This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 12 IEEE JOURNAL OF PHOTOVOLTAICS Mohammad Ryyan Khan received the B.Sc. degree in electrical and electronic engineering from the Bangladesh University of Engineering and Technology, Dhaka, Bangladesh, in Since Fall 2009, he has been working toward the Ph.D. degree with the Alam CEED Group, School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN. His work focuses on optical designing and modeling of solar cells. Charles Black (SM 05) received the Ph.D. degree in physics from Harvard University, Cambridge, MA, in He is a Scientist and Group Leader for Electronic Nanomaterials with the Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY, where he researches applications for nanostructured materials in photovoltaic devices. From 1996 to 2006, he was a Research Staff Member with the IBM Thomas J. Watson Research Center, Yorktown Heights, NY. His research at IBM involved using self-assembly to address device fabrication challenges in high-performance semiconductor electronics. Dr. Black is a Fellow of the American Physical Society. Muhammad Ashraful Alam (M 96 SM 01 F 06) received the Master s and Doctoral degrees from Clarkson University, NY, and Purdue University, West Lafayette, IN, in 1991 and 1995, respectively. He is a Professor of electrical and computer engineering and a University Faculty Scholar with Purdue University, where his research and teaching focus on physics, simulation, characterization, and technology of classical and emerging electronic devices. From 1995 to 2001, he was with Bell Laboratories, Murray Hill, NJ, as a Technical Staff Member with the Silicon ULSI Research Department. From 2001 to 2003, he was a Distinguished Technical Staff Member with Agere Systems, Murray Hill, NJ. During his time in industry, he made important contributions to reliability physics of electronic devices, metalorganic chemical vapor deposition crystal growth for optoelectronic integrated circuits and performance limits of directly modulated semiconductor lasers. After joining Purdue University in 2004, his research has broadened to include nanocomposite flexible electronics, organic solar cells, and performance limits of nanobiosensors. He has published more than 150 papers in international journals and has presented many invited and contributed talks at international conferences. Dr. Alam is a Fellow of the American Physical Society and the American Association for the Advancement of Science. He received the 2006 IEEE Kiyo Tomiyasu Award for contributions to device technology for communication systems.