Nanostructured Electrodes for Organic Solar Cells: Analysis and Design Fundamentals

318 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 3, NO. 1, JANUARY 2013

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 ab-sorption and charge collection in photovoltaic (PV) devices. Tra-ditionally, the electrodes have been designed exclusively for higheroptical absorption. Such an optical design of the electrodes doesnot necessarily ensure better charge collection. Since the efficiencyof organic PV (OPV) devices is hindered by the low carrier mobil-ity of the organic semiconductors, the charge collection propertyof the NEs provides an interesting design alternative. The goal ofthis paper is the formulation of the essential design rules for NEsto improve charge collection in the low-mobility organic materi-als. We use detailed optoelectronic device simulation to explorethe physics of NEs embedded in the organic semiconductors andquantify its effect on the performance gain of organic solar cells.Our analysis suggests that an optimum codesign of electrodes andmorphology is essential for significant performance improvement(mainly through fill factor) in OPV cells.

Index Terms—Bulk heterojunction (BHJ), fill factor (FF), mor-phology, nanostructured electrodes (NEs), organic photovoltaic(OPV) cell.

I. INTRODUCTION

ORGANIC photovoltaics (OPV) is a relatively new tech-nology that promises low-cost solar energy conversion

and the possibility of novel PV applications (e.g., portable cells,building-integrated PV). Successful commercialization of thistechnology, however, will require significant improvement inefficiency and lifetime. The power conversion efficiency η ofany solar cell is determined by three parameters: short-circuitcurrent JSC , open-circuit voltage VOC , and fill factor FF, i.e.,η = JSCVOCFF/Pin , where Pin is the input power from the sun.JSC and VOC are mainly dependent on the energy band profile ofthe absorbing materials. FF, on the other hand, is related to the

Manuscript received July 24, 2012; revised September 5, 2012; acceptedSeptember 13, 2012. Date of publication November 12, 2012; date of currentversion December 19, 2012. This work was supported in part by the Center forRe-Defining Photovoltaic Efficiency Through Molecule Scale Control, an En-ergy Frontier Research Center funded by the U.S. Department of Energy Officeof Science, and in part by the Office of Basic Energy Sciences under AwardDE-SC0001085. The computational resources for this work were provided bythe Network of Computational Nanotechnology under Award EEC-0228390from the National Science Foundation.

B. Ray, M. R. Khan, and M. A. Alam are with the School of Electri-cal and Computer Engineering, Purdue University, West Lafayette, IN 47906USA (e-mail: [email protected]; [email protected]; [email protected]).

C. Black is with the Center for Functional Nanomaterials, Brookhaven Na-tional Laboratory, Upton, NY 11973 USA (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JPHOTOV.2012.2220529

efficiency of charge extraction from the cell and depends on themobility of charge carriers and their recombination rates. Overthe past few years [1]–[8], there have been several breakthroughsin developing new absorbing polymers [also called donors (D)]with lower band gap (hence higher JSC ) and improved bandalignment with acceptor (A) molecules (hence higher VOC ).These improvements in JSC and VOC have raised the cell effi-ciency continually, with the current record being more than 10%[48]. Despite material innovations, however, the FF of OPV cellsremains stagnant at (0.6–0.7) [1]–[10], much lower than the in-organic counterparts (∼0.85) [6]. The OPV efficiency cannotreach its theoretical limit unless FF is improved significantly.

Fill factor of a solar cell reflects the ability of the photo-generated charge carriers to be collected by the respective con-tacts. Thus, it is defined by the carrier mobility and the re-combination properties of the active material [11], [12]. Mostorganic semiconductors have very low mobility (e.g., 10−5–10−3 cm2 ·V−1 ·s−1) [13], [14], which makes the charge extrac-tion inefficient, especially under the operating (or maximumpower point) bias condition when the internal field is low. Var-ious approaches have been adopted to improve the carrier mo-bility in the OPV materials. One approach involves increasingthe nanoscale crystallinity and molecular packing of the poly-mer film by controlling the annealing conditions [15]. Anotherapproach involves percolation-doping [16]–[18] of the polymerfilm by carbon nanotubes or conducting nanowires. While bothapproaches improve the carrier mobility in the organic films,the improvement is often marginal. Indeed, the requirement ofsolution processing precludes many film growth techniques thatmay otherwise improve the material mobility significantly.

Recently [19]–[21], there have been several efforts for the ef-ficient charge collection from the low-mobility semiconductingmaterials by the insertion of electrodes in the active layer. Hsuet al. [19] have shown that embedding the ITO nanoelectrodeinside the organic material can “balance” the carrier transportby increasing the effective hole mobility, which is the slowercarrier in a typical OPV cell. Similarly, Allen et al. [20] demon-strated improved carrier collection by inserting the electrode inthe active materials for radial charge collection. However, theperformance gain in both approaches was low, because the elec-trode design was not optimized. Similarly, nanostructuring of thefront/back contacts [22]–[29] has also been used to enhance pho-ton absorption in organic solar cells (photonic crystals [22]–[25]and plasmonic structures [26], [28]). For example, Niggemannet al. [23] have shown increased absorptance by embeddingcomb-like array of Al electrodes in the photoactive polymerblend. Similarly, Ko et al. [24] have shown that by embedding

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RAY et al.: NANOSTRUCTURED ELECTRODES FOR ORGANIC SOLAR CELLS: ANALYSIS AND DESIGN FUNDAMENTALS 319

a photonic crystal geometry made of nanocrystalline ZnO (alsoacts as a cathode for electron collection), the band-edge absorp-tion in OPV can be enhanced significantly. These recent studiesimply that optimizing the design of nanostructured electrodes(NEs) may improve OPV efficiency by simultaneously increas-ing light absorption (high JSC ) and by efficient charge collection(improved FF).

The optimization of NEs for the high-efficiency OPV cells isnot straightforward: The inserted electrodes not only alter theoptical field (hence photogeneration), but also redistribute theelectrical field that affects charge collection. Most of the the-oretical works [27], [30] regarding the optimized design of theelectrodes have focused exclusively on the optical absorption,and hence, electrode dimensions have been tailored as a functionof light wavelength. However, for low-mobility organic mate-rials, the potential of efficient charge collection by NE offersan intriguing design possibility. Although several experimentalresults are available, unfortunately there is no theoretical workthat explores the charge transport or recombination dynamics inthe complex organic materials in the presence of inserted elec-trodes, and hence, NEs have never been optimized to improvecharge collection in OPV cells. That is why, we believe, mostof the reported works have failed to demonstrate simultaneousimprovement in all the three solar cell performance matrices(JSC , VOC , and FF) after the insertion of electrodes.

The objective of this paper is to explore the fundamentalphysics of electrode insertion in the organic semiconductors inorder to formulate the general design principles for this con-cept. With this goal, we use a detailed and systematic opto-electronic 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 ex-traction length and hence do improve the FF of the OPV cell.Second, the field distribution (and carrier density) inside thecell is altered by the insertion of NEs in such a manner that itcan either improve or degrade the performance based on the de-tails of active-layer morphology. In general, performance gainis achieved if the inserted electrodes exclusively remain in asingle material, typically the donor which has lower mobility.Thus, a planar heterojunction (PHJ) [see Fig. 1(a)] structureis more suited than BHJ [see Fig. 1(c)] morphology for theimplementation of this concept. Third, the design criterion forabsorption (mainly band-edge) enhancement not necessarily en-sures better charge transport and vice versa. In other words,the transport-oriented electrode design is different from thephotonic crystal design. However, we find that electrode de-sign for the better transport also provides optical enhancementwhich compensates the loss of active volume due to electrodeinsertion.

This paper is organized as follows. We first describe the ba-sic device structure of an OPV cell and its working principle.Next, the optoelectronic modeling approach is presented. Theoptoelectronic simulation framework is then applied to study theeffect of electrode insertion on the short-circuit current, open-circuit voltage, FF, etc., for various OPV morphologies. Finally,we discuss the essential design rules for the NEs in order toachieve 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) En-ergy band diagram of a PHJ cell under the short-circuit condition. Thevarious current fluxes are shown by the arrows. The current componentsare exciton diffusion flux Jex , generation-dependent recombination cur-rent Jrec , dark or injection current Jdark , and the photocurrent Jph .(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 assumeμe = μh = μ.

II. DEVICE STRUCTURE AND WORKING PRINCIPLE OF

ORGANIC PHOTOVOLTAIC

The light-absorbing layer of an organic solar cell consists oftwo organic semiconductors, which are called donor (D) andacceptor (A). In the PHJ [31] type OPV cells, these two D–Asemiconductors are deposited (thermal evaporation) on top ofeach other [see Fig. 1(a)]. However, the more commonly usedstructure for the OPV devices is the BHJ [32] [BHJ, Fig. 1(c)],which consists of randomly intermixed donor–acceptor materi-als that are fabricated by spin-coating. The operation of an OPVcell has four sequential steps [numbered in Fig. 1(a)]. First, whenthe photon transmits through the transparent glass substrate andthe electrode (TCO), it is absorbed in the active layer gener-ating a strongly bound electron–hole pair called exciton. Exci-tons, being charge neutral, diffuse in the active material (step 2)until they encounter an interface, where they form a chargetransfer (CT) state (step 3) with the electron in the acceptor ma-terial and the hole in the donor. However, if excitons cannot findthe interface within the diffusion length (Lex ≈ (5−10) nm)[33], they are irreversibly lost to self-recombination. Thus,the BHJ morphology ensures that regardless of the point ofphotoexcitation, all the excitons are collected by the large in-terfacial area. Finally, the CT states dissociate into free carriers(electrons and holes) which are transported toward the respec-tive electrodes by the built in field (step 4).


Ideally, the electron-carrying acceptor material should be con-tacted exclusively by the cathode (see Al in Fig. 1). Likewise, thehole-carrying donor material should be in contact only with theanode (ITO/PEDOT). If the cathode (or anode) directly contactsthe donor (or acceptor), it would act as interface recombinationcenters. Thus, interlayer, minority-carrier blocking materials areused along with the electrodes (e.g., LiF on Al, and PEDOT: PSSon ITO) to minimize the contact recombination loss, especiallyin BHJ devices where both the D/A materials touch both theelectrodes. The interlayer material selectively allows only themajority carrier (e or h) to escape and prevents the recombi-nation of the minority carrier in the wrong contact by a highenergy barrier.

The current conduction in OPV devices is unipolar [34], withhole and electron currents exclusively confined within the donorand acceptor materials, respectively. Only at the D/A interface,electron and hole can come together and recombine. We il-lustrate the various current components in Fig. 1(c) using theenergy band diagram of the PHJ device. Here, Jex is the excitondiffusion flux or the rate of charge generation (assuming thatexciton dissociation efficiency is unity), Jph is the photocurrentor the rate of charge extraction, and Jrec is the recombinationrate at the interface, such that Jex ≡ Jph (V ) + Jrec(V ). Thedetailed analytical derivation of the photo-current is given inour previous publication [49]. Since Jph ∝ μe,h , the Jrec mustcompensate the poor Jph in a low mobility μ material. Thecarrier profile [see Fig. 1(d)] obtained by numerical simulationconfirms this hypothesis by showing how carriers pile up at theinterface in a low-μ material. This increase in carrier concen-trations leads to high recombination (Jrec ∼ γnp) loss. Here,n and p are the electron and hole densities, respectively, and γis the bimolecular recombination coefficient [35].

III. MODEL SYSTEM AND MODEL EQUATIONS

A. Optics

Optical absorption in different layers of the OPV cell is calcu-lated by the full-wave solution of Maxwell’s equations with theinput of AM1.5 illumination. The materials in different layersof the cell are characterized by the complex refractive indicesηmed that are obtained from measurements [36]. Transfer matrixmethod (TMM) [37] calculations are used for the optical studiesof the planer electrode structure. In this approach, the structureis modeled using a series of interface and phase matrices. Theinterface matrices are defined by Fresnel complex refection andtransmission coefficients. The phase matrix describes the changein phase of the electromagnetic waves as it flows through a layer.The central quantity which is calculated in this approach is thepoint-wise optical absorptance [A(λ, r)] inside various layers ofthe cell. The optical absorption for the NEs is implemented us-ing COMSOL RF-module [38] in 2-D grid space with periodicboundary conditions. We study the results for both transverseelectric (TE) and transverse magnetic (TM) waves for normalincidence. The wavelength range of 300–900 nm is used for ourcalculations. We consider power absorption only in the poly-mer blend. Absorption in the top ITO, back contact (Al), andthe projected electrodes (ITO) are subtracted from the total ab-

TABLE IEQUATIONS FOR CARRIER TRANSPORT

sorption of the system under AM1.5 illumination. The opticalmodel is comprehensive, but the equations and approach aretraditional—we make no claim for novelty in this regard.

B. Transport

The transport of carriers (excitons, electrons, and holes) ismodeled by generalized drift-diffusion formalism, which is de-scribed in detail in the previous publications [39]–[42]. Forcompleteness, we offer the following summary. Exciton gener-ation is calculated from the optical absorption profile discussedpreviously. The diffusion and recombination of the net gener-ated exciton is modeled by the finite exciton diffusion length.Dissociation of the CT excitons is assumed to be field indepen-dent, consistent with recent experiments [11], [43]–[47]. Theelectron and hole transport inside the cell morphology is sim-ulated by a self-consistent solution of Poisson and continuityequations. The generation term in the e–h continuity equationsis calculated from the solution of exciton transport. The chargedcarrier recombination term in the continuity equations is imple-mented by the bimolecular recombination [35]. Since the D–Ainterface is the only place where free carriers can recombine aswell as generate, the generation and recombination terms in thee–h continuity equations are nonzero only at the D–A interfa-cial nodes. We made no new contribution to model development;rather, we use the well-calibrated and well-tested model equa-tions [39]–[42] (see Table I) and simulation parameters (seeTable II) to explore the implications of electrode insertion onthe performance of organic solar cells.


Fig. 2. Structure and functionality of the nano-structured electrodes (NEs).(a) Schematic of comb-like NE geometry which is assumed for simulation inthis 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). Thearrows in (b) represent the path of electron (in acceptor) and hole (in donor)current. The potential redistribution inside the cell with the inserted electrodesis shown by color coding in (c).

IV. RESULTS AND DISCUSSION

We now explore the effect of nanostructured projected elec-trodes on the performance of organic solar cells. For thisanalysis, we choose typical material parameters representingP3HT:PCBM system (summarized in Table II). The results pre-sented here are, however, applicable for any other material sys-tem. For simplicity, we choose a periodic comb-like electrodestructure which is characterized by three geometric parameters:height Helec , width Welec , and spacing Selec ; see Fig. 2(a). Forthe systematic explanation, we first analyze the effects of elec-trode insertion on the carrier transport (assuming that the opticalabsorption is unaltered), and then, we discuss how optical ab-sorption is affected by inserted electrodes.

A. Effect of the Nanostructured Electrodes on CarrierTransport

1) Planar Heterojunction Cell: Conceptually, it is easier toexplain the effect of NEs by exploring its implication for thePHJ morphology. We will later translate many of the conclu-sions derived from PHJ-OPV to BHJ-OPV. Fig. 2(b) showsthe device structure of a PHJ-OPV with electrode inserted inthe donor material. We assume that the inserted electrodes are

Fig. 3. Effect of inserted electrode height Helec on the performance of aPHJ-based OPV cell. Various solar cell performance matrices are plotted as afunction of electrode height. (a) Efficiency, (b) short-circuit current, (c) open-circuit voltage, and (d) FF. The electrode dimensions [see Fig. 2(a)] are Selec =100 nm and Welec = 10 nm. The thicknesses of the donor (TD ) and acceptor(TA ) layers are 50 nm each. The JSC value reflects AM1.5 illumination andexciton diffusion length of 25 nm. However, in this plot we did not consider anyeffect on optical absorption profile with the electrode insertion.

made of optically transparent conducting oxide (e.g., ITO) withconformal coating of appropriate minority carrier blocking lay-ers (e.g., PEDOT-PSS). Typically, holes in the donor materialare the slower carrier, and hence, it is advantageous to haveelectrodes inserted into lower mobility material. Due to theperiodicity/symmetry of the assumed electrode structure [seeFig. 2(a)], it will be sufficient to analyze only one half of theperiodic structure in the 2-D geometry.

From the point of charge transport, inserted electrodes havetwo important effects: First, they reduce the average carrier ex-traction time by providing low resistive pathways [illustrated inFig. 2(b)] and, hence, enhance the FF. Second, they alter thepotential and charge carrier distribution inside the cell [illus-trated by color coding in Fig. 2(c)] in such a way that holes areattracted toward the electrode, and electrons are pushed awayfrom it. The first effect (reduced carrier collection length) sig-nificantly improves the I−V characteristics mainly under themaximum power point condition when the effective field in thedevice is low. The second effect (redistributed potential andcharge carriers) affects the free carrier recombination and hencealters the I−V curve primarily under the short-circuit condition,when the built in field in the device is the maximum. Taken to-gether, the NEs make the charge extraction faster and improvethe OPV performance, as shown in Fig. 3(a). In Fig. 3, weplot the efficiency and related solar cell performance matrices(JSC , VOC , and FF) as a function of the height of the insertedelectrode Helec . Below, we explain the effect of the NEs on eachof these performance matrices.

Short-Circuit Current JSC : For the transport analysis inFig. 3, we assume that optical absorption remains unalteredwith the NEs. Thus, as shown in Fig. 3(b), JSC remains almost


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 withinthe 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, itrepresents electrons. The arrows represent the electric field distribution. (d) Current–voltage characteristics corresponding to the three cells. (e) Electron (n) andhole (p) density at the interface of D–A region is plotted for the three cell structures, and the corresponding position-dependent recombination rates are shownin (f).

unchanged with electrode height. Only a small improvementin current is possible with increasing electrode height (butHelec < TD ) purely from better electrical transport. This is be-cause the built-in electric field at the SC condition is high, andhence, the transport gain is not significant. However, once theelectrode crosses the interface (Helec > TD ), it induces signifi-cant recombination loss (as explained in detail in Fig. 4) whichreduces JSC .

Open-Circuit Voltage VOC : In Fig. 3(c), we plot VOC againstHelec which shows that VOC remains unchanged with the elec-trode height. This behavior of VOC can be explained as follows:Under the open-circuit condition, the net current in the cell iszero. Since transport in OPV is mostly unipolar [41], the elec-tron current in acceptor and hole current in donor both are zero.Thus, at the VOC point, the quasi-fermi levels in the donor andacceptor are flat (∇Fe/h = 0). This implies that VOC is almostindependent of carrier mobility and mainly dictated by the ma-terial properties of the D–A interface [41]. Since the insertedelectrode effectively improves carrier mobility (or shortens thecarrier path length), which has no effect on the VOC point, thusVOC remains unchanged with electrode height. However, a keyassumption in this analysis is that we have assumed zero re-combination at the electrode surface (or perfect minority carrierblocking). If we include electrode surface recombination, thenonce the electrode penetrates through the D–A interface, VOCwill degrade sharply.

Fill Factor FF: In Fig. 3(d), we plot the variation of the FFwith the electrode height. At the maximum power point (or FFpoint) the built-in field is low, and hence, the transport gain dueto the NEs is most prominently reflected on FF. With increas-ing Helec , the photocarrier collection path becomes shorter, andhence, FF increases rapidly. However, beyond a certain electrodeheight (Helec ∼ thickness of the donor layer), FF degrades withHelec due to the significant interface recombination loss (ex-plained in detail in Fig. 4). Since under the assumptions of thisanalysis 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 byexploring in detail the physics associated with three representa-tive points (P0, P1, and P2) in Fig. 3(a).

In Fig. 4(a)–(c), we show electric field (arrows) and chargecarrier (color coding) distribution inside the D–A layers for threedifferent electrode heights, i.e., usual planar electrode (cell P0),inserted electrode only in the donor (cell P1), and inserted elec-trode breaching the D–A interface (cell P2). The correspond-ing current–voltage characteristics are plotted in Fig. 4(d). TheI−V characteristics illustrate the improvement in FF (and slightincrease in JSC) for cell P1 but a significant degradation in per-formance (both JSC and FF) for cell P2. To explain these I−Vcharacteristics, we plot the charge carrier densities and the re-combination rates along the D–A interface in Fig. 4(e) and (f),respectively. The inserted electrodes alter the electric field in


Fig. 5. Effect of the electrode spacing Selec on the performance of a PHJ-based OPV cell. Various solar cell performance metrics are plotted as a functionof Selec . (a) Efficiency, (b) short-circuit current, (c) open-circuit voltage, and(d) FF. The other electrode dimensions are Helec = 40 nm and Welec = 10 nm.The thicknesses of the donor and acceptor layers are 50 nm each. JSC remainsflat since we have not considered any effect on the absorption profile with theNEs.

such a way that holes are attracted toward the electrode, whilethe electrons are pushed away from it. Thus, as long as the in-serted electrodes remain in the donor (e.g., cell P1), the freecarrier density along the D–A interface remains lower [see thered dashed line in Fig. 4(e)] than the usual PHJ cell (black solidline). The reduction of electron and hole densities at the inter-face reduces charge recombination at the interface [see the reddashed line in Fig. 4(f)] and improves the cell efficiency. How-ever, once the electrode crosses the heterojunction (e.g., cellP2), the electric field forces accumulation of free holes alongthe interface, especially closer to the inserted electrodes [see theblue dotted line in Fig. 4(e)]. Thus, the recombination increasesthroughout 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 [(Selecin Fig. 2(a)] on the device performance. The height of the elec-trodes is kept fixed (Helec = 40 nm). The figure clearly showsthat the benefit of inserted electrode in terms of carrier transportis minimal for higher spacing (Selec > 200 nm). However, theoptical absorption enhancement is possible with higher elec-trode spacing, as recently demonstrated with various photoniccrystal structures [22]–[28]. Since the goal of this study is to un-derstand and optimize the NEs for the transport enhancement,we have assumed constant absorption in these simulations, andhence, JSC remains flat with electrode spacing in Fig. 5(b).In the later sections, we will use the closely spaced electrodestructure to explore its effect on optical absorption.

2) Bulk Heterojunction Cell: BHJ-based OPV cells havecomplex intermixed morphology, as shown in the schematicof Fig. 6(a). However, it is easy to see (and we have confirmedit 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 atypical 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 functionof electrode height for B1 and B2. (b) Efficiency, (c) short-circuit current,(d) open-circuit voltage, and (e) FF. The electrode dimensions are Selec =100 nm and Welec = 10 nm. The thicknesses of the active layer are 100 nm.The JSC value is higher than that in the PHJ case, because we have assumedall the photogenerated excitons are collected by the BHJ structure with averageD/A domain width ∼50 nm (=2Lex ).

solar cell parameters (such as JSC and VOC ) of the complexBHJ cells can be accurately analyzed with the equivalent reg-ularized geometric transform. Since the goal of this study is toformulate the general design guidelines, we focus our analysison four representative sections of the morphology [shown by thedashed lines in Fig. 6(a)]. The four representative sections are asfollows: B0 is the ordered vertical junction cell with usual pla-nar electrodes; B1 represents the circumstances when insertedelectrode (ITO) remains exclusively in the donor; B2 representsthe instances where the inserted electrode remains in the accep-tor; and B3 indicates the situations when the inserted electrodecrosses the D–A interface. The instances that are represented byB3 are equivalent to the PHJ devices, and the conclusions that


Fig. 7. Carrier concentration and recombination dynamics in the ordered BHJ-OPV cells with inserted electrodes under the short-circuit condition. (a)–(c) 2-Dcarrier 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 theacceptor, it represents only electrons. The arrows in the diagram represent the electric field distribution. (d) Current–voltage characteristics corresponding to thethree 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-dependentrecombination 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 functionof electrode height in Fig. 6(b)–(e). The figure clearly showsthat if the electrode remains in the donor (red dashed line), thenthere will be significant improvement in FF (and slight improve-ment in JSC ) and hence in performance of the BHJ cell. On thecontrary, if the electrodes are in the acceptor region (blue dottedline), then JSC degrades significantly, while the other parameters(FF and VOC ) remain essentially unchanged. Let us emphasizethat the electrodes are conformally coated with minority car-rier blocking layer. Therefore, any performance loss should notbe (mistakenly) attributed to minority carrier recombination inthe electrode surface. In the next paragraph, we show that theperformance loss arises from the nontrivial remote electrostaticeffect by the inserted electrodes, which causes higher carrierrecombination at the DA interface.

In Fig. 7(a)–(c), we illustrate the change in carrier distribu-tion inside the cell depending on the position of the insertedelectrodes. Fig. 7(a) represents the ordered (vertical junction)cell with planar electrode geometry, and Fig. 7(b) and (c) showthe carrier redistributions in the presence of electrode repre-senting the two cases (B1 and B2) discussed in Fig. 6(a). Thecorresponding I−V characteristics are shown in Fig. 7(d). TheI−V characteristics show performance improvement for the in-serted electrode in donor (red dashed line) but degradation inperformance when the electrodes reside in the acceptor (blue

dotted line). This efficiency variation can be interpreted by thecarrier distribution plots that are shown in Fig. 7(a)–(c). In thecase of cell B1, inserted electrodes attract the holes from theinterface [see the arrows in Fig. 7(b)] and push the electronsaway from the interface. Thus, the carrier concentrations atthe vertical interface are reduced [see the red dashed line inFig. 7(e)], leading to lower recombination loss [see the reddashed line in Fig. 7(f)] and improved charge collection (highFF) and overall higher efficiency. In the case of cell B2, thedirection of horizontal electric field is reversed [see the arrowsin Fig. 7(c)], which pushes the electrons (in the acceptor ma-terial) toward the interface as well as attracts the holes (fromthe donor material) toward the interface, leading to significantenhancement of recombination at the vertical interface [see theblue dotted line in Fig. 7(f)]. This recombination loss is re-flected in dramatic reduction in JSC and FF [see the blue line inFig. 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 ofthe time. Thus, this analysis of the idealized vertical junctioncells indicates that in the random BHJ morphology, projectedelectrodes will improve the device FF if placed (statistically)in the donor region, but at the same time, there will be somedegradation in the JSC value when the electrodes are in theacceptor region. As a result, we conclude that there will be no


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 carrierdistribution (under the short-circuit condition) inside the cell is plotted with color coding in (b) Helec = 0 and (c) Helec > HD . Carrier profile in the donorrepresents 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 Selec = 100 nm and Welec = 10 nm. Thethicknesses of the active layer are 100 nm, with HA =HD = 25 nm.

significant improvement in the overall efficiency of the BHJcells with this concept of NEs.

3) Optimum Bulk Heterojunction Morphology: In our previ-ous publication [39], we have explored the theoretical optimummorphology, which resembles a fin-like structure, see Fig. 8(a).We found that the performance gain with such morphologyis not very significant compared with the (optimized) randomBHJ structure. However, the NEs offer additional transport ad-vantage for the fin morphology which is not accessible to therandom BHJ cells as discussed in the previous section. There-fore, in this section, we explore the implication of the NEs for finmorphology.

In Fig. 8(d)–(g), we summarize the expected performancegains with the various heights of the inserted electrodes in a fin-like morphology. As expected from our previous discussion, theinserted electrode (ITO in donor) improves FF significantly. Re-markably and counterintuitively, however, Fig. 8(d) also showsa reduction of efficiency when Helec > HD (the donor offset),even though the electrode is still immersed exclusively in thedonor material. The reason for such reduction in JSC is ex-plained in Fig. 8(c), where we show pile up of holes close tothe D–A interface at the donor offset (HD ). This pile up of holedensity causes recombination loss at JSC , which is analogous tothe situation that inserted electrode crossing the D–A interfacediscussed in the PHJ cell. Thus, even though the electrode isstill in the donor material, its remote electrostatic effect in theneighboring junction leads to performance degradation. Thus,the design of fin morphology with projected electrodes shoulduse an asymmetric morphology (HD > HA ) with the electrodeheight, Helec < HD .

B. Effect of the Nanostructured Electrodes on the OpticalAbsorption

The analysis of the concept of projected electrodes in theprevious sections was focused on carrier transport assumingoptical absorption unaltered. However, electrode insertion inthe 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 onthe optical absorption in the active layer of OPV cells.

Organic materials have very high absorption coefficient, andhence, almost all the photons (with sufficient energy) are ab-sorbed in a film of 100–200 nm thickness. However, the band-edge absorption can still be improved with proper nanostruc-turing of the electrodes as reported by various groups in recentyears [22]–[28]. However, the electrode spacing/periodicity insuch optimized photonic crystal geometry is generally large, andhence it does not impact the transport property of the cell sig-nificantly (see Fig. 5). Since the goal of this paper is to evaluatethe potential improvement of the charge transport property, weutilize the closely spaced electrode structure (Selec ∼ 100 nm)to explore its effect on photon absorption instead of optimizingthe photonic crystal dimensions for absorption enhancement.

In Fig. 9(a), we plot the optical field distributions inside a PHJcell under AM1.5 illumination for the P3HT:PCBM materialsystem. In Fig. 9(b), we show the photon absorption profile alongthe horizontal line [shown as a dashed line in Fig. 9(a)] for twocases: without inserted electrode (solid line) and with insertedelectrode (dashed line). We find that even though the optical field(hence photon absorption) enhances in the close proximity of


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 absorptionprofile is shown by color coding. (b) 1-D cut of the absorption profile in the fourdifferent layers: ITO, donor, acceptor, and Al. (c) Absorption profile in D–Ablend with the inserted electrodes. (d) Photon absorption in the various layersof the BHJ cell. Solid lines represent the results without NEs, and dashed linesrepresent 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. Solidline: optimized planar electrode (PE) ((LITO = 100 nm; Lblend = 100 nm;LAl = 100 nm); dotted line: un-optimized PE (LITO = 100 nm, Lblend =140 nm, LAl = 100 nm) and dashed line: comb-like NE (LITO = 100 nm,Lblend = 100 nm, LAl = 100 nm, Helec = 50 nm, Selec = 100 nm andWelec = 20 nm). (b) Total photon absorption (expressed as maximum JSC ))in D-A blend as a function of active layer thickness. The solid blue line is forplanner electrode (PE), the black dashed line represents NE with ITO, and thered dotted line represents NE with Al. Electrode heights are assumed half of thefilm thicknes.

the inserted electrode, but the field remains relatively unalteredin rest of the active layer. Similar analysis for BHJ cells inFig. 9(c) and (d) also leads to the same conclusion.

Next, we explore the effect of the NEs on the absorptionspectra (A(λ)) of 1:1 P3HT: PCBM blend in Fig. 10(a). Notethat we first optimize various layer thicknesses for maximumabsorption in the planar electrode-based typical BHJ-OPV cell[dimensions given in the caption of Fig. 10(a)] and then compareits absorption property in the presence of inserted electrodes.The figure also shows that even though the inserted electrodesreduce the active volume by 10%, the overall absorption remainsrelatively unaltered. If the layer thicknesses are not properlyoptimized, even a thicker active layer may absorb less [see thedotted line in Fig. 10(a)]. The NEs in such unoptimized cellswill apparently show higher optical gain [see Fig. 10(b)].

For more quantitative analysis of the effects of the NEs onoptical performance, we express the integrated absorption inthe active layer in terms of the maximum possible short-circuitcurrent as follows:

JSC(max) = q

∫A(λ)I0(λ)

hc/λdλ. (1)

Here, A (λ) is the absorption spectrum in the blend calculatedby the procedure described in the model system, and I0 (λ) is theAM1.5 spectrum. q, h, and c are electron charge, Planck’s con-stant, and speed of light, respectively. We calculate JSC(max)for various thicknesses of the active layer (keeping the thick-ness of the other layers fixed) and plot them in Fig. 10(b). In thisfigure, the solid line represents the results that are obtained forusual planar electrodes with different active layer thicknesses.The dashed line (or dotted line) represents the total absorptionin the presence of inserted ITO (or back electrode Al) elec-trodes. Electrode heights are assumed to be half of the filmthickness. The plot shows that the inserted electrodes can in-crease (slightly) or decrease (slightly) the optical absorption,depending on the thickness of the active layer. For example, inFig. 10(b) higher absorption is observed with the NEs for 150 nmfilm thickness, while slightly degrading effect in absorption isobserved for 100 nm film thickness. Thus, the key point hereis the fact that even though the inserted electrodes displace theabsorbing volume (by 10% in the simulation), the integrated op-tical absorption still remains almost unchanged due to the fieldenhancement closer to the electrodes.

If one nano-structures the metallic electrode instead of theITO, the absorption of the TE waves is diminished. Thus, nanos-tructured metallic electrodes will have much lower absorptionfor a given active layer thickness compared to that of ITO elec-trode [see Fig. 10(b)]. Therefore, we must design the projectedelectrode structure with optically transparent electrodes (ITO).

V. DESIGN FUNDAMENTALS AND CONCLUSION

The optoelectronic analysis of the electrode insertion conceptin OPV shows that the design space for optical enhancementand transport enhancement is not necessarily the same. For thesignificant enhancement of the charge transport, inserted elec-trodes need to be very closely spaced (<100 nm), which wouldnot represent a photonic crystal design. Moreover, the transportanalysis of the effect of projected electrode shows that electrodeinsertion significantly enhances the interfacial recombination inthe BHJ structure. Regardless, we find that for the PHJ struc-ture, an inserted electrode significantly enhances the fill factorof the device. Thus, the ideal design with the projected electrodeshould involve the interdigitized fin-like morphology embeddedwith a projected electrode, which exploits the advantages of BHJmorphology as well as the better transport property of the in-serted electrode. The essential physics of the electrode insertion(explored in the previous two sections) can be summarized asfollows.

1) We find that for the efficient extraction of the charged carri-ers from the low-mobility organic materials, the electrodedimensions need to be designed quite differently from the


TABLE IISIMULATION PARAMETERS

photonic crystal design which improves optical absorp-tion. We find that for better charge collection, the spacingbetween the electrodes needs to be very close (∼100 nm),and electrode heights need to be approximately half thefilm thickness.

2) Our analysis shows significant recombination loss when-ever the projected electrode crosses the D–A interface.This restricts the electrode design exclusively in a singlematerial. Since hole mobility in the donor polymer is low,it is evident that the inserted electrode should be designedto collect the holes in a donor polymer. This design con-sideration can be easily implemented for PHJ cells, but inBHJ cells, additional care (such as fin morphology, etc.)needs to be taken.

3) The inserted electrodes enhance the optical absorption inthe proximity of the electrode surface. However, this lo-cal enhancement is compensated by the active volumeloss due to the finite volume of the electrodes. Hence, wefind that the overall integrated absorption remains rela-tively unaltered with inserted electrodes. However, inser-tion of a metal electrode can degrade the absorption. Thus,nanostructuring of the electrode needs to be done for theoptically transparent electrodes (e.g., ITO) as the metallicelectrode degrades absorption of TE waves.

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Biswajit Ray (S’12) received the B.Tech. degreein electrical and electronics engineering from theNational Institute of Technology, Trichy, India, andthe M.Sc.(Eng.) degree from the Indian Institute ofScience, Bangalore, India, in 2006 and 2008, re-spectively. Since 2008, he has been working to-ward the Ph.D. degree with the School of Electricaland Computer Engineering, Purdue University, WestLafayette, IN.

His research interests include semiconductor de-vice physics and electronic transport in organic and

amorphous materials.Mr. Ray received the Technoinventor Award in 2009 from the Indian Semi-

conductor Association for his master’s thesis. He also received the Best PosterAward in the area of Organic Photovoltaics at the 38th IEEE Photovoltaic Spe-cialist Conference, in 2012.


Mohammad Ryyan Khan received the B.Sc. de-gree in electrical and electronic engineering fromthe Bangladesh University of Engineering and Tech-nology, Dhaka, Bangladesh, in 2009. Since Fall2009, he has been working toward the Ph.D. degreewith the Alam CEED Group, School of Electricaland Computer Engineering, Purdue University, WestLafayette, IN.

His work focuses on optical designing and mod-eling of solar cells.

Charles Black (SM’05) received the Ph.D. degree in physics from HarvardUniversity, Cambridge, MA, in 1996.

He is a Scientist and Group Leader for Electronic Nanomaterials with theCenter for Functional Nanomaterials, Brookhaven National Laboratory, Upton,NY, where he researches applications for nanostructured materials in photo-voltaic devices. From 1996 to 2006, he was a Research Staff Member with theIBM Thomas J. Watson Research Center, Yorktown Heights, NY. His researchat IBM involved using self-assembly to address device fabrication challengesin 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 fromClarkson University, NY, and Purdue University,West Lafayette, IN, in 1991 and 1995, respectively.

He is a Professor of electrical and computer engi-neering and a University Faculty Scholar with PurdueUniversity, where his research and teaching focus onphysics, simulation, characterization, and technologyof classical and emerging electronic devices. From1995 to 2001, he was with Bell Laboratories, MurrayHill, NJ, as a Technical Staff Member with the Silicon

ULSI Research Department. From 2001 to 2003, he was a Distinguished Tech-nical Staff Member with Agere Systems, Murray Hill, NJ. During his time inindustry, he made important contributions to reliability physics of electronic de-vices, metalorganic chemical vapor deposition crystal growth for optoelectronicintegrated circuits and performance limits of directly modulated semiconductorlasers. After joining Purdue University in 2004, his research has broadened toinclude nanocomposite flexible electronics, organic solar cells, and performancelimits of nanobiosensors. He has published more than 150 papers in internationaljournals and has presented many invited and contributed talks at internationalconferences.

Dr. Alam is a Fellow of the American Physical Society and the AmericanAssociation for the Advancement of Science. He received the 2006 IEEE KiyoTomiyasu Award for contributions to device technology for communicationsystems.

Nanostructured Electrodes for Organic Solar Cells: Analysis and Design Fundamentals

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