Investigation of the Photocurrent in Bulk Heterojunction Solar Cells M. Limpinsel, A. Wagenpfahl, M. Mingebach, and C. Deibel a Experimental Physics VI, Julius-Maximilians-University of W¨urzburg, D-97074 W¨urzburg V. Dyakonov Experimental Physics VI, Julius-Maximilians-University of W¨urzburg, D-97074 W¨urzburg and Functional Materials for Energy Technology, Bavarian Centre for Applied Energy Research (ZAE Bayern), D-97074 W¨urzburg (Dated: July 30, 2018) We investigated the photocurrent in poly(3-hexylthiophene-2,5-diyl) (P3HT):[6,6]-phenyl-C$_{61}$ butyric acid methyl ester (PCBM) solar cells by applying a pulsed measurement technique. For annealed samples, a point of optimal symmetry (POS) with a corresponding voltage V$_{POS}$ of 0.52–0.64 V could be determined. Based on macroscopic simulations and results from capacitance–voltage measurements, we identify this voltage with flat band conditions in the bulk of the cell, but not the built-in voltage as proposed by [Ooi et al., J. Mater. Chem. 18 (2008) 1644]. We calculated the field dependent polaron pair dissociation after Onsager–Braun and the voltage dependent extraction of charge carriers after Sokel and Hughes with respect to this point of symmetry. Our analysis allows to explain the experimental photocurrent in both forward and reverse directions. Also, we observed a voltage–independent offset of the photocurrent. As this offset is crucial for the device performance, we investigated its dependence on cathode material and thermal treatment. From our considerations we gain new insight into the photocurrent‘s voltage dependence and the limitations of device efficiency. PACS numbers: 71.23.An, 72.20.Jv, 72.80.Le, 73.50.Pz, 73.63.Bd Keywords: organic semiconductors; polymers; photovoltaic effect; photocurrent; polaron pair dissociation Organic solar cells have improved greatly in the last years, reaching 5–6 % power conversion efficiency (PCE) today. 1 However, the Shockley diode equation cannot explain the voltage dependent photocurrent in organic solar cells based on a physical model. 2 The detailed process leading from pho- toinduced polaron pairs to extracted charge carriers and ex- ternal photocurrent needs better understanding to push devel- opment of these devices systematically. 3 The first step in this process is singlet exciton formation upon absorption of a pho- ton, usually on the polymer. Then, the exciton has to diffuse to a polymer-fullerene interface within its lifetime, where, due to the high electron affinity of the fullerene, a polaron pair is created via ultrafast charge-transfer. 4 These polaron pairs are still Coulomb-bound due to a low dielectric constant e$_{r}$ of the organic material system (typically 3–4), and have to be disso- ciated to free polarons. Provided the free polarons arrive at their respective electrodes, the last step is charge extraction. In this paper, we investigate the symmetry and voltage de- pendence of the photocurrent, and compare this to a model that takes field dependent polaron pair dissociation and volt- age dependent charge extraction into account. The photocur- rent J$_{Ph}$ , defined as the difference of illuminated and dark cur- rent, J$_{light}$ − J$_{dark}$ , can experimentally be accessed using pulsed illumination (inset in Figure 1). This is necessary to avoid a major overestimation due to device heating. 5 We find the photocurrent of annealed P3HT:PCBM solar cells to have a point of optimal symmetry (POS). The pho- tocurrent shows a point symmetry with respect to POS (see Figure 1), and the corresponding voltage V$_{POS}$ is in the range a deibel@physik.uni-wuerzburg.de In order to describe the voltage dependence of J$_{Ph}$ , we use a combination of Braun–Onsager 6,7 theory and charge extrac- tion as calculated by Sokel and Hughes. 8 This combination was proposed by Mihailetchi et al. 9 and could for the first time explain the experimental photocurrent in reverse direc- tion. However, they calculated effective voltage and field with respect to the physically ill-defined voltage V$_{0}$ , at which J$_{Ph}$ = 0. As we will show, this is correct only in the special case where V$_{0}$ coincides with V$_{POS}$ . In general, contact effects result in a lower value of V$_{POS}$ . Consequently, we consider voltage and electric field relative to V$_{POS}$ instead of V$_{0}$ . Cal- culating polaron pair dissociation and charge extraction with respect to the point of symmetry now allows to describe the experimental photocurrent for solar cells with different elec- trode material. Using a pulsed measurement technique also makes the photocurrent in forward direction accessible, and shows that the model can describe the data in both directions. As shown in Figure 1, the photocurrent is composed of two contributions. The first is voltage-dependent and symmetric with respect to POS. The second contribution is a voltage- independent offset. This constant offset is usually negative, thereby increasing the short-circuit current J$_{SC}$ and PCE. As the magnitude of this offset is crucial for device performance, we investigated its dependence on thermal treatment, cathode material and active layer thickness in detail. of 0.52–0.64 V. While these values agree with results of Ooi et al.$^{5}$, our interpretation differs. We identify this voltage as the quasi flat band case–with flat bands in the bulk of the so- lar cell–which is well below the built-in voltage. Accordingly, our considerations lead to new insights into the origin of the photocurrent. I. INTRODUCTION arXiv:1001.2546v1 [cond-mat.mtrl-sci] 14 Jan 2010