(Un)avoidable energy loss during carrier extraction in polymer:fullerene solar cells

Armantas Melianas1,  Fabian Etzold2,  Tom J. Savenije3,  Frédéric Laquai2,  Olle Inganäs1,  Martijn Kemerink4
1Biomolecular and Organic Electronics, Department of Physics, Chemistry and Biology, Linköping University, 58183 Linköping, Sweden, 2Max Planck Research Group for Organic Optoelectronics, Max Planck Institute for Polymer Research, Ackermannweg 10, Mainz, 55128, Germany, 3Optoelectronic Materials Section, Department of Chemical Engineering, Delft University of Technology, 2628 BL Delft, The Netherlands, 4a) Complex Materials and Devices, Department of Physics, Chemistry and Biology, Linköping University, 58183 Linköping, Sweden b) Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands

Abstract

Compared to other photovoltaic systems, organic bulk-heterojunction solar cells (OSC) suffer from large photo-voltage losses. Although various rules of thumb exist to estimate the magnitude of this loss, its origin is still debated. Here we investigate the energy loss due to relaxation of photogenerated charge-carriers in the disordered density of states (DOS). Combining experimental and numerical techniques we find that this loss channel can amount to 0.1-0.3eV for both the electrons and the holes, i.e. 0.2-0.6eV in total, with large variation between materials. More specifically, by a combination of time-resolved optical/electro-optical experiments and kinetic Monte Carlo simulations we show that as photo-generated charge carriers are transported to the extracting electrode they gradually lose energy to continuous thermalization in the DOS. In fact, the charge carriers are extracted before even reaching equilibrium. The free charge carrier thermalization mechanism is fundamentally different from that in inorganic photovoltaic devices. We identify it as a two-step process: 1) Following charge-transfer a fast thermalization loss of the order of ~1-2σ occurs (σ is the DOS width 0.05-0.1eV ), during which an average free-charge-carrier makes multiple hops but does effectively not move any closer to the extracting electrode. The excess energy is wasted by diffusion, which dominates the drift component at the early time scales of motion. This fraction of the loss is unavoidable. 2) Gradually charge-carrier drift overcomes diffusion. The charge carrier is transported to the extracting electrode, its remaining excess energy is continuously lost by further thermalization in the DOS; an additional loss of the order of 0.5-1σ occurs. This loss is reduced in thinner devices. Since thermalization occurs downhill in energy it boosts charge carrier motion, leading to a strongly time-dependent mobility, which we independently confirm by direct experiments. We identify the time and distance scales which are relevant for charge extraction in OPV devices and show that experimental techniques which probe the mobility of (almost) relaxed charge-carriers are not meaningful to OPV device operation. Therefore to correctly describe the device physics of operating OPV devices non-equilibrium effects related to the gradual thermalization of the charge carrier populations must be taken into account.