Two-dimensional simulations of CuPc-PCTDA solar cells:: The importance of mobility and molecular π stacking

An existing two-dimensional microkinetical model for the photovoltaic effect of molecular-based solar cells has been extended to include electron-hole pair recombination between donor and acceptor sites. Simulations of the short circuit current for simple two-dimensional model heterojunction structures composed of copper phthalocyanine (CuPc) and 3,4,9,10-perylenetetracarboxylic dianhydride (PTCDA) are presented. The short circuit current was investigated as a function of the thickness of the photoactive layer for different choices of mobility for CuPc and PTCDA. The hole mobility of CuPc and/or the electron mobility of PTCDA limits the photovoltaic performance if chosen below a certain threshold determined by the net electron-hole generation rate at the CuPc-PTCDA interface. Also, the mobilities should be of the same order of magnitude. The effect of changing the interplanar separation alpha between the pi stacking molecules was investigated, and it was found that increasing alpha from 0.33 to 0.6 nm increases the short circuit current up to 5 orders of magnitude. This was rationalized in terms of the charge separation energetics of geminate electron-hole pairs and its dependence on alpha. As mobilities decrease with increasing alpha and thus opposes this effect, an optimum for alpha similar to 0.66 nm was found for the CuPc-PTCDA heterojunction model structures. The simulations are interpreted in a simple kinetic picture of an electron-hole pair generation step at the CuPc-PTCDA interface and subsequent transport in the CuPc and PTCDA domains. It is argued that an optimal device configuration involves an amorphous region at the CuPc-PTCDA interface and a gradual increase of the molecular order as the electrodes are approached in the respective CuPc and PTCDA transport regions.