Ideal diode equation for organic heterojunctions. I. Derivation and application

The current-voltage characteristics of organic heterojunctions (HJs) are often modeled using the generalized Shockley equation derived for inorganic diodes. However, since this description does not rigorously apply to organic semiconductor donor-acceptor (D-A) HJs, the extracted parameters lack a clear physical meaning. Here, we derive the current density-voltage (J-V) characteristic specifically for D-A HJ solar cells and show that it predicts the general dependence of dark current, open-circuit voltage (V(oc)), and short-circuit current (J(sc)) on temperature and light intensity as well as the maximum Voc for a given D-A material pair. We propose that trap-limited recombination due to disorder at the D-A interface leads to the introduction of two temperature-dependent ideality factors and show that this describes the dark current of copper phthalocyanine/C(60) and boron subphthalocyanine/C(60) cells at low temperature, where fits to the generalized Shockley equation break down. We identify the polaron pair recombination rate as a key factor that determines the J-V characteristics in the dark and under illumination and provide direct measurements of this process in our companion paper II [N. C. Giebink, B. E. Lassiter, G. P. Wiederrecht, M. R. Wasielewski, and S. R. Forrest, Phys. Rev. B 82, 155306 (2010)]. These results provide a general physical framework for interpreting the J-V characteristics and understanding the efficiency of both small molecule and polymer organic, planar and bulk HJ solar cells.