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

Abstract

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 $(J\text{\ensuremath{-}}V)$ 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 ${V}_{oc}$ 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/${\text{C}}_{60}$ and boron subphthalocyanine/${\text{C}}_{60}$ 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 $J\text{\ensuremath{-}}V$ 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 $J\text{\ensuremath{-}}V$ characteristics and understanding the efficiency of both small molecule and polymer organic, planar and bulk HJ solar cells.