Numerical simulation of organic semiconductor devices with high carrier densities

We give a full description of the numerical solution of a general charge transport model for doped disordered semiconductors with arbitrary field- and density-dependent mobilities. We propose a suitable scaling scheme and generalize the Gummel iterative procedure, giving both the discretization and linearization of the van Roosbroeck equations for the case when the generalized Einstein relation holds. We show that conventional iterations are unstable for problems with high doping, whereas the generalized scheme converges. The method also offers a significant increase in efficiency when the injection is large and reproduces known results where conventional methods converge.

💡 Research Summary

The paper presents a comprehensive numerical framework for solving the charge transport equations governing doped, disordered organic semiconductor devices, with particular emphasis on regimes of high carrier density and strong injection. The authors start from the generalized van Roosbroeck system, which couples Poisson’s equation for the electrostatic potential with drift‑diffusion continuity equations for electrons and holes. Unlike conventional treatments that assume constant mobility, the model incorporates arbitrary field‑ and density‑dependent mobilities μ(E,n) and respects the generalized Einstein relation D = (kT/q) μ