Numerical simulation of organic semiconductor devices with high carrier densities

TL;DR

This paper presents a comprehensive numerical method for simulating charge transport in doped disordered semiconductors, addressing stability and efficiency issues in high doping scenarios.

Contribution

It introduces a generalized Gummel iterative scheme with a new scaling approach, improving convergence and efficiency for high carrier density simulations.

Findings

The generalized scheme converges where conventional methods fail.

The method is more efficient with large injection currents.

It accurately reproduces known results in standard cases.

Abstract

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.