A coarse‐grained electrothermal model for organic semiconductor devices

Abstract

We derive a coarse‐grained model for the electrothermal interaction of organic semiconductors. The model combines stationary drift‐diffusion‐ based electrothermal models with thermistor‐type models on subregions of the device and suitable transmission conditions. Moreover, we prove existence of a solution using a regularization argument and Schauder's fixed point theorem. In doing so, we extend recent work by taking into account the statistical relation given by the Gauss–Fermi integral and mobility functions depending on the temperature, charge‐carrier density, and field strength, which is required for a proper description of organic devices.

A drift‐diffusion based electrothermal model for organic thin‐film devices including electrical and thermal environment

“…We take advantage of properties of Gauss–Fermi integrals established, for example, in ref. [10, Subsection 2.1], and [22, Appendix]. First, we consider arbitrary parameters $$-N_{p0}<C<N_{n0}$$, $$E_L,\,E_H\in {\mathbb {R}}$$, $$\sigma _n,\,\sigma _p>0$$, and $$T>0$$ and discuss properties of the solution to the local charge neutrality condition ().…”