Hybrid finite-volume/finite-element schemes for p(x)-Laplace thermistor models

Abstract

We introduce an empirical PDE model for the electrothermal description of organic semiconductor devices by means of current and heat flow. The current flow equation is of p(x)-Laplace type, where the piecewise constant exponent p(x) takes the non-Ohmic behavior of the organic layers into account. Moreover, the electrical conductivity contains an Arrhenius-type temperature law. We present a hybrid finite-volume/finite-element discretization scheme for the coupled system, discuss a favorite discretization of the p(x)-Laplacian at hetero interfaces, and explain how path following methods are applied to simulate S-shaped current-voltage relations resulting from the interplay of self-heating and heat flow.