A bulk‐surface model for the electrothermal feedback in large‐area organic light‐emitting diodes

Abstract

This work deals with an effective bulk‐surface thermistor model describing the electrothermal behavior of large‐area thin‐film organic light‐emitting diodes (OLEDs). This model was rigorously derived from a ‐Laplace thermistor model by dimension reduction and consists of the heat equation in the three‐dimensional glass substrate and two semi‐linear equations describing the current flow through the electrodes coupled to algebraic equations that express the continuity of the electrical fluxes through the organic layers. The electrical problem lives on the surface of the glass substrate where the OLED is mounted. The source terms in the heat equation result from Joule heating and are concentrated on the part of the boundary where the current‐flow problem is formulated. Schauder's fixed‐point theorem is used to establish the existence of weak solutions to this effective system. Since the heat source terms at the surface are a priori only in L1, the concept of entropy solutions for the heat equation is worked with.