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Subject: Arrhenius-like conductivity law ×

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    Analysis of p(x)-Laplace thermistor models describing the electrothermal behavior of organic semiconductor devices
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Glitzky, Annegret; Liero, Matthias
    We study a stationary thermistor model describing the electrothermal behavior of organic semiconductor devices featuring non-Ohmic current-voltage laws and selfheating effects. The coupled system consists of the current-flow equation for the electrostatic potential and the heat equation with Joule heating term as source. The self-heating in the device is modeled by an Arrhenius-like temperature dependency of the electrical conductivity. Moreover, the non-Ohmic electrical behavior is modeled by a power law such that the electrical conductivity depends nonlinearly on the electric field. Notably, we allow for functional substructures with different power laws, which gives rise to a p(x)-Laplace-type problem with piecewise constant exponent. We prove the existence and boundedness of solutions in the two-dimensional case. The crucial point is to establish the higher integrability of the gradient of the electrostatic potential to tackle the Joule heating term. The proof of the improved regularity is based on Caccioppoli-type estimates, Poincaré inequalities, and a Gehring-type Lemma for the p(x)-Laplacian. Finally, Schauders fixed-point theorem is used to show the existence of solutions.
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    p-Laplace thermistor modeling of electrothermal feedback in organic semiconductors
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Liero, Matthias; Koprucki, Thomas; Fischer, Axel; Scholz, Reinhard; Glitzky, Annegret
    In large-area Organic Light-Emitting Diodes (OLEDs) spatially inhomogeneous luminance at high power due to inhomogeneous current flow and electrothermal feedback can be observed. To describe these self-heating effects in organic semiconductors we present a stationary thermistor model based on the heat equation for the temperature coupled to a p-Laplace-type equation for the electrostatic potential with mixed boundary conditions. The p-Laplacian describes the non-Ohmic electrical behavior of the organic material. Moreover, an Arrhenius-like temperature dependency of the electrical conductivity is considered. We introduce a finite-volume scheme for the system and discuss its relation to recent network models for OLEDs. In two spatial dimensions we derive a priori estimates for the temperature and the electrostatic potential and prove the existence of a weak solution by Schauder's fixed point theorem.
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    Self-heating, bistability, and thermal switching in organic semiconductors
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Fischer, Axel; Pahner, Paul; Lüssem, Björn; Scholz, Reinhard; Koprucki, Thomas; Gärtner, Klaus; Glitzky, Annegret
    We demonstrate electric bistability induced by the positive feedback of self-heating onto the thermally activated conductivity in a two-terminal device based on the organic semiconductor C60. The central undoped layer with a thickness of 200 nm is embedded between thinner n-doped layers adjacent to the contacts minimizing injection barriers. The observed current-voltage characteristics follow the general theory for thermistors described by an Arrhenius-like conductivity law. Our findings including hysteresis phenomena are of general relevance for the entire material class since most organic semiconductors can be described by a thermally activated conductivity.