| 1. |
- Glitzky, Annegret, et al.
(författare)
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A hybrid model for the electrothermal behavior of semiconductor devices
- 2021
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Ingår i: Proceedings in Applied Mathematics and Mechanics. - : Wiley-Blackwell. - 1617-7061. ; 20:1, s. 1-2
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a hybrid model for the electro-thermal behavior of semiconductor heterostructures. It combines a model based on drift-diffusion with thermistor type models in different subregions of the semiconductor device. The aim of this hybrid modeling approach is to be physically as accurate as necessary and at the same time as computationally efficient as possible. Our existence proof uses a regularization method, a priori estimates, and Schauder's fixed point theorem.
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| 2. |
- Glitzky, Annegret, et al.
(författare)
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Analysis of a bulk-surface thermistor model for large-area organic LEDs
- 2021
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Ingår i: Portugaliae Mathematica. - : European Mathematical Society Publishing House. - 0032-5155 .- 1662-2758. ; 78:2, s. 187-210
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Tidskriftsartikel (refereegranskat)abstract
- The existence of a weak solution for an effective system of partial differential equations describing the electrothermal behavior of large-area organic light-emitting diodes (OLEDs) is proved. The effective system consists of the heat equation in the threedimensional bulk glass substrate and two semilinear equations for the current flow through the electrodes coupled to algebraic equations for the continuity of the electrical fluxes through the organic layers. The electrical problem is formulated on the (curvilinear) surface of the glass substrate where the OLED is mounted. The source terms in the heat equation are due to Joule heating and are hence concentrated on the part of the boundary where the current-flow equation is posed. The existence of weak solutions to the effective system is proved via Schauder’s fixed-point theorem. Moreover, since the heat sources are a priori only in $L^1$, the concept of entropy solutions is used.
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| 3. |
- Glitzky, Annegret, et al.
(författare)
-
Dimension reduction of thermistor models for large-area organic light-emitting diodes
- 2021
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Ingår i: Discrete and Continuous Dynamical Systems. Series S. - : American Institute of Mathematical Sciences. - 1937-1632 .- 1937-1179. ; 14:11, s. 3953-3971
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Tidskriftsartikel (refereegranskat)abstract
- An effective system of partial differential equations describing the heat and current flow through a thin organic light-emitting diode (OLED) mounted on a glass substrate is rigorously derived from a recently introduced fully three-dimensional $p(x)$-Laplace thermistor model. The OLED consists of several thin layers that scale differently with respect to the multiscale parameter $ε>0$, which is the ratio between the total thickness and the lateral extent of the OLED. Starting point of the derivation is a rescaled formulation of the current-flow equation in the OLED for the driving potential and the heat equation in OLED and glass substrate with Joule heat term concentrated in the OLED. Assuming physically motivated scalings in the electrical flux functions, uniform a priori bounds are derived for the solutions of the three-dimensional system which facilitates the extraction of converging subsequences with limits that are identified as solutions of a dimension reduced system. In the latter, the effective current-flow equation is given by two semilinear equations in the two-dimensional cross-sections of the electrodes and algebraic equations for the continuity of the electrical fluxes through the organic layers. The effective heat equation is formulated only in the glass substrate with Joule heat term on the part of the boundary where the OLED is mounted.
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