| 1. |
- Fuhrmann, Jürgen, et al.
(författare)
-
Unipolar Drift-Diffusion Simulation of S-Shaped Current-Voltage Relations for Organic Semiconductor Devices
- 2020
-
Ingår i: Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. FVCA 2020. - Cham : Springer. - 9783030436506 - 9783030436513 ; , s. 625-633
-
Bokkapitel (refereegranskat)abstract
- We discretize a unipolar electrothermal drift-diffusion model for organic semiconductor devices with Gauss–Fermi statistics and charge carrier mobilities having positive temperature feedback. We apply temperature dependent Ohmic contact boundary conditions for the electrostatic potential and use a finite volume based generalized Scharfetter-Gummel scheme. Applying path-following techniques we demonstrate that the model exhibits S-shaped current-voltage curves with regions of negative differential resistance, only recently observed experimentally.
|
|
| 2. |
- Glitzky, Annegret, et al.
(författare)
-
A coarse‐grained electrothermal model for organic semiconductor devices
- 2022
-
Ingår i: Mathematical methods in the applied sciences. - : John Wiley & Sons. - 0170-4214 .- 1099-1476.
-
Tidskriftsartikel (refereegranskat)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.
|
|
| 3. |
- Glitzky, Annegret, et al.
(författare)
-
A hybrid model for the electrothermal behavior of semiconductor devices
- 2021
-
Ingår i: Proceedings in Applied Mathematics and Mechanics. - : Wiley-Blackwell. - 1617-7061. ; 20:1, s. 1-2
-
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.
|
|
| 4. |
- Glitzky, Annegret, et al.
(författare)
-
An existence result for a class of electrothermal drift-diffusion models with Gauss–Fermi statistics for organic semiconductors
- 2020
-
Ingår i: Analysis and Applications. - : World Scientific. - 0219-5305 .- 1793-6861. ; 19:02, s. 275-304
-
Tidskriftsartikel (refereegranskat)abstract
- This work is concerned with the analysis of a drift-diffusion model for the electrothermal behavior of organic semiconductor devices. A “generalized Van Roosbroeck” system coupled to the heat equation is employed, where the former consists of continuity equations for electrons and holes and a Poisson equation for the electrostatic potential, and the latter features source terms containing Joule heat contributions and recombination heat. Special features of organic semiconductors like Gauss–Fermi statistics and mobility functions depending on the electric field strength are taken into account. We prove the existence of solutions for the stationary problem by an iteration scheme and Schauder’s fixed point theorem. The underlying solution concept is related to weak solutions of the Van Roosbroeck system and entropy solutions of the heat equation. Additionally, for data compatible with thermodynamic equilibrium, the uniqueness of the solution is verified. It was recently shown that self-heating significantly influences the electronic properties of organic semiconductor devices. Therefore, modeling the coupled electric and thermal responses of organic semiconductors is essential for predicting the effects of temperature on the overall behavior of the device. This work puts the electrothermal drift-diffusion model for organic semiconductors on a sound analytical basis.
|
|
| 5. |
- Glitzky, Annegret, et al.
(författare)
-
Analysis of a bulk-surface thermistor model for large-area organic LEDs
- 2021
-
Ingår i: Portugaliae Mathematica. - : European Mathematical Society Publishing House. - 0032-5155 .- 1662-2758. ; 78:2, s. 187-210
-
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.
|
|
| 6. |
- Glitzky, Annegret, et al.
(författare)
-
Analysis of a hybrid model for the electro-thermal behavior of semiconductor heterostructures
- 2022
-
Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier. - 0022-247X .- 1096-0813. ; 507:2
-
Tidskriftsartikel (refereegranskat)abstract
- We prove existence of a weak solution for a hybrid model for the electro-thermal behavior of semiconductor heterostructures. This hybrid model combines an electro-thermal model based on drift-diffusion with thermistor type models in different subregions of the semiconductor heterostructure. The proof uses a regularization method and Schauder's fixed point theorem. For boundary data compatible with thermodynamic equilibrium we verify, additionally, uniqueness. Moreover, we derive bounds and higher integrability properties for the electrostatic potential and the quasi Fermi potentials as well as the temperature.
|
|
| 7. |
- Glitzky, Annegret, et al.
(författare)
-
Dimension reduction of thermistor models for large-area organic light-emitting diodes
- 2021
-
Ingår i: Discrete and Continuous Dynamical Systems. Series S. - : American Institute of Mathematical Sciences. - 1937-1632 .- 1937-1179. ; 14:11, s. 3953-3971
-
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.
|
|
