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Article
A Weighted Hybridizable Discontinuous Galerkin Method for Drift-Diffusion Problems
In this work, we propose a weighted hybridizable discontinuous Galerkin method (W-HDG) for drift-diffusion problems. By using specific exponential weights when computing the
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Chapter and Conference Paper
Mathematical Modeling of Semiconductors: From Quantum Mechanics to Devices
AbstractWe discuss recent progress in the mathematical modeling of semiconductor devices. The central result of this paper is a combined quantum-classical model that self-consistently couples van Roosbroeck’s ...
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Article
Do** optimization for optoelectronic devices
We present a mathematical and numerical framework for the optimal design of do** profiles for optoelectronic devices using methods from mathematical optimization. With the goal to maximize light emission and...
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Chapter and Conference Paper
Minisymposium: Charge Transport in Semiconductor Materials: Emerging and Established Mathematical Topics
Modern electronic devices would be unthinkable without semiconductor materials. Few inventions have shaped our modern society like they have. There are emerging fields such as organic semiconductors, where the...
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Chapter and Conference Paper
On Some Extension of Energy-Drift-Diffusion Models: Gradient Structure for Optoelectronic Models of Semiconductors
We derive an optoelectronic model based on a gradient formulation for the relaxation of electron-, hole- and photon-densities to their equilibrium state. This leads to a coupled system of partial and ordinary ...
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Article
Error Analysis of a B-Spline Based Finite-Element Method for Modeling Wind-Driven Ocean Circulation
We present the results of an error analysis of a B-spline based finite-element approximation of the stream-function formulation of the large scale wind-driven ocean circulation. In particular, we derive optima...
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Article
On thermodynamic consistency of a Scharfetter–Gummel scheme based on a modified thermal voltage for drift-diffusion equations with diffusion enhancement
Driven by applications like organic semiconductors there is an increased interest in numerical simulations based on drift-diffusion models with arbitrary statistical distribution functions. This requires numer...
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Article
Geometrical and physical optimization of a photovoltaic cell by means of a genetic algorithm
A methodology for the geometrical and physical optimization of a photovoltaic cell is proposed, which makes use of a detailed distributed model for the device simulation and a genetic algorithm. For the numeri...
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Article
On the Tractability Index of a Class of Partial Differential-Algebraic Equations
We consider a class of nonlinear partial-differential-algebraic equations, where the nonlinearity is present only in the PDEs and in the coupling conditions, and some additional structural conditions hold. For...
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Chapter and Conference Paper
An Existence Result for Index-2 PDAE System Arising in Semiconductor Modeling
We consider an electric network modeled via Modified Nodal Analysis, which is refined by a nonlinear multi-dimensional elliptic partial differential equations as semiconductor device model. This coupled system...
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Chapter and Conference Paper
Diffusive Limit of a MEP Hydrodynamical Model Obtained from the Bloch-Boltzmann-Peierls Equations for Semiconductors
We consider a MEP hydrodynamical model obtained from a set of transport equations for the distribution functions of electrons in conduction band and phonon. We assume that the MEP model contains equations for ...
