Projects

Projects

The Berlin Mathematics Research Center MATH+ project AA2-21
(January 2024 - December 2025)

Strain engineering for functional heterostructures: Aspects of elasticity

Strain engineering for semiconductor devices or lithium-ion batteries requires a good understanding of elastic effects. We consider some problems in the modelling of such devices, related to the choice of the free energy density and dimension reduction.

Simulation by Yiannis Hadjimichael

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The Berlin Mathematics Research Center MATH+ project AA2-10
(January 2021 - December 2022)

Electro-mechanical coupling for semiconductor devices

We establish nonlinear PDE models for coupled charge-carrier transport and elasticity using the framework of GENERIC. Within the project existence, regularity, and boundedness properties of solutions are derived. Moreover, new simulation techniques are developed to validate the theory.

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The Berlin Mathematics Research Center MATH+ project AA2-1
(January 2019 - December 2020)

Hybrid models for the electrothermal behavior of organic semiconductor devices

We establish, study, and implement hybrid PDE models for the description of charge and heat flow in organic semiconductor devices. These models combine drift-diffusion and coarser thermistor systems for device subregions with the goal to be as accurate as necessary but as computationally inexpensive as possible.

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MATH+ transition project SE18
(January 2019 - September 2019)

Models for heat and charge-carrier flow in organic electronics

The main aim of the prolongation of SE18 is to ensure a reliable, stable, and well tested simulation code for the electrothermal behavior of organic semiconductor devices based on a drift-diffusion description of the charge transport coupled to the heat flow. In particular, it is expected to form a solid base for the treatment of hybrid models for organic semiconductor devices. The theoretical results and the simulation tool under construction in the project enable us to investigate real structures and novel device concepts from our cooperation partner, the Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP) and to take more actively part in applied research in the field of organics.

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ECMath-project SE18 in Research Center Matheon
(June 2017 - December 2018)

Models for heat and charge-carrier flow in organic electronics

The aim of the project is to develop a thermodynamically correct energy-drift-diffusion model for organic semiconductor devices and its discretization and implementation in a simulation tool. The outcome of the project is a fundamental building block for a more efficient multi-scale and multi-physics description and simulation of organic devices. First, the transport of charge carriers in the isothermal case will be described on the basis of a drift-diffusion model, taking the distinctive features of organic materials into account. Second, the model will be extended in a thermodynamically consistent way to include the self-heating and the resulting feedback as well. In both points, the aspects of modeling, analysis, numerics, and simulation are considered.

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Inhomogeneous luminance of a lighting panel

ECMath-project SE2 in Research Center Matheon

Electrothermal modeling of large-area OLEDs

<-- Inhomogeneous luminance of a large-area organic LED

The aim of the Matheon project SE2 is to find adequate spatially resolved PDE models for the electrothermal description of organic semiconductor devices describing self-heating and thermal switching phenomena. Moreover, the project intends to investigate their analytical properties, derive suitable numerical approximation schemes, and provide simulation results which can help to optimize large-area organic light emitting diodes.

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Modeling of Electronic Properties of Interfaces in Solar Cells

to the MATHEON-Project D22

<-- Principle of solar cells: photons generate electron-hole pairs, electrons/holes move to the contacts. The aim consists in minimizing the recombination losses.

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Voronoi Finite Volume Methods for Semiconductor Problems

to the project: Numerical Analysis for Drift-Diffusion Problems

<-- Notation in Voronoi finite volume schemes

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Semiconductor Models with Spin-Polarization

to the project: Spin-Polarized Drift-Diffusion Models

<-- Scheme of a magnetic bipolar diode. The p-region is magnetic, the n-region is nonmagnetic, but spin-polarized by a spin source.

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WIAS-TeSCA-Simulationen von Halbleiterlasern

zum Projekt: Monolithisch integrierter direkt-modulierter 40 Gb/s Transmitter-Laser OIEC (diMOLA)

<-- Buried heterostructure multi quantum well laser. Elektrische Stromdichte in der Umgebung der aktiven Zone

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Energiemodelle für heterogene Halbleiterstrukturen

<-- Schematischer Querschnitt eines SiGe Heterobipolartransistors

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WIAS-TeSCA applications:

Laser diodes

see also WIAS Annual Research Report 2002

<-- Cross section of a RW laser - different materials, intensity distribution of two optical modes

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Zur Analysis von thermodynamischen Modellen des Stoff-, Ladungs- und Energietransports in heterogenen Halbleitern

<-- Reaktionen in einem Paar - Diffusions - Modell

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Modelling and simulation of power devices for high voltage integrated circuits

<-- Scheme of a High Voltage MOS Transistor (alpha microelectronics gmbh Frankfurt (Oder))

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Analytische Untersuchungen von Elektro - Reaktions - Diffusionsgleichungen mit nichtglatten Daten

<-- Energie - Band - Diagramm einer typischen Hetero - Struktur

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Reaction diffusion equations in heterostructures with application to semiconductor technology

<-- Atomic force micrograph of a SiGe Heterojunction Bipolar Transistor (IHP Frankfurt (Oder))

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