Numerical solution of nonlinear PDEs

• Finite volume schemes for convection-dominated problems
• Complete flux and Scharfetter-Gummel schemes for nonlinear diffusion
• Physics preserving methods

Semiconductor simulation

• Charge transport models
• Drift diffusion simulation tool ddfermi
• Applications such as bent nanowires, perovskites, spintronics and quantum wells

Meshfree methods

• RBF collocation and interpolation
• Convergence and stability for multilevel methods
• Anisotropic (surface) mesh improvement

Perovskites

About ten years ago engineers showed for the first time that low-cost perovskites could be used to convert sunlight into electricity. Since then their efficiency has greatly improved, giving hope to replace or modify (via tandem solar cells) less efficient yet widely-used silicon-based solar cells soon. Simulating perovskite solar cells is extremely challenging due to stiffness: Apart from electrons and holes a third ionic species has to be considered which moves about twelve orders of magnitude more slowly. This means that different time scales are present in the model which leads to numerical difficulties.

Cooperations: RG1, RG3, Helmholtz Zentrum Berlin, University of Oxford, Inria Lille/Universty of Lille

Imaging techniques

We model several semiconductor-based imaging techninques to predict fluctuations in doping profiles such as the laser beam induced current (LBIC) or the lateral photovoltage scanning (LPS) method. Mathmatically, we need to solve an inverse problem which we achieve via machine learning techniques.

Cooperations: RG3, Institut für Kristallzüchtung, University of Florence, SISSA (Trieste, Italy)

Nanowires

In order to build even smaller MOS transistors, nanowires Useful electronic properties of these thin wires can be controlled via elastic strain. For example, bending nanowires changes the band gap. However, deformation-related, piezoelectric, and in particular flexoelectric contributions create a complicated potential landscape which is poorly understood and leads to unexpectedly slow charge carrier transport. Careful simulations are needed to explain the cause.

Cooperations: RG1, RG3, Paul-Drude-Institut

Quantum wells

We model and simulate random alloy fluctuations in band edge profiles within a full device. To achieve this, we combine random atomic fluctuations in band edges with macroscale drift diffusion processes. The spatially randomly varying band edges are implemented in ddfermi. Quantum effects are taken into account via localization landscape theory (LLT).

Cooperations: RG1, Tyndall National Institute (Cork, Ireland)

Lasers

Semiconductor lasers are needed in many areas: For example, semiconductor-based LiDAR (light detection and ranging) sensors improve autonomous driving as they are accurate, comparatively small and thus mass market friendly. Moreover, high precision lasers are needed in quantum metrology and quantum computing. Since building new laser prototypes is costly, it is important to understand for all these cases how a new setup works before production. Thus simulations of semiconductor lasers will not only provide scientific insights but also help to reduce development costs. To achieve this, the group will extend the van Roosbroeck model to incorporate more than two charge-carrier species and include additional physical effects (heterostructures, heat transport and light emission).

Cooperations: RG1, RG2, RG3, Ferdinand-Braun-Institut

Neural networks/surrogate models

The core of machine learning algorithms consists of a (usually high-dimensional) optimization problem. To find a minimizer within such complex structures it is often beneficial to resort to surrogate models, which will be minimized instead of the original problem. Due to the curse of dimensionality it is often not feasible to build meshes. For this reason meshfree methods help to efficiently build surrogate models for high-dimensional problems. In particular, we will focus on positive definite kernels within an efficient multilevel residual correction scheme. Additionally, we solve inverse problems arising semiconductor-based imaging techniques via machine learning techniques.

Cooperations: WG DOC, University of Florence, SISSA