Séminaire du pôle Analyse

Abstract: Mathematical semiconductor models are used to describe the evolution of charge carrier densities in electronic devices. For industrial applications, the most commonly used model is based on two convection-diffusion equations coupled with a Poisson equation. Numerical simulations are often performed using two-points finite volume methods, which are very robust and ensure the positivity of the computed densities.

In this talk, I will consider a situation in which the device is immersed into an exterior magnetic field, which induces a rotation of the charges. In this framework, the convection-diffusion equations become anisotropic, and the classical two-points schemes are not able to compute reliable solutions anymore.

In order to get a reliable numerical method, which can handle both anisotropy and general meshes, I will introduce a nonlinear scheme based on the Hybrid Finite Volume method.

This scheme is devised to preserve at the discrete level the entropy structure of the continuous problem, therefore ensuring the good properties of the method (existence, robustness, positivity of the solution).

I will also present numerical results demonstrating the practical robustness of the method.

Finally, I will also discuss the use of general meshes in order to produce local refinements, and its interest in computing relevant physical quantities, such as current–voltage curves.