The mini-workshop will take place in the “Salle de réunion” at the Laboratoire Paul Painlevé on June 17, 2025 from 14:00 to 16:30.
Program:
- 14:00 – 14:45: Dilara Abdel (WIAS Berlin) – Charge transport in perovskites solar cells: modeling, numerical analysis and simulations: While crystalline silicon dominates today’s solar market, metal halide perovskites are promising due to their high efficiency and low manufacturing costs. However, key questions remain to realize their full potential, particularly regarding empty sites in the crystalline semiconductor lattice, so-called vacancies, which contribute to the charge transport. This talk explores the impact of vacancy dynamics on device performance through a three-stage theoretical framework: modeling, numerical analysis, and simulation of drift-diffusion charge transport equations. Key contributions include a physically accurate model for limiting vacancy accumulation, a rigorous existence proof for discrete solutions of an implicit-in-time two-point-flux finite volume scheme, and the investigation of experimentally relevant phenomena using a self-developed open-source simulation tool.
- 14:45 – 15:30: Julien Moatti (INP Bordeaux) – Structure preserving finite volume schemes for anisotropic semiconductor models: 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.
- Coffee Break
- 15:45 – 16:30 Claire Chainais-Hillairet (University of Lille) – Corrosion of iron in an underground repository: a new thermodynamically consistent model and some theoretical and numerical results: The modelling and the numerical simulation of corrosion take part in the general description of the nuclear waste repository. The derivation of models that are accurate in the long-time regime is a challenge, especially in this context. In this talk, I will start by recalling the Diffusion Poisson Coupled Model introduced by Bataillon et al. en 2010 and I will show how some minor corrections lead to a thermodynamically consistent model. This model consists in a drift-diffusion-Poisson system of equations on a moving domain. I will review the mathematical results we recently obtained for this model and the main issues we are currently considering.
