CE46 - Modèles numériques, simulation, applications

Cross-diffusion systems in moving domains – COMODO

Submission summary

This proposal aims at developping appropriate models and efficient accurate numerical methods for the high-performance simulation and the optimization of the fabrication process of thin film solar cells.

The production of the thin film inside of which occur the photovoltaic phenomena accounting for the efficiency of the whole solar cell is done via a Physical Vapor Deposition (PVD) process. More precisely, a substrate wafer is introduced in a hot chamber where the different chemical species composing the film are injected under a gaseous form. Molecules deposit on the substrate surface, so that a thin film layer grows. In addition, the different components diffuse inside the bulk of the film, so that the local volumic fractions of each chemical species evolve through time. The efficiency of the final solar cell crucially depends on the final chemical composition of the film, which is freezed once the wafer is taken out of the chamber. A major challenge consists in optimizing the fluxes of the different atoms injected inside the chamber during the process in order for the final local volumic fractions in the layer to be as close as possible to target profiles.

Two different phenomena have to be taken into account in order to correctly model the evolution of these local volumic fractions: 1) the cross-diffusion phenomena between the various components occuring inside the bulk of the film; 2) the evolution of the surface of the thin film layer.
In the context of a collaboration with IPVF (French Photovoltaic Institute), Virginie Ehrlacher [PI] and a PhD student, proposed a one-dimensional cross-diffusion system defined on a moving domain in order to model the evolution of the local concentrations of the different components inside the film during the PVD process. Comparisons between numerical simulations and experimental measurements yielded encouraging results on the relevance of this approach.

However, the model studied by the PI and her student suffers from several limitations. Because of its one-dimensional nature, it is not currently possible to study geometrical effects due to surface tension or surfacic cross-diffusion phenomena which occur at the surface of the film. These phenomena are nevertheless extremely important to take into account, in particular for the production of curved solar cells for building-integrated photovoltaics. There is a crucial need for overcoming these limitations and proposing a multi-dimensional model for the PVD process along with an accurate numerical scheme for the approximation of its solutions, which can be used in order to optimize the production process of such thin film solar cells. This represents a significant scientific advance with respect to the existing models and numerical methods which we wish to address in this proposal.

Four main tasks are identified to tackle this challenging problem:
1) identifying appropriate models for the evolution of the local volumic fractions of the various chemical species inside the film and of its surface. Such models read as cross-diffusion systems defined on a domain with moving boundary, taking into account surface cross-diffusion phenomena;
2) developing numerical schemes for the simulation of such models, which should respect the mathematical properties of the considered systems;
3) parallelizing the obtained numerical schemes, using time-space domain decomposition methods and parareal algorithms;
4) designing accurate and efficient reduced-order models, which will be used for the calibration of the parameters entering the model with experimental data and for the optimization of the PVD process.

Project coordinator

Madame Virginie Ehrlacher (Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

CERMICS Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

Help of the ANR 213,810 euros
Beginning and duration of the scientific project: December 2019 - 48 Months

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