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Quantum Transport in Nanostructures – QUATRAIN

Submission summary

In order to comply with the growing needs of ultra fast, low consumption and high functionality operation, it is no secret information that microelectronics industry produces highly miniaturized devices with very small characteristic length scales. In such devices, quantum effects such as interferences or tunneling effect become important and more and more predominant. Consequently, since the standard numerical tools used in the industry are based on classical physics, a wide field of research is open in order to design suitable quantum transport models and corresponding efficient numerical methods. Numerical simulations based on the Schrödinger equation in the context of nanoelectronics have to face difficulties due to the specific properties of this equation: oscillatory behavior of the solutions, presence of resonances, many particles effects and scattering phenomena. The contribution of mathematics is then required at several levels. This project proposes to explore several directions of research linked to the mathematical and numerical issues raised by applications from emerging fields of nanoelectronics and physics at the nanometer scale. Some target-applications have been identified and feed the mathematical issues raised in this project: double-gate mosfets, nanowires, carbon nanotubes and bio-inspired nanostructures, spintronics, and also the Bose-Einstein condensates. The objective of our project is to combine theorical and numerical studies in order to obtain accurate enough, numerically tractable and rigorously justified models, then to develop sound numerical methods to discretize the obtained models and apply them to the simulation of realistic devices. To will be done, by looking at reduced dimensionality models for strongly confined electron ensembles, by including and justifying an asymptotic description of resonances which reduces even more the dimensionality of the problem, by pursuing the effort in deriving hybrid models coupling quantum and classical transport equations, by thoroughly studying the quantum fluid models derived from entropy principles, and by defining and implementing novel multiscale numerical schemes for quantum transport. The extension of the approaches to spin polarized transport opens a new research direction to be mathematically developed with a promising interplay of transport and micromagnetism phenomena. It is also planned to design an integrated simulator, fed with these hybrid models and the various numerical methods presented above. The final aim is to used this simulator as a tool for interdisciplinary research.

Project coordination

Florian MEHATS (Université)

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

Help of the ANR 210,000 euros
Beginning and duration of the scientific project: - 48 Months

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