In this lecture, we study mathematical theory of model equations for semiconductor.
In this lecture, we study the basic concepts and methods to study the mathematical structure of model equations for semiconductor.
Model equations for semiconductor, relaxation time limit
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
The lectures provide the fundamentals of partial differential equations for semiconductor.
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Class 1 | This lecture provides a recent study of mathematical research on semiconductor equations. With recent developments in semiconductor technology, several mathematical models have been established to analyze and to simulate the behavior of electron flow in semiconductor devices. Among them, a hydrodynamic, an energy-transport and a drift-diffusion models are frequently used for the device simulation with the suitable choice, depending on the purpose of the device usage. Hence, it is interesting and important not only in mathematics but also in engineering to study a model hierarchy, relations among these models. The model hierarchy has been formally understood by relaxation limits letting the physical parameters, called relaxation times, tend to zero. In this lecture, we concentrate ourself on the mathematical justification of the relaxation limit of the hydrodynamic model. More precisely, we show that the time global solution for the hydrodynamic model converges to that for the drift-diffusion model as the relaxation time tends to zero. | Understand the contents covered by the lecture. |
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Shinya Nishibata, Masahiro Suzuki, Hierarchy of Semiconductor Equations: Relaxation Limits with Initial Layers for Large Initial Data (Tokyo: The Mathematical Society of Japan, 2011)
By scores of reports.
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