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- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
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School of Environment and Society
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- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematical and Computing Science
- Instructor(s)
- Suzuki Masahiro
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Intensive ()
- Group
- -
- Course number
- MCS.T415
- Credits
- 2
- Academic year
- 2016
- Offered quarter
- 3-4Q
- Syllabus updated
- 2016/9/23
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
In this lecture, we study mathematical theory of model equations for semiconductor.
Student learning outcomes
In this lecture, we study the basic concepts and methods to study the mathematical structure of model equations for semiconductor.
Keywords
Model equations for semiconductor, relaxation time limit
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
The lectures provide the fundamentals of partial differential equations for semiconductor.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| 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. |
Textbook(s)
None
Reference books, course materials, etc.
Shinya Nishibata, Masahiro Suzuki, Hierarchy of Semiconductor Equations: Relaxation Limits with Initial Layers for Large Initial Data (Tokyo: The Mathematical Society of Japan, 2011)
Assessment criteria and methods
By scores of reports.
Related courses
- MCS.T401 ： Analysis on Continuous Systems
- MCS.T311 ： Applied Theory on Differential Equations
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None
