Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-81-35-M-7

Mathematical Models for Semiconductor Devices (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-81-35-M-7 Mathematical Models for Semiconductor Devices 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-TEMA] Industrial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V MAT-81-35-K-7
Mathematical Models for Semiconductor Devices
P 28 h 107 h - - PL1 4.5 irreg.
  • About [MAT-81-35-K-7]: Title: "Mathematical Models for Semiconductor Devices"; Presence-Time: 28 h; Self-Study: 107 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86298 ("Mathematical Models for Semiconductor Devices")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

Microscopic and macroscopic models in the hierarchy of models for semiconductors are derived and explained. Both, classical and quantum mechanical approaches for ultra-small components are considered. In particular, the focus is on:
  • fundamentals of Semiconductor Physics: charge transport, interactions, electrostatics,
  • microscopic models: Newton, Liouville and Fokker-Planck equations, Schrödinger equations,
  • classical macroscopic models: drift-diffusion equations, hydrodynamic models, energy transport systems,
  • macroscopic quantum models: Madelung transformation, quantum drift diffusion, quantum energy transport.

Competencies / intended learning achievements

Upon successful completion of this module, the students know and understand advanced mathematical models for semiconductors. In particular, they are familiar with microscopic and macroscopic models in the hierarchy of models. They understand both, classical and quantum mechanical modeling. They can apply the models and methods learnt in the lecture to concrete examples. They are able to name and to prove the essential propositions of the lecture as well as to classify and to explain the connections.

Literature

  • P. Markowich, Ch. Ringhofer, Ch. Schmeiser: Semiconductor Equations,
  • A. Jüngel: Quasi-hydrodynamic Semiconductor Equations,
  • S. Selberherr: Analysis and Simulation of Semiconductor Devices.

Requirements for attendance (informal)

Modules:

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-81-35-M-7]

Module-Pool Name
[MAT-81-MPOOL-7] Specialisation Partial Differential Equations (M.Sc.)
[MAT-8x-MPOOL-7] Specialisation Modelling and Scientific Computing (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)