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227-0158-00L 4 Credits BSC , MSC D-ITET , D-MATH , D-MAVT
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Semiconductor Transport Theory and Monte Carlo Device Simulation

Halbleitertransporttheorie und Monte Carlo Bauelementesimulation

Lecturers: Prof. em. Dr. Andreas Schenk, PD Dr. Fabian Bufler
Examiners: PD Dr. Fabian Bufler
VVZ CR n/a

Last Updated: 2026-02-05 15:29:09

Abstract

The first part deals with semiconductor transport theory including the necessary quantum mechanics.In the second part, the Boltzmann equation is solved with the stochastic methods of Monte Carlo simulation.The exercises address also TCAD simulations of MOSFETs. Thus the topics include theoretical physics,numerics and practical applications.

Objective

On the one hand, the link between microscopic physics and its concrete application in device simulation is established; on the other hand, emphasis is also laid on the presentation of the numerical techniques involved.

Content

Quantum theoretical foundations I (state vectors, Schroedinger and Heisenberg picture). Band structure (Bloch theorem, one dimensional periodic potential, density of states). Pseudopotential theory (crystal symmetries, reciprocal lattice, Brillouin zone). Semiclassical transport theory (Boltzmann transport equation (BTE), scattering processes, linear transport).
Monte Carlo method (Monte Carlo simulation as solution method of the BTE, algorithm, expectation values).
Implementational aspects of the Monte Carlo algorithm (discretization of the Brillouin zone, self-scattering according to Rees, acceptance- rejection method etc.). Bulk Monte Carlo simulation (velocity-field characteristics, particle generation, energy distributions, transport parameters). Monte Carlo device simulation (ohmic boundary conditions, MOSFET simulation). Quantum theoretical foundations II (limits of semiclassical transport theory, quantum mechanical derivation of the BTE, Markov-Limes).

Resources

Lecture Notes

Lecture notes (in German)

General Information

Language
English
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 30 minutes

Course Components

Type Title Time & Place Hours
lecture Halbleitertransporttheorie und Monte Carlo Bauelementesimulation
  • Tue 09:45-11:30 (HPP G 6)
2 h weekly
exercise Halbleitertransporttheorie und Monte Carlo Bauelementesimulation
HPP G 6: Rechnenübungen HPV F7.1: Computerübungen
  • Tue 11:45-12:30 (HPP G 6)
  • Tue 11:45-12:30 (HPV F 7.1)
1 h weekly

Offered In