Aim of the course is to discuss the techniques used for the numerical simulation of semiconductor materials and devices, and to teach the student both to use proficiently a commercial CAD suite and to write specialized device simulation codes - critical competences for engineers expert in (opto)electronic devices and nanotechnologies. The course presents the derivation, implementation and limitations of the most important semiclassical models of electron transport in semiconductors (drift-diffusion, energy balance, hydrodynamic), and provides an introduction to quantum transport models. Particular emphasis is placed on numerical laboratories.

Knowledge of the semiclassical models derived from Boltzmann transport equation for the physics-based simulation of semiconductor devices, of their different application domains, and of the numerical techniques involved in their implementation.
Knowledge of the quantum transport models based on the non-equilibrium Green’s function (NEGF) formalism.
Ability to use commercial CAD programs for the physics-based simulation of semiconductor (opto)electronic devices.
Ability to implement a one-dimensional (1D) solver based on the finite-element method (FEM) for Poisson’s equation in semiconductor devices.
Ability to implement a 1D FEM quantum transport simulation code based on NEGF.

Basics of quantum mechanics and solid-state physics.
Operating principles of the most important electronic semiconductor devices.
Fundamentals of Matlab programming.

1. Semiclassical models for carrier transport in semiconductors: from the Boltzmann transport equation (BTE) to the hydrodynamic, energy-transport and drift-diffusion models. Numerical issues and fundamental limitations in the simulation of (opto)electronic devices with semiclassical models based on systems of partial differential equations (1 ECTS)
2. Simulation of semiconductor devices at equilibrium: implementation of a 1D FEM solver for Poisson’s equation (1 ECTS)
3. Physics-based semiclassical simulation of (opto)electronic devices with commercial CAD suites (1.5 ECTS)
4. Introduction to quantum transport models. The NEGF formalism. Implementation of a 1D FEM quantum transport simulation code based on NEGF (2.5 ECTS)

The theory presented in class (both with transparencies and at the blackboard) will be applied in four numerical laboratories, devoted to the implementation of simulation codes (in Matlab) or to the use of commercial physics-based CAD suites (most recently, TCAD Sentaurus by Synopsys). Each laboratory will be organized in two or more 3-hour sessions. The lab reports and the numerical codes written by the students will be graded and discussed during the oral exam.

Detailed week-by-week syllabus, lecture notes, and laboratory/homework assignments will be posted on the course website. Supplementary texts include:
D. Vasileska, S. M. Goodnick, and G. Klimeck, Computational Electronics. Semiclassical and Quantum Device Modeling and Simulation, CRC Press 2010.
M. Fischetti and W. G. Vandenberghe, Advanced Physics of Electron Transport in Semiconductors and Nanostructures, Springer 2016.

Oral examination (30 minutes) focused on the reports of the numerical laboratories. The grading will take into account the quality of the lab reports, and the ability of the student to discuss the specific issues involved in each laboratory and her/his personal approach.