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 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. Ability to use commercial CAD programs for the multiphysics simulation of semiconductor (opto)electronic devices.

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. Lab 1: Simulation of semiconductor devices at equilibrium. The goal of this lab is to present the limitations of "textbook" closed-form approximations by guiding the student towards the implementation of a 1D FEM solver for Poisson's equation. Starting from a basic Poisson-Boltzmann solver, it is shown how and when Fermi-Dirac statistics and incomplete ionization of doping impurities can affect the device electrostatics. To this aim, the solver is applied to the simulation of pn diodes and nin structures. (1 ECTS) 3. Lab 2: introduction to quantum transport models. Students are guided towards implementing a genuine quantum transport simulator with a step-by-step approach. First, relying on the experience acquired in Lab 1, a FEM eigensolver for Schroedinger equation is implemented, aimed at evaluating numerically the stationary states of quantum wells and comparing them with (semi)analytical solutions. Then, this code is modified to describe tunneling through a potential barrier, first by a scattering states picture, then by the nonequilibrium Green's function approach. This tool allows to simulate quantum effects such as resonant tunneling in double-barrier diodes and miniband transport in type-II superlattices, emphasizing the connection with the Landauer-Buttiker formalism. The final part of the laboratory is focused on the interaction between quantum and electrostatic effects by coupling the Poisson solver, developed in Lab 1, with the Schroedinger and NEGF solvers. (2.5 ECTS) 3. Lab 3: multiphysics semiclassical simulation of optoelectronic devices with commercial CAD suites. The first part of this lab, common to all students, will take as reference device the pixel of a realistic infrared imaging array, guiding the students through its simulation in dark and under illumination, and comparing alternative approaches for the description of light propagation in the photodetector. The second part of the lab will be devoted to "individual" projects, which are defined each year (1.5 ECTS)

The theory presented in class is immediately applied in three numerical laboratories, devoted to the implementation of simulation codes (in Matlab) or to the use of commercial multiphysics CAD suites (most recently, TCAD Sentaurus by Synopsys). Each laboratory is organized in several 3-hour sessions. Every student is expected to deliver her/his codes and results to the instructors at the end of each laboratory. These codes and results will be 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: S. Datta, "Electronic transport in mesoscopic systems," Cambridge University Press 1995 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.

Lecture slides; Lecture notes; Lab exercises; Simulation tools;

Exam: Compulsory oral exam;

The individual oral examination (30 minutes) is devoted to the discussion of the three numerical laboratories. The final grade takes into account the ability of the student to discuss the numerical and physical issues involved in each laboratory, the approach adopted to reach the goals suggested for the labs, the quality of the codes/projects developed by the student and the corresponding numerical results. Specifically: - for Lab 1, the student should be able to discuss the numerical strategies (FEM, Newton’s methods) adopted to solve electrostatic problems, and to describe the impact of some common approximations on the results of the simulations, supporting the discussion (when required) with the derivations introduced during the lectures; - for Lab 2, the student should master the main NEGF concepts and outputs, e.g., local density of states (LDOS), spectral electron densities, spectral current densities, relating them with the Green's functions and with single-particle properties; - for Lab 3, the student should be able to discuss the relative advantages of the alternative approaches used in the multiphysics analysis of the infrared pixel, and to present her/his individual project.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.