The first part of this course revisits a number of basic concepts from band theory, many-particle physics and statistical physics which are paramount for deriving the electron and hole densities in semiconductor structures as well as the corresponding potential profile (the so-called "band diagrams" and their "band bending" phenomena. As a straightforward benchmark, we discuss the calculation of the above profiles for an ideal pn-junction and a simplified version of the field-effect transistor (MOS capacitor) while ignoring transport (i.e. sticking to thermal equilibrium) for the sake of simplicity.
The next part briefly touches a few essential concepts and tools from statistical physics and field theory that are needed to set up a theoretical background for
studying transport of mobile electric charges in semiconductors: phase space, the density matrix or statistical operator, the classical Liouville equation and its
quantum counterpart, distribution functions. As a first application, classical transport theory based on the Boltzmann equation is treated in the framework of the Lagrange-Charpit method that employs classical (Newtonian) trajectories to trace the time dependent Boltzmann distribution function. Simple and/or idealized conduction models, such as the Drude model, are included. Next, we select one or two items from a list of quantum transport formalisms, e.g. the quantum mechanical energy and momentum balance equations, the Wigner-Liouville and Wigner-Boltzmann equations, the Kubo-Greenwoord formalism (low-field transport) etc.
Finally, we apply the techniques and machinery developed to deal with classical and quantum transport to a number of specific devices, such as the planar MOSFET, the double-gate MOSFET and the junctionless nanowire FET (or pinch-off FET).