Deterministic Solvers for the Boltzmann Transport Equation

The book covers all aspects from the expansion of the Boltzmann transport equation with harmonic functions to application to devices, where transport in the bulk and in inversion layers is considered. The important aspects of stabilization and band structure mapping are discussed in detail. This is done not only for the full band structure of the 3D k-space, but also for the warped band structure of the quasi 2D hole gas. In the latter case the k p-Schrödinger equation has to be solved in addition to the Boltzmann transport equation and Poisson equation. Efficient methods for building the Schrödinger equation for arbitrary surface or strain directions, gridding of the 2D k-space and solving it together with the other two equations are presented. The features of the deterministic solvers for the 2D and 3D k-space are demonstrated by application to SOI NMOSFETs, THz SiGe HBTs and SiGe heterostructure DG PMOSFETs. For example, in the case of the PMOSFETs optimum surface/channel directions and strain conditions are investigated.