TABLE OF CONTENTS The use of III-V compound semiconductor materials for manufacturing semiconductor devices becomes more and more important owing to their excellent velocity characteristics. These features permit the operation of devices at very high frequencies. Especially InP is increasingly used as the bulk material for many electronic devices, whose performance exceed those fabricated of GaAs regarding velocity and frequency response.
Due to the enhanced functional integration of such modern electron devices, the traditional drift diffusion models [Markowich et al. (1990)] fail in describing the occurring high-field and sub-micron phenomena. Therefore, the semi-classical Boltzmann transport equations must be applied for dealing with phenomena of hot electrons [Ferry (1991)]. Moreover, non-equilibrium longitudinal-optical phonons have been found to strongly affect the electron distribution function (hot phonon phenomena) in polar semiconductors [Vaissiere et al. (1992); Vaissiere et al. (1996)]. Consequently, one must also include kinetic equations for the evolution of phonon populations in an accurate description of such materials.
The numerical solution of these BBP equations is not an easy task, because these transport equations are of integro-differential type in six phase space and one time variables. Besides the well-established Monte Carlo techniques [Jacoboni and Lugli (1989); Gonz lez S nchez et al. (1991); Jungemann and Meinzerhagen (2003)], newly developed deterministic methods are nowadays used for solving the BTEs under transient transport conditions. Here, the publications of Fatemi and Odeh [Fatemi and Odeh (1993)], Niclot et al. [Niclot et al. (1988)], Majorana and Pidatella [Majorana and Pidatella (2001)], Carrillo et al. [Carrillo et al.
