TABLE OF CONTENTS In this chapter, we introduce deterministic multigroup model equations to the BBP equations, which are based on a general carrier dispersion law and contain the full quantum statistics of both, the carriers and the phonons. We study the spatially homogeneous case with vanishing electric field, but we construct the multigroup equations in a way that they allow the description of particle distributions of arbitrary anisotropy with respect to a main direction imposed, for example, by an electric field. Hence, the transport model can easily be extend to describe field dependent, spatially inhomogeneous problems by including multigroup formulations of the advection terms in the BBP equations following the receipts given in chapter 3.
Since the reliability of a deterministic transport model increases with the amount of mathematical properties, which the model equations and the original BBP equations possess in common grounds, it is the main goal of this paper to investigate the most important features of our multigroup transport model. Therefore, we show the boundedness of the distribution coefficients, which reflects the Pauli principle as it is found in the BBP equations [Markowich et al. (1990)]. The conservational properties of the multigroup model are discussed and a Boltzmann H-theorem for the obtained evolution equations is proved, similar to that of the BBP equations [Rossani (2002)]. We consider the equilibrium distribution of our multigroup equations and find that it is given by a set of discretized Fermi-Dirac and Bose-Einstein distributions for non-drifting particles, which corresponds to the features of the...
