TABLE OF CONTENTS On a semi-classical level the transport of carriers in semiconductors can be well described by the BE. For device simulation the time- and position-dependent BE needs to be considered.
This equation is posed in the simulation domain D and has to be supplemented by boundary and initial conditions. In semiconductor physics the distribution function is commonly normalized as
where N D denotes the number of carriers contained in the semiconductor domain of volume V D. This normalization is based on the notion of discrete states in k-space having a of density 2 V D/(2 ?) 3, such that f can be viewed both as an occupation probability of the discrete state k and a density function in the continuous k-space. In both cases, however, with respect to r, f is to be interpreted as a density function.
In (19) the carrier's group velocity v is related to the band energy ?( k) by v = h ?1 ? k ?( k). The force field F takes into account electric and magnetic fields. If only an electric field E is present, the force field is given by F = q E/ ?, where q is the charge of the carrier. The scattering operator Q = Q g ? Q l consists of a gain and a loss term, respectively. If...
