Non-parabolic macroscopic transport models for semiconductor device simulation

We present a formulation of non-parabolic macroscopic transport models which avoids the commonly used relaxation time approximation by using an expansion of the scattering integral into the odd moments of the distribution function. The parameters of this expansion and the closure relations required in the final transport model are directly calculated via analytical models of the distribution function. These models are obtained by displacing an isotropic distribution function with an energy-dependent displacement and expanding the displaced distribution function up to second-order. This allows, for instance, to investigate the commonly neglected second-order contributions to the energy tensor in more detail. In addition, new models for the non-parabolicity corrections of the streaming terms are suggested. In a detailed discussion non-parabolic macroscopic transport models of order four and six are compared.