2. A Six Moments Model for the Boltzmann Equation

In this chapter we introduce the Boltzmann transport equation (BTE) which is the fundamental relationship describing transport of free carriers in semiconductors. We discuss the solution of the Boltzmann equation by the method of moments. The arising hierarchy of equations is simplified assuming the diffusion approximation. Truncation of the hierarchy at a finite order leads to a closure problem. Closure in the scattering operator is achieved by using the macroscopic relaxation time approximation. Models for mobilities and relaxation times consistent with bulk data are introduced. Discussion of the closure in the highest order moment is treated in Chapter 3.