Simulation of Bulk Properties of Solids

Abstract

When the band structure, the phonon spectrum and the interaction between them are known, the Monte Carlo method can be used to calculate the bulk transport properties of a semiconductor. We need to know the shape of the energy bands, the values of the effective masses, the phonon energies, phonon deformation potentials and the dielectric constant. These values have been collected in the semiconductor tables edited by Landolt-Börnstein (1982) or from several individual publications mentioned in Chapter 4. Several authors have calculated the drift velocity and mobility of the carriers for bulk material, the population ratio of the various minima of the conduction band, the energy and momentum relaxation times and the mean free paths by means of Monte Carlo simulation. Comparing the physical constants they use, we note some differences in the choice of values between the authors. Some of these values, e.g. some deformation potentials, may be difficult to ascertain because the transport is not very sensitive to their value. However, when we have decided on a set yielding macroscopic bulk quantities in agreement with measured ones, our chosen value can be considered representative. The author’s set for silicon and gallium arsenide have been quoted in Tables 6.1 and 6.2. Once a set has been established, it should not be changed during the simulation of devices. The selection of basic constants is referred to as priming the model.