CHAPTER II

                 BAND STRUCTURE AND EFFECTIVE MASS


2.1 Introduction

     The interpretation of transport properties in silicon and the modeling.of silicon junction devices depend on an accurate knowledge of values of effective mass. The complex valence band structure of silicon leads to difficulties in the study of transport properties of holes in this material. Thus the development of a model incorporating the nonparabolic nature of the band into'a single parameter, the combined hole effective mass, would greatly simplify the study of mobility, resistivity, and the Hal.l effect in silicon. Including the band nonparabolicity in calculations of relaxation time via the effective mass formulation is a reasonable procedure and has been applied effectively by Radcliffe [18] to study acoustic phonon scattering, and by Barrie [19] to study optical phonon and impurity scattering in nonparabolic bands. In this chapter we will derive such a theoretical model for hole effective mass calculations in silicon.

     Lax and Mavroides [20] have derived expressions for density-of-states effective masses m*l and m*2 for the heavy-hole band and the light-hole band, respectively, which lead to the generally accepted and quoted value, m*   0.591 mo. This value, however, can only be considered applicable at 4.2 K, where m* = 0.537 m0 and m* = 0.153 m. A number of experimental data have been published which indicate both electron and hole effective mass to be dependent both on temperature and dopant
                                  6