The effective densities of states, N _c and N _? , in Eqs. (2.4) and (2.5) relate the electron concentration in the conduction band and the hole concentration in the valence band to the Fermi level in the bandgap. In this appendix, we derive an expression for the effective density of states, using electrons in the conduction band as an example.

To determine the density of electronic states within a certain energy range, it is first necessary to determine the number of different momentum values that can be acquired by electrons in this energy range. Based on quantum mechanics, there is one allowed state in a phase space of volume ( ? x ? p _x)( ? y ? p _y)( ? z ? p _z)= h ³, where p _x , p _y , p _z are the x-, y-, z- components of the electron momentum and h is Planck s constant. If we let N(E)dE be the number of electronic states per unit volume with an energy between E and E+dE in the conduction band, then

(A3.1)

where dp _x dp _y dp _z is the volume in the momentum space within which the electron energy lies between E and E+dE, g is the number of equivalent minima in the conduction band, and the factor of two arises from the two possible directions of electron spin. The conduction band of silicon has a sixfold...