temperatures considered here, the assumption of parabolicity for the heavy-hole band based on Kane's model [27] is reasonable. Other studies [35,36] support the validity of-this model for the valence band of silicon.
2.3 Effective Mass Formulation
In the case of spherically symmetric energy surfaces all of the
carriers respond in the same way to a given set of applied forces. The effective mass then acts as a scalar and thus has the same value for the Hall effect, conductivity, and density of states. For nonspherical energy surfaces, however, this is not the case. The mixed response of carriers to a set of applied forces is reflected in differences between the different kinds of effective masses. The density-of-states effective mass, mi, is defined from the relationship
4 2,fkoTm*i 3/2
pi 4 2 k Di F1 2( ) (2.6)
where
I
Fl/2(n) = I + exp (- ) (2.7)
a =(EV - E)/koT, n (Ev EF)/koT, k° is the Boltzmann constant, EV is the top of the valence band, and i = 1, 2, 3 refers to the heavy-hole, light-hole, and split-off bands, respectively.
The electric current density in the presence of electric and magnetic fields can be expressed by [20]
Ji = gjkEk + CjkQEkfH + Ojk.Zm'k HkHm + .
(2.8)