Substituting equations (2.9) and (2.10) into equations (2.26) and (2.27) it follows that
rfl~ 3/2 M <2 m23/2 i <> [m* )3/2 ~~1
m=C m* m m-- --- c __ D) C 2 t m * mC3)
(2.28)
and
3/2 .T 2> 3/2 D <'T > m*J 2 1
m 2 <2.2 J H m m J m*32
H2 H3
(2.29)
Equations (2.25), (2.28) and (2.29) were evaluated numerically as functions of temperature and acceptor doping density for p-type silicon. Values of the band parameters, IAI = 4.27, IBI = 0.63 and CI = 4.93, were determined at 4.2 K by Hensel and Feher [22] and Balslev and Lewaetz [29]. In order to simplify the calculations and maintain tractability, anisotropies in the relaxation time were ignored. A rigorous analysis of the conductivities for nonisotropic scattering would be extremely difficult to carry out because no relaxation time is expected to exist in the usual sense [38].
Figure 2.2 shows the dependence of m* with temperature in the range from 100 to 400 K. The slight temperature dependence due to the explicit temperature variation of the curvature at the edge of the band results in an effective mass increase of about 5 percent in each band at 400 K. This can be seen in the slope of m*l. The temperature
dependence of m3 is more pronounced since here we also have the
D3
effects of energy displacement at T = 0. The temperature dependence due to nonparabolicity is very apparent in the shape of the m*2 curve.
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