2.4 Discussion
The idea of temperature-dependent effective mass is supported by
a number of experimental data. Cardona et al. [21] found an increase of about 12 percent in optical effective mass between 90 and 300 K in hea.vily-doped p-type silicon. Cyclotron-resonance studies conducted by Hensel and Feher [22] show that when'carrier heating populates deeper regions'of the light-hole band, the nonparabolic nature of this band at higher values of T results in an increase in the effective mass of holes.
The model used here in the calculation of hole density-of-states. effective mass is identical to that of Barber [25], and consequently our results for mi and m* are in excellent agreement with those of Barber [25]. We have extended Barber's work to the calculations of m* and m* in p-type silicon. The increase of m* by 36 percent at 400 K shown in Figure 2.3 is much larger than that reported by Costato and Reggiani (9 percent) [26]. Their calculation was done over a similar range of temperatures, and their value at 100 K, mc=0.342 m0, is somewhat lower than our calculated value (.3604 m ). The discrepancies between our results and those of Costato and Reggiani are due mainly to the correction of m* for the explicit temperature-dependence of the energy gap, the inclusion of the split-off band, and the consideration of unequal relaxation times in the three bands. Note that our calculations of effective masses were achieved through more rigorous mathematical derivations, while those of Costato and Reggiani followed a more empirical curve-fitting type of procedure.
The experimental values of density-of-states effective masses of holes in p-type silicon have been published by numerous authors [21,22, 39,40], but very little data can be found for the conductivity and the