Effective masses for nonparabolic bands in p-type silicon

Abstract

The nonparabolic nature of the valence bands of silicon gives rise to an explicit temperature dependence in the density of states effective mass as defined through the carrier concentration as well as an energy dependence in the mass defined through the density of states itself. Both masses are important to those researchers interested in fitting electronic transport data. In the past the temperature dependent effective mass of Barber has been most commonly used. The approximations that have gone into the Barber mass are somewhat oversimplified in that he only approximated the actual band structure. We present a more complete calculation, and compare it with the results of Barber for nondegenerate p-type silicon. There is a significant difference, a factor of about 1.4, between our results and his in the temperature range 300–600 K. The difference is quite noticeable in calculating electronic transport quantities such as carrier concentration or conductivity mobility.