Two-band galvanomagnétic effects in gray tin

Abstract

A study of the temperature, magnetic field, and doping dependence of the conductivity, Hall coefficient, and magnetoresistance of gray tin has been interpreted within the framework of the Groves-Paul band structure model allowing the determination of several of its parameters as well as an investigation of the charge carrier scattering mechanisms. Suitable choice of temperature and doping limited conduction to at most two bands so that the single-band characteristics could be obtained using standard two-band theory. In a series of filaments having donor concentrations, N d , between 5×10 16 and 2·5×10 19 cm −3 the 4·2 0K values of Hall number, number from oscillatory magnetoresistance period, low field magnetoresistance, and Γ 8 + electron mobility all exhibit discontinuous behavior as functions of N d at a critical concentration, N c 5×10 17 cm −3, at which the 〈111〉 minima begin to be populated. The observed mobility enhancement is in good qualitative agreement with screened-ionized-impurity scattering theory. The energy separation of the two conduction bands is evaluated ( E μ =0·092 eV), and an upper limit is placed on the 〈111〉 density of states effective mass ( m 1d <-0·21 m e ). For N d < N c the mobility agrees well with the above theory if a doping dependent dielectric constant is employed. Between 4·2 and 100 oK samples having 2×10 17<- N d >-2·5×10 18 cm −3 exhibit an increasing Hall coefficient with temperature due to thermal transfer of electrons from the 〈000〉 to the 〈111〉 minima. This is consistent with the above energy separation and mass values. We also show that d E g /d T<-−4×10 −5 eV/ oK. For intrinsic single crystal samples the hole mobility follows a T −3/2 dependence down, to 20 oK and has an absolute value compatible with acoustic phonon scattering.