Nonparabolicity of the Gray-TinΓ8+Conduction Band

Abstract

Oscillatory magnetoresistance measurements on gray tin have been extended to Sb-doped samples in the concentration range $8\times {10}^{15}\le N_d\le 1\times {10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$. The field-modulation technique was used, and period and amplitude measurements were made with the field in principal crystallographic planes. The field and temperature dependence of the amplitude was analyzed in terms of an empirically modified expression which incorporates the inhomogeneity temperature $T_i$. The analysis yielded principal values of the effective mass, the Dingle temperature, and $T_i$. The observed increase in effective mass with carrier concentration is compared with the predictions of Kane's theory for InSb. For ${{\Gamma }_8}^{+}$ electron concentrations $n_0$ less than 4.7×${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$, the observed nonparabolicity is consistent with Kane's theory with the following parameters: bandedge density-of-states mass, $0.0236m_e$; ${{\Gamma }_7}^{-}-{{\Gamma }_8}^{+}$ energy gap, 0.634 eV; and matrix-element energy $E_P=39\mathrm{}$ eV. For larger $n_0$ values, at which the ${L_6}^{+}$ subsidiary minima are populated, the mass increases more rapidly than predicted. The Fermi level is evaluated taking account of the observed nonparabolicity.