Carrier-Concentration Dependence of Electron-Phonon Scattering in Te-Doped GaSb at Low Temperature

The thermal conductivity $K$ between 5 and 100°K was measured on Te-doped samples with excess donor concentrations $n$ ranging between ∼${10}^{17}$ and 2×${10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$. At temperatures below that of the peak, $K$ was observed to decrease with increasing $n$, this behavior being associated to electron-phonon scattering. The dependence of $K$ on $n$ was investigated by calculating the additional thermal resistivity $W_{\mathrm{ep}}=\frac{1}{K}-\frac{1}{K_0}$ at 6°K, where $K$ and $K_0$ are, respectively, the experimental and theoretical values of the thermal conductivity. The theoretical conductivity was deduced from the Callaway model, using as parameters the Casimir-boundary mean free path, point-defect scattering calculated from the Klemens relation, and phonon-phonon scattering deduced empirically from the results at higher temperatures. $W_{\mathrm{ep}}$ was found to vary approximately as ${{{n_{300}}^{\circ }}_{\mathrm{K}}}^{1.7}$ or ${{{n_{\sim 6}}^{\circ }}_{\mathrm{K}}}^{2.2}$. The excess thermal resistivity is most likely due to scattering of phonons by an electron gas. On the basis of the Ziman model, it is suggested that the observed $W_{\mathrm{ep}}\mathrm{}\left(n\right)\mathrm{}$ behavior may arise from a variation of the effective mass $m^{*}$ with $n$, due to the nonparabolic (000) band. Tentatively, an alternative argument is considered. The low-temperature thermal conductivity of undoped $p$-type samples with hole concentrations of about 1.5×${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$ was found to be much lower than that of Te-doped samples with comparable electron concentrations. This indicates that the strength of hole-phonon scattering in undoped material is more pronounced than that of electron-phonon scattering in Te-doped material.