Electron and Phonon Scattering in GaAs at High Temperatures

Abstract

The electrical resistivity $\rho$, the Seebeck coefficient $Q$, and the thermal conductivity $\kappa$, were measured in a series of GaAs samples in the temperature range 300-900°K. Values of $Q$ were combined with room-temperature values of the Hall coefficient in order to derive the relative weights of the polar scattering ($\tau \sim E^r$, $0<~r<~0.5$) and the ionized-impurity scattering ($\tau \sim E^{\frac{3}{2}}$) in a self-consistent manner. The partial mobilities ${\mu }_P$ (polar mobility) and ${\mu }_I$ (ionized-impurity mobility) were then derived from the measured $\rho$. The Brooks-Herring formula for ${\mu }_I$ was found to overestimate screening effects. The temperature dependencies of these mobilities were ${\mu }_P\sim T^{-2.3\mathrm{}}$ and ${\mu }_I\sim T^{\frac{3}{2}}$. Knowledge of the Fermi levels and of the degree of "mixing" of the two scattering mechanisms made it possible to assess exactly the electronic contributions to $\kappa$. It was found that ${\kappa }_{\mathrm{lattice}}$ was proportional to $T^{-1.25\mathrm{}}$, and that it decreased as the free-carrier concentrations in the samples increased, thus showing the influence of scattering of phonons by electrons. The value of ${\kappa }_{\mathrm{lattice}}$ at the Debye temperature in the undoped material is used to confirm the contribution due to scattering of acoustical by optical phonons.