Electron and Phonon Scattering in GaAs at High Temperatures

Abstract

The electrical resistivity $\ensuremath{\rho}$, the Seebeck coefficient $Q$, and the thermal conductivity $\ensuremath{\kappa}$, were measured in a series of GaAs samples in the temperature range 300-900\ifmmode^\circ\else\textdegree\fi{}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 ($\ensuremath{\tau}\ensuremath{\sim}{E}^{r}$, $0<~r<~0.5$) and the ionized-impurity scattering ($\ensuremath{\tau}\ensuremath{\sim}{E}^{\frac{3}{2}}$) in a self-consistent manner. The partial mobilities ${\ensuremath{\mu}}_{P}$ (polar mobility) and ${\ensuremath{\mu}}_{I}$ (ionized-impurity mobility) were then derived from the measured $\ensuremath{\rho}$. The Brooks-Herring formula for ${\ensuremath{\mu}}_{I}$ was found to overestimate screening effects. The temperature dependencies of these mobilities were ${\ensuremath{\mu}}_{P}\ensuremath{\sim}{T}^{\ensuremath{-}2.3}$ and ${\ensuremath{\mu}}_{I}\ensuremath{\sim}{T}^{\frac{3}{2}}$. 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 $\ensuremath{\kappa}$. It was found that ${\ensuremath{\kappa}}_{\mathrm{lattice}}$ was proportional to ${T}^{\ensuremath{-}1.25}$, 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 ${\ensuremath{\kappa}}_{\mathrm{lattice}}$ at the Debye temperature in the undoped material is used to confirm the contribution due to scattering of acoustical by optical phonons.