Electrical Properties of the GaAsX1CMinima at Low Electric Fields from a High-Pressure Experiment

Hall-effect measurements at pressures extending to 60 kbar were made on single crystals of $n$-type GaAs grown by liquid epitaxy, vapor epitaxy, and bulk techniques over the carrier-concentration range ${10}^{13}$-${10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$ and with Se, Si, Sn, and Te dopants. The $X_{1C}$ Hall mobility at 50 kbar for material in the ${10}^{14}$-${10}^{17}$-${\mathrm{cm}}^{-3\mathrm{}}$ range was 375±45 ${\mathrm{cm}}^2$/V sec after transfer from the ${\Gamma }_{1C}$ minimum. [The labeling of states follows the notation of Wigner where the added subscripts $C$ (as used in $X_{1C}$) and $V$ (used in ${\Gamma }_{15V}$) refer to conduction- and valence-band states, respectively.] Extrapolation to atmospheric pressure gives a conductivity mobility of 328±50 ${\mathrm{cm}}^2$/V sec. Theoretical fits for the high-pressure data indicate a subband gap ($X_{1C}-{\Gamma }_{1C}$) of 0.38±0.01 eV and a density-of-states ratio of ${\left(\frac{N_x}{N_{\Gamma }}\right)}_{P=0\mathrm{}}=45\mathrm{}$, which implies $X_{1C}$ density-of-states effective mass of $(0.\mathrm{}85\pm 0.10)m_e$. The loss of carriers at high pressures to impurity levels associated with the $X_{1C}$ minima has been observed. The activation energies relative to the $X_{1C}$ minima are estimated at 0.045±0.01 eV for ${10}^{17}$-${\mathrm{cm}}^{-3\mathrm{}}$ material with Si, Se, Te doping. Results have been analyzed in terms of the simple hydrogenic model. Ionized-impurity scattering in the $X_{1C}$ minima has been shown to be unimportant for material with carrier concentrations below ${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$.