Electron transport and band structure of ${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ alloys

Measurements of electrical conductivity $\sigma$ and Hall coefficient $R_H$ have been made as a function of temperature in the range room to 230 °C on epitaxial $n$-type samples of ${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ with carrier concentrations in the range 5 × ${10}^{21}$ to 1.6 × ${10}^{24}$ ${\mathrm{m}}^{-3\mathrm{}}$. Theoretical calculations of $\sigma$ and $R_H$ have been made on a three-band ($\Gamma$, $L$, $X$) model using the method of Fletcher and Butcher, and the resulting values fitted to the experimental data by using the band-energy differences and various parameters in the electron-scattering equations as adjustable parameters. Thus the relative energy values of the three bands have been determined as a function of composition $x$, and values of such parameters as dielectric constant, deformation potentials, intervalley and interband coupling coefficients have been found. Different parameters dominate the results in different composition ranges, e.g., for $0<x<\mathrm{}0.20\mathrm{}$, the $\Gamma$ and $L$ bands have greatest effect, while for $0.7<x<\mathrm{}1.0\mathrm{}$ the $X$ band is of major importance. However, the requirement that the various parameters vary smoothly with $x$ has been used to extend the composition ranges for which the various parameters have been determined.