Pressure and compositional dependences of the Hall coefficient inAlxGa1−xAsand their significance

The Hall coefficients have been measured in ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ as a function of hydrostatic pressure, temperature, and the compositional parameter $x$, and are shown to consist of two contributions. These result from (1) the electron distribution in the $\Gamma$, $L$, and $X$ conduction-band minima and (2) the freeze out of electrons to the donor levels due to an increase in the donor ionization energy with pressure or Al concentration. We have analyzed the experimental data for $R_H$ in terms of the three-band model to separate out these contributions and have shown that $R_H^{*}$ representing purely contribution (1) goes through a maximum near the $\Gamma -X$ crossover pressure. The donor ionization energy rises from 6 to 101 meV under hydrostatic pressure in ${\mathrm{Al}}_{0.15}$ ${\mathrm{Ga}}_{0.85}$As. As a function of composition the ionization energy increases from 6 to 101 meV with a peak at 130 meV near the composition $x=0.45\mathrm{}$ at which a crossover from the direct to the indirect energy gap occurs. From these results it is shown that the donor levels attached to the $\Gamma$, $L$, and $X$ minima are 6, 150, and 101 meV below the respective minima. The variation of the Hall coefficient, the mobility, and the donor ionization energy with composition or pressure are shown to be consistent with the direct-indirect crossover effect.