Comprehensive analysis of Si-doped ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ ($x=0\mathrm{} \mathrm{to} 1$): Theory and experiments

Temperature-dependent Hall-effect measurements were carried out both in dark and in ambient light on Si-doped ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ layers grown by molecular-beam epitaxy over the entire composition range. Above 150 K, the measured Hall carrier densities (different from actual electron densities near the direct-indirect transition) show an exponential dependence on temperature. A shallow donor (≤15 meV) tied to the $\Gamma$ band and a deep donor level tied to the $L$ band were observed. The deep donor is dominant for $x>\mathrm{}0.2\mathrm{}$, and its activation energy $E_d$ rises dramatically up to the direct-indirect band-gap crossover and peaks at 160 meV for $x\sim 0.48$. As the A1 fraction increases further, $E_d$ decreases, reaching 57 meV for AlAs. The error due to multivalley conduction on the measured values of $E_d$ is shown to be negligible. The variation in $E_d$ of the dominant donor level with $x$ is accounted for by our theoretical calculations using a multivalley effective-mass model. A decrease of $E_d$ with increasing doping densities is also observed. At high substrate-growth temperature, the incorporation of Si atoms was found to decrease. The persistent-photoconductivity (PPC) effect was observed with an increase in mobilities over the dark values in the entire composition range. The effect was most pronounced in the range $0.20\le x\le 0.40$. Traps related to the Si-doping density appear to be responsible for the observed photoconductivity effect. The ratio of the PCC traps and the Si atomic density is maximum at $x\sim 0.32$ and is minimum in the direct-indirect band-gap crossover region.