Comprehensive analysis of Si-doped<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Al</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ga</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mi mathvariant="normal">As</mml:mi></mml:math>(<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mn/><mml:mi> </mml:mi><mml:mi mathvariant="normal">to</mml:mi><mml:mi> </mml:mi><mml:mn>1</mml:mn></mml:math>): Theory and experiments

Temperature-dependent Hall-effect measurements were carried out both in dark and in ambient light on Si-doped ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ 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 (\ensuremath{\le}15 meV) tied to the $\ensuremath{\Gamma}$ band and a deep donor level tied to the $L$ band were observed. The deep donor is dominant for $x&gt;0.2$, and its activation energy ${E}_{d}$ rises dramatically up to the direct-indirect band-gap crossover and peaks at 160 meV for $x\ensuremath{\sim}0.48$. 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 $0.20\ensuremath{\le}x\ensuremath{\le}0.40$. 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 $x\ensuremath{\sim}0.32$ and is minimum in the direct-indirect band-gap crossover region.