We present results for a method to measure directly the energy relaxation time (${\tau }_e$) for electrons in a single ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}/\mathrm{GaAs}$ heterojunction; measurements were performed from 1.6 to 15 K under quasiequilibrium conditions. We find ${\tau }_e\alpha T^{-1\mathrm{}}$ below 4 K, and ${\tau }_e$ independent of $T$ above 4 K. We have also measured the energy-loss rate, $〈Q〉$, by the Shubnikov-de Haas technique, and find $〈Q〉\alpha (T_e^3-T^3)$ for $T<~4.2$ K; $T_e$ is the electron temperature. The values and temperature dependence of ${\tau }_e$ and $〈Q〉$ for $T<\mathrm{}4\mathrm{}$ K agree with calculations based on piezoelectric and deformation potential acoustic phonon scattering. At 4.2 K, we can also estimate the momentum relaxation time, ${\tau }_m$, from our measured ${\tau }_e$. This leads to a preliminary estimate of the phonon-limited mobility at 4.2 K of $\mu =3\mathrm{}\times {10}^7$ ${\mathrm{cm}}^2$/Vs ($n_s=4.2\mathrm{}\times {10}^{11}$ ${\mathrm{cm}}^{-2\mathrm{}}$), which agrees well with published numerical calculations, as well as with an earlier indirect estimate based on measurements on a sample with much higher mobility.

• Received 30 June 1995

DOI:https://doi.org/10.1103/PhysRevB.53.R7592