Energy Relaxation in the Bloch-Gruneisen Regime Probed by Weak Antilocalization (WAL) Measurements in GaN Heterostructures

Electron-phonon (e-p) interaction was investigated in wurtzite Al$_{0.15}$Ga$_{0.85}$N/AlN/GaN and Al$_{0.83}$In$_{0.17}$N/AlN/GaN heterostructures with polarization induced two dimensional electron gases in the Bloch-Gruneisen regime. WAL and Shubnikov-de Haas measurements were performed on gated Hall bar structures at temperatures down to 0.3 K. With gate voltage, we cover a carrier density range from 3.41$\times $10$^{12}$cm$^{-2}$ to 4.92$\times $10$^{12}$cm$^{-2}$. Moreover, we used the WAL as a thermometer to measure the electron temperature T$_{e}$ as a function of the bias current. We find the power dissipated per electron P$_{e}$ is proportional to T$_{e}^{4 }$ due to piezoelectric acoustic phonon emission by hot electrons. We calculated P$_{e}$ as a function of T$_{e}$ without using any adjustable parameters for both static and dynamic screening cases of piezoelectric e-p coupling. In the temperature range of this experiment the static screening case is expected to be applicable; however, our data are in better agreement with the dynamic screening case.