Acoustic phonon scattering in a low density, high mobility AlGaN/GaN field effect transistor

We report on the temperature dependence of the mobility, $\mu$, of the two-dimensional electron gas in a variable density AlGaN/GaN field effect transistor, with carrier densities ranging from 0.4$\times10^{12}$ cm$^{-2}$ to 3.0$\times10^{12}$ cm$^{-2}$ and a peak mobility of 80,000 cm$^{2}$/Vs. Between 20 K and 50 K we observe a linear dependence $\mu_{ac}^{-1} = \alpha$T indicating that acoustic phonon scattering dominates the temperature dependence of the mobility, with $\alpha$ being a monotonically increasing function of decreasing 2D electron density. This behavior is contrary to predictions of scattering in a degenerate electron gas, but consistent with calculations which account for thermal broadening and the temperature dependence of the electron screening. Our data imply a deformation potential D = 12-15 eV.