  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.
