Highly Ga-doped ZnO (GZO) films of thicknesses d = 5, 25, 50, and 300 nm, grown on 160-nmZnO buffer layers by molecular beam epitaxy, had 294-K Hall-effect mobilities μH of 64.1, 43.4, 37.0, and 34.2 cm2/V-s, respectively. This extremely unusual ordering of μH vs d is explained by the existence of a very high-mobility Debye tail in the ZnO, arising from the large Fermi-level mismatch between the GZO and the ZnO. Scattering theory in conjunction with Poisson analysis predicts a Debye-tail mobility of 206 cm2/V-s at the interface (z = d), falling to 58 cm2/V-s at z = d + 2 nm. Excellent fits to μH vs d and sheet concentration ns vs d are obtained with no adjustable parameters.