High quality gallium doped ZnO ͑Ga:ZnO͒ thin films were grown on c-Al 2 O 3 ͑1000͒ by plasma-assisted molecular beam epitaxy, and Ga concentration N Ga was controlled in the range of 1 ϫ 10 18-2.5ϫ 10 20 /cm 3 by adjusting/changing the Ga cell temperature. From the low-temperature photoluminescence at 10 K, the donor bound exciton I 8 related to Ga impurity was clearly observed and confirmed by comparing the calculated activation energy of 16.8 meV of the emission peak intensity with the known localization energy, 16.1 meV. Observed asymmetric broadening with a long tail on the lower energy side in the photoluminescence ͑PL͒ emission line shape could be fitted by the Stark effect and the compensation ratio was approximately 14-17% at N Ga ജ 1 ϫ 10 20 /cm 3. The measured broadening of photoluminescence PL emission is in good agreement with the total thermal broadening and potential fluctuations caused by random distribution of impurity at N Ga lower than the Mott critical density.