A series of Mg-doped GaN films were grown by plasma-assisted molecular beam epitaxy at different temperatures and the resulting surface morphology, crystallinity, and electrical propel ties were examined. Although the films were grown under N-rich conditions which usually do not give rise to high quality films, very smooth surfaces were obtained at high temperatures (T(s)greater than or equal to 650 degrees C) when doped with Mg. From the information on grain size measured with an atomic force microscope, the activation energy for Ga diffusion was determined to be similar to 1.0 eV. This low value is considered to be responsible for promoting the diffusion of Ga atoms on the growing surface and facilitating two-dimensional growth at high temperatures. It was found, with no surprise, that the concentration of Mg incorporated into the film depends on the growth temperature and that the type of electrical conduction in the films is determined by the competition between the background electron concentration and Mg-doping. Mg-doped GaN films grown at temperatures between 650 degrees C and 700 degrees C exhibited the p-type electrical properties with smooth surfaces (root-mean-square roughness similar to 2 nm) and good crystallinity (full width at half maximum less than or equal to 20 arcmin).