The nucleation anti buffer growth of GaN on (0001) sapphire by molecular beam epitaxy are investigated using the design of experiments approach. Six factors are simultaneously varied: time and temperature for: nitridation, buffer growth temperature, Ga cell temperature, growth time, and nitrogen plasma power during buffer growth. In situ reflection high-energy electron diffraction is utilized to monitor these steps. The quality of the epitaxial layers obtained is examined by means of electron mobility and atomic force microscopy. It is shown that the buffer layer growth rate has the greatest influence on improving the electrical properties of the subsequent GaN epitaxial layer. Depending on the growth conditions, the Hall mobility of the GaN epitaxial layer varies from 24 to 238 cm(2)/Vs. Changes in surface morphology are correlated with improvements in electron mobility. We also discuss interaction effects between the factors. A trend extracted from a least-squares model reveals that 300 K Hall mobility is greatly improved at high growth rate and low nitrogen plasma power during buffer growth.