  Diffusion mechanism of beryllium in gallium nitride was investigated by
analyzing temperature-dependent diffusion profiles from an infinite source.
Beryllium atoms were implanted into a high structural quality gallium nitride
layer crystallized by halide vapor phase epitaxy on an ammonothermal gallium
nitride substrate. Post-implantation annealing was performed at different
temperatures, between 1000{\deg}C and 1400{\deg}C, under high nitrogen
pressure. Beryllium profiles were analyzed in the as-implanted and annealed
samples by secondary ion mass spectrometry. It was shown that the diffusion of
the dopant results from the combination of two mechanisms: rapid interstitial
and slow interstitial-substitutional diffusion. The pre-exponential factor as
well as activation energy for both diffusion paths were determined. Moreover,
from the characteristic features of beryllium depth profiles, the formation
energies of gallium vacancy and beryllium in interstitial position were
calculated and compared to the theoretical values.
