Quantum statistics effects in surface diffusion: application to diffusion of nitrogen adatoms over GaN(0001) surface

It has been demonstrated that quantum effects play an important role in nitrogen adatom diffusion over partially Ga-covered GaN(0001) surfaces. This is partially related to the bonding in both the initial and activated complex states. It is shown that wurtzite gallium nitride is bonded differently from standard semiconductors having two separate valence subbands: upper by gallium 4sp³ hybridized orbitals and nitrogen resonant 2p states, and lower by gallium 3d and nitrogen 2s orbitals. Second, the diffusion energy barrier may be changed owing to the quantum statistics of electrons governed by the Fermi energy, as shown in the case of nitrogen diffusion over a clean and gallium-covered Ga-terminated GaN(0001) surface. Under fractional Ga coverage of the GaN(0001) surface, the nitrogen diffusion energy barrier is at the saddle point. The barrier affects the electron redistribution between the surface quantum states at both the initial and saddle points. In the case of full GaN coverage, the diffusion path is from the top N adatom configuration to the H3 site, which corresponds to the maximal energy. Therefore the diffusion barrier is ΔE_bar = 1.18 eV for clean and ΔE_bar = 0.92 eV for (1/6) ML to finally ΔE_bar = 1.23 eV for full Ga coverage. Thus, the overall barrier was ΔE_bar = 0.92 eV. The identified stable N-on-top configuration for Ga coverage is essential for the GaN growth mechanism.