Theoretical studies of self-diffusion and dopant clustering in semiconductors

Density functional theory studies have been performed to investigate the mechanisms of serf-diffusion in Ge and the clustering of B in Si. In the case of self-diffusion of Ge, we find within the harmonic transition state theory a diffusion prefactor for the vacancy mechanism which is in good agreement with experimental values. However, the activation energy is underestimated by nearly 1 eV when the PW91 functional is used. We propose a duster correction procedure involving the hybrid B3LYP functional which leads to an activation energy of 3.1 eV in agreement with experiment. The contribution of interstitial and exchange mechanisms is negligible. The reaction pathway for the B duster formation in Si has also been studied. The cluster B₃I₂ has been identified as an intermediary in the formation of B₃I^-, a dominant cluster. The dimer method is found to be effective for finding transition states for complex systems. All of the steps identified to date have been shown to be diffusion limited.