Quantum transition-state theory, based upon the path-integral formalism, was used to study the jump rate of atomic H and D in crystalline Si. This technique provided a method for studying the effect of vibrational mode quantization and quantum tunnelling upon the impurity jump rate. The atomic interactions were modelled by using potentials which had been fitted to earlier  ab initio  pseudopotential calculations. The Si nuclei were treated as quantum particles, up to second-nearest neighbors of the impurity. The H jump rate obeyed an Arrhenius law, and could be described by classical transition-state theory at temperatures above 100K. At about 80K, a change in the slope of the Arrhenius plot was observed in the case of H. This was attributed to the onset of a diffusion regime that was controlled by phonon-assisted tunnelling of the impurity. In the case of D, no change in slope was observed at temperatures ranging down to 40K.

C.P.Herrero: Physical Review B, 1997, 55[15], 9235-8