Quantum transition-state theory, based upon the path-integral formalism, was used to study the jump rate of atomic hydrogen and deuterium in crystalline silicon. This permitted study of the influence of vibrational mode quantization and quantum tunneling upon the impurity jump rate. The atomic interactions were modeled by effective potentials, fitted to earlier ab initio pseudopotential calculations. Silicon nuclei were treated as quantum particles up to second-nearest neighbors of the impurity. The hydrogen jump rate obeyed an Arrhenius law, described by classical transition-state theory at above 100K. At about 80K, a change in the slope of the Arrhenius plot was found for hydrogen, as expected for the onset of a diffusion regime controlled by phonon-assisted tunneling of the impurity. For deuterium, no change in slope was observed at temperatures down to 4K.

Thermally Assisted Tunneling of Hydrogen in Silicon: a Path-Integral Monte Carlo Study. C.P.Herrero: Physical Review B, 1997, 55[15], 9235-8