Thermally assisted tunneling of hydrogen in silicon: A path-integral Monte Carlo study

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Abstract
Quantum transition-state theory, based on the path-integral formalism, has been applied to study the jump rate of atomic hydrogen and deuterium in crystalline silicon. This technique provides a methodology to study the influence of vibrational mode quantization and quantum tunneling on 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 follows an Arrhenius law, describable with classical transition-state theory, at temperatures higher than 100 K. At ∼80 K, a change in the slope of the Arrhenius plot is obtained for hydrogen, as expected for the onset of a diffusion regime controlled by phonon-assisted tunneling of the impurity. For deuterium, no change of slope is observed in the studied temperature range (down to 40 K).