Thermally Assisted Tunneling of the B-H Complex in Silicon

Jump rate constants of atomic hydrogen and deuterium in boron-doped crystalline silicon are calculated using quantum transition-state theory, based on the path-integral centroid formalism. A break in the slope of the Arrhenius plot for the jump rate of hydrogen is obtained at $T\sim 60$ K, indicating a crossover from thermally activated quasiclassical motion over a barrier to thermally assisted quantum tunneling, in good agreement with previous experimental results. For deuterium, no deviation from an Arrhenius law is found down to 30 K. It is shown that the defect complex undergoing quantum tunneling consists of hydrogen, boron, and the nearest silicon atoms.