State and motion of hydrogen in crystalline silicon

The open-shell version of the modified intermediate neglect-of-differential-overlap molecular-orbital method has been used to obtain the equilibrium positions of H, ${\mathrm{H}}^{+}$, and ${\mathrm{H}}_2$ in a 32-atom cyclic silicon cluster. Two shells of silicon neighbors around the defect have been allowed to relax and reconstruct while the potential surface for the hydrogen was mapped. The absolute minimum has been found for both H and ${\mathrm{H}}^{+}$ at the bond-centered interstitial (BC) site. The H (or ${\mathrm{H}}^{+}$) breaks the lattice bond only if lattice relaxation is allowed. The energy of the H atom relative to the lattice is 0.1 eV lower at this point than its energy in a ${\mathrm{H}}_2$ molecule located on the tetrahedral interstitial ($T_d$) site. An additional local minimum for the atomic hydrogen has been found at a distance of 0.42 Å from the $T_d$ site in the 〈111〉 direction toward the next silicon atom, the antibonding (AB) site. This site is 0.92 eV higher in energy than the BC site. Saddle-point calculations show that the activation energy for diffusion of H is about 0.8 eV from the BC site, and about 0.4 eV for diffusion between AB sites. No gap levels arise with the H atom on the BC site. A donor level emerges above the valence-band edge when the H atom moves from one BC site to another. This can be ionized in a p-type material. The ionized system exhibits the same diffusion path for hydrogen.