A first-principles molecular dynamics simulation is applied to an H-terminated Si(111) surface subjected to Si-H $\overrightarrow{\sigma }{\sigma }^{*}$ excitation which was mimicked by promoting the electron occupations. To take the finite lifetime of the excited state into account, the time-dependent electronic Schrödinger equation has been solved and coupled with the classical Newton equation of ions. Density functional theory with use of the local density approximation (LDA) and the generalized gradient approximation (GGA) was adopted to express the Hamiltonian. To study influence of localization of the excited state and height of the density of state (DOS) of the system on the simulated results, systematic calculations using clusters and slab models with several sizes were performed. Strong localization of the excited state in cluster models caused stronger forces compared to those in slab models. Such overestimation of the localization indicates that cluster models have been found to be inappropriate for expressing electronic excited states on solid surfaces. On the other hand, the computed lifetime of the excited state was found to become shorter as the cluster became larger and as the slab became thicker. This fact was attributed to higher DOS in extended systems that opened many decay paths. The obtained lifetime in slab models was on the order of (or less than) 10 fsec, which was too short to induce a direct H dissociation and consistent with the very low yield of the dissociated H atoms in recent experiments. The decay of the excited state was due to relaxation of the Si-valence electrons to the Si-H $\sigma$-hole state, but neither due to the direct recombination of ${\sigma }^{*}\to \sigma$ nor relaxation of the ${\sigma }^{*}$ state into the Si conduction bands. Finally, detailed comparison between LDA and GGA results are also presented.

• Received 15 June 1999

DOI:https://doi.org/10.1103/PhysRevB.62.2039