First-principles study of the local vibrational properties of $H_2$ and $H_2^*$ complexes in crystalline Si

Abstract

We study the local vibrational properties of $H_2$ and $H_2^*$ complexes in crystalline Si through first-principles pseudopotential calculations within the local-density-functional approximation. The vibrational modes and frequencies are determined by the full dynamical matrix constructed using a supercell geometry. Including gradient corrections for the exchange-correlation potential, we find the vibrational frequencies of 2071 and $1784 cm^{-1}$ for the stretch modes of the $H_2^*$ complex, while 784 and $598 cm^{-1}$ for the wagging modes, consistent with experimentally measured values. For the $H_2$ molecule at a tetrahedral site, we examine the [100], [110], and [111] orientations, and find the stretch modes in the range of $3556 - 3643 cm^{-1}$, in good agreement with previous calculations and experiments. We also predict new soft local modes for the $H_2$ molecule at $650 - 700 cm^{-1}$, which lies above the bulk phonon band.