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Vibrational zero point energy for H-doped Silicon

Most of the studies addressed to computations of hydrogen parameters in semiconductor systems, such as silicon, are performed at zero temperature T=0 K and do not account for contribution of vibrational zero point energy (ZPE). For light weight atoms such as hydrogen (H), however, magnitude of this parameter might be not negligible. This work is devoted to clarify the importance of accounting the zero-point vibrations when analyzing hydrogen behavior in silicon and its effect on silicon electronic properties. For this, we estimate the ZPE for different locations and charge states of H in Si. We show that the main contribution to the ZPE is coming from vibrations along the Si-H bonds whereas contributions from other Si atoms apart from the direct Si-H bonds play no role. It is demonstrated that accounting the ZPE reduces the hydrogen formation energy by ~0.17 eV meaning that neglecting ZPE at low temperatures one can underestimate hydrogen solubility by few orders of magnitude. In contrast, the effect of the ZPE on the ionization energy of H in Si is negligible. The results can have important implications for characterization of vibrational properties of Si by inelastic neutron scattering, as well as for theoretical estimations of H concentration in Si.