Erratum: Raman scattering and photoluminescence in boron-doped and arsenic-doped silicon

Abstract

The deformation potentials and $g$ values of the ground state of the boron acceptor in silicon have been determined from a study of the stress and Zeeman splitting of the electronic Raman scattering in this material. The stress splitting of the Raman line results from a twofold splitting of the ${\ensuremath{\Gamma}}_{8}$ ground state only and yields the shear deformation potentials ${b}^{\ensuremath{'}}=\ensuremath{-}1.46\ifmmode\pm\else\textpm\fi{}0.06$ eV and ${d}^{\ensuremath{'}}=\ensuremath{-}4.16\ifmmode\pm\else\textpm\fi{}0.12$ eV. The temperature dependence of the Zeeman spectra indicates that the observed Zeeman components arise only from a splitting of the acceptor ground state. This conclusion is supported by the anisotropy of the Zeeman pattern which is characteristic of the splitting of a ${\ensuremath{\Gamma}}_{8}$ level. An analysis of the Zeeman splittings yields the phenomenological average $g$ value squared ${M}^{2}=1.23\ifmmode\pm\else\textpm\fi{}0.04$ and the anisotropy parameter $\ensuremath{\epsilon}=\ensuremath{-}0.07\ifmmode\pm\else\textpm\fi{}0.02$. The corresponding parameters of the Luttinger spin Hamiltonian are $K=0.84\ifmmode\pm\else\textpm\fi{}0.09$ and $L=0.13\ifmmode\pm\else\textpm\fi{}0.08$ in contrast to the values of $K=1.21\ifmmode\pm\else\textpm\fi{}0.01$ and $L=0.00\ifmmode\pm\else\textpm\fi{}0.01$ obtained by Feher, Hensel, and Gere using paramagnetic resonance in uniaxially stressed samples. The $g$ values obtained from magneto-Raman measurements on stressed samples are consistent with the zero-stress magneto-Raman results, and the discrepancy between the two sets of experimental results remains unexplained. The Zeeman splitting of the photoluminescence of excitons bound to neutral arsenic donors has been interpreted in terms of a simplified model of the silicon band structure. For the $g$ value of the hole in the bound-exciton complex we obtain ${M}^{2}=1.44\ifmmode\pm\else\textpm\fi{}0.07$ and $\ensuremath{\epsilon}=\ensuremath{-}0.12\ifmmode\pm\else\textpm\fi{}0.04$ corresponding to $K=0.74$ and $L=0.22$; for the $g$ value of the ground state of the arsenic donor we get ${g}_{e}=1.85\ifmmode\pm\else\textpm\fi{}0.06$. The electronic $g$ value is in disagreement with electron-spin-resonance results. A quadratic diamagnetic shift of the bound exciton is also observed.