Correlation of electrical and optical properties of the vanadium-related C level in silicon

Abstract

Gibb's free energies due to hole transitions between the C level of Si:V and the valence band have been determined for eleven different temperatures within the range 190 K\ensuremath{\leqslant}T\ensuremath{\leqslant}270 K on the basis of simultan- eous measurements of corresponding thermal hole capture coefficients and emission rates. Zero-phonon binding energies have been determined from the low-energy part of photoionization cross-section spectra at five different temperatures within the range 75 K\ensuremath{\leqslant}T\ensuremath{\leqslant}170 K. The temperature dependence of these binding energies can be described by a Varshni-type analytical formula with a zero-temperature level position of ${\mathrm{E}}_{\mathrm{v}}$ +0.361 eV (\ifmmode\pm\else\textpm\fi{}0.003 eV). The associated ratio of the temperature-induced change of this level position with respect to the one of the band-gap energy is about 0.80 (\ifmmode\pm\else\textpm\fi{}0.10). The inherent correlation between electrical and optical level position parameters was used to calculate the temperature dependence of the zero-phonon binding energy, ${\mathrm{J}}_{\mathrm{p}}$ (T), the Gibb's free energy, ${\mathrm{G}}_{\mathrm{p}}$ (T), and the enthalpy, ${\mathrm{H}}_{\mathrm{p}}$ (T), from 0 K to room temperature. Using two photoionization cross-section spectra, the associated Franck-Condon shift was estimated to be about 0.04 eV.