Excitation cross section of erbium in semiconductor matrices under optical pumping

Abstract

Based on a detailed consideration of excitation mechanisms of erbium in crystalline and amorphous matrix we present an analysis of the physical meaning of the Auger excitation cross section of ${\mathrm{Er}}^{3+}$ ions in semiconductor. It is demonstrated that large values of Auger excitation cross sections under optical pumping in semiconductor matrices are due to large values of band-to-band absorption coefficient exceeding by several orders of magnitude the absorption coefficient of erbium in dielectric ${\mathrm{SiO}}_{2}$ and ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ matrix. The Auger excitation cross section of ${\mathrm{Er}}^{3+}$ in semiconductor matrices is roughly given by the ratio of the matrix absorption coefficient to concentration of ${\mathrm{Er}}^{3+}$ ions. While the analysis of the excitation cross section is carried out for Er-doped crystalline and amorphous silicon, the results are expected to be applicable to the other rare-earth doped semiconductors. Based on low-temperature experimental results for crystalline silicon we get the Auger excitation coefficient of ${c}_{A}^{\mathrm{cryst}}\ensuremath{\approx}7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10} {\mathrm{cm}}^{3}{\mathrm{s}}^{\ensuremath{-}1}$ and the effective excitation cross section ${\ensuremath{\sigma}}_{\mathrm{eff}}^{\mathrm{cryst}}=(2\ensuremath{-}8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12} {\mathrm{cm}}^{2}.$ For amorphous silicon at 100 K we obtain ${\ensuremath{\sigma}}_{\mathrm{eff}}^{\mathrm{amorph}}\ensuremath{\approx}1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14} {\mathrm{cm}}^{2}.$