Two-Photon Excitation Rate in Indium Antimonide

Abstract

Kane's wave functions for InSb are used with second-order perturbation theory to obtain an accurate expression for the two-photon transition rate. The statistics of the crystal electrons are included in the general expression. A simplified expression is obtained under assumptions that fit our experimental conditions well, namely, the valence-band states and the conduction-band states involved in the transitions are completely filled and completely empty, respectively. The transition rate per unit volume at 77 \ifmmode^\circ\else\textdegree\fi{}K is $0.36{\mathfrak{g}}^{2}$ and $0.064{\mathfrak{g}}^{2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ with irradiation wavelengths $\ensuremath{\lambda}=9.6 \mathrm{and} 10.6$ \ensuremath{\mu}m, respectively, and at 2 \ifmmode^\circ\else\textdegree\fi{}K the rate is $0.25{\mathfrak{g}}^{2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ with $\ensuremath{\lambda}=9.6$ \ensuremath{\mu}m, for irradiation intensity $\mathfrak{g}$ in erg ${\mathrm{sec}}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{\ensuremath{-}2}$. The rate for $T=77$ \ifmmode^\circ\else\textdegree\fi{}K and $\ensuremath{\lambda}=10.6$ \ensuremath{\mu}m previously reported by Danishevskii is one order of magnitude larger than the present result. This discrepancy in the calculated values is rationalized. Measurements of the transition rates are described and the obtained values are given for the two temperatures and two wavelengths mentioned above. The agreement between our measured and theoretical values is within the experimental accuracy.