Radiative Recombination of Electron-Hole Pairs Generated by Two-Photon Absorption in Indium Antimonide

The radiative-recombination coefficient $r$ of electron-hole pairs in InSb generated by irradiation with a C${\mathrm{O}}_2$ laser is calculated and compared with measurements at liquid-He and -${\mathrm{N}}_2$ temperatures. To obtain the theoretical $r$, the spontaneous transition rate is calculated using Kane's wave functions with the assumption of parabolic energy bands. Thermal equilibrium, within each band and between the two valence bands, is also assumed. Measurements of the decay of excess conductivity yield $r\approx 1\times {10}^{-9\mathrm{}}$ ${\mathrm{cm}}^3$ ${\sec }^{-1\mathrm{}}$ at both 2 and 4 °K. No value for $r$ could be measured at 77 °K since the decay is dominated by a monomolecular recombination process at this temperature. The experimental values of $r$ are between one and two orders of magnitude smaller than the theoretical values. This large discrepancy is caused by the nonparabolicity of the heavy-hole band. The possibility of acquiring accurate information about the shape of the warped valence band by measuring the decay of excess-carrier densities at liquid-He temperatures is discussed.