Effects of energy gap and band structure on free-carrier nonlinear susceptibilities in semiconductors

Abstract

Using dispersion relations from the Kane band model, we obtain limiting forms for the third-order nonlinear susceptibilities due to nonparabolicity, thermal-carrier generation, and nonequilibrium optical-carrier generation. We show that whereas χ(3)’s for all three processes increase with decreasing energy gap, there is no further benefit once Eg becomes smaller than either the Fermi or thermal energies. In fact, simultaneous optimization of both the magnitude of χ(3) and the saturation properties favors materials with a large direct gap and large effective mass, coupled with a smaller thermal gap which may be indirect in either real or momentum space.