3RD-ORDER NONLINEAR-OPTICAL SUSCEPTIBILITIES OF GROUP-IV AND GROUP-III-V COMPOUND SEMICONDUCTORS

We calculate the third-order nonlinear optical susceptibility (chi(3)) of tetrahedrally coordinated solids by adopting a simple method of linear combination of hybrids developed by us. We have constructed a basis state for the valence bands which is a linear combination of hybrids forming a bond in which their relative phase factors, heretofore neglected, have been properly included. We have also constructed the basis states for the conduction bands which are orthogonal to the valence band functions. We have used our basis states in the expression for the nondispersive part of chi(3)) at T = 0 K to derive an expression for chi(xxxx)(3) of tetrahedral semiconductors. We have used the Hall-Weaire-Thorpe approximation to calculate the matrix elements between different hybrids and made an average-energy-gap ansatz (E(g)) for the energy gap denominator occurring in the expression for chi(3). Our expression for chi(3) is obtained in a tractable form in term of matrix elements between intrasite hybrids and between adjacent hybrids forming a bond. We have calculated chi(xxxx)(3), for a large number of tetrahedral semiconductors. Our results yield the correct sign and reasonable agreement in magnitude with experiment, unlike the earlier chemical-bond models.