Equivalence between the LCHO Model and the Phillips Theory. I. The SHG Constant χ₁₂₃⁽²⁾ of the Semiconductors of Sphalerite Type

Abstract

By following straightforwardly the model originally proposed by Phillips and Van Vechten and revised afterwards by Kleinman for explaining the nonlinear optical constants of zinc-blende type semiconductors, without their important but invalid assumption ⟨a|ξ|a⟩+⟨b|ξ|b⟩=0, we have proved that their model is essentially equivalent to the primitive LCHO–MO model and the combination parameter λ and the overlapping integral S in the latter model are related with the two parameters E_h and C, the homopolar and heteropolar energy gaps, in the former model, in a simple form λ={(E_g+E_h)\sqrt1−S+C\sqrt1+S}⁄{(E_g+E_h)\sqrt1−S−C\sqrt1+S}. Observed values of the SHG constant χ₁₂₃⁽²⁾ of several semiconductors are compared with the calculated values by introducing the reduction factor 2/3 on the heteropolar energy gap C.