Abstract
The polarization (P) dependence of the exchange-correlation energy () of semiconductors results in an effective field (/∂)P≡P in the Kohn-Sham equations [Gonze et al., Phys. Rev. Lett 74, 4035 (1995)]. This effective field is absent in local-density approximations such as LDA and GGA. We show that in the long-wavelength limit ≃- where χ is the linear susceptibility. We find that scales roughly linearly with average bond length suggesting a simple, weakly material-dependent function [P]. For medium-gap group IV and III-V semiconductors is remarkably constant: =-0.25±0.05. Using the average LDA band gap mismatch Δ and the average quasiparticle gap a simplified quasiparticle approach yields -≃-Δ/(χ)=-0.27 *0.10 in good agreement with the value of . However, for materials containing first-row elements (B,C,N,O) varies by a factor of 2 while Δ/(χ) is roughly constant. That is, the simple quasiparticle estimate fails to reproduce the polarization dependence of [P]. For nonlinear response functions, an analysis of [P] leads to Miller-like expressions ≃[/, n= 2, 3, where the formula for is valid only when =0. For , this estimate works well for all the materials including those containing first-row elements. © 1996 The American Physical Society.
- Received 24 April 1996
DOI:https://doi.org/10.1103/PhysRevB.54.8540
©1996 American Physical Society