Ab initio calculation of linear and nonlinear optical properties of semiconductor structures

Abstract

The theoretical and numerical approaches are discussed for ab initio calculations of optical properties. The density functional theory DFT combined with the local-density approximation LDA allows the calculation of the geometry of crystalline solids and their surfaces with a precision of about one percent. The DFT-LDA band structure and single-electron states therefore provide a reasonable starting point for the calculation of linear and nonlinear susceptibilities within the independent-particle approximation. However, this approach has to be improved by taking into account many-body interactions: self-energy e ects, local-eld corrections, and electron-hole attraction. Three types of optical spectra are studied: the frequency-dependent dielectric function, the second-harmonic generation, and surface re ectance anisotropy spectra. The systems considered are two-atomic semiconductors, their polytypes and their surfaces. I IntroductionThe recent major advances in the quantitative computation of ground-state properties of solids are essentially related to the development of density-functional theory DFT in local-density approximation LDA 1 . However, spectroscopic properties, as optical spectra, are not accessible in this theory, since its single-particle eigenvalues or di erences of them cannot be directly identi ed with electronic excitation energies. For instance, energy gaps of semiconductors and insulators are remarkably underestimated within DFT-LDA 2 . Instead, quasiparticle QP energies have to be computed. The basic approach to quasiparticles is Hedin's GW approximation 3 , in which the spatially nonlocal and energy-dependent exchange-correlation XC selfenergy is approximated by a convolution of singleparticle Green function G and dynamically screened Coulomb i n teraction W. Vertex corrections are neglected. Full numerical calculations of the singleparticle excitations can now be performed on real crystals starting from the DFT-LDA results 4,5 .Despite of the complications with the inclusion of the many-body e ects, DFT-LDA has been used to determine the atomic structure and to de ne a reasonable starting point for the description of the electronic structure. Optical spectra have been calculated 6 within the independent-particle approximation 7 . Meanwhile, quasiparticle shifts have been included also in calculations of the complete dielectric function 6,8 . Moreover, the e ects of XC b e y ond the independentparticle approximation have been demonstrated within DFT-LDA for bulk semiconductors, and local-eld effects are taken into account 9 . Very recently the compensation e ect of the dynamical screening in quasiparticle and vertex corrections has been found 10 . Furthermore, the Coulomb attraction of excited electrons and holes has been indeed calculated in the limit of static screening 11 .In the last years such kind of ab initio calculations in the framework of DFT-LDA and the independentparticle approximation has been also applied to nonlinear optical properties of semiconductors, e.g. the second-harmon...