Exchange and Correlation in Semiconductors and Insulators.

Adequate treatment of exchange and correlation in the motion of the electrons in solid state systems is a many body problem of longstanding difficulty both for the evaluation of ground state energies and spectroscopic properties. The density functional theory addresses the former, but a first principles approach to excitation energies applicable in practice is an outstanding problem. The primary goal of the present dissertation is to give a first principles theory for the quasiparticle energies and band gaps in semiconductors and insulators. Secondarily, work has been done on exchange-correlation functionals that go beyond the usual local density approximation (LDA). To formulate excitation energies, exchange and correlation are included in the electron self energy operator, Sigma. The quasiparticle properties are calculated from Dyson's equation. Here Sigma is evaluated in the GW approximation: the first term in an expansion of Sigma in terms of the dynamically screened Coulomb interaction and the dressed Green's function. Quasiparticle energies are calculated for the homopolar materials diamond, Si and Ge as well as the ionic compound LiCl. The results are in excellent agreement with available experimental data. It is shown that the full dielectric screening matrix must be included, i.e. local field effects are essential. The local fields in diamond, Si, Ge and LiCl are illustrated for the response to an applied external electric field as well as an added point charge (electron) at various sites in the unit cell. The latter illustrates the role of local fields in modifying the screening cloud around the quasi-particles e.g. distinguishing those in the bond region from those in the interstitial region. The energy dependence of Sigma is also crucial and the role of dynamical renormalization is illustrated. In the density functional approach a weighted density approximation is applied here to Si and Ge. It is based on an improved description of the exchange-correlation hole that explicitly accounts for the charge inhomogeneity as well as the qualitatively different screening in semiconductors. The resulting functional yields excellent structural properties. Comparison of the eigenvalues to spectroscopic data shows no significant improvement over the LDA results.