Coulomb correlations in semiconductors

We use tight-binding theory to demonstrate how $k\cdot p$ theory and local-density approximation (LDA) energies should be corrected to incorporate Coulomb correlation corrections. Applications to the enhanced band gap for the creation of quasiparticles, to the effective mass of carriers, and to the static dielectric susceptibility are given. We find that, in the $k\cdot p$ calculations of effective masses, use of the enhanced gap is only accurate for small-gap semiconductors. In the expression for the static dielectric constant, one should use the unenhanced LDA gap for the leading term and the enhanced gap for the metallization term.