First-principles self-energy calculations of carrier-induced band-gap narrowing in silicon

We calculate the band-gap narrowing in silicon caused by the introduction of additional electrons, using a first-principles self-energy approach within the GW approximation. We include full local-field effects and the nonlocal and energy-dependent dielectric function of the intrinsic material. We also analyze our calculations to test the approximations normally used in simple models of this effect: local-field effects are found to be unimportant, but the inclusion of the energy dependence of the dielectric response of the intrinsic material, which is normally neglected in model calculations, is found to be crucial at high carrier concentrations.