High-Resolution Study of the One-Electron Spectrum of Si

In the present paper we reexamine the one-particle interband transition contribution to the optical absorption spectrum in Si. In particular we introduce a k·p extrapolation of the pseudopotential method. This allows us to truncate greatly the secular equations appearing in that method. Combining this with a method of zone integration proposed by Gilat and Raubenheimer for phonon spectra, we get ${\epsilon }_2\left(\omega \right)$ curves which show an improvement in computational resolution of ∼${10}^2$. The high speed of our present techniques allows us to examine carefully several models which have been proposed to explain the 3.4-eV fundamental edge in Si. In particular we find dramatic changes in the line shape which depend on the relative position of ${\Gamma }_{{25}^{\prime }}-{\Gamma }_{15}$ and $L_{3^{\prime }}-L_1$. For all models examined, an extremely complex nest of critical points is predicted near the fundamental edge. This indicates that efforts to interpret the fundamental edge from a model of one or two special points in the zone probably cannot be successful.