Optical Properties and Electronic Structure of Solid Silicon

The existence of an empty (conduction) band 1. 5 or 2. 0 volts above the highest filled band in metallic-looking semi-conductors such as silicon and certain sulfides is inferred from the optical properties of these substances. Reflectivity data of silicon are examined with the aid of the expression for the complex index of refraction as given by classical electromagnetic theory. Through use of this expression, which is checked for internal consistency, an oscillator strength of 1. 6 electrons is calculated for the absorption, and a dielectric constant at low frequencies of 12. 5 is computed. The Wigner-Seitz-Slater method of computing electronic energy bands in crystals is used to determine the band structure of silicon. A combination of one s, three p, and three d functions for each of the two atoms in the unit cell is made, and through use of boundary conditions of continuity of value, of normal, and of tangential derivatives, a solution is obtained for the plane x=y. The resulting band structure closely resembles that obtained by Kimball for the diamond, except that silicon is more nearly metallic than is the diamond. The 3s level of the silicon atom splits into two bands, the 3p level into six bands, and the 3d level into six bands; the two 3s bands and the lowest two 3p bands are completely filled by electrons. At the observed half-distance between nearest neighbors, the gap between the uppermost filled band and the lowest empty band is much greater than that expected from consideration of the optical data. The form of the optical absorption as expected from band structure considerations is proposed. The width of the filled bands as observed in soft x-ray emission spectra is about equal to the width of the computed bands.