Local-pseudopotential calculation for optical properties and photoemission valence-band spectrum of silicon

A simple analytic local pseudopotential has been suggested for silicon. This pseudopotential has four adjustable parameters ( beta 1/ beta 2, C1, C2, C3) of which two are taken to give the values of W(111) and W(311) used by Cohen and Bergstresser (1966) and beta 1/ beta 2 is taken from Animalu and Heine (1965), leaving one parameter which the authors choose to obtain a fit. The band structure, reflectivity spectrum and valence density of states were calculated on the basis of this pseudopotential and compared with the experimental results and the corresponding non-local pseudopotential calculations. It is shown that the local pseudopotential approach to silicon can give at least as good results as the more complicated non-local approaches of recent years. This is due to the inclusion of form factors for larger reciprocal lattice vectors (g2>(2 pi /a)211) which other workers have taken as zero. From the results of the present paper it becomes apparent that an adequate estimate of the influence of non-local features can be made only after investigations of the possibilities of the local pseudopotential.