Electronic charge distribution in crystalline diamond, silicon, and germanium

Recent refinement studies of a consolidated set of Si structure factors have produced information on the Si charge density with an unprecedented level of accuracy, unmatched by any other crystallographic study to date. In this work we examine the extent to which an accurate implementation of the local-density formalism can describe the charge distribution in silicon, as well as that of the experimentally less-refined data on diamond and germanium. Results of a refinement study of recent germanium and diamond measurements are presented and compared with the ab initio calculations. Our ab initio calculated structure factors for Si show a twofold to fivefold improvement in the R factor over previous local-density calculations. We describe in detail, total, valence, and deformation charge-density maps for C, Si, and Ge. We analyze the effects of high-momentum components (currently outside the range of the high-precision measurements) as well as dynamic structure factors on the ensuing charge-density maps.