Gilat-Raubenheimer scheme

The approach most commonly used, and used extensively in the curves in this book, is the Gilat-Raubenheimer scheme (Raubenheimer and Gilat, 1966). In this scheme, the idea is to replace the true bands by approximate bands, but then to calculate the density of levels for that spectrum accurately. This is done by dividing up the Brillouin Zone, or a forty-eighth of the /one for cubic symmetry, into cells of the order of fifty may be appropriate Raubenheimer and Gilat used cells in the shape of cubes. They then fit each band in each cell by a linear expression,... 

In the Gilat-Raubenheimer scheme it is inconvenient to obtain the nece.ssary values of the gradient of the energy with respect to wave number in each cell, and the cubes do not fit the Brillouin Zone section exactly, so there are problems in calculating the energy at the surface of the. section. For this reason Jepsen and Andersen (1971) and later, independently, Lehman and Taut (1972) replaced... 

A schematic representation of the Gilat-Raubenheimer scheme for calculating densities of states. The energy bands (a) are replaced by linear bands (b) in each cell. The contribution by each cell to each of a set of small energy intervals (c) is then obtained analytically. 

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