Static limit co 0 spatial dependence of screening processes

Static limit co = 0 spatial dependence of screening processes 

In semi-conductors, screening effects have been described in a much less detailed way, using an assumption of spatial homogeneity and isotropy of space, and a simplified account of the electronic structure (Penn, 1962 Bechstedt and Enderlein, 1979 Levine and Louie, 1982 Cappellini et al, 

For example, Cappellini et al. (1993) have proposed for e q,co = 0) the following expression (C an empirical parameter)  

At q = 0, e q,oj = 0) is equal to the optical dielectric constant foo-Equation (4.2.9) gives the contribution of free electrons for large q  

By comparing their model to experimental results obtained in Si, Ge, GaAs, and ZnSe, the authors have found that the empirical parameter C is roughly constant in the series C 1-56. They deduce, from (4.2.9), the coulomb hole expression as a function of the local density p(r), the Fermi fep and Thomas-Fermi wave vectors. 

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