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Bisi et al. / Surface Science Reports 38 (2000) 1±126 47 Fig. 48. Comparison of the dielectric function of PS layers prepared on various substrates differing in doping level as indicated. From Ref. . thin or if the material has a large dispersion, other methods should be employed. A more complete evaluation requires simulation of experimental spectra. The square root of the dielectric function resulting from the ®t is the refractive index of the PS layer . The simulation approach requires sharp interfaces, which depends often on the type and quality of substrate.
Porosity obtained from pÀ -and p -type doped Si substrates , and is shown in Fig. 51. The absorption of the p -type doped samples occurs at higher energy compared to pÀ -type doped samples, and the only signi®cant difference in the two samples is the average dimensions of the nanocrystals (about 10 nm for p -type and 3 nm for pÀ -type doped material). A more precise lineshape analysis of the absorption coef®cient shows that the energy dependence of a follows a trend like that of an indirect gap semiconductor very similar to that of Si, even though displaced to higher energy (see Fig.
The refractive index of PS is expected to be lower than that of bulk Si, and decreases with increasing porosity, because PS is basically a mixture of air and Si. However, the averaging of the dielectric functions of the individual components is not trivial, but depends on the microtopology of the material. The application of different effective medium theory leads to different formulas [170±172]. For example, the widely used Bruggemann  formula leads to the following symmetric expression: E À Eeff EM À Eeff 1 À f 0Y (6) f E 2Eeff EM 2Eeff Fig.