Semiconductor dielectric function, excitons and the Penn model

DIEGO JULIO CIRILO

PHILOSOPHICAL MAGAZINE

TAYLOR & FRANCIS LTD

Lugar: Londres; Año: 2015

1478-6435

Improved computation of the dielectric function considering excitonic effectsand long wavelength is performed and compared with the nearly free electronband approximation, similarly with the Penn?s model case. New expressionsfor the real and imaginary part of the dielectric function are presented and thereal part compared with the Penn?s result. The obtained functions satisfy theKramers?Krönig relations, in contrast with earlier results in the literature. Inaddition, our improved dielectric function presents a coefficient of 2/3 for smallgapapproximation (different from the value of 1 in the original Penn model) isvery close to the value 0.62 obtained in [Can. J. Phys. 53 (1975) p.2549] from purenumerical procedures. The obtained dielectric function also is used in a rough andstimative analysis of the metal?insulator transition in molecular hydrogen beingthe critical densities determinated near the experimental values for the hydrogencoming from other approach. The approximated expressions and critical valuesare given and the usefulness of the rough methods involved in the determinationof the critical points briefly discussed.