Semiconductor dielectric function, excitons and the Penn model

Abstract

Improved computation of the dielectric function considering excitonic effects and long wavelength is performed and compared with the nearly free electron band approximation, similarly with the Penn’s model case. New expressions for the real and imaginary part of the dielectric function are presented and the real part compared with the Penn’s result. The obtained functions satisfy the Kramers–Krönig relations, in contrast with earlier results in the literature. In addition, our improved dielectric function presents a coefficient of 2/3 for small-gap approximation (different from the value of 1 in the original Penn model) is very close to the value 0.62 obtained in [Can. J. Phys. 53 (1975) p.2549] from pure numerical procedures. The obtained dielectric function also is used in a rough and stimative analysis of the metal–insulator transition in molecular hydrogen being the critical densities determinated near the experimental values for the hydrogen coming from other approach. The approximated expressions and critical values are given and the usefulness of the rough methods involved in the determination of the critical points briefly discussed.

Keywords:

• exciton dielectric function
• Penn model
• metal-insulator transition
• Kramers-Kronig

Acknowledgements

We are very grateful to the people of the Bogoliubov Laboratory of Theoretical Physics (BLTP) and JINR Directorate for their hospitality and financial support and to the reviewers for their suggestions.