Modified Lorentz oscillator on modeling the dielectric function of Si and Ge

Abstract

The classical Lorentz model is widely used for modeling the dielectric function of insulators. However, it has failed to reproduce the experimental spectra of semiconductors in certain cases. The dielectric response over a wide range of photon energies can be easily understood using the equation of motion for electrons at different energies, particularly those below the optical bandgap. In this study, the Lorentz oscillator was modified to satisfy the Clausius–Mossotti relation, enabling the derivation of a modified Lorentz oscillator suitable for semiconductors. The dielectric response was then analyzed within the framework of the proposed dielectric function model for both the fundamental interband region and the region below the optical bandgap. The fitting results for crystalline silicon (Si) and germanium (Ge) showed that this model can provide satisfactory fitting results from above the reststrahlen region to the interband region. The properties of the dielectric function then can be better understood in terms of the motion of electrons in regions with different photon energies. In addition, the proposed model was used to calculate the static dielectric constants of Si and Ge, the values of which are very close to the actual value. The results indicate that the proposed model is an effective method for determining the static dielectric constant.