Correlation between the static refractive index and the optical bandgap: Review and new empirical approach

Highlights

• New empirical relation correlates the static refractive index to the optical bandedge.

• Bandgap structure.

• Empirical relation between the static refractive index to the optical bandgap/band edge.

• Comparative study.

• New empirical relation correlates the static refractive index and the optical bandgap/band edge.

Abstract

The static refractive index n_o of different types of materials, like semiconductors, insulators, oxides, thin-films, and glasses, has been reported in many publications in attempts to estimate how it can be correlated to the optical bandgap. Reviewing of the previous studies to correlate the optical refractive index and energy gap led to concluded that Reddy Ahmmed approximation was selected to develop a new realized form that can give a good fit to the experimental data and, hence, be used directly as an accurate formula in the theoretical studies. The obtained formula correlates the optical/static refractive index to the energy bandgap and the oxygen atom's electronegativity. Such a new relation has been used to calculate the refractive indices for more than 96 materials (elements/compounds) with a high agreement with the experimental data.

Introduction

The refractive index, or the index of refraction, is used to measure the bending of the electromagnetic radiation when transiting between two different mediums. In other words, the refractive index of a substance shows how much is bending in the path of radiation in such a substance. The refractive index is dependent on the optical absorption of the material, where its atoms can absorb and re-emit electromagnetic radiation. The materials of the high absorption coefficients should have high refractive indices and vice versa. It's well known that optical absorption is strongly dependent on the electronic transitions over the energy gap E_g. From this point of view, the relation between the refractive index and the optical bandgap has arisen. Generally, the bandgap describes the maximum energy at which the transparency of a substance starts to increase. When the energy of light increases toward the optical bandgap value, the refraction index should be increased. The refractive index of the different categories of materials such as thin films, nanocomposites, nanopowder, chalcogenide glasses, oxide glasses, and all other semiconductors has been important in their potential and advanced applications. In many fields of electronic and Opto-electronic devices like linear and non-linear optics, light-emitting diodes, photovoltaic cells, photo-detectors, lasers, modulators, integrated circuits, and optical filters, the refractive index is utilized.

Furthermore, the optical refractive index is an important macroscopic parameter related to many microscopic properties, like; the internal local field and the matter's electronic polarizability [[1], [2], [3], [4], [5], [6], [7]]. Many researchers have attempted to propose, develop, and obtain simplified relations related to the optical refractive index to the energy bandgap [[8], [9], [10], [11], [12], [13], [14]]. Moss, Revindra et al. and Reddy et al. have proposed mathematical relations [[15], [16], [17], [18]] that correlate the optical refractive index of the matter to its plasmon’ energy bandgap. Also, they successfully used such relation to calculate some different parameters like bond length, bond energy, …, etc., for the set of semiconductors. All these models showed an ability to calculate the optical refractive index with high accuracy for a limited number of materials and limited energy ranges. Every day, there are many attempts to propose new models or modify the oldest one to cover many materials and long ranges of energy. In general, the refractive index of a material is a function of energy, dopants, thickness, voids, grain boundaries, etc. To minimize these variations, the authors consider only the static/optical refractive index due to the time-independent component of the light and electric field. This study may be considered as a brief overview of the understanding of the know-how of correlations between the optical bandgap of semiconductors and their static refractive indices. The models of Moss and Penn and the relation of Ravindra are reviewed and briefly discussed based on the previous publication approaches. So, this work was performed to get more accurate comparison between the static refractive index and the optical energy bandgap for the best fit of the experimental data. The data of the refractive index and the bandgap were collected from many publications for different materials. Subsequently, all data were simulated using each relation, separately, for comparison with the suggested relation, to know the high accuracy and the correlation between the refractive index to the energy bandgap.