Size-dependent refractive index of semiconducting nanomaterials: A semi-empirical model

Abstract

This study presents a semi-empirical model for predicting the refractive index of semiconducting nanomaterials based on size and dimension. The model uses the bond energy model to calculate dimensional-dependent refractive index, relating nanomaterial energy band gap to refractive index at the nanoscale. It incorporates the relaxation factor for dangling bonds, critical size, and relevant size of the nanosolid to study optical behaviour of semiconducting nanomaterials. The Herve and Vandamme relation, correlating refractive index and band gap for bulk materials, is adapted for nanomaterials by incorporating the size-dependent band gap expression from the bond energy model. The model predicts refractive indices of Si, CdS, CdSe, and CdTe at the nanoscale, showing a nonlinear reciprocal relationship between refractive index and material size. Results indicate the refractive index decreases as nanomaterial size reduces, with a sharp drop below the exciton Bohr diameter and gradual decrease above it. This decrease is attributed to the increased proportion of weakly bound surface atoms in nanomaterials, which respond more quickly to the optical field, resulting in higher light transmission velocity compared to bulk structure. The model provides a straightforward approach to predict size-dependent refractive index of semiconducting nanomaterials and is expected to be valuable for researchers fabricating nanodevices.