# A Modified Model Dielectric Function for Analyzing Optical Spectra of InGaN Nanofilms on Sapphire Substrates

## TL;DR

This paper introduces a modified model to analyze the optical properties of InGaN nanofilms on sapphire, enabling accurate predictions of their behavior for photonic applications.

## Contribution

A semiempirical approach combining inter-band transitions and transfer matrix method for simulating InGaN/Sapphire optical spectra.

## Key findings

- The model accurately predicts x-dependent energy gap shifts in InxGa1−xN.
- Simulated reflectivity and transmission spectra align well with experimental data.
- The method avoids computationally intensive electronic band structure calculations.

## Abstract

Due to a lower InN bandgap energy Eg~0.7 eV, InxGa1−xN/Sapphire epifilms are considered valuable in the development of low-dimensional heterostructure-based photonic devices. Adjusting the composition x and thickness d in epitaxially grown films has offered many possibilities of light emission across a wide spectral range, from ultraviolet through visible into near-infrared regions. Optical properties have played important roles in making semiconductor materials useful in electro-optic applications. Despite the efforts to grow InxGa1−xN/Sapphire samples, no x- and d-dependent optical studies exist for ultrathin films. Many researchers have used computationally intensive methods to study the electronic band structures Ejk→, and subsequently derive optical properties. By including inter-band transitions at critical points from Ejk→, we have developed a semiempirical approach to comprehend the optical characteristics of InN, GaN and InxGa1−xN. Refractive indices of InxGa1−xN and sapphire substrate are meticulously integrated into a transfer matrix method to simulate d- and x-dependent reflectivity RE  and transmission TE spectra of nanostructured InxGa1−xN/Sapphire epifilms. Analyses of RE and TE have offered accurate x-dependent shifts of energy gaps for InxGa1−xN (x = 0.5, 0.7) in excellent agreement with the experimental data.