GaAs Optical Properties & Band Gap Analysis

Overview

This project performs a computational analysis of the dielectric function ($\epsilon_2$) for Gallium Arsenide (GaAs) in two structural phases:

1. Crystalline (c-GaAs): Ordered zincblende structure with sharp optical transitions.
2. Amorphous (a-GaAs): Disordered structure with broadened absorption features.

The MATLAB script fits experimental data using non linear least squares optimization (fminsearch) to extract physical parameters, specifically the Optical Band Gap ($E_g$).

Theoretical Models

1. Lorentz Oscillator Model

Used as a baseline to model the classical electron-cloud oscillation. $$\epsilon_2(\omega) = \sum_{j=1}^{N} \frac{A_j \gamma_j \omega}{(\omega_{0,j}^2 - \omega^2)^2 + \gamma_j^2 \omega^2}$$

• Best for: General shape fitting.
• Limitation: Does not account for the band gap onset (predicts absorption at $E=0$).

2. Tauc-Lorentz Model

Used to extract the Optical Band Gap ($E_g$). This model enforces zero absorption below the band gap energy. $$\epsilon_2(\omega) \propto \frac{(\omega - E_g)^2}{\omega}$$

• Best for: Amorphous materials and determining the fundamental gap in semiconductors.

How to Run

Setup MATLAB: Ensure all .txt data files are in the Current Folder or added to the MATLAB path.

Execute: Run the main script in the MATLAB Command Window

Note: To test the fit, you will need experimental measurements for GaAs from spectroscopic ellipsometers.

eg: In natural units: (ω (Photon Energy), Re(Epsilon), Im(Epsilon))

1.567eV 18.750000 6.875000| 1.577eV 18.747999 6.878000| 1.587eV 18.743999 6.886000| 1.597eV 18.736000 6.900000|

Expected Results

Upon running, the script generates a $2 \times 2$ plot window and outputs the following analysis to the console:

Crystalline GaAs (c-GaAs):
  > Found Eg:      [Value calculated by fit] eV
  > Theoretical Eg: 1.424 eV (at 300 K)

Amorphous GaAs (a-GaAs):
  > Found Eg:      [Value calculated by fit] eV
  > Theoretical Eg: 1.5 - 1.7 eV

References

1. Fujiwara, H. Spectroscopic Ellipsometry: Principles and Applications. Springer, 2007.

2. Aspnes, D. E. "Optical functions of semiconductors." Handbook on Semiconductors, 1982.

3. Jellison, G. E., and Modine, F. A. "Parameterization of the optical functions of amorphous materials." Applied Physics Letters, vol. 69, no. 3, 1996, pp. 371–373.