Modeling the Optical Constants of Ternary Alloys Using Modified Oscillator Model: Application to AlxGa1?xN

Abstract

The optical constants of hexagonal Al x Ga 1--x N alloys for the perpendicular polarization (E ? c) have been modeled in the energy range up to 10 eV for compositions 0x 1. The model employed for describing the dielectric function is the modified oscillator model. The main difference between the employed model and the conventional oscillator model is the use of an adjustable broadening function instead of the Lorentzian one. One additional adjustable parameter per oscillator determines the type of broadening. The adjustable broadening enables us to model transitions with inhomogeneous broadening (i.e. broadening which is not purely Lorentzian) with a single oscillator, while in the conventional oscillator model superposition of several oscillators would be required. We employ a total of five oscillators, giving 21 parameters for each composition, i.e. 84 parameters for the entire composition range 0x 1. This is significantly less than the number of parameters used in modeling the optical constants of Al x Ga 1--x As using harmonic oscillators, where 144 parameters were employed (F. L. Terry, Jr., J. Appl. Phys. 70, 409 (1991)).