Modeling the optical constants of ternary alloys using modified oscillator model:: Application to AlxGa1-xN

The optical constants of hexagonal AlxGa1-xN alloys for the perpendicular polarization (E perpendicular to c) have been modeled in the energy range up to 10 eV for compositions 0 less than or equal to x less than or equal to 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 fur the entire composition range 0 less than or equal to x less than or equal to 1. This is significantly less than the number of parameters used in modeling the optical constants of AlxGa1-xAs using harmonic oscillators, where 144 parameters were employed (F. L. Terry, Jr., J. Appl. Phys. 70, 409 (1991)).