A modified harmonic oscillator approximation scheme for th;e dielectric constants of AI,Ga, -Xes

The dielectric functions of Al,Gai _ As have recently been measured for several Al mole fractions over the 1.5-6.0 eV wavelength range [D.E. Aspnes, S. M. Kelso, R. A. Logan, and R. Bhat, J. Appl. Phys. 60, 754 (1986)]. To make use of this data to perform optical modeling for spectroscopic ellipsometry analysis of AIXGal _ As-containing samples, and for other optical modeling purposes, a reasonable interpolation scheme is required to estimate the dielectric functions of-intermediate compounds. In this work, we will present a modified version of the harmonic oscillator approximation (HOA) of Erman et al. [M. Erman, J. B. Theeten, P. Chambon, S. M. Kelso, and D. E. Aspnes, J. Appl. Phys. 56, 2664 (1984)] to model the experimental data and interpolate between the known compositions over the 1.5-5.0 eV range. Our model uses additional harmonic oscillators and allows each oscillator to have -an independent phase. These modifications significantly improve the accuracy of the approximation for photon energies at and below the fundamental band-gap energy. This allows much more accurate modeling of reflection problems for multilayer GaAs/AlGaAs structures. We will present test of this approach with simulations of spectroscopic ellipsometry data using known data, and with measured spectroscopic ellipsometer data on AIXGal -&-containing samples grown by molecular-beam epitaxy and organometallic chemical vapor deposition.