A MODIFIED HARMONIC-OSCILLATOR APPROXIMATION SCHEME FOR THE DIELECTRIC-CONSTANTS OF ALXGA1-XAS

The dielectric functions of Al(x)Ga1-xAs 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 Al(x)Ga1-xAs-containing samples, and for other optical modeling purposes, a resonable 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 Al(x)Ga1-xAs-containing samples grown by molecular-beam epitaxy and organometallic chemical vapor deposition.