A modified harmonic oscillator approximation scheme for the dielectric constants of AlxGa1−xAs

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Abstract
The dielectric functions of AlxGa1−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 AlxGa1−xAs‐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 AlxGa1−xAs‐containing samples grown by molecular‐beam epitaxy and organometallic chemical vapor deposition.