Investigation of effective-medium approximation, alloy, average-composition, and graded-composition models for interface analysis by spectroscopic ellipsometry

We critically test the capabilities of the effective-medium approximation (EMA) and alloy models to describe multilayer samples with gradual interfaces by analyzing spectroscopic ellipsometric (SE) data of two AlGaAs samples grown expressly for this purpose. The dielectric functions epsilon of the interfaces are calculated in the EMA and alloy models, and the interfaces themselves simulated either as a single layer of Al0.5Ga0.5As or a stack of layers of AlxGa1-xAs with x increasing or decreasing between 0.1 and 0.9 in increments of 0.1. The EMA essentially fails completely for either interface representation. For the alloy model the stepwise-graded representation is significantly better, not only simulating the data more accurately but also yielding thicknesses in essential agreement with those obtained by cross-sectional transmission electron microscopy. The results highlight the types of errors that are encountered with the different models, and show that the analysis of SE data can provide information about these interfaces. (C) 2007 American Institute of Physics.