Abstract

For stratified samples where material is being uniformly deposited or removed at a known rate, I show that the dielectric function o of the outermost region is determinable exactly and analytically at any given wavelength from the value and the thickness derivative of the complex reflectances for p-polarized, s-polarized, or normally incident light without any knowledge of the underlying structure. This minimal-data approach greatly simplifies analysis compared with the standard procedure, in which dielectric functions are determined sequentially from a combination of new data and previously established sample parameters. It is also robust, eliminating cumulative error and error propagation that can cause conventional analysis to fail. An interferometric method for acquiring complex-reflectance data is proposed, although to achieve the necessary level of accuracy with present technology would be a formidable challenge. For ellipsometric measurements these technical obstacles do not exist, but an equivalent exact solution is not possible. However, I develop a common-pseudosubstrate approximation (CPA) that in applications to semiconductor crystal growth is accurate to better than 0.1%. The minimal-data approach also provides new insights about how sample parameters are determined from measured optical functions. For example, to determine deposition rates one needs to establish the second derivative (curvature) as well, which places additional constraints on measurement accuracy and/or the amount of data required. Also, the small-term expansion of the ellipsometrically determined pseudodielectric function 〈〉, originally derived as a thin-film limit of the three-phase model, is shown to be more generally valid. This result provides a theoretical basis for the direct analysis of several phenomena, including interface mixing, from 〈〉 data obtained during epitaxial growth. Using the CPA, I derive expressions that allow one to assess whether the performance of a given ellipsometer is adequate for growth control. Finally, the influence of selvage layers on determined values of 0 is briefly discussed.

© 1993 Optical Society of America

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