Numerical ellipsometry: enhancement of new algorithm for real-time, in situ film growth monitoring

Abstract

The equations associated with the popular models of film deposition of a material on a substrate tend not to be invertible in practical situations. Thus, development of numerical techniques for obtaining approximate solutions to these equations has become necessary. The variably damped least squares (VDLS) algorithm of Levenberg and Marquardt is commonly used, although it requires accurate initial estimates and is typically to slow for real-time applications. Another algorithm combines the speed of an artificial neural network (ANN) for accurate initial estimates, and the real-time refinement capability of VDLS for real-time performance; however, substantial off-line processing (from hours to days) is necessary to train ANNs. A third algorithm (called 2C) has been developed, which is fast enough for reliable real-time solutions without requiring either accurate initial estimates or any off-line processing. The algorithm 2C employs the techniques of dynamic step adjustment, overrelaxation and reduction in dimensions, as well as curve following and curve intersection location techniques developed by the authors. The performance of the new 2C algorithm in terms of speed and convergence is comparable with the ANN-VDLS algorithms for Ni and BK7 glass.