NUMERICAL ELLIPSOMETRY - ENHANCEMENT OF NEW ALGORITHMS FOR REAL-TIME,IN-SITU FILM GROWTH MONITORING

The equations associated with the popular models of film deposition of a material on a substrate tend not to be invertible in practical situ ations. Thus, development of numerical techniques for obtaining approx imate solutions to these equations has become necessary. The variably damped least squares (VDLS) algorithm of Levenberg and Marquardt is co mmonly used, although it requires accurate initial estimates and is ty pically too slow for real-time applications. Another algorithm combine s the speed of an artificial neural network (ANN) for accurate initial estimates, and the real-time refinement capability of VDLS for real-t ime 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 p rocessing. The algorithm 2C employs the techniques of dynamic step adj ustment, 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.