A Combined Topographical Search Strategy with Ellipsometric Application

Abstract

A comparison deals with the advantages and disadvantages of the classical random-base, exhaustive and gradient searches and presents a precise local search combined global search control strategy including a new, systematic point selection which makes possible the escape from local minima by time. As a demonstration electrochemically etched porous silicon (PS) samples were investigated by spectroscopic ellipsometry (SE). The evaluation process (a global optimisation task) was made in different ways to see the difficulties and the differences among the evaluating possibilities. The new, topographical search (named Gradient Cube search) was compared with some classical methods (Grid search, Random or Monte-Carlo search, and Levenberg-Marquardt gradient search) and with two more complex algorithms (Genetic Algorithms and Simulated Annealing) by evaluating real measurements. The application results prove that the classical methods have difficulties to give enough reliability and precision at the same time in global optimisation tasks if the error surface is hilly. There is therefore a hard need of escaping from local minima, and a need of a systematic evaluation to avoid the uncertainty of random-base evaluation. The Gradient Cube search is an effective, systematic hill-climbing search with high precision and so it can be useful in ellipsometry.