Numerical techniques useful in the practice of ellipsometry

While well-established methods for sample preparation and measurement make ellipsometry attractive for surface and film investigations, development of reliable methods for computing unknown physical attributes of reflecting surfaces is just beginning, This situation has arisen because the equations of ellipsometry are transcendental, have not been inverted and thus require numerical techniques for solution in all but the simplest of reflecting surface configurations. The problem of data analysis is by no means solved and remains one of the key issues in ellipsometry. This paper presents a survey of numerical techniques and principles for approximating solutions to problems, and illustrates an application of these techniques in the development of a new algorithm to address the problem.