Real-time combined reflection and transmission ellipsometry for film-substrate systems

摘要

Combined reflection and transmission ellipsometry of film-substrate systems provides a wealth of experimental information that proves helpful with extracting the system parameters. In such a technique, both the reflection and transmission ellipsometric functions are simultaneously measured. The technique itself requires a special design of the sample for fixed and for multiple angles of incidence measurements. The data reduction could be done using numerical methods which are tedious and time consuming resulting in an overall slower technique. A closed-form inversion for the system parameters (film thickness, film optical constant, and substrate optical constant) would render a fast technique that is suitable for real-time applications. The sample used is a three-film-thickness sample and measurements are carried out at two angles of incidence. Real simple closed-form equations are derived through successive transformations and algebraic manipulations to obtain the optical constants of the film and the substrate, in addition to the film thickness. We propose the use of obtained several values of the film thickness to provide a measure of the accuracy of the experimental measurements. In addition, the special case of a bare-substrate system is considered, and the use of the several values of the substrate refractive index to provide a measure of the accuracy of the experimental measurements in such a case is also proposed. A simple software program, with a limited number of code lines, is developed and tested yielding perfect results.