Beam deviation errors in ellipsometric measurements; an analysis

The types of error produced by beam deviation in the optical elements of an ellipsometer are examined. It is shown that there are two types of error that may be significant-systematic errors due to a variation in the plane of incidence and in the angle of incidence at the specimen and errors due to the combined effects of beam displacement and nonuniformities in either the detector response or the optical properties of the specimen, the compensator, the polarizer, the analyzer, or the specimen cell. Analytic expressions for the variation in the plane of incidence and in the angle of incidence are given in terms of parameters that can be determined experimentally. A method by which these parameters can be measured is described. It is shown that the azimuthal variation in the angle of incidence produces fundamental errors in conventional zone averaging techniques because the values of psi and Delta are averaged at different angles of incidence in different zones. Methods of experimentally predetermining when such errors are likely to be significant are discussed, and a procedure that cancels most systematic errors due to beam deviation in each zone is described. The combined effects of beam deviation in the polarizer, the compensator, the cell windows, and the analyzer are considered in several commonly used configurations, and the configurations that minimize beam deviation errors are described.