Automatic alignment and error compensation in rotating analyzer ellipsometer

Abstract

A novel precision structure was developed in an ellipsometer. The kinematic-coupling principle was used to have high repeatability and precision for alignment of incident angle. All 3-D optical paths were modeled with homogeneous transformation matrix (HTM). Geometrical error analysis, that calculates the position of the light spot reached at the aperture of detector, showed the sensitivities of each component error. As a result, the rotational error of light source was most dominant on the error of the detected signal. The error bound was ±0.08 degree for light source. The translational errors of the ellipsometric components didn’t affect the final position of the spot. The manufactured mainframe has high repeatability and low manufacturing cost, and low uncertainty, less than 0.0014 degree, for incident angle. The designed specimen stage has one translation and two tilt motions; 60㎚ resolution and 25㎜ range for translation motion, $10^{-6}$ degree resolution and 20 degree range. We developed a 3-step auto-alignment algorithm for a specimen stage of an ellipsometer without any auxiliary equipment but with a capability of variable angle of incidence. By using our specially designed 3-axis specimen stage, we could simplify the alignment procedure. Our algorithm can also perform auto-alignment, even if the reflected light spot is far away from the aperture of the detector in case of huge initial errors at the specimen stage. Alignment at two different angles of incidence resulted in correct estimation of the values of translation error and the tilt angle error at the specimen stage. Computer simulation showed that our auto-alignment algorithm worked perfectly, and experiment with our home made rotating analyzer type ellipsometer also proved the precise performance of our algorithm. We have modeled most errors, which affect measurement, with Jones matrix. We characterized the errors as the thickness of specimen changes from 1nm to 600nm. A careful on error ana...