Alternative methods for uncertainty evaluation in EUV scatterometry

The precise and accurate determination of critical dimensions of photo masks and their uncertainties is important in the lithographic process to ensure operational reliability of electronic compounds. Scatterometry is known as a fast, non-destructive optical method for the indirect determination of geometry parameters. In recent years novel methods for solving the inverse problem of scatterometry have enabled a more reliable determination of grating parameters. In this article we present results from maximum likelihood parameter estimations based on numerically simulated EUV scatterometry data. We approximately determine uncertainties of these parameters by a Monte Carlo method with a limited amount of samplings and by employing the Fisher information matrix. Furthermore, we demonstrate that the use of incomplete mathematical models may lead to severe distortions in the calculations of the uncertainties by the approximate Fisher matrix approach as well as to substantially larger uncertainties for the Monte Carlo method.