Statistical Aspects of Size Functions for the Description of Random Shapes : Applications to Problems of Lithography in Microelectronics

Here the Theory of Size Functions is introduced and joined to some statistical techniques in order to build confidence regions for a family of random shapes. An algorithm for the computation of the discrete counterpart of the Size Functions is also introduced. The method is applied to the quality control of shapes impressed with a laser on a silicon wafer, in microelectronics. The robustness of the Size Functions in the description of random shapes has led to good experimental results, and thus to the possibility of enclosing this method into an automatic procedure for the quality control of electronic devices.