Identification of complicated shape objects by fractal characteristic variables - categorizing dust particles on LSI wafer surface

This paper describes a mathematical model of dust particles having complex shapes, and an algorithm to identify them, aiming mainly at categorizing types of dust on an LSI wafer surface. Fractal dimension is used to represent the dust features. A conventional fractal dimension applied to specimens as a whole, however, does not sufficiently represent the shapes of dust in each category of the model. This paper introduces a local fractal dimension into a global fractal dimension so that the feature of a mathematical model can be represented. Also proposed is a method based on Mahalanobis' distance using a fractal characteristic valuable to categorize the data. The proposed method has been tested successively by using real data.