A LOWER BOUND ON ALIGNMENT ACCURACY AND SUBPIXEL RESOLUTION IN LITHOGRAPHY

In wafer alignment, subpixel resolution methods have been used in an attempt to increase the accuracy of the wafer positioning algorithm. These methods produce line positions that are between the pixels of the rasterized image of the alignment pattern. In this paper we provide a lower bound on the error variance of any alignment algorithm for a given alignment system and develop a method of ranking alignment patterns for their suitability for the task. We show that the use of a nonsymmetric alignment pattern will cause a decrease in accuracy unless information about the amplitude of the alignment pattern is known. An expression for the maximum useful subpixel resolution of any alignment system is derived and it is shown that with pixel resolution higher than this maximum value the subpixel methods produce no significant increase in accuracy. Examples of the use of the bound will be given.