Iterative algorithm for automatic alignment by object transformation

Mathematical model for automatic alignment of wafers was derived under the assumption of the ideal condition of alignment marks. Because wafers were fabricated under non-ideal conditions at the factory level, the wafers were difficult to align during the manufacturing process. The errors from the distortion were reduced by repeated application of an ideal alignment sequence algorithm. The alignment algorithm, which was modified to be iterative, is based on the object transformation and is composed of matrix operations like a linear model. The convergence speed of the iteration could be varied by use the convergence constant η. The accuracy of the algorithm was demonstrated by a dicing machine used in an experiment. The alignment was repeated until the error was under the tolerance level of the inspection system. The convergence constant was varied to monitor its effect on iterative alignment speed. The result showed that this iterative algorithm was simple but accurate enough for application at the manufacturing level.