Exploiting structure in positioning of nonsymmetric signals

One of the most crucial emerging challenges in lithography is achieving rapid and accurate alignment under a wide variety of conditions brought about by different processing steps. Current alignment algorithms assume symmetric alignment signals. In this paper, we propose a new algorithm based on subspace decomposition of alignment signals. We assume that the process-induced asymmetries are small enough so that only linear effects need to be considered. We first find the subspace of alignment signals using a set of signals with pre-known positions. The position of a new signal is calculated considering that, if shifted correctly, it will lie in the same subspace of previous signals. Since this method exploits the structure of the signals, it results in more accurate measurement of the position. Simulation results show that the alignment error is about an order of magnitude smaller than that achieved with conventional maximum likelihood or phase-fitting approaches