Abstract: 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 overlying films occluding the marks. The problem is exacerbated by planarizing processes such as Chemical Mechanical Polishing (CMP) and asymmetric processes such as metal deposition and photoresist coating. These processes give rise to displacement of the perceived position of the alignment mark. Thus, any effective algorithm must be based on the history of such displacements. A new approach based on subspace decomposition of the alignment signals is described. The method only applies to imaging and/or scanning based alignment signals. The main assumption is that the process-induced asymmetries are small enough such that only linear effects need to be considered. We first find the subspace of alignment signals using a set of alignment signals with pre-known positions. The positions of the new signals are measured based on the fact that, if shifted correctly, they will lie in the same subspace as the previous signals. Current alignment algorithms assume symmetric alignment signals. Since this method exploits the structure of the signals, it results in more accurate measurement of the position than the current algorithms. 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. The computational complexity also increases linearly with the dimension of the subspace and is linearly proportional to signal bandwidth. !4
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