A Genetic Algorithm-Enhanced Sensor Marks Selection Algorithm for Wavefront Aberration Modeling in Extreme-UV (EUV) Photolithography

Abstract

In photolithographic processes, nanometer-level-precision wavefront-aberration models enable the machine to be able to meet the overlay (OVL) drift and critical dimension (CD) specifications. Software control algorithms take as input these models and correct any expected wavefront imperfections before reaching the wafer. In such way, a near-optimal image is exposed on the wafer surface. Optimizing the parameters of these models, however, involves several time costly sensor measurements which reduce the throughput performance of the machine in terms of exposed wafers per hour. In that case, photolithography machines come across the trade-off between throughput and quality. Therefore, one of the most common optimal experimental design (OED) problems in photolithography machines (and not only) is how to choose the minimum amount of sensor measurements that will provide the maximum amount of information. Additionally, each sensor measurement corresponds to a point on the wafer surface and therefore we must measure uniformly around the wafer surface as well. In order to solve this problem, we propose a sensor mark selection algorithm which exploits genetic algorithms. The proposed solution first selects a pool of points that qualify as candidates to be selected in order to meet the uniformity constraint. Then, the point that provides the maximum amount of information, quantified by the Fisher-based criteria of G-, D-, and A-optimality, is selected and added to the measurement scheme. This process, however, is considered “greedy”, and for this reason, genetic algorithms (GA) are exploited to further improve the solution. By repeating in parallel the “greedy” part several times, we obtain an initial population that will be the input to our GA. This meta-heuristic approach outperforms the “greedy” approach significantly. The proposed solution is applied in a real life semiconductors industry use case and achieves interesting industry as well as academical results.

Keywords

• photolithography
• optimal design of experiments
• optimal experimental design
• G-optimal
• D-optimal
• A-optimal