Probability distribution-based method for aberration budgeting in EUV lithography

Extreme ultraviolet (EUV) lithography is one of the most indispensable technologies in semiconductor manufacturing for 7 nm and smaller technology nodes. However, many key parameters in the lithography system may deviate from target values, and there are extremely complex coupling effects among these parameters. Additionally, aberrations that far exceed expectations damage lithography results severely. These accidents pose significant challenges in achieving satisfactory lithography outcomes. To investigate the impact of aberrations coupled with multiple key parameters on lithography results, and to provide quantitative and precise direction for the research and development of lithography systems, this paper proposes a methodology of budget analysis of aberrations based on probability distribution. First, a rapid prediction model of lithography results is established by multilayer perceptron. Then, the lithography results under different parameter conditions are obtained according to the prediction model. Subsequently, the aberration combinations that meet lithography requirements are filtered out. Finally, the impact of each aberration on lithography results and their budget range can be determined according to the general distribution and joint probability distribution of aberrations coupled with multiple key parameters. For patterns commonly used in EUV single exposure at the 5 nm technology node, this paper finds that aberrations such as Z2 and Z4 exhibit significant impacts on lithography results under the coupling of multiple key parameters. Additionally, all the budget ranges of aberrations are obtained. Specifically, for example, Z2, Z4, and Z5, their budget ranges are -18∼15mλ, 10∼45mλ, 7∼43mλ, respectively. While items such as Z1 and Z27, their budget ranges are -40∼40mλ consistently. This method can obtain the impact and budget range of aberrations under the coupling of multiple key parameters in the lithography system quickly and accurately. It can provide a reliable guideline for aberration compensation and optimization, and the research and development of lithography systems. Moreover, the budget ranges obtained by this method can also serve as a clear indicator for aberration monitoring.