Optimization Design Method for Flexible Support Structure of Lens Based on Astigmatism Constraints

With the rapid development of semiconductor technology，the manufacturing level of ultra large scale integrated circuits is constantly changing，and the manufacturing level of integrated circuits depends on high-precision semiconductor manufacturing equipment and cutting-edge lithography technology. In high-precision semiconductor manufacturing equipment，both deep ultraviolet and extreme ultraviolet lithography projection lenses require extremely high accuracy，which requires extremely high precision for the optical components in their optical systems. How to design and optimize the support structure of optical components is one of the problems that must be solved to meet the surface shape accuracy indicators. This paper focuses on high-precision optical systems， such as 193 nm lithography projection objective，and provides a detailed theoretical introduction to the support principle of spring and the analysis principle of surface shape error. On the premise of fully considering the design specifications of the opto-mechanical system，in order to improve the surface shape accuracy of the optical components after support，an integrated multi spring positioning optical lens support structure is designed，taking into account factors such as impact，vibration，pressure，and temperature. And through theoretical analysis and calculation of the support of the spring，the flexible deformation value of the spring is controlled. Under static conditions，finite element analysis is used to calculate the natural frequency of the overall structure and the influence of the support structure on the accuracy of lens surface shape. The first-order frequency reaches 366.13 Hz，the peak-to-valley value of the lens surface shape is 13.923 nm，and the root-mean-square value is 2.499 nm. The overall structure meets the design requirements under static conditions. In response to the issue of change in the surface shape accuracy of optical components during the integration process of the lens group and how to optimize and improve it，the degradation degree of lens surface shape caused by deformation of the support structure is analyzed based on the astigmatic constraint condition. The peak-to-valley value deteriorates to 119.62 nm，and the root-mean-square value deteriorates to 20.69 nm. The main cause for degradation is due to the influence of astigmatism constraints on the bottom reference plane of the lens group. And the shape of lens deformation is related to the type of bottom constraints of the lens support structure，exhibiting a distribution of astigmatism. A method for optimizing the lens support structure is proposed to improve the accuracy of lens surface shape. Firstly，through sensitivity analysis of lens support structure parameters，parameters with high sensitivity can be given special consideration，which can reduce the design space of the optimization process，obtain optimization results as soon as possible，and save time and cost. Secondly，a high-order response surface approximation model is constructed to describe the functional relationship between input parameters and response values. The analysis of fit goodness proves that the response surface model has high accuracy and can better map the relationship between design variables and optimization objectives. Finally，genetic algorithm optimization is used to improve the accuracy of lens surface shape. The improvement rates of peak-to-valley value and root-mean-square value are about 18% and 19%，respectively. The Zeiss gantry coordinate measuring instrument is used to detect the flatness of the lens holder，and the ZYGO 12 inch vertical interferometer is used to detect the surface shape error of the lens. Through experimental results and comparison of optimization results，the deviation rate of the peak-to-valley value relative to the detection result is about 9%，and the deviation rate of the root-mean-square value relative to the detection result is about 12%，which accurately verifies the optimization design conclusion. The research results indicate that the proposed lens support structure，integrated surface analysis and optimization method can provide reference for the support design of optical components in high-precision optomechanical systems. © 2024 Chinese Optical Society. All rights reserved.