Linearized EUV mask optimization based on the adjoint method

Mask optimization, a compensation method for the thick mask effect and the optical proximity effect in projection lithography, is essential for advanced EUV-enabled production nodes. However, owing to high computation costs and the absence of gradient calculations, it is challenging to optimize EUV masks under rigorous consideration of the thick mask effect. In this work, a linearized EUV mask optimization method based on the adjoint method is proposed to provide fast and effective optimizations. The adjoint method is introduced to calculate the gradient of the EUV mask model. Additionally, a linearized gradient is proposed to quickly compensate for wafer pattern distortion caused by the prominent thick mask effect. Two examples of the EUV mask optimization implemented with a two-step strategy were provided, from which it was observed that the linearized gradient can improve the efficiency by about 40% in the coarse optimization step. The proposed method is promising for accurate full-chip EUV mask optimization.