A neural network assisted etch model for mask process correction

Etch bias correction method is essential to meet the critical dimension (CD) uniformity requirements for mask process correction (MPC), and it has evolved along with the development of process technologies. For matured nodes, rule-based etch bias corrections are adopted. However, this method suffers from limited accuracy and cannot meet the tight CD controls requirement over various patterns for advanced process nodes. To model nontrivial etching process effects such as the aperture effect and the microloading effect, Ref. 1 proposed a variable etch bias (VEB) model. This edge-based semi-empirical model has been widely used in many applications in production and demonstrates good model fits for various layout features and process conditions. In addition, compared to physical etch models, the VEB model is easier to calibrate and requires less runtime. However, for more advanced nodes with EUV masks, and high sensitivity photoresists, only a complex VEB model might be able to meet the precise CD accuracy requirements. The main source of error for the VEB model is the residual error that results from all aspects of the etching process, and a semi-empirical model cannot fully capture it. To overcome this challenge, we propose a neural network assisted etch (N2E) model for MPC. The N2E model is a two-stage etch model that contains a VEB model followed by a neural network assisted model (NNAM).2 With NNAM, the VEB model in the two-stage N2E model can be simpler than the conventional VEB model while maintaining the same accuracy. In addition, compared to the conventional VEB model, the calibrated N2E model is able to achieve a smaller root mean square error (RMSE) between the measured and predicted etch CDs. Besides, the N2E model produces a small RMSE for the validation dataset and generalizes well. Therefore, the N2E model has the potential to simplify the VEB model part and improve the overall accuracy of MPC.