## 4 Optimization Results
### Simulation Results
#### 4.2.1 Line Space Pattern  
The validity of the proposed SNPCO method is first demonstrated for pattern 1. The ideal MAT is 68 nm and the ideal SWA is 90\({}^{\circ}\). Figure 3 presents the simulation results of the MPLCO and the SNPCO in the case of pattern 1. From top to bottom, Figure 3 shows the corresponding simulation results of the MPLCO and the SNPCO. From left to right, Figure 3 exhibits the optimized source patterns, mask patterns, resist profiles for the ideal system, and the system with MAT = 63 nm and SWA = 95\({}^{\circ}\). The corresponding NA and process parameters optimization results are listed in Table 3. From the comparison results, it can be seen that the optimized SNPCO source is obviously different from the MPLCO source. The PEB durations, development time, and NA of the SNPCO are all smaller than that of the MPLCO. For the ideal system, the CDEs of the two methods are \(-\)0.04 nm and 0.01 nm, respectively. In this case, the image fidelities of the two methods are very close. However, for the system with the MAT = 63 nm, the CDEs of the two cases are \(-\)3.43 nm and \(-\)1.30 nm. In this case, the CDEs of the SNPCO is 62.1% smaller than that of the MPLCO. For the system with the SWA = 95\({}^{\circ}\), the CDEs of the two cases are 5.35 nm and 2.20 nm. In such circumstance, the CDEs of the SNPCO is 58.9% lower than that of the MPLCO.  
Figure 4 shows the exposure latitude (EL) versus DOF curves of the MPLCO and the SNPCO method. Figure 4a-c are the EL versus DOF curves for the ideal system, the system with MAT = 63 nm, and the system with SWA = 95\({}^{\circ}\), respectively. We use the dashed lines to indicate the DOF at EL = 5% in the figure. For the ideal system, the DOFs at EL = 5% of the MPLCO and SNPCO methods are 166 nm and 294 nm, respectively. The DOF of the proposed SNPCO method is 43.5% larger than that of the MPLCO. For the system with MAT = 63 nm, the DOFs at EL = 5% of the MPLCO and SNPCO are 176 nm and 295 nm. In this case, the DOF of the SNPCO is 40.3% larger than that of the MPLCO, and for the system with SWA = 95\({}^{\circ}\), the DOFs at EL = 5% of the MPLCO and SNPCO are 185 nm and  
Figure 2: Two test patterns used in the simulation. Pattern 1 represents the 1D line space mask pattern, and pattern 2 represents the 2D contact hole mask pattern.  
291 nm, respectively. In such circumstance, the DOF of the proposed method is 36.4% larger than that of the MPLCO.  
Figure 5 illustrates the mask absorber errors dependencies of the CDEs of the two methods for pattern 1. The MAT and SWA dependencies of the CDEs are presented in Figure 5a,b, respectively. In Figure 5a, it can be observed that the CDE of the proposed SNPCO method is generally smaller than that of the MPLCO with the same MAT error. When the MAT error is less than \(-\)4.25 nm, the corresponding CDE of the MPLCO exceeds 2.8 nm. It does not meet the requirements of the current lithography technology node (within 10% CD). Under the  
of the MPLCO with the same SWA error. When the SWA error is larger than 2.5\({}^{\circ}\), the corresponding CDE of the MPLCO is larger than 2.8 nm. In the corresponding situation, the CDE of the SNPCO is still less than 2.8 nm. This means that the pattern fidelity of the proposed SNPCO is more robust with regards the mask absorber errors than that of the MPLCO for pattern 1.  
Comparisons between the simulation results of the two methods for pattern 1 clearly demonstrate that the proposed SNPCO method improves the image fidelity and increases the PW of the lithography system with random mask absorber errors effectively. It indicates that the impacts of the mask absorber errors on lithography performance are mitigated by our SNPCO method. This can be attributed to the application of higher flexibility source along with the alternate optimization of source, NA, and process parameters, which incorporate the impact of random mask absorber errors.