## 4 Optimization Results
### Simulation Results
#### 4.2.2 Contact Hole Pattern  
To demonstrate the universality of the SNPCO method, another set of simulations for pattern 2 are provided in Figure 6. The ideal MAT is 80 nm and the ideal SWA is 90\({}^{\circ}\). From top to bottom, Figure 6 shows the corresponding simulation results of the MPLCO and the SNPCO method. From left to right, Figure 6 exhibits the optimized source patterns, mask patterns, resist profiles for the ideal system and the system with MAT = 75 nm and SWA = 94\({}^{\circ}\). The corresponding NA and process parameters optimization results are listed in Table 4. It is observed that the optimized SNPCO source is different from the MPLCO source. The optimized NA and process parameters of the SNPCO are all smaller than that of the MPLCO. For the ideal system, the CDEs of the two methods are 0.02 nm and 0.03 nm, respectively. In this case, the image fidelities of the two methods are still very close. However, for the system with MAT = 75 nm, the CDEs of the two cases are 5.53 nm and 4.42 nm. In this case, the CDEs of the SNPCO is 20.1% smaller than that of the MPLCO. For the system with SWA = 94\({}^{\circ}\), the CDEs of the two cases are \(-\)11.34 nm and \(-\)6.95 nm. In such circumstance, the CDEs of the SNPCO are 38.7% lower than that of the MPLCO. Figure 7 shows the exposure latitude (EL) versus DOF curves of the MPLCO and the SNPCO method for pattern 2. Figure 7a-c are the EL versus DOF curves for the ideal system, the system with MAT = 75 nm and the system with SWA = 94\({}^{\circ}\), 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 64 nm and 124 nm, respectively. The DOF of the proposed SNPCO method is 48.4% larger than that of the MPLCO. For the system with MAT = 75 nm, the DOFs at EL = 5% of the MPLCO and SNPCO are 36 nm and 76 nm. In this case, the DOF of the SNPCO is 52.6% larger than that of the MPLCO, and for the system with SWA = 94\({}^{\circ}\), the DOFs at EL = 5% of the MPLCO and SNPCO are  
Figure 5: The mask absorber errors dependencies of the critical dimension errors (CDEs) of the MPLCO (blue curve) and the SNPCO (red curve) in the case of pattern 1. (**a**) The MAT error dependencies of the CDEs; (**b**) the SWA error dependencies of the CDEs. 37 nm and 85 nm, respectively. In such circumstance, the DOF of the proposed method is 56.5% larger than that of the MPLCO. Figure 8 illustrates the mask absorber errors dependencies of the CDEs of the two methods for pattern 2. The MAT and SWA dependencies of the CDEs are presented in Figure 8a,b, respectively. In Figure 8a, it is observed that the CDE of the proposed SNPCO method is generally smaller than that of the MPLCO with same MAT error. When the MAT error is less than -2.77 nm or greater than 2.50 nm, the corresponding CDE of the MPLCO exceeds 4.00 nm. It does not meet the requirements of the current lithography technology node (within 10% CD). Under the same circumstance, the CDEs of the SNPCO are 2.47 nm and-2.29 nm, respectively. As can be seen in Figure 8b, the CDE of the SNPCO is also smaller than that of the MPLCO with the same SWA error. When the SWA error is larger than 2.0\({}^{\circ}\), the corresponding CDE of the MPLCO is less than \(-4.00\) nm. In the corresponding situation, the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Pattern** & **Parameters** & **MPLCO Results** & **SNPCO Results** \\ \hline \multirow{4}{*}{Contact hole} & Hotplate duration (s) & 64 & 61 \\  & Transition duration (s) & 12 & 9 \\  & Chill plate duration (s) & 35 & 29 \\  & Development time (s) & 40 & 32 \\  & NA & 1.35 & 1.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: NA and process parameters optimization results of pattern 2. Figure 6: Simulation results of the MPLCO and the SNPCO in the case of pattern 2. Top to bottom: Simulations for the MPLCO and the SNPCO. Left to right: optimized source, mask, resist profile for the ideal system and the system with MAT = 75 nm and SWA = 94\({}^{\circ}\).