3D Rigorous Simulation of Defective Masks used for EUV Lithography via Machine Learning-Based Calibration

Heng Zhang; Sikun Li; Xiangzhao Wang; Wei Cheng

doi:10.3788/AOS201838.1222002

Acta Optica Sinica, Volume. 38, Issue 12, 1222002(2018)

3D Rigorous Simulation of Defective Masks used for EUV Lithography via Machine Learning-Based Calibration

Heng Zhang^1,2、*, Sikun Li^1,2、*, Xiangzhao Wang^1,2、*, and Wei Cheng^1,2

¹ Laboratory of Information Optics and Optelectronic Technology, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

² University of Chinese Academy of Sciences, Beijing 100049, China

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Figures & Tables(9)

Fig. 1. Schematic of EUVL 3D mask. (a) 3D view; (b) side view

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Fig. 2. Schematic of mask simulation model. (a) Absorber model; (b) multilayer model

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Fig. 3. Flow chart of training and predicting process employed in machine learning methods

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Fig. 4. Comparison of simulation results for fast models with and without model parameter calibration using different machine learning methods

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Fig. 5. Comparison of the simulation accuracy of a parameter calibrated fast model and an advanced single-surface approximation model

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Fig. 6. Comparison of the aerial images of mask simulations. (a) Rigorous simulation of a defect-free mask; (b) rigorous simulation of defective uncompensated mask; (c) defect compensation using a rigorous model; (d) defect compensation using a fast model

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Table 1. Training data for different masks

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Table 1. Training data for different masks

Data index	Mask parameter						Model parameter
Data index	Mask pitch /nm	Contact size /nm	$\begin{matrix} {h_{top}}_{} \end{matrix}$ /nm	$\begin{matrix} {w_{top}}_{} \end{matrix}$ /nm	$\begin{matrix} {h_{bot}}_{} \end{matrix}$ /nm	$\begin{matrix} {w_{bot}}_{} \end{matrix}$ /nm	g_best
1	176	91	2	5	20	30	1.104
2	144	70	6	19	20	42	1.082
3	128	60	10	19	23	24	1.073
…	…	…	…	…	…	…	…
582	144	67	2	15	8	24	1.069
583	176	89	4	10	4	12	9.802
584	176	92	8	11	20	44	1.098

Table 2. Testing data for different masks

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Table 2. Testing data for different masks

Data index	Mask pitch /nm	Contact size /nm	$\begin{matrix} {h_{top}}_{} \end{matrix}$ /nm	$\begin{matrix} {w_{top}}_{} \end{matrix}$ /nm	$\begin{matrix} {h_{bot}}_{} \end{matrix}$ /nm	$\begin{matrix} {w_{bot}}_{} \end{matrix}$ /nm	Model parameter
Data index	Mask pitch /nm	Contact size /nm	$\begin{matrix} {h_{top}}_{} \end{matrix}$ /nm	$\begin{matrix} {w_{top}}_{} \end{matrix}$ /nm	$\begin{matrix} {h_{bot}}_{} \end{matrix}$ /nm	$\begin{matrix} {w_{bot}}_{} \end{matrix}$ /nm	Original	KNN	Best
1	176	93	6	12	10	21	1.10	1.19	1.23
2	176	89	10	18	18	25	1.10	1.15	1.15
3	176	83	8	9	8	37	1.10	1.10	1.10
…	…	…	…	…	…	…	…	…	…
48	144	80	9	7	11	35	1.10	1.09	1.08
49	200	95	6	6	28	33	1.10	1.12	1.10
50	160	83	5	10	11	23	1.10	1.10	1.10

Table 3. Comparison of simulation accuracy of different parameter calibration methods
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Table 3. Comparison of simulation accuracy of different parameter calibration methods
Method name RMS mean RMS median RMS min RMS max RMS SD deviation
DT 2.19 1.68 0.54 10.2 1.70
KNN 1.82 1.55 0.23 5.48 1.09
RF 2.10 1.56 0.55 8.23 1.68
Original 3.32 2.53 0.53 9.77 2.58
Best 1.07 0.98 0.16 4.45 0.62

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Heng Zhang, Sikun Li, Xiangzhao Wang, Wei Cheng. 3D Rigorous Simulation of Defective Masks used for EUV Lithography via Machine Learning-Based Calibration[J]. Acta Optica Sinica, 2018, 38(12): 1222002

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