Moustapha Godi Tchéré, Stéphane Robert, Zaki Sabit Fawzi, Bernard Bayard, Damien Jamon, and Cécile Gourgon, "Experimental identification of a grating profile using neural network classifiers in optical scatterometry," Appl. Opt. 60, 7929-7936 (2021)
In this paper, we develop a new technique, to the best of our knowledge, of grating characterization based on two separate steps. First, an artificial neural network (ANN) is implemented in a classifier mode to identify the shape of the geometrical profile from a measured optical signature. Then, a second ANN is used in a regression mode to determine the geometrical parameters corresponding to the selected geometrical model. The advantage of this approach is highlighted by discussions and studies involving the error criterion that is used widely in scatterometry. In addition, experimental tests are provided on diffraction grating structures with a period of 500 and 750 nm.
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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Geometrical Parameter Ranges for the , , and Training
Table 2.
Performances of the Differently Trained MLPs: , , and
Table 3.
Results of the Real Sample ANN Characterization
MLP
SEM
Geometrical parameters
Quality of characterization
Table 4.
Confusion Matrix of the MLP_C Focused to Detect the Particular Rectangular Profile Noted as
Real Class
Precision
Predicted class
450
28
94.1
0
422
100%
Sensitivity
100%
93.8%
Accuracy: 96.9%
Table 5.
Details of the ANN Row Outputs ( for Class and for Class) Concerning the Set of Misclassified Profiles Supplemented by the Calculated Geometrical Deviation
Misclassified Signatures
0.92
0.86
0.86
0.83
0.72
0.95
0.96
0.76
0.57
0.8
0.08
0.14
0.14
0.17
0.28
0.05
0.04
0.24
0.43
0.2
Geometrical deviation ()
56.14
192.01
104.86
63.35
49.97
66.41
116.81
62.66
247.51
61.7
Misclassified signatures
0.59
0.75
0.88
0.9
0.52
0.81
0.75
0.69
0.83
0.83
0.41
0.25
0.12
0.1
0.48
0.19
0.25
031
0.17
0.17
Geometrical deviation ()
240.34
37.31
66.61
49.61
238.03
97.09
94.14
134.25
141.67
164.67
Misclassified signatures
0.92
0.72
0.72
0.63
0.93
0.93
0.62
0.62
0.08
0.28
0.28
0.37
0.07
0.07
0.38
0.38
Geometrical deviation ()
74.38
123.11
123.66
361.42
100.15
92.12
267.75
63
Table 6.
Output Results of the MLP_C Corresponding to Samples and a
Optical Signatures
Sample
0.00
1.00
Sample
0.00
1.00
Class ${{\rm{C}}_1}$ corresponds to the rectangular profiles, and class ${{\rm{C}}_2}$ includes all the others.
Table 7.
Geometrical Parameter Ranges for Different Profile Shapes Belonging to Classes , , and
Table 8.
Confusion Matrix of the MLP_P Focused to Identify a Particular Geometrical Profilea
Real Class
Precision
Predicted class
450
0
19
95.9%
0
450
0
100%
0
0
431
100%
Sensitivity
100%
100%
95.8%
Accuracy: 98.6%
Class ${{\rm{C}}_1}$ corresponds to the rectangular profiles, and Classes ${{\rm{C}}_2}$ and ${{\rm{C}}_3}$ correspond, respectively, to the trapezoidal profile and the rectangular profile rounded at the top.
Table 9.
Raw Output Results of the MLP_P for Samples , , , and
Optical Signatures
Sample
0.00
0.00
1.00
Sample
0.00
0.00
1.00
Sample
0.00
0.00
1.00
Sample
0.56
0.00
0.44
Table 10.
Results of ANN Characterization of Samples , , and Operating in the Regression Mode for a Profile Shape Fixed by Previous Classifiers 1 and
Samples
Geometrical Parameters
Quality of Characterization
Geometrical Parameters
Quality of Characterization
SEM Parameters
= 209.61 ± 0.66 nm
= 0.12 = 5230.4 nm2
= 0.63 = 217 nm = 383 nm
= 365.88 ± 0.66 nm
= 0.16 = 1.474e4 nm2
= 0.24 = 344 nm = 527 nm
= 246.44 ± 0.03 nm
= 597.23 nm2
= 245.76 ± 0.66 nm
= 0.16 = 1251.4 nm2
= 237 nm = 562 nm
Tables (10)
Table 1.
Geometrical Parameter Ranges for the , , and Training
Table 2.
Performances of the Differently Trained MLPs: , , and
Table 3.
Results of the Real Sample ANN Characterization
MLP
SEM
Geometrical parameters
Quality of characterization
Table 4.
Confusion Matrix of the MLP_C Focused to Detect the Particular Rectangular Profile Noted as
Real Class
Precision
Predicted class
450
28
94.1
0
422
100%
Sensitivity
100%
93.8%
Accuracy: 96.9%
Table 5.
Details of the ANN Row Outputs ( for Class and for Class) Concerning the Set of Misclassified Profiles Supplemented by the Calculated Geometrical Deviation
Misclassified Signatures
0.92
0.86
0.86
0.83
0.72
0.95
0.96
0.76
0.57
0.8
0.08
0.14
0.14
0.17
0.28
0.05
0.04
0.24
0.43
0.2
Geometrical deviation ()
56.14
192.01
104.86
63.35
49.97
66.41
116.81
62.66
247.51
61.7
Misclassified signatures
0.59
0.75
0.88
0.9
0.52
0.81
0.75
0.69
0.83
0.83
0.41
0.25
0.12
0.1
0.48
0.19
0.25
031
0.17
0.17
Geometrical deviation ()
240.34
37.31
66.61
49.61
238.03
97.09
94.14
134.25
141.67
164.67
Misclassified signatures
0.92
0.72
0.72
0.63
0.93
0.93
0.62
0.62
0.08
0.28
0.28
0.37
0.07
0.07
0.38
0.38
Geometrical deviation ()
74.38
123.11
123.66
361.42
100.15
92.12
267.75
63
Table 6.
Output Results of the MLP_C Corresponding to Samples and a
Optical Signatures
Sample
0.00
1.00
Sample
0.00
1.00
Class ${{\rm{C}}_1}$ corresponds to the rectangular profiles, and class ${{\rm{C}}_2}$ includes all the others.
Table 7.
Geometrical Parameter Ranges for Different Profile Shapes Belonging to Classes , , and
Table 8.
Confusion Matrix of the MLP_P Focused to Identify a Particular Geometrical Profilea
Real Class
Precision
Predicted class
450
0
19
95.9%
0
450
0
100%
0
0
431
100%
Sensitivity
100%
100%
95.8%
Accuracy: 98.6%
Class ${{\rm{C}}_1}$ corresponds to the rectangular profiles, and Classes ${{\rm{C}}_2}$ and ${{\rm{C}}_3}$ correspond, respectively, to the trapezoidal profile and the rectangular profile rounded at the top.
Table 9.
Raw Output Results of the MLP_P for Samples , , , and
Optical Signatures
Sample
0.00
0.00
1.00
Sample
0.00
0.00
1.00
Sample
0.00
0.00
1.00
Sample
0.56
0.00
0.44
Table 10.
Results of ANN Characterization of Samples , , and Operating in the Regression Mode for a Profile Shape Fixed by Previous Classifiers 1 and
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