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Analysis of pattern-dependent image placement of single-membrane stencil masks for electron-beam lithography
Microelectronic Engineering 84 (2007) 825–828 www.elsevier.com/locate/mee
Analysis of pattern-dependent image placement of single-membrane stencil masks for electron-beam lithography Hisatake Sano a,*, Naoko Kuwahara b, Minoru Kitada a, Satoshi Yusa b, Horoshi Fujita a, Tadahiko Takikawa b, Morihisa Hoga b a b
Dai Nippon Printing Co., Ltd., Kashiwa-shi 277–0871, Japan Dai Nippon Printing Co., Ltd., Fujimino-shi 356–8507, Japan Available online 27 January 2007
Abstract Large single-membrane stencil masks have been developed for electron-beam lithography. Since a large membrane induces large image placement (IP) error, which is pattern dependent, a method of correcting EB data has been studied to compensate the membrane distortion. In this study, firstly, the effect of crystal anisotropy of a Si membrane to the distortion is examined by making masks from blanks with different orientations. The influence of the anisotropy is found to be small and simulation based on isotropic modeling should be applicable. Secondly, a finite element method (FEM) called ANSYS and Pseudo-FEM are used to predict distortions for three masks with 8 mm-, 12 mm-, or 18 mm-square die of an opening ratio of 0.2 on a 24 mm-square membrane. The simulation results are compared with the results obtained in the experiment on anisotropy and a previous experiment. Qualitative agreement is observed between simulation and experiment but quantitative agreement is obtained only after introduction of adjustment factors. A suggestion is made to improve the IP correction scheme for EB data. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Electron-beam lithography; Stencil mask; Membrane distortion; Image placement; Finite element method; Anisotropy
1. Introduction Large single-membrane stencil masks [1] have been developed for electron-beam lithography, especially for low-electron proximity projection lithography. Fig. 1 shows an example of a 200 mm/, 0.725 mm-thick stencil mask with a single 24 mm-square, 1 lm thick-membrane. When the membrane gets larger, however, image placement (IP) error also becomes larger. It is because the internal stress of the membrane distorts the membrane when stencil patterns are formed on it and because this in-plane distortion becomes larger for a larger membrane. In order to reduce such a pattern-dependent distortion several correction methods have been proposed. One method is to make a send-ahead mask, to measure the distortion of the membrane, to make an IP map, to correct EB data so as to com*
Corresponding author. Tel: +81 4 7134 1762; fax: +81 4 7133 9290. E-mail address: [email protected] (H. Sano).
0167-9317/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2007.01.040
pensate the distortion and then to make a final mask. However, the IP map so obtained is usually limited to be global due to the limitation of IP mark insertion. The IP map specifying local displacement is often necessary to reduce IP errors. Moreover, every new layout requires a new send-ahead mask. Another method is to estimate the distortion by simulation, and then to correct EB data. Several groups have reported numerical [2,3] and experimental [4,5] evaluation results on the latter method. However, no group has ever obtained quantitative agreement between simulation and experiment. In our previous study [1], we examined the latter method with the simulation based on a pseudo finite element method (hereafter, referred to as ‘‘Pseudo-FEM’’), where a part of membrane with a thickness t0 of opening ratio q was replaced by a part of solid membrane with the reduced thickness (1 q)t0. We made three masks with an 8 mm-, 12 mm-, or 18 mm-square die (or block) at the centre of the membrane. The (perforated) hole in each die was a 200 nm square and its array x-/y-
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H. Sano et al. / Microelectronic Engineering 84 (2007) 825–828
Fig. 1. Example of a stencil mask for a hp 65 nm hole layer: (a) photograph of a 200 mm/ stencil mask; (b) photograph of 24 mm-square membrane with 16 blocks of pattern; (c) SEM image of a part of hp 65 nm hole pattern (with a window opened by an SII NanoTechnology FIB repair system).
pitch was 450 nm. Therefore, the opening ratio of each die was 20% (q = 0.2). We could observe only qualitative agreement between simulation and experiment. Therefore, we believe that it is too risky to depend solely on the simulation. In this study, the experimental results mentioned above are compared with results obtained using another FEM together with those of Pseudo-FEM in order to find a practical way to improve the IP correction scheme for EB data. 2. Experiment on anisotropy Before that, we investigated the influence of crystal anisotropy of Si membrane. We made each of the two types of masks with a 8 mm-square die; one was similar as that reported in the previous paper [1] and the other was made from a mask blank rotated by an angle of 45°, as shown in
the upper part of Fig. 2. The blanks belonged to a lot different from that reported in the previous paper. Fig. 2 also shows the experimental results. We conclude that the influence of the anisotropy is small and that simulation based on isotropic modeling should be applicable. 3. Simulation In order to understand the membrane distortion, we adopted another simulation software called ANSYS 10.0A10 [6] (hereafter, referred to as ‘‘ANSYS FEM’’). Cybernet Systems Co., Ltd. ran the software. In test runs, the convergence of the simulated values with a decrease of the hole size was confirmed in three cases of hole sizes, 1000 lm, 500 lm, and 50 lm, covering a 12 mm-square die for q = 0.25. In the simulation for q = 0.2, 45 lmsquare holes were placed with an x-/y-ptich of 100 lm,
<110>
<100>
<110> 8 mm 24 mm
<100>
Ope nin g rat io: 0.20
Normal
45-degree rotated
a
80
70
Normal <110>
60
Rotation45 <100>
50 40 30 20 10
50 40 30 20 10 0
-10
-10
6 10 2 4 8 Distance from the origin along the line parallel to the membrane edge (mm)
12
b
Rotation45 <110>
60
0 0
Normal <100>
70 Displacement (nm)
Displacement (nm)
80
0
2 6 8 10 12 14 16 4 Distance from the origin along the line diagonal to the membrane edge (mm)
Fig. 2. Mask layouts and the effect of the crystalline anisotropy to the displacement along the line (a) parallel and (b) diagonal to the membrane edge.
H. Sano et al. / Microelectronic Engineering 84 (2007) 825–828
covering a 8 mm-, 12 mm-, or 18 mm-square die. Therefore, the original hole was enlarged by a factor of 250. The mesh sizes were 22.5 lm and 27.5 lm. The simulation area was the 1st quadrant because of the system symmetry. We used 120 GPa, 0.28, and 13 MPa for elastic modulus, Poisson’s ratio, and (internal) stress of the membrane, respectively. Fig. 3 shows contour maps and displacement curves along the two lines, y = 0 and y = x. The contours are smooth except at the corner and edges of the die.
4. Discussion and suggestion Two cases are discussed. Firstly, in Fig. 4 we compare the experimental results shown in Fig. 2 and simulation results. In the die area, both ANSYS FEM and Pseudo-FEM curves fit to the experimental values (averaged over h1 1 0i and h1 0 0i) within 4 nm when they are multiplied by adjustment factors of 0.68 and 1.75, respectively for the two lines, y = 0 and y = x. This means that both simulations can predict the experimental IP map except for its magnitude. Secondly, in
( nm) 0 10.5 21.0 31.5 42.0 52.5 63.0 73.4 83.9 94.4
12 mm
4 mm
0
6 mm
along the line parallel to the membrane edge (y=0) along the line diagonal to the membrane edge (y=x)
80 60 40 20
0
100
0
9 mm 12 mm Point of the maximum displacement
along the line parallel to the membrane edge (y=0) along the line diagonal to the membrane edge (y=x)
120 Displacement (nm)
Displacement (nm)
100
12 mm
Point of the maximum displacement
Point of the maximum displacement 120
(n m ) 0 9.1 18.3 27.4 36.6 45.7 54.8 64.0 73.1 82.3
( nm ) 0 12.4 24.7 37.1 49.5 61.9 74.2 86.6 99.0 1 11. 0
80 60 40 20
100
a
8 10 12 14 16 18 2 4 6 D is ta n c e fr o m th e o r ig in (mm)
80 60 40 20 0
0
0
along the line parallel to the membrane edge (y=0) along the line diagonal to the membrane edge (y=x)
120 Displacement (nm)
0
827
0
2
b
4 6 8 10 1 2 14 1 6 D is ta n c e fr o m th e o r ig i n (m m )
0
18
2
c
4
6
8
10
12 14
16 18
D is ta n c e fr o m th e o r ig in (mm)
Fig. 3. Contour maps and displacements along the two lines, y = 0 and y = x: (a) 8 mm-square die; (b) 12 mm-square die; (c) 18 mm-square die.
In the die 100
In the die 90
ANSYS FEM
ANSY S F EM
ANSYS FEM *0.68 Pse udo-FEM *1.75 Pse udo-FEM Expe rime nt (av e )
60
ANSY S F EM *0.68
70 Displacement (nm)
Displacement (nm)
80
40 20
0
Pse u d o - F EM *1.75 Pse u d o - F EM
50
Exp e r ime n t ( av e )
30
10 -10
0
2
4 6 8 10 Distance fr om the or igin along the line par allel to the menbr ane edge (mm)
12
0
2
4
6
8
10
12
14
16
18
Distance fr om the or igin along the line diagonal to the menbr ane edge (mm)
Fig. 4. Comparison between the experimental results and the results of Pseudo-FEM and ANSYS FEM: displacement along the line (a) parallel and (b) diagonal to the membrane edge; ANSYS FEM*0.68 stands for ANSYS FEM value multiplied by 0.68.
828
H. Sano et al. / Microelectronic Engineering 84 (2007) 825–828 ANSYS FEM Pse udo-FEM *1.47 Expe rime nt
Maximum displacement along the x-axis (nm)
120
ANSYS FEM *0.59 Pse udo-FEM
100 80 60 40 20 0 0
2
4
6
8
10
12
H alf die siz e (mm)
Fig. 5. Comparison between the experimental results and the results of Pseudo-FEM and ANSYS FEM; maximum displacement along the x-axis is plotted as a function of the half die size.
Fig. 5 we compare the results reported in the previous paper [1] and ANSYS FEM results together with those of PseudoFEM. In the die area, ANSYS FEM and Pseudo-FEM curves, respectively, fit to the experimental values within 4 nm and 7 nm when they are multiplied by adjustment factors of 0.59 and 1.45. Since the displacement is proportional to the stress, the biggest cause of the uncertainty in the experiment lies on the degree of the control of the stress for each mask blank. We obtained 13 ± 5 MPa for the stress for one sample in the blank lot by the bulge method. Blank-toblank variation, which was not considered in this study, may explain the slight difference between the experimental values and the simulated values after adjustment. We found that the ANSYS FEM could not reproduce the experimental displacements, but will place the task of finding the cause in another study.
We suggest the following procedure to make masks for a layer of several blocks of single opening ratio with small IP errors (less than 10 nm): (1) control the stress to a degree of ±2 MPa or measure the stress before patterning for each mask blank; (2) make a send-ahead mask with IP marks for a representative layout and make a global IP map by measuring them; (3) apply an FEM (ANSYS FEM, Pseudo-FEM, or another) to make a local IP map together with a global map by comparison with the global experimental IP map; and (4) make a mask with IP correction based on the global and local IP maps. The combination of a send-ahead mask and the simulation can give a practical way to reduce IP errors both globally and locally. Acknowledgements The authors would like to thank Nobuyasu Horiuchi, Masahiro Shoji, and Tomoyuki Chikanaga (Nippon Control System Corporation) for providing us the simulation tool for IP correction and helpful discussion, and Katsumi Hashimoto (Dai Nippon Printing) for fruitful discussion about simulation. References [1] M. Kitada, S. Yusa, N. Kuwahara, H. Fujita, T. Takikawa, H. Sano, M. Hoga, in: Proceedings of the SPIE 5992 (2005) 59924R-1–12. [2] I. Ashida, S. Omori, H. Ohnuma, Proc. SPIE 4754 (2002) 847–856. [3] K. Nakayama, K. Tsuchiya, S. Ohnuma, Proc. SPIE 5446 (2004) 932– 940. [4] J. Sawamura, K. Suzuki, S. Omori, I. Ashida, H. Ohnuma, J. Vac. Sci. Technol. B22 (2004) 3092–3096. [5] H. Eguchi, T. Susa, T. Sumida, T. Kurosu, T. Yoshii, K. Itoh, R.L. Engelestad, E.G. Lovell, X. Azkorra, A. Mikkelson, J. Chang, S.M. Janowshi, J. Vac. Sci. Technol. B22 (2004) 3087–3091. [6] ANSYS 10.0A10 is a product of ANSYS Inc.(www.ansys.com).
Analysis of pattern-dependent image placement of single-membrane stencil masks for electron-beam lithography Hisatake Sano a,*, Naoko Kuwahara b, Minoru Kitada a, Satoshi Yusa b, Horoshi Fujita a, Tadahiko Takikawa b, Morihisa Hoga b a b
Dai Nippon Printing Co., Ltd., Kashiwa-shi 277–0871, Japan Dai Nippon Printing Co., Ltd., Fujimino-shi 356–8507, Japan Available online 27 January 2007
Abstract Large single-membrane stencil masks have been developed for electron-beam lithography. Since a large membrane induces large image placement (IP) error, which is pattern dependent, a method of correcting EB data has been studied to compensate the membrane distortion. In this study, firstly, the effect of crystal anisotropy of a Si membrane to the distortion is examined by making masks from blanks with different orientations. The influence of the anisotropy is found to be small and simulation based on isotropic modeling should be applicable. Secondly, a finite element method (FEM) called ANSYS and Pseudo-FEM are used to predict distortions for three masks with 8 mm-, 12 mm-, or 18 mm-square die of an opening ratio of 0.2 on a 24 mm-square membrane. The simulation results are compared with the results obtained in the experiment on anisotropy and a previous experiment. Qualitative agreement is observed between simulation and experiment but quantitative agreement is obtained only after introduction of adjustment factors. A suggestion is made to improve the IP correction scheme for EB data. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Electron-beam lithography; Stencil mask; Membrane distortion; Image placement; Finite element method; Anisotropy
1. Introduction Large single-membrane stencil masks [1] have been developed for electron-beam lithography, especially for low-electron proximity projection lithography. Fig. 1 shows an example of a 200 mm/, 0.725 mm-thick stencil mask with a single 24 mm-square, 1 lm thick-membrane. When the membrane gets larger, however, image placement (IP) error also becomes larger. It is because the internal stress of the membrane distorts the membrane when stencil patterns are formed on it and because this in-plane distortion becomes larger for a larger membrane. In order to reduce such a pattern-dependent distortion several correction methods have been proposed. One method is to make a send-ahead mask, to measure the distortion of the membrane, to make an IP map, to correct EB data so as to com*
Corresponding author. Tel: +81 4 7134 1762; fax: +81 4 7133 9290. E-mail address: [email protected] (H. Sano).
0167-9317/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2007.01.040
pensate the distortion and then to make a final mask. However, the IP map so obtained is usually limited to be global due to the limitation of IP mark insertion. The IP map specifying local displacement is often necessary to reduce IP errors. Moreover, every new layout requires a new send-ahead mask. Another method is to estimate the distortion by simulation, and then to correct EB data. Several groups have reported numerical [2,3] and experimental [4,5] evaluation results on the latter method. However, no group has ever obtained quantitative agreement between simulation and experiment. In our previous study [1], we examined the latter method with the simulation based on a pseudo finite element method (hereafter, referred to as ‘‘Pseudo-FEM’’), where a part of membrane with a thickness t0 of opening ratio q was replaced by a part of solid membrane with the reduced thickness (1 q)t0. We made three masks with an 8 mm-, 12 mm-, or 18 mm-square die (or block) at the centre of the membrane. The (perforated) hole in each die was a 200 nm square and its array x-/y-
826
H. Sano et al. / Microelectronic Engineering 84 (2007) 825–828
Fig. 1. Example of a stencil mask for a hp 65 nm hole layer: (a) photograph of a 200 mm/ stencil mask; (b) photograph of 24 mm-square membrane with 16 blocks of pattern; (c) SEM image of a part of hp 65 nm hole pattern (with a window opened by an SII NanoTechnology FIB repair system).
pitch was 450 nm. Therefore, the opening ratio of each die was 20% (q = 0.2). We could observe only qualitative agreement between simulation and experiment. Therefore, we believe that it is too risky to depend solely on the simulation. In this study, the experimental results mentioned above are compared with results obtained using another FEM together with those of Pseudo-FEM in order to find a practical way to improve the IP correction scheme for EB data. 2. Experiment on anisotropy Before that, we investigated the influence of crystal anisotropy of Si membrane. We made each of the two types of masks with a 8 mm-square die; one was similar as that reported in the previous paper [1] and the other was made from a mask blank rotated by an angle of 45°, as shown in
the upper part of Fig. 2. The blanks belonged to a lot different from that reported in the previous paper. Fig. 2 also shows the experimental results. We conclude that the influence of the anisotropy is small and that simulation based on isotropic modeling should be applicable. 3. Simulation In order to understand the membrane distortion, we adopted another simulation software called ANSYS 10.0A10 [6] (hereafter, referred to as ‘‘ANSYS FEM’’). Cybernet Systems Co., Ltd. ran the software. In test runs, the convergence of the simulated values with a decrease of the hole size was confirmed in three cases of hole sizes, 1000 lm, 500 lm, and 50 lm, covering a 12 mm-square die for q = 0.25. In the simulation for q = 0.2, 45 lmsquare holes were placed with an x-/y-ptich of 100 lm,
<110>
<100>
<110> 8 mm 24 mm
<100>
Ope nin g rat io: 0.20
Normal
45-degree rotated
a
80
70
Normal <110>
60
Rotation45 <100>
50 40 30 20 10
50 40 30 20 10 0
-10
-10
6 10 2 4 8 Distance from the origin along the line parallel to the membrane edge (mm)
12
b
Rotation45 <110>
60
0 0
Normal <100>
70 Displacement (nm)
Displacement (nm)
80
0
2 6 8 10 12 14 16 4 Distance from the origin along the line diagonal to the membrane edge (mm)
Fig. 2. Mask layouts and the effect of the crystalline anisotropy to the displacement along the line (a) parallel and (b) diagonal to the membrane edge.
H. Sano et al. / Microelectronic Engineering 84 (2007) 825–828
covering a 8 mm-, 12 mm-, or 18 mm-square die. Therefore, the original hole was enlarged by a factor of 250. The mesh sizes were 22.5 lm and 27.5 lm. The simulation area was the 1st quadrant because of the system symmetry. We used 120 GPa, 0.28, and 13 MPa for elastic modulus, Poisson’s ratio, and (internal) stress of the membrane, respectively. Fig. 3 shows contour maps and displacement curves along the two lines, y = 0 and y = x. The contours are smooth except at the corner and edges of the die.
4. Discussion and suggestion Two cases are discussed. Firstly, in Fig. 4 we compare the experimental results shown in Fig. 2 and simulation results. In the die area, both ANSYS FEM and Pseudo-FEM curves fit to the experimental values (averaged over h1 1 0i and h1 0 0i) within 4 nm when they are multiplied by adjustment factors of 0.68 and 1.75, respectively for the two lines, y = 0 and y = x. This means that both simulations can predict the experimental IP map except for its magnitude. Secondly, in
( nm) 0 10.5 21.0 31.5 42.0 52.5 63.0 73.4 83.9 94.4
12 mm
4 mm
0
6 mm
along the line parallel to the membrane edge (y=0) along the line diagonal to the membrane edge (y=x)
80 60 40 20
0
100
0
9 mm 12 mm Point of the maximum displacement
along the line parallel to the membrane edge (y=0) along the line diagonal to the membrane edge (y=x)
120 Displacement (nm)
Displacement (nm)
100
12 mm
Point of the maximum displacement
Point of the maximum displacement 120
(n m ) 0 9.1 18.3 27.4 36.6 45.7 54.8 64.0 73.1 82.3
( nm ) 0 12.4 24.7 37.1 49.5 61.9 74.2 86.6 99.0 1 11. 0
80 60 40 20
100
a
8 10 12 14 16 18 2 4 6 D is ta n c e fr o m th e o r ig in (mm)
80 60 40 20 0
0
0
along the line parallel to the membrane edge (y=0) along the line diagonal to the membrane edge (y=x)
120 Displacement (nm)
0
827
0
2
b
4 6 8 10 1 2 14 1 6 D is ta n c e fr o m th e o r ig i n (m m )
0
18
2
c
4
6
8
10
12 14
16 18
D is ta n c e fr o m th e o r ig in (mm)
Fig. 3. Contour maps and displacements along the two lines, y = 0 and y = x: (a) 8 mm-square die; (b) 12 mm-square die; (c) 18 mm-square die.
In the die 100
In the die 90
ANSYS FEM
ANSY S F EM
ANSYS FEM *0.68 Pse udo-FEM *1.75 Pse udo-FEM Expe rime nt (av e )
60
ANSY S F EM *0.68
70 Displacement (nm)
Displacement (nm)
80
40 20
0
Pse u d o - F EM *1.75 Pse u d o - F EM
50
Exp e r ime n t ( av e )
30
10 -10
0
2
4 6 8 10 Distance fr om the or igin along the line par allel to the menbr ane edge (mm)
12
0
2
4
6
8
10
12
14
16
18
Distance fr om the or igin along the line diagonal to the menbr ane edge (mm)
Fig. 4. Comparison between the experimental results and the results of Pseudo-FEM and ANSYS FEM: displacement along the line (a) parallel and (b) diagonal to the membrane edge; ANSYS FEM*0.68 stands for ANSYS FEM value multiplied by 0.68.
828
H. Sano et al. / Microelectronic Engineering 84 (2007) 825–828 ANSYS FEM Pse udo-FEM *1.47 Expe rime nt
Maximum displacement along the x-axis (nm)
120
ANSYS FEM *0.59 Pse udo-FEM
100 80 60 40 20 0 0
2
4
6
8
10
12
H alf die siz e (mm)
Fig. 5. Comparison between the experimental results and the results of Pseudo-FEM and ANSYS FEM; maximum displacement along the x-axis is plotted as a function of the half die size.
Fig. 5 we compare the results reported in the previous paper [1] and ANSYS FEM results together with those of PseudoFEM. In the die area, ANSYS FEM and Pseudo-FEM curves, respectively, fit to the experimental values within 4 nm and 7 nm when they are multiplied by adjustment factors of 0.59 and 1.45. Since the displacement is proportional to the stress, the biggest cause of the uncertainty in the experiment lies on the degree of the control of the stress for each mask blank. We obtained 13 ± 5 MPa for the stress for one sample in the blank lot by the bulge method. Blank-toblank variation, which was not considered in this study, may explain the slight difference between the experimental values and the simulated values after adjustment. We found that the ANSYS FEM could not reproduce the experimental displacements, but will place the task of finding the cause in another study.
We suggest the following procedure to make masks for a layer of several blocks of single opening ratio with small IP errors (less than 10 nm): (1) control the stress to a degree of ±2 MPa or measure the stress before patterning for each mask blank; (2) make a send-ahead mask with IP marks for a representative layout and make a global IP map by measuring them; (3) apply an FEM (ANSYS FEM, Pseudo-FEM, or another) to make a local IP map together with a global map by comparison with the global experimental IP map; and (4) make a mask with IP correction based on the global and local IP maps. The combination of a send-ahead mask and the simulation can give a practical way to reduce IP errors both globally and locally. Acknowledgements The authors would like to thank Nobuyasu Horiuchi, Masahiro Shoji, and Tomoyuki Chikanaga (Nippon Control System Corporation) for providing us the simulation tool for IP correction and helpful discussion, and Katsumi Hashimoto (Dai Nippon Printing) for fruitful discussion about simulation. References [1] M. Kitada, S. Yusa, N. Kuwahara, H. Fujita, T. Takikawa, H. Sano, M. Hoga, in: Proceedings of the SPIE 5992 (2005) 59924R-1–12. [2] I. Ashida, S. Omori, H. Ohnuma, Proc. SPIE 4754 (2002) 847–856. [3] K. Nakayama, K. Tsuchiya, S. Ohnuma, Proc. SPIE 5446 (2004) 932– 940. [4] J. Sawamura, K. Suzuki, S. Omori, I. Ashida, H. Ohnuma, J. Vac. Sci. Technol. B22 (2004) 3092–3096. [5] H. Eguchi, T. Susa, T. Sumida, T. Kurosu, T. Yoshii, K. Itoh, R.L. Engelestad, E.G. Lovell, X. Azkorra, A. Mikkelson, J. Chang, S.M. Janowshi, J. Vac. Sci. Technol. B22 (2004) 3087–3091. [6] ANSYS 10.0A10 is a product of ANSYS Inc.(www.ansys.com).