- Email: [email protected]
Optimum design of processing condition and experimental investigation of grating fabrication with hot embossing lithography
Acta Mechanica Solida Sinica, Vol. 22, No. 6, December, 2009 Published by AMSS Press, Wuhan, China.
ISSN 0894-9166
OPTIMUM DESIGN OF PROCESSING CONDITION AND EXPERIMENTAL INVESTIGATION OF GRATING FABRICATION WITH HOT EMBOSSING LITHOGRAPHY Jianguo Zhu1
Huimin Xie1
Minjin Tang1
Xiaojun Li2
1
( AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China) (2 National Center for Nanoscience and Technology, Beijing 100084, China)
Received 1 July 2009; revision received 23 October 2009
ABSTRACT The cross-section profiles of polymer deformation in the hot embossing lithography process were studied by finite element method for various temperature, time and pressure. In order to successfully fabricate high-frequency grating lines, an optimal imprint condition was selected and the related experiments were carried out. The fabricated gratings were illuminated by the SEM image and AFM analysis, which agree well with the simulated results. Therefore, the finite element methods are helpful for a better comprehension of the polymer flow phenomena governing the pattern definition and the design of optimum processing conditions for successful grating fabrication.
KEY WORDS grating fabrication, hot embossing lithography, finite element, experiment
I. INTRODUCTION Gratings are straight, parallel, and equispaced grooves. As a basic optical component, it is being used in various optical technologies, such as moir´e method, moir´e interferometry and various microscopic moir´e methods, to measure the surface deformation on the object[1, 2] . As a conventional grating fabrication method developed in the early 1960s[3], holography lithography technique (HLT) is based on the interference of two coherent beams of light and the exposure of photoresist. However, the complex arrangement of optical components resulted in a very low manufacturability, and accordingly restrained its wide applications. In recent years, researchers have investigated a number of microfabrication technologies to fabricate gratings, such as X-ray lithography[4] , electron beam writing[5] , focus ion beam writing[6] and SPM lithography[7]. Although high-resolution alignment can be created, the low throughput and the high cost make it impractical for commercialization. Since the middle 1990s, hot embossing lithography (HEL) or nanoimprint lithography (NIL), initially proposed and developed by Chou’s group[8, 9], has emerged as one of the most promising technologies for nanoscale patterning[10] . It can create micro- and nanosacle patterns in a resist material with
Corresponding author. Email: [email protected] Project supported by the National Basic Research Program of China (Grant No.2010CB631005), National Natural Science Foundation of China (Grant Nos.10625209, 10732080, 90916010), Beijing Natural Sciences Foundation (Grant No.3072007), and Program for New Century Excellent Talents (NCET) in Universities and Chinese Ministry of Education (Grant No.NCET-05-0059).
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Fig. 1. Schematic diagram of the grating fabrication with HEL process.
rapid-processing and high-throughput, and it is capable of sub-micron alignment over a large area. Furthermore, the mould can be used repeatedly for hundreds of imprints, thus, the cost is very low and it is more feasible for mass production[11] . As illustrated in Fig.1, a thin film of a thermoplastic polymer cast on a substrate is physically deformed, and the grating fabrication with HEL process involves an imprint step using a rigid stamp under pressure and elevated temperature above the glass transition temperature (Tg ). Then, processes of solidification and demoulding are performed after the polymer is cooled to a temperature below Tg . With the Patterns transferred to the polymer, a metal layer was deposited before it is used as reflective gratings. In recent years, a number of studies have been addressed to investigate the HEL using numerical simulations. Hirai et al. studied the cross-section profiles of resists under various processing conditions with hyperelastic finite element method (FEM). They assumed that the polymer resist was a hyperelastic material and used Mooney-Rivlin constitutive law[12–14] . Young developed a simulation model based on the assumption of a viscous fluid at a fixed temperature over Tg to predict the polymer flow during the imprinting process[15]. Hirai et al. developed a simulator using generalized Maxwell model as the viscoelastic constitutive model in conventional FEM[16, 17] . Kim et al. performed a viscoelastic FE analysis to investigate the behavior of polymer of low temperature thermal NIL and studied the effects of imprinting speed and patterns on the process[18]. In this paper, the commercial finite element code ABAQUS was used to analyze the grating fabrication in the HEL process. The polymer is polymethyl methacrylate (PMMA), which was assumed to be a viscoelastic material. With a clear understanding of the polymer behaviour, the embossing conditions, such as temperature, pressure, and time, are all considered in developing the new lithography methodologies. Based on the simulations, an optimal imprint condition was selected and the related experiment was carried out. The simulated results were compared with experimental ones observed by SEM and AFM systems, showing good replication fidelity for the fabrication of nanoscale periodical structures.
II. SIMULATION In the study, a Si mould with fixed array of grating lines was used. Since gratings are periodical line structures with the constant cross-section profile in one direction, it is practical to assume a twodimensional plain-strain model of a unit cell, as shown in Fig.2. The depth (h) and width (W ) of the mould cavity are 80 nm and 150 nm, respectively. The line width (L = W + S) is 333 nm in accordance with a frequency of 3000 lines/mm grating lines. Symmetric boundaries were used on the two sides of the model and fixed displacement was applied at the bottom surface of the polymer because the polymer was prebaked to strongly adhere to the substrate. As the mould is much stiffer than the polymer, it was considered to be a rigid body. At point C, a small arc was incorporated to improve the convergence of the simulation. For a polymer material at a temperature above Tg , the application of a constant load results in a deformation that can involve instantaneous deformation (elastic effect) followed by continual deformation over time (viscous effect), which results in the decay of the applied load and is termed as relaxation[19]. Viscoelastic stress relaxation can be illustrated with mechanical elements, that is, springs and dashpots, where the spring represents the elastic behavior and the dashpot represents viscous behavior. A generalized Maxwell model was used to represent the stress relaxation behaviour of the polymer during the HEL process[20, 21] , as shown in Fig.3.
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Fig. 2. Boundary conditions and dimensions.
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Fig. 3. Generalized Maxwell model.
Fig. 4. Deformation of profile and Von Mises stress distribution of demoulded PMMA at temperature of (a) 120◦ C, (b) 130◦ C, (c) 140◦ C (t = 120 s, p = 2 MPa).
The molecular weight (Mw ) of PMMA is 950 k and its initial thickness is 100 nm which is similar to the mould depth to avoid excess layers[22]. According to its rectangle section, the polymer was fine meshed using four-node bilinear quadrilateral elements. The interaction type was defined by a surface-to-surface contact with a frictionless contact property and finite sliding was considered in the simulation[23] . The simulation of HEL process consists of three steps: heating and pressing process, cooling process, and demoulding process.
III. SIMULATION RESULTS Figure 4 shows the simulation results of HEL when the temperature is elevated from 120 to 160 centigrade at the processing condition of t = 120 s, and p = 2 MPa. The imprinted depth of the mould was very small, but increases dramatically as the temperature begins to arise from 120 centigrade. As the temperature continuously arises, however, the increased depth decreases slightly. Above 140 centigrade, the depth of the mould reached the maximum and was kept as a constant value even when the temperature is increased to 160 centigrade. This agrees with the stress relaxation of the polymer changing from the glassy state to the rubbery state: dropping rapidly in modulus when temperature arises from above Tg and remaining relatively constant in the rubber-elastic plateau region[20] . The imprinted depth of the mould was recorded and plotted as a function of temperature at the processing conditions of various pressures, as shown in Fig.5. As the temperature below 140 centigrade, the deformation profile of PMMA was not sufficiently conformed to the mould. While above 140 centigrade, the deformation profile remains relatively unchanged with increased temperature. Consequently, the optimal imprinted temperature is 140 centigrade. Fig. 5 Depth of mould at temperature from 120 to 160◦ C.
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Fig. 6. Deformation of profile and Von Mises stress distribution of demoulded PMMA after imprint for (a) 5 s, (b) 10 s, (c) 60 s, (d) 120 s (p = 3 MPa, T = 140◦ C).
Next, the PMMA profile was evaluated with various imprint time from 0 to 120 s with the application of a 3 MPa pressure. The temperature was set constant: T = 140◦ C. At the time of 5, 10, 60 and 120 s, we can see the mould depth slowly increases under a constant pressure of 3 MPa, as illuminated in Fig.6. Although there is slightly increased creep deformation of the polymer as a function of imprint time, the von Mises stress distribution in the polymer clearly indicates that the concentrated stress on the bottom surface reduces gradually. This can be ascribed to the stress relaxation phenomena of the viscoelastic polymer. The creep deformation of the polymer and Von Mises stress distribution under constant imprint pressures of 1 and 2 MPa were also studied. Though they were not shown here to avoid tediousness, the mould depths in terms of imprint time were plotted in Fig.7 and similar stress relaxation phenomena can be observed. The influence of imprint pressure on the deformation of the polymer was demonstrated at constant temperature of T = 140◦C and the imprint time of, t = 120 s, as shown in Figs.8(a) to (d). ◦ It is clear at glance that more and more polymer Fig. 7 Depth of mould in terms of imprint time (T = 140 C). flows into the groove as the imprint pressure increases. However, the filling rate of the polymer is not proportional to the applied pressure. It becomes difficult to fully fill the entire groove when the filling rate reaches 60 percent, as shown in Fig.9. This is similar to the results studied by Hirai et al.[13] . With the same imprint pressure of Fig.8(d), the Von Mises stress distribution of un-demoulded PMMA at the end of pressing process was shown in Fig.8(e). Relatively high stress concentration appears on the bottom surface of the polymer. As assumed the polymer is fixed on the substrate, the concave polymer becomes difficult to flow into the groove with the continuously increasing imprint pressure. Considerable stress concentration also appears in the polymer near the arc of the mould in the pressing process, as shown in Fig.8(e). Obviously, it is harmful to the nanoscale patterns on the mould
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Fig. 8. Deformation of profile and Von Mises stress distribution of demoulded PMMA at pressure of (a) 1 MPa, (b) 2 MPa, (c) 3 MPa, (d) 4 MPa, (e) 4 MPa (undemoulded) (T = 140◦ C, t = 120 s).
Fig. 9. The filling rate at different pressures (T = 140◦ C, t = 120 s).
surface, thus, it is not wise to excessively increase the pressure to obtain a best filling rate[13] . And a low pressure with a moderate deformation of the polymer is recommended[24] .
IV. EXPERIMENT RESULTS The grating fabrication with HEL was carried out on the hot embossing system HEX01 in the National Center for Nanoscience and Technology in China. According to the simulation, the imprint conditions chosen were T = 140◦ C, t = 120 s, p = 2 MPa. Before the imprint experiment, an initial thickness of 100 nm PMMA was spin-coated onto the substrate of a silicon wafer, followed by prebaking to enhance its adherence to the substrate. Additionally, in order to provide stamps with good anti-sticking surface properties, anti- Fig. 10 SEM image of grating lines fabricated with HEL. adhesive coatings were deposited using silane chemistry[25] .
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Fig. 11. AFM image and section analysis of grating lines fabricated with HEL.
After the HEL experiment, the samples were observed with a CSM950 SEM from Opton Corporation of Germany. Figure 10 shows a SEM image of grating lines which are straight, parallel, and equispaced. To investigate the cross-section profile of imprinted polymer, AFM (NanoScope IIIa) observations were also carried out. Section analysis manifests that the line frequency is 3000/mm and the period is about 333 nm, as shown in Fig.11. This is perhaps because of thermal match between a Si mould and Si substrate which results in good replication fidelity for the HEL process. However, the vertical distance analyzed by AFM is about 47.7 nm, which is smaller than the simulation result of 66.3 nm. The possible reason is the simplified simulation model such as the frictionless contact property, perfect demoulding without sticking of polymer in the mould grooves, and so on.
V. CONCLUSIONS In order to successfully fabricate high-frequency grating lines, the cross-section profiles of polymer deformation were studied by finite element method for various temperature, time and pressure with HEL process. Based on the simulations, an optimal imprint condition was selected and the related experiment was carried out. The theoretical and experimental results were compared with each other. We can conclude: (1) The modulus of the polymer drops quickly above the temperature of Tg and stays relatively constant in the rubber-elastic plateau region. (2) The creep deformation of polymer under constant imprint pressures in terms of imprint time was very little, but the concentrated stress on the bottom surface reduces gradually. (3) The filling rate of the polymer is not simply proportional to the applied pressure. Perfect polymer deformation needs even higher pressure. (4) The fabricated gratings with HEL were illuminated by the SEM image and AFM analysis, which agree well with the simulated results. Therefore, the finite element methods are helpful for a better understanding of the polymer flow phenomena governing the pattern definition and the optimization of processing conditions for successful grating fabrication. Acknowledgements The authors deeply thank NIL Technology APS for providing stamp and National Center for Nanoscience and Technology for providing experimental equipment.
References [1] Chen,Y.M., He,Y.M., Hu,E.Y. and Zhu,H.M., Deformation measurement using dual-frequency projection grating phase-shift profilometry. Acta Mechanica Solida Sinica, 2008, 21(2): 110-115. [2] Li,X.L., Kang,Y.L., Qiu,W. and Xiao,X., Application of the digital moire method in fracture analysis of a cracked rubber sheet. Acta Mechanica Solida Sinica, 2006, 19(3): 241-247. [3] Anderson,E.H., Horwitz,C.M. and Smith,H.I., Holographic lithography with thick photoresist. Applied Physics Letters, 1983, 43(9): 874-875. [4] Ritucci,A., Reale,A., Zuppella,P., Reale,L., Tucceri,P., Tomassetti,G., Bettotti,P. and Pavesi,L., Interference lithography by a soft x-ray laser beam: Nanopatterning on photoresists. Journal of Applied Physics, 2007, 102(3): 034313-1∼4.
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[5] Xie,H.M., Kishimoto,S. and Shinya,N., Fabrication of high-frequency electron beam moire grating using multi-deposited layer techniques. Optics and Laser Technology, 2000, 32(5): 361-7. [6] Xie,H.M., Li,B., Geer,R., Xu,B. and Castracane,J., Focused ion beam moire method. Optics and Lasers in Engineering, 2003, 40(3): 163-177. [7] Liu,Z.W., Xie,H.M., Fang,D.N., Shang,H.X., and Dai,F.L. , A novel nano-moire method with scanning tunneling microscope (STM). Journal of Materials Processing Technology, 2004, 148(1): 77-82. [8] Chou,S.Y., Krauss,P.R. and Renstrom,P.J., Imprint of sub-25nm vias and trenches in polymers. Applied Physics Letters, 1995, 67(21): 3114-3116. [9] Chou,S.Y., Krauss,P.R. and Renstrom,P.J., Imprint lithography with 25-nanometer resolution. Science, 1996, 272(5258): 85-87. [10] Schift,H., Nanoimprint lithography: An old story in modern times? A review. Journal of Vacuum Science & Technology B, 2008, 26(2): 458-480. [11] Guo,L.J., Recent progress in nanoimprint technology and its applications. Journal of Physics D-Applied Physics, 2004, 37(11): R123-R141. [12] Hirai,Y., Fujiwara,M., Okuno,T., Tanaka,Y., Endo,M., Irie,S., Nakagawa,K. and Sasago,M., Study of the resist deformation in nanoimprint lithography. Journal of Vacuum Science & Technology B, 2001, 19(6): 2811-2815. [13] Hirai,Y., Konishi,T., Yoshikawa,T. and Yoshida,S., Simulation and experimental study of polymer deformation in nanoimprint lithography. Journal of Vacuum Science & Technology B, 2004, 22(6): 3288-3293. [14] Hocheng,H., and Nien,C.C., Numerical analysis of effects of mold features and contact friction on cavity filling in the nanoimprinting process. Journal of Microlithography Microfabrication and Microsystems, 2006, 5(1): 011004-1∼7. [15] Wen-Bin,Y., Analysis of the nanoimprint lithography with a viscous model. Microelectronic Engineering, 2005, 77(3): 405-411. [16] Hirai,Y., Onishi,Y., Tanabe,T., Nishihata,M., Iwasaki,T., Kawata,H. and Iriye,Y., Time dependent analysis of the resist deformation in thermal nanoimprint. Journal of Vacuum Science & Technology B, 2007, 25(6): 2341-2345. [17] Hirai,Y., Onishi,Y., Tanabe,T., Nishihata,M., Iwasaki,T., Kawata,H. and Iriye,Y., Pressure and resist thickness dependency of resist time evolutions profiles in nanoimprint lithography. Microelectronic Engineering, 2008, 85(5-6): 842-845. [18] Kim,N.W., Kim,K.W. and Sin,H.C., Finite element analysis of low temperature thermal nanoimprint lithography using a viscoelastic model. Microelectronic Engineering, 2008, 85(9): 1858-1865. [19] Christensen,R.M., Theroy of Viscoelasticity: An Introduction. London: Academic Press INC. LTD., 1982. [20] Zhang,T.Y., ed., Theory of Thermo-Viscoelasticity. Tianjin: Tianjin University Press, 2002. [21] Yan,W., Ying,J. and Chen,W.Q., A three-dimensional solution for laminated orthotropic rectangular plates with viscoelastic interfaces. Acta Mechanica Solida Sinica, 2006, 19(2): 181-188. [22] Bogdanski,N., Wissen,M., Mollenbeck,S. and Scheer,H.C., Thermal imprint with negligibly low residual layer. Journal of Vacuum Science & Technology B, 2006, 24(6): 2998-3001. [23] Zhuang,Z., You,X.C., Liao,J.H., Ceng,S., Sheng,X.P. and Liang,M.G., ed., Finite Element Analysis and Its Applications Based on ABAQUS. Beijing: Tsinghua University Press, 2008. [24] Lazzarino,F., Gourgon,C.,Schiavone,P. and Perret,C., Mold deformation in nanoimprint lithography. Journal of Vacuum Science & Technology B, 2004, 202(6): 3318-3322. [25] Jaszewski,R.W., Schift,H., Schnyder,B., Schneuwly,A. and Gr¨oning,P., The deposition of anti-adhesive ultra-thin teflon-like films and their interaction with polymers during hot embossing. Applied Surface Science, 1999, 143(1-4): 301-308.
ISSN 0894-9166
OPTIMUM DESIGN OF PROCESSING CONDITION AND EXPERIMENTAL INVESTIGATION OF GRATING FABRICATION WITH HOT EMBOSSING LITHOGRAPHY Jianguo Zhu1
Huimin Xie1
Minjin Tang1
Xiaojun Li2
1
( AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China) (2 National Center for Nanoscience and Technology, Beijing 100084, China)
Received 1 July 2009; revision received 23 October 2009
ABSTRACT The cross-section profiles of polymer deformation in the hot embossing lithography process were studied by finite element method for various temperature, time and pressure. In order to successfully fabricate high-frequency grating lines, an optimal imprint condition was selected and the related experiments were carried out. The fabricated gratings were illuminated by the SEM image and AFM analysis, which agree well with the simulated results. Therefore, the finite element methods are helpful for a better comprehension of the polymer flow phenomena governing the pattern definition and the design of optimum processing conditions for successful grating fabrication.
KEY WORDS grating fabrication, hot embossing lithography, finite element, experiment
I. INTRODUCTION Gratings are straight, parallel, and equispaced grooves. As a basic optical component, it is being used in various optical technologies, such as moir´e method, moir´e interferometry and various microscopic moir´e methods, to measure the surface deformation on the object[1, 2] . As a conventional grating fabrication method developed in the early 1960s[3], holography lithography technique (HLT) is based on the interference of two coherent beams of light and the exposure of photoresist. However, the complex arrangement of optical components resulted in a very low manufacturability, and accordingly restrained its wide applications. In recent years, researchers have investigated a number of microfabrication technologies to fabricate gratings, such as X-ray lithography[4] , electron beam writing[5] , focus ion beam writing[6] and SPM lithography[7]. Although high-resolution alignment can be created, the low throughput and the high cost make it impractical for commercialization. Since the middle 1990s, hot embossing lithography (HEL) or nanoimprint lithography (NIL), initially proposed and developed by Chou’s group[8, 9], has emerged as one of the most promising technologies for nanoscale patterning[10] . It can create micro- and nanosacle patterns in a resist material with
Corresponding author. Email: [email protected] Project supported by the National Basic Research Program of China (Grant No.2010CB631005), National Natural Science Foundation of China (Grant Nos.10625209, 10732080, 90916010), Beijing Natural Sciences Foundation (Grant No.3072007), and Program for New Century Excellent Talents (NCET) in Universities and Chinese Ministry of Education (Grant No.NCET-05-0059).
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Fig. 1. Schematic diagram of the grating fabrication with HEL process.
rapid-processing and high-throughput, and it is capable of sub-micron alignment over a large area. Furthermore, the mould can be used repeatedly for hundreds of imprints, thus, the cost is very low and it is more feasible for mass production[11] . As illustrated in Fig.1, a thin film of a thermoplastic polymer cast on a substrate is physically deformed, and the grating fabrication with HEL process involves an imprint step using a rigid stamp under pressure and elevated temperature above the glass transition temperature (Tg ). Then, processes of solidification and demoulding are performed after the polymer is cooled to a temperature below Tg . With the Patterns transferred to the polymer, a metal layer was deposited before it is used as reflective gratings. In recent years, a number of studies have been addressed to investigate the HEL using numerical simulations. Hirai et al. studied the cross-section profiles of resists under various processing conditions with hyperelastic finite element method (FEM). They assumed that the polymer resist was a hyperelastic material and used Mooney-Rivlin constitutive law[12–14] . Young developed a simulation model based on the assumption of a viscous fluid at a fixed temperature over Tg to predict the polymer flow during the imprinting process[15]. Hirai et al. developed a simulator using generalized Maxwell model as the viscoelastic constitutive model in conventional FEM[16, 17] . Kim et al. performed a viscoelastic FE analysis to investigate the behavior of polymer of low temperature thermal NIL and studied the effects of imprinting speed and patterns on the process[18]. In this paper, the commercial finite element code ABAQUS was used to analyze the grating fabrication in the HEL process. The polymer is polymethyl methacrylate (PMMA), which was assumed to be a viscoelastic material. With a clear understanding of the polymer behaviour, the embossing conditions, such as temperature, pressure, and time, are all considered in developing the new lithography methodologies. Based on the simulations, an optimal imprint condition was selected and the related experiment was carried out. The simulated results were compared with experimental ones observed by SEM and AFM systems, showing good replication fidelity for the fabrication of nanoscale periodical structures.
II. SIMULATION In the study, a Si mould with fixed array of grating lines was used. Since gratings are periodical line structures with the constant cross-section profile in one direction, it is practical to assume a twodimensional plain-strain model of a unit cell, as shown in Fig.2. The depth (h) and width (W ) of the mould cavity are 80 nm and 150 nm, respectively. The line width (L = W + S) is 333 nm in accordance with a frequency of 3000 lines/mm grating lines. Symmetric boundaries were used on the two sides of the model and fixed displacement was applied at the bottom surface of the polymer because the polymer was prebaked to strongly adhere to the substrate. As the mould is much stiffer than the polymer, it was considered to be a rigid body. At point C, a small arc was incorporated to improve the convergence of the simulation. For a polymer material at a temperature above Tg , the application of a constant load results in a deformation that can involve instantaneous deformation (elastic effect) followed by continual deformation over time (viscous effect), which results in the decay of the applied load and is termed as relaxation[19]. Viscoelastic stress relaxation can be illustrated with mechanical elements, that is, springs and dashpots, where the spring represents the elastic behavior and the dashpot represents viscous behavior. A generalized Maxwell model was used to represent the stress relaxation behaviour of the polymer during the HEL process[20, 21] , as shown in Fig.3.
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Fig. 2. Boundary conditions and dimensions.
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Fig. 3. Generalized Maxwell model.
Fig. 4. Deformation of profile and Von Mises stress distribution of demoulded PMMA at temperature of (a) 120◦ C, (b) 130◦ C, (c) 140◦ C (t = 120 s, p = 2 MPa).
The molecular weight (Mw ) of PMMA is 950 k and its initial thickness is 100 nm which is similar to the mould depth to avoid excess layers[22]. According to its rectangle section, the polymer was fine meshed using four-node bilinear quadrilateral elements. The interaction type was defined by a surface-to-surface contact with a frictionless contact property and finite sliding was considered in the simulation[23] . The simulation of HEL process consists of three steps: heating and pressing process, cooling process, and demoulding process.
III. SIMULATION RESULTS Figure 4 shows the simulation results of HEL when the temperature is elevated from 120 to 160 centigrade at the processing condition of t = 120 s, and p = 2 MPa. The imprinted depth of the mould was very small, but increases dramatically as the temperature begins to arise from 120 centigrade. As the temperature continuously arises, however, the increased depth decreases slightly. Above 140 centigrade, the depth of the mould reached the maximum and was kept as a constant value even when the temperature is increased to 160 centigrade. This agrees with the stress relaxation of the polymer changing from the glassy state to the rubbery state: dropping rapidly in modulus when temperature arises from above Tg and remaining relatively constant in the rubber-elastic plateau region[20] . The imprinted depth of the mould was recorded and plotted as a function of temperature at the processing conditions of various pressures, as shown in Fig.5. As the temperature below 140 centigrade, the deformation profile of PMMA was not sufficiently conformed to the mould. While above 140 centigrade, the deformation profile remains relatively unchanged with increased temperature. Consequently, the optimal imprinted temperature is 140 centigrade. Fig. 5 Depth of mould at temperature from 120 to 160◦ C.
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Fig. 6. Deformation of profile and Von Mises stress distribution of demoulded PMMA after imprint for (a) 5 s, (b) 10 s, (c) 60 s, (d) 120 s (p = 3 MPa, T = 140◦ C).
Next, the PMMA profile was evaluated with various imprint time from 0 to 120 s with the application of a 3 MPa pressure. The temperature was set constant: T = 140◦ C. At the time of 5, 10, 60 and 120 s, we can see the mould depth slowly increases under a constant pressure of 3 MPa, as illuminated in Fig.6. Although there is slightly increased creep deformation of the polymer as a function of imprint time, the von Mises stress distribution in the polymer clearly indicates that the concentrated stress on the bottom surface reduces gradually. This can be ascribed to the stress relaxation phenomena of the viscoelastic polymer. The creep deformation of the polymer and Von Mises stress distribution under constant imprint pressures of 1 and 2 MPa were also studied. Though they were not shown here to avoid tediousness, the mould depths in terms of imprint time were plotted in Fig.7 and similar stress relaxation phenomena can be observed. The influence of imprint pressure on the deformation of the polymer was demonstrated at constant temperature of T = 140◦C and the imprint time of, t = 120 s, as shown in Figs.8(a) to (d). ◦ It is clear at glance that more and more polymer Fig. 7 Depth of mould in terms of imprint time (T = 140 C). flows into the groove as the imprint pressure increases. However, the filling rate of the polymer is not proportional to the applied pressure. It becomes difficult to fully fill the entire groove when the filling rate reaches 60 percent, as shown in Fig.9. This is similar to the results studied by Hirai et al.[13] . With the same imprint pressure of Fig.8(d), the Von Mises stress distribution of un-demoulded PMMA at the end of pressing process was shown in Fig.8(e). Relatively high stress concentration appears on the bottom surface of the polymer. As assumed the polymer is fixed on the substrate, the concave polymer becomes difficult to flow into the groove with the continuously increasing imprint pressure. Considerable stress concentration also appears in the polymer near the arc of the mould in the pressing process, as shown in Fig.8(e). Obviously, it is harmful to the nanoscale patterns on the mould
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Fig. 8. Deformation of profile and Von Mises stress distribution of demoulded PMMA at pressure of (a) 1 MPa, (b) 2 MPa, (c) 3 MPa, (d) 4 MPa, (e) 4 MPa (undemoulded) (T = 140◦ C, t = 120 s).
Fig. 9. The filling rate at different pressures (T = 140◦ C, t = 120 s).
surface, thus, it is not wise to excessively increase the pressure to obtain a best filling rate[13] . And a low pressure with a moderate deformation of the polymer is recommended[24] .
IV. EXPERIMENT RESULTS The grating fabrication with HEL was carried out on the hot embossing system HEX01 in the National Center for Nanoscience and Technology in China. According to the simulation, the imprint conditions chosen were T = 140◦ C, t = 120 s, p = 2 MPa. Before the imprint experiment, an initial thickness of 100 nm PMMA was spin-coated onto the substrate of a silicon wafer, followed by prebaking to enhance its adherence to the substrate. Additionally, in order to provide stamps with good anti-sticking surface properties, anti- Fig. 10 SEM image of grating lines fabricated with HEL. adhesive coatings were deposited using silane chemistry[25] .
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Fig. 11. AFM image and section analysis of grating lines fabricated with HEL.
After the HEL experiment, the samples were observed with a CSM950 SEM from Opton Corporation of Germany. Figure 10 shows a SEM image of grating lines which are straight, parallel, and equispaced. To investigate the cross-section profile of imprinted polymer, AFM (NanoScope IIIa) observations were also carried out. Section analysis manifests that the line frequency is 3000/mm and the period is about 333 nm, as shown in Fig.11. This is perhaps because of thermal match between a Si mould and Si substrate which results in good replication fidelity for the HEL process. However, the vertical distance analyzed by AFM is about 47.7 nm, which is smaller than the simulation result of 66.3 nm. The possible reason is the simplified simulation model such as the frictionless contact property, perfect demoulding without sticking of polymer in the mould grooves, and so on.
V. CONCLUSIONS In order to successfully fabricate high-frequency grating lines, the cross-section profiles of polymer deformation were studied by finite element method for various temperature, time and pressure with HEL process. Based on the simulations, an optimal imprint condition was selected and the related experiment was carried out. The theoretical and experimental results were compared with each other. We can conclude: (1) The modulus of the polymer drops quickly above the temperature of Tg and stays relatively constant in the rubber-elastic plateau region. (2) The creep deformation of polymer under constant imprint pressures in terms of imprint time was very little, but the concentrated stress on the bottom surface reduces gradually. (3) The filling rate of the polymer is not simply proportional to the applied pressure. Perfect polymer deformation needs even higher pressure. (4) The fabricated gratings with HEL were illuminated by the SEM image and AFM analysis, which agree well with the simulated results. Therefore, the finite element methods are helpful for a better understanding of the polymer flow phenomena governing the pattern definition and the optimization of processing conditions for successful grating fabrication. Acknowledgements The authors deeply thank NIL Technology APS for providing stamp and National Center for Nanoscience and Technology for providing experimental equipment.
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Vol. 22, No. 6
Jianguo Zhu et al.: Grating Fabrication with Hot Embossing Lithography
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