Study of the resist deformation in nanoimprint lithography

Transcription

1 Study of the resist deformation in nanoimprint lithography Yoshihiko Hirai, a) Masaki Fujiwara, Takahiro Okuno, and Yoshio Tanaka Department of Mechanical System Engineering, Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Sakai, Osaka, Japan Masataka Endo, Sigeo Irie, Kazuo Nakagawa, and Masaru Sasago ULSI Process Technology Development Center, Semiconductor Company, Matsushita Electric Corporation, 19 Nishikujo-Kasugacho, Minami-ku, Kyoto, Kyoto, Japan Received 1 June 2001; accepted 10 September 2001 Numerical simulations and experimental studies are carried out to understand the deformation process of thin polymer film in nanoimprint lithography. Deformation of a thin polymer above its glass transition temperature is studied for various imprinting conditions such as the aspect ratios of a mold pattern, initial thickness of the polymer, and imprinting pressure. Cross-sectional profiles of the deformed polymers are simulated by the finite element method based on a rubber elastic model. The results are compared with experimental data. The areal penetration ratio of the polymer into the recessed groove of the mold and residual thickness underneath the mold are quantitatively evaluated. The simulations and the experimental results agree well with each other American Vacuum Society. DOI: / I. INTRODUCTION Imprint lithography is one of the promising technologies for nanometer scale lithography fabricate ultralarge-scale integration ULSI systems. 1,2 There are many published reports on nanoimprint lithography including novel methods and applications. These can be classified into two major methods. One is thermal curing method of a polymer film that was proposed by Chou et al. 1 and the other is ultraviolet UV curing method proposed by Colburn et al. 2 In the former process, a resist polymer is heated above the glass transition temperature and deformed by pressing a mold into a polymer, while in the latter method the liquid-like polymer flows into a recessed groove of the mold and is cured by ultraviolet exposure. In these processes, the resolution and cross-sectional profile of the resist polymer may be characterized by deformation or viscous liquid flow processes to the recessed groove of the mold. However, detailed experimental or theoretical studies have not been reported for these deformation processes in imprinting lithography. We have focused on polymer deformation by the thermal curing method and have studied resist cross-sectional profiles under various imprinting conditions by both numerical simulations and experiments. In imprint lithography, a thin polymer film suffers large deformation from a mechanical stress. The cross-sectional profile of the deformed polymer dominates the resolution and the quality of imprint lithography. Also, a residual thickness after imprinting affects the subsequent fabrication process. We studied the cross-sectional profile of the deformed polymer and residual thickness for various process conditions, such as the imprinting pressure, the aspect ratio of the recessed groove, and the polymer s initial thickness. Our simulated results are compared with experimental results. a Electronic mail: hirai@mecha.osakafu-u.ac.jp II. RESIST DEFORMATION SIMULATION In imprint lithography, a resist polymer and a mold are preheated above the glass transition temperature of the polymer. Next, the mold is pressed into the polymer and held at the pressure and the temperature. Then, the polymer and the mold are cooled down, keeping the imprinting pressure. Finally, the mold is released from the polymer. The deformed polymer profile is principally determined in the pressing process and the deformed polymer profile is retained by cooling it down before release. We assume the retained polymer pattern is approximately the same as the deformed. The resist deformation process is simulated by the finite element method FEM using the MARC program. 3 We used rectangular plane strain elements for the polymer and rigid body for the mold. The polymer is assumed to be a rubber elastic material above its glass transmission temperature. The Moony Rivlin model 4 6 is applied for rubber elastic dynamics. According to the Moony Rivlin model, the stress is expressed as i i W i, FIG. 1. Schematic of the system analyzed J. Vac. Sci. Technol. B 19 6, NovÕDec Õ2001Õ19 6 Õ2811Õ5Õ$ American Vacuum Society 2811

2 2812 Hirai et al.: Resist deformation in nanoimprint lithography 2812 where is the expansion rate and W is a strain density function which is expressed as W C 10 I 1 3 C 01 I 2 3, 2 I , I , 4 where the C 01 and C 10 are Moony constants. They are derived from the following approximated relations: 6 C C 10, 6 C 10 C 01 E, 6 where E is an elastic coefficient of the polymer. The rubber elastic shows nonlinear stress strain behavior. A schematic of the system to be analyzed is shown in Fig. 1. Line and space patterns are simulated by taking symmetric 3 5 boundary conditions into account. The angular corner of the mold is rounded to avoid failure due to interaction between the mold and polymer. Friction between the mold and polymer is ignored. The elastic coefficient E of the polymer poly methyl methacrylate PMMA is assumed to be 10 MPa above its glass transition temperature. 7 9 The areal penetration ratio R p, which is defined by the ratio of the penetrated cross section of the polymer S p to the total cross section of the groove S 0, and residual thickness h r are evaluated for various initial thicknesses of the resist polymer h 0, the depth of the mold groove h m, the linewidth of the mold w m, and imprinting pressure P. Figure 2 shows the simulated cross-sectional profiles and the primary principal stress distribution in arbitrary units that vary with the aspect ratio ( h m /w 1 ) of the groove, the initial polymer thickness h 0, and the imprinting pressure FIG. 2. Simulated cross-sectional profiles and the primary principal stress distribution in arbitrary units for various values of the aspect ratio. a 0.5, b 1.0, and c 1.5. J. Vac. Sci. Technol. B, Vol. 19, No. 6, NovÕDec 2001

3 2813 Hirai et al.: Resist deformation in nanoimprint lithography 2813 thick for each aspect ratio of the groove. On the other hand, the polymer is successfully deformed into the groove at higher pressure with thicker polymer (h 0 1.5h m ). Residual thickness exists in all cases even if the pressure P is high and the initial thickness h 0 is thin because the polymer is assumed to be a rubber elastic element, which shows nonlinear strain behavior under applied stress. In cases in which the initial thickness of the polymer is thin, the strain for the polymer underneath the mold becomes large for equivalent displacement of the mold and the pressure required increases. The polymer is not linearly compressed underneath the mold as the imprinting pressure increased. When the initial thickness of the polymer is thin (h 0 0.5h m ) and the aspect ratio of the mold is small ( 0.5), a polymer at the mold edge bunches up. This is because the compressed polymer underneath the mold moved toward the lateral direction and the polymer near the edge bunches up locally. In cases in which the mold edges are close to each other, the polymer between the edges bunches up and the groove of the mold becomes filled with the polymer. FIG. 3. Simulation results for various initial polymer thicknesses h 0, the aspect ratios of the groove, and the imprinting pressures P. a Areal penetration ratio R p ; b residual thickness h r. P. The value of is varied from 0.5 to 1.5 and the h 0 from 0.5 to 1.5h m and the P is from 3.0 to 9.0E, where E is an elastic coefficient of the polymer. Figure 3 summarizes the simulation results of the areal penetration ratio R p and the residual thickness for various initial polymer thicknesses and aspect ratio of the groove. The symbols show simulated results and the solid line shows a geometric relation when the polymer is deformed like a noncompressive liquid. When the imprinting pressure is low and the initial resist thickness h 0 is thin, the polymer cannot be deformed sufficiently along the groove. The areal penetration ratio R p ( S p /S 0 ) is low and the residual thickness ratio h r /h 0 is III. EXPERIMENTS We use an air press machine with thermal control bases for the mold and substrate. 10 They are put into a vacuum chamber. The experimental procedure is as follows. PMMA (M w ) is coated on Si substrates. The thickness of the PMMA are 120, 250, and 360 nm. They are prebaked at 170 C for 30 min on a hot plate. Then, the polymer and the mold are heated to 170 C. Next, the mold is pressed into the polymer on the substrate at 30, 60, and 90 MPa and held for 5 min. Then, the mold and the substrate are cooled down by water to 60 C and held 5 min, keeping the imprinting pressure. Finally, the mold is released from the polymer. The experiments are carried out in vacuum ambient. The mold is fabricated by conventional photolithography and by a dry etching process using Si materials. The crosssectional profiles of the molds are shown in Fig. 4. The widths of the recessed grooves are 1000, 350, and 200 nm. The depth of the groove is 270 nm for each mold. The aspect ratios of the recessed grooves are 0.27, 1.1, and 1.35 for molds A, B, and C, respectively. To avoid sticking to the polymer in the releasing process, a5nmthick fluorinated ethylene-propylene FEP copolymer film is coated onto the mold surface by vacuum evaporation. 11 IV. RESULTS AND DISCUSSIONS Figure 5 shows cross-sectional profiles of the imprinted polymers. When the initial thickness of the polymer is thin and the aspect ratio of the mold is low, the cross-sectional profiles showed that the polymer bunches up near the mold s edge. These profiles agree very well with the simulation results. Form the image of these profiles, the penetration ratio R p ( S p /S 0 ) and the residual thickness ratio h r /h 0 are evaluated and they are summarized in Fig. 6. JVST B-Microelectronics and Nanometer Structures

4 2814 Hirai et al.: Resist deformation in nanoimprint lithography 2814 FIG. 4. Cross-sectional profiles of the molds. a Mold A ( 0.27); b mold B ( 1.1); c mold C ( 1.35). Figure 6 a shows penetration ratio R p and residual thickness ratio h r /h 0 for various initial thicknesses of the polymer, aspect ratios of the grooves, and imprinting pressures. The solid lines show the simplified relation between the initial polymer thickness and the penetration ratio when the polymer is assumed to be a noncompressive liquid. The symbols in color show the experimental results and black symbols show simulated results for an value of 1.0. When the initial thickness of the polymer is thin, the R p does not become large even if the imprinting pressure increases. If the initial thickness of the polymer is thick and so is the mold depth, the R p is over 0.8 under high-pressure conditions. These results agree with the simulation results. The residual thickness is shown in Fig. 6 b. As the initial thickness increases, the residual thickness is increases. However, the values are less than the values predicted by the FIG. 5. Experimental results for various values of the aspect ratio. a 0.27, b 1.1, and c FIG. 6. Simulation and experimental results for the polymer deformation process for various aspect ratios of the grooves and imprinting pressures. a The relation between the penetration ratio R p and the initial thickness h 0. b The residual thickness h r and the initial thickness h 0. J. Vac. Sci. Technol. B, Vol. 19, No. 6, NovÕDec 2001

5 2815 Hirai et al.: Resist deformation in nanoimprint lithography 2815 simulations or by the geometrically derived results solid lines. This shows that volume compression occurs in the polymer. V. CONCLUSIONS Cross-sectional profiles of deformed polymers in imprint lithography were studied by simulation based on a rubber elastic model and were compared with experimental results for various imprinting conditions such as the aspect ratios of the mold pattern, initial thickness of the polymer, and imprinting pressures. The penetration ratio of the polymer to the recessed groove of the mold and the residual thickness of the deformed polymer underneath the mold were quantitatively evaluated. The cross-sectional profiles from the simulation results agreed quantitatively with the experimental results qualitatively for various geometrical and pressure conditions. Also, the penetration ratios and the cross-sectional profiles agreed relatively well with the experiments. This indicates that when the polymer is above its glass transition temperature it shows rubber-like elastic dynamics as discussed by the simulation. However, volume compression is observed under the high-pressure condition and with thick polymers. We believe these results can be very useful for optimizing nanoimprint process conditions and mold design for integrated variety patterns such as ULSI patterns. ACKNOWLEDGMENTS The authors thank Dr. K. Murata and Dr. A. Okamoto of the Technology Research Institute TRI of the Osaka prefecture for their help. 1 S. Y. Chou, P. R. Krauss, and P. J. Renstrom, Appl. Phys. Lett. 67, M. Colburn et al., Proc. SPIE 3676, M. Moony, J. Appl. Phys. 11, R. S. Rivin, Philos. Trans. R. Soc. London, Ser. A 242, User Information A, MARC Analysis Research Corporation, Palo Alto, CA L. E. Nielsen, Soc. Plastic Eng. J. 16, N. A. Fleck, W. J. Stronge, and J. H. Liu, Proc. R. Soc. London, Ser. A 429, F. Hurtado-Laguna and J. V. Aleman, J. Polym. Sci., Part A: Polym. Chem. 26, Y. Hirai, T. Kanemaki, M. Fujuwara, T. Yostuya, and Y. Tanaka, J. Photopolym. Sci. Technol. 13, Y. Hirai, S. Yoshida, A. Okamoto, Y. Tanaka, M. Endo, S. Irie, H. Nakagawa, and M. Sasago, J. Photopolym. Sci. Technol. 14, JVST B-Microelectronics and Nanometer Structures