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Profile evolution during thermal nanoimprint
Microelectronic Engineering 83 (2006) 843–846 www.elsevier.com/locate/mee
Profile evolution during thermal nanoimprint H.-C. Scheer a
a,*
, N. Bogdanski a, M. Wissen a, T. Konishi b, Y. Hirai
b
Microstructure Engineering, Faculty of Electrical, Information and Media Engineering, University of Wuppertal, Rainer-Gruenter-Str. 21, 42119 Wuppertal, Germany b Physics and Electronics Engineering, Osaka Prefecture University, Osaka, Japan Available online 3 March 2006
Abstract The evolution of the profile of an imprinted line under squeeze-flow dominated thermal nanoimprint is investigated experimentally. The results indicate, that in the very first moment the stamp intrusion into the polymer is fast due to shear thinning at the periphery of the feature, proceeding along with the build-up of internal stress in the feature centre. Relaxation of this stress proceeds according to the flow time constants. At processing times that are short compared to the time constants, stress relaxation will not be completed. Then the polymer recovers its initial shape in parts, and this recovery is responsible for the final profile shape. As time constants can be tuned by temperature, these investigations are helpful to define adequate low temperature imprint conditions when mixed pattern sizes are imprinted into spin-coated layers. 2006 Elsevier B.V. All rights reserved. Keywords: Thermal nanoimprint; Profile evolution; Time constants; Elastic recovery; Stress relaxation
1. Introduction During thermal nanoimprint [1] a thermoplastic polymer has to conform to a mould at an elevated temperature under pressure. Typically, thermoplastic polymers feature viscoelastic behaviour, i.e., polymer response depends on the time constants responsible for viscous flow and elastic response of the material at the processing temperature. Therefore, in particular for low temperature NIL (nanoimprint lithography), a subtle tuning of temperature and time is required to result in an accurate imprint for a given range of pattern sizes. Recovery effects may arise, which have been investigated in detail recently [2,3]. Thermoplastic polymers like polystyrene behave according to the well known time–temperature correspondence principle [4]: at different processing temperatures, the imprint proceeds in the same way but at a different time scale. We make use of this principle to experimentally
*
Corresponding author. Tel.: +49 202 439 1040; fax: +49 202 439 1804. E-mail address: [email protected] (H.-C. Scheer).
0167-9317/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2006.01.255
observe the profile evolution during the imprint of elevated stamp patterns. Results with different imprint times in combination with simulations of the elastic effects, which govern polymer behaviour within the first moments of deformation, facilitate the discussion of profile evolution during squeeze-flow dominated thermal nanoimprint. 2. Experimental We used commercial polystyrene (Sigma Aldrich, Tg = 95 C, Mw = 350 kg/mol), referred to as PS 350k, which was characterised [5] before imprinting. From the complex shear modulus master curves the response time constants were derived [6]. At 170 C, the time constant for elastic response is se < 0.1 ms, the time constant for the onset of flow is sc = 1.7 s and the final (longest) flow time constant is s0w = 20 s. The imprint experiments were performed in a simple manual press at 100 bar to make use of shear thinning effects [7,8]. Temperature was reduced to 130 and 140 C to get time constants comparable to well-controllable processing times. Visualization of the imprint process was
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H.-C. Scheer et al. / Microelectronic Engineering 83 (2006) 843–846
realised by conducting a series of imprint experiments where the imprint time was increased from about 10 s to about 25 min, including about 3 s for pressure build-up. After quick cooldown the pressure was released at 70 C. In order to ensure crucial squeeze flow conditions with elastic effects, (i) we imprinted into thin layers (130 nm) where macroscopic polymer characterisation may meet its limits, and (ii) we evaluated the imprint of a 40 lm wide isolated line of 500 nm height (2 · 2 cm2 fully patterned stamp). With only two exceptions the results were taken at identical locations. Elastic behaviour of the polymer was simulated with a commercially available software package (MARC, MSC Software), treating the polymer as a homogeneous, isotropic, continuous, incompressible elastic body according to the classical Mooney–Rivlin equations for the non-linear behaviour of a rubber at high strain [4,9]. 3. Results and discussion For the two processing temperatures the characteristic parameters differ by a factor of 8 [6,7], sc = 12 and 1.5 min, s0w = 150 and 18 min and g0 = 5 · 107 and 6.5 · 106 Pa s for 130 and 140 C, respectively, where g0 is the zero shear viscosity of the polymers. Elastic response is still below 1 s, so elastic effects are quasi-instantaneous, whereas flow-related effects evolve with time. Fig. 1 shows profilometer measurements across the 40 lm line for the two processing temperatures. The measurements are levelled with respect to the initial polymer height d0. With ongoing time the imprint depth increases. The steep polymer wall besides the imprinted line refers to material which has climbed up the stamp [10]. There the stamp cavity is filled in all cases to its full height –
stamp height is marked by the shaded rectangle. (The ‘overshoots’ at the peaks are due to profilometer inertia and potential polymer stretching during separation.) With increasing imprint depth the stamp cavity along the line is filled laterally (see increased width of the peaks). In accordance with earlier findings [6,8] and in accordance with other groups [2,3] the centre of the imprinted line recovers to its full initial height. Along the line periphery a plastic deformation remains, increasing in width with time. At high enough temperature and/or imprint time the central tip decreases (140 C, 24 min) and finally vanishes – for 150 C the imprinted line is flat already after 1 min. The initial depth and final depth of the imprint, marked as di and d1, are comparable for the two temperatures. In contrast to other groups [3] we do not assign the difference between di and d1 to recovery. A steep decrease of the polymer height in the beginning of the imprint and a severe slowdown after short time, as suggested by the profiles of Fig. 1, can be anticipated from calculations in [7]. Simulation of the elastic behaviour shown in Fig. 2 is a further indication. Stress components (a) and strain components (b) are shown when a wide line (only half of it is visible, together with a part of the adjacent cavity) is pressed into an elastomeric layer. The state of deformation (Fig. 2b) indicates, that in the centre of the imprinted line there is some horizontal elongation combined with vertical compression (volume remains constant), but no shear deformation. Towards the periphery of the imprinted line all deformations increase. At the periphery elongation/ compression reduces again, but highest shear deformations occur. We believe, that this high shear deformation within very short time (se) gives rise to strong shear thinning and thus to a low local viscosity and efficient outflow of the polymer. As at 140 C the viscosity is lower than for
Fig. 1. Profiles (Dektak) across an imprinted 40 lm line (500 nm stamp height, see shading), in a 130 nm polystyrene layer after imprint times of 10 s to 24 min: (a) imprint temperature 130 C; (b) imprint temperature 140 C (bottom part of profiles only). d0 is the initial polymer height, di is the initial imprint depth after 10 s, and d1 is the final imprint depth after long imprint time.
H.-C. Scheer et al. / Microelectronic Engineering 83 (2006) 843–846
845
Fig. 2. Components of stress (a) and strain (b) during elastic deformation of a polymer according to the Mooney–Rivlin Model.
130 C the width of the outflow region is wider on the cost of the recovered region in the 10 s imprints of (Fig. 1). Recovery effects can be expected within a region of high built-in stress, when there was not sufficient time available at high temperature to relax these stresses. The stress state (Fig. 2a) indicates, that in the centre of the imprinted line, the highest normal compressional stresses in horizontal as well as in vertical direction prevail. In particular the horizontal stress decreases towards the line periphery, where both normal stresses are low. Therefore recovery is expected in the line centre, but not at the periphery. The local difference between horizontal and vertical stress components together with the shear stress determines the specific shape of the recovered region. The lateral width decrease of the recovered centre region in Fig. 1 with time is assumed to result from stress relaxation according to the flow time constants. With increasing time the polymer loses the memory for its initial shape. Thus the differences observed for the two temperatures should reflect the differences in the respective flow time constants s0w, 150 and 18 min for 130 and 140 C, respectively. This illustrates, that even after 24 min at 140 C there is still recovery. From the profile similarity of the 130 C/24 min experiment and the 140 C/(3–8) min experiment a factor of 3–8 can be derived. Though somewhat too low, this is in acceptable agreement with the expectations.
behaviour of the polymer were performed. The investigations lead to the following view of the imprint procedure. In a thermal nanoimprint process under squeeze flow dominated conditions with shear thinning, the stamp intrudes into the polymer quickly up to a specific depth di, which we attribute mainly to the pressure applied. In the first moment the polymer acts like an elastic body, and its forced deformation under volume conservation leads to the built-up of internal stresses. These compressional stresses are highest in the centre of the imprinted feature and decrease towards its periphery, where high shear deformation occurring elastically within short time results in a local viscosity reduction due to shear thinning in the very initial phase of the imprint. With ongoing imprint time the polymer molecules disentangle according to the flow time constants, where the longest time constant s0w will dominate the process, until the stresses are relaxed and no more recovery occurs. The results are valid for any imprint independent of the processing temperature. An increase of temperature merely accelerates the imprint process: at 200 C the final flow time constant is in the 1– 2 s range. The investigations evidence that knowledge of the polymer flow time constants in addition to the viscosity is vital to define adequate low processing temperatures. No evidence is given that polymer data derived from macroscopic characterisation should be invalid for the thin layers imprinted here.
4. Conclusion References Imprint sequences with increasing imprint times have been performed at low temperatures to visualise the time evolution of a thermal nanoimprint process in a commercial thermoplastic polymer with medium molecular weight and a broad molecular weight distribution. To understand the observed recovery effects, simulations of the elastic
[1] S.Y. Chou, P.R. Krauss, P.J. Renstrom, Appl. Phys. Lett. 67 (1995) 3114. [2] C.M. Martin, L. Ressier, J.P. Peyrade, Physica E 17 (2003) 523. [3] L. Ressier, C. Martin, J.P. Peyrade, Microelectron. Eng. 71 (2004) 272. [4] R.R. Schwarzl, Polymermechanik, Springer, Berlin, 1990.
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H.-C. Scheer et al. / Microelectronic Engineering 83 (2006) 843–846
[5] H. Schulz, M. Wissen, N. Bogdanski, H.-C. Scheer, K. Mattes, Ch. Friedrich, Microelectron. Eng. 78–79 (2005) 625. [6] H.-C. Scheer, N. Bogdanski, M. Wissen, T. Konishi, Y. Hirai, J. Vac. Sci. Technol. B23 (2005) 2963. [7] H.-C. Scheer, N. Bogdanski, M. Wissen, Jpn. J. Appl. Phys. 44 (2005) 5609.
[8] H. Schulz, M. Wissen, N. Bogdanski, H.-C. Scheer, K. Mattes, Ch. Friedrich, Microelectron. Eng. 83 (2006) 259. [9] Y. Hirai, T. Konishi, T. Yoshikawa, S. Yoshida, J. Vac. Sci. Technol. B 22 (2004) 3288. [10] L.J. Heyderman, H. Schift, C. David, J. Gobrecht, T. Schweitzer, Microelectron. Eng. 54 (2000) 229.
Profile evolution during thermal nanoimprint H.-C. Scheer a
a,*
, N. Bogdanski a, M. Wissen a, T. Konishi b, Y. Hirai
b
Microstructure Engineering, Faculty of Electrical, Information and Media Engineering, University of Wuppertal, Rainer-Gruenter-Str. 21, 42119 Wuppertal, Germany b Physics and Electronics Engineering, Osaka Prefecture University, Osaka, Japan Available online 3 March 2006
Abstract The evolution of the profile of an imprinted line under squeeze-flow dominated thermal nanoimprint is investigated experimentally. The results indicate, that in the very first moment the stamp intrusion into the polymer is fast due to shear thinning at the periphery of the feature, proceeding along with the build-up of internal stress in the feature centre. Relaxation of this stress proceeds according to the flow time constants. At processing times that are short compared to the time constants, stress relaxation will not be completed. Then the polymer recovers its initial shape in parts, and this recovery is responsible for the final profile shape. As time constants can be tuned by temperature, these investigations are helpful to define adequate low temperature imprint conditions when mixed pattern sizes are imprinted into spin-coated layers. 2006 Elsevier B.V. All rights reserved. Keywords: Thermal nanoimprint; Profile evolution; Time constants; Elastic recovery; Stress relaxation
1. Introduction During thermal nanoimprint [1] a thermoplastic polymer has to conform to a mould at an elevated temperature under pressure. Typically, thermoplastic polymers feature viscoelastic behaviour, i.e., polymer response depends on the time constants responsible for viscous flow and elastic response of the material at the processing temperature. Therefore, in particular for low temperature NIL (nanoimprint lithography), a subtle tuning of temperature and time is required to result in an accurate imprint for a given range of pattern sizes. Recovery effects may arise, which have been investigated in detail recently [2,3]. Thermoplastic polymers like polystyrene behave according to the well known time–temperature correspondence principle [4]: at different processing temperatures, the imprint proceeds in the same way but at a different time scale. We make use of this principle to experimentally
*
Corresponding author. Tel.: +49 202 439 1040; fax: +49 202 439 1804. E-mail address: [email protected] (H.-C. Scheer).
0167-9317/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2006.01.255
observe the profile evolution during the imprint of elevated stamp patterns. Results with different imprint times in combination with simulations of the elastic effects, which govern polymer behaviour within the first moments of deformation, facilitate the discussion of profile evolution during squeeze-flow dominated thermal nanoimprint. 2. Experimental We used commercial polystyrene (Sigma Aldrich, Tg = 95 C, Mw = 350 kg/mol), referred to as PS 350k, which was characterised [5] before imprinting. From the complex shear modulus master curves the response time constants were derived [6]. At 170 C, the time constant for elastic response is se < 0.1 ms, the time constant for the onset of flow is sc = 1.7 s and the final (longest) flow time constant is s0w = 20 s. The imprint experiments were performed in a simple manual press at 100 bar to make use of shear thinning effects [7,8]. Temperature was reduced to 130 and 140 C to get time constants comparable to well-controllable processing times. Visualization of the imprint process was
844
H.-C. Scheer et al. / Microelectronic Engineering 83 (2006) 843–846
realised by conducting a series of imprint experiments where the imprint time was increased from about 10 s to about 25 min, including about 3 s for pressure build-up. After quick cooldown the pressure was released at 70 C. In order to ensure crucial squeeze flow conditions with elastic effects, (i) we imprinted into thin layers (130 nm) where macroscopic polymer characterisation may meet its limits, and (ii) we evaluated the imprint of a 40 lm wide isolated line of 500 nm height (2 · 2 cm2 fully patterned stamp). With only two exceptions the results were taken at identical locations. Elastic behaviour of the polymer was simulated with a commercially available software package (MARC, MSC Software), treating the polymer as a homogeneous, isotropic, continuous, incompressible elastic body according to the classical Mooney–Rivlin equations for the non-linear behaviour of a rubber at high strain [4,9]. 3. Results and discussion For the two processing temperatures the characteristic parameters differ by a factor of 8 [6,7], sc = 12 and 1.5 min, s0w = 150 and 18 min and g0 = 5 · 107 and 6.5 · 106 Pa s for 130 and 140 C, respectively, where g0 is the zero shear viscosity of the polymers. Elastic response is still below 1 s, so elastic effects are quasi-instantaneous, whereas flow-related effects evolve with time. Fig. 1 shows profilometer measurements across the 40 lm line for the two processing temperatures. The measurements are levelled with respect to the initial polymer height d0. With ongoing time the imprint depth increases. The steep polymer wall besides the imprinted line refers to material which has climbed up the stamp [10]. There the stamp cavity is filled in all cases to its full height –
stamp height is marked by the shaded rectangle. (The ‘overshoots’ at the peaks are due to profilometer inertia and potential polymer stretching during separation.) With increasing imprint depth the stamp cavity along the line is filled laterally (see increased width of the peaks). In accordance with earlier findings [6,8] and in accordance with other groups [2,3] the centre of the imprinted line recovers to its full initial height. Along the line periphery a plastic deformation remains, increasing in width with time. At high enough temperature and/or imprint time the central tip decreases (140 C, 24 min) and finally vanishes – for 150 C the imprinted line is flat already after 1 min. The initial depth and final depth of the imprint, marked as di and d1, are comparable for the two temperatures. In contrast to other groups [3] we do not assign the difference between di and d1 to recovery. A steep decrease of the polymer height in the beginning of the imprint and a severe slowdown after short time, as suggested by the profiles of Fig. 1, can be anticipated from calculations in [7]. Simulation of the elastic behaviour shown in Fig. 2 is a further indication. Stress components (a) and strain components (b) are shown when a wide line (only half of it is visible, together with a part of the adjacent cavity) is pressed into an elastomeric layer. The state of deformation (Fig. 2b) indicates, that in the centre of the imprinted line there is some horizontal elongation combined with vertical compression (volume remains constant), but no shear deformation. Towards the periphery of the imprinted line all deformations increase. At the periphery elongation/ compression reduces again, but highest shear deformations occur. We believe, that this high shear deformation within very short time (se) gives rise to strong shear thinning and thus to a low local viscosity and efficient outflow of the polymer. As at 140 C the viscosity is lower than for
Fig. 1. Profiles (Dektak) across an imprinted 40 lm line (500 nm stamp height, see shading), in a 130 nm polystyrene layer after imprint times of 10 s to 24 min: (a) imprint temperature 130 C; (b) imprint temperature 140 C (bottom part of profiles only). d0 is the initial polymer height, di is the initial imprint depth after 10 s, and d1 is the final imprint depth after long imprint time.
H.-C. Scheer et al. / Microelectronic Engineering 83 (2006) 843–846
845
Fig. 2. Components of stress (a) and strain (b) during elastic deformation of a polymer according to the Mooney–Rivlin Model.
130 C the width of the outflow region is wider on the cost of the recovered region in the 10 s imprints of (Fig. 1). Recovery effects can be expected within a region of high built-in stress, when there was not sufficient time available at high temperature to relax these stresses. The stress state (Fig. 2a) indicates, that in the centre of the imprinted line, the highest normal compressional stresses in horizontal as well as in vertical direction prevail. In particular the horizontal stress decreases towards the line periphery, where both normal stresses are low. Therefore recovery is expected in the line centre, but not at the periphery. The local difference between horizontal and vertical stress components together with the shear stress determines the specific shape of the recovered region. The lateral width decrease of the recovered centre region in Fig. 1 with time is assumed to result from stress relaxation according to the flow time constants. With increasing time the polymer loses the memory for its initial shape. Thus the differences observed for the two temperatures should reflect the differences in the respective flow time constants s0w, 150 and 18 min for 130 and 140 C, respectively. This illustrates, that even after 24 min at 140 C there is still recovery. From the profile similarity of the 130 C/24 min experiment and the 140 C/(3–8) min experiment a factor of 3–8 can be derived. Though somewhat too low, this is in acceptable agreement with the expectations.
behaviour of the polymer were performed. The investigations lead to the following view of the imprint procedure. In a thermal nanoimprint process under squeeze flow dominated conditions with shear thinning, the stamp intrudes into the polymer quickly up to a specific depth di, which we attribute mainly to the pressure applied. In the first moment the polymer acts like an elastic body, and its forced deformation under volume conservation leads to the built-up of internal stresses. These compressional stresses are highest in the centre of the imprinted feature and decrease towards its periphery, where high shear deformation occurring elastically within short time results in a local viscosity reduction due to shear thinning in the very initial phase of the imprint. With ongoing imprint time the polymer molecules disentangle according to the flow time constants, where the longest time constant s0w will dominate the process, until the stresses are relaxed and no more recovery occurs. The results are valid for any imprint independent of the processing temperature. An increase of temperature merely accelerates the imprint process: at 200 C the final flow time constant is in the 1– 2 s range. The investigations evidence that knowledge of the polymer flow time constants in addition to the viscosity is vital to define adequate low processing temperatures. No evidence is given that polymer data derived from macroscopic characterisation should be invalid for the thin layers imprinted here.
4. Conclusion References Imprint sequences with increasing imprint times have been performed at low temperatures to visualise the time evolution of a thermal nanoimprint process in a commercial thermoplastic polymer with medium molecular weight and a broad molecular weight distribution. To understand the observed recovery effects, simulations of the elastic
[1] S.Y. Chou, P.R. Krauss, P.J. Renstrom, Appl. Phys. Lett. 67 (1995) 3114. [2] C.M. Martin, L. Ressier, J.P. Peyrade, Physica E 17 (2003) 523. [3] L. Ressier, C. Martin, J.P. Peyrade, Microelectron. Eng. 71 (2004) 272. [4] R.R. Schwarzl, Polymermechanik, Springer, Berlin, 1990.
846
H.-C. Scheer et al. / Microelectronic Engineering 83 (2006) 843–846
[5] H. Schulz, M. Wissen, N. Bogdanski, H.-C. Scheer, K. Mattes, Ch. Friedrich, Microelectron. Eng. 78–79 (2005) 625. [6] H.-C. Scheer, N. Bogdanski, M. Wissen, T. Konishi, Y. Hirai, J. Vac. Sci. Technol. B23 (2005) 2963. [7] H.-C. Scheer, N. Bogdanski, M. Wissen, Jpn. J. Appl. Phys. 44 (2005) 5609.
[8] H. Schulz, M. Wissen, N. Bogdanski, H.-C. Scheer, K. Mattes, Ch. Friedrich, Microelectron. Eng. 83 (2006) 259. [9] Y. Hirai, T. Konishi, T. Yoshikawa, S. Yoshida, J. Vac. Sci. Technol. B 22 (2004) 3288. [10] L.J. Heyderman, H. Schift, C. David, J. Gobrecht, T. Schweitzer, Microelectron. Eng. 54 (2000) 229.