Size-Dependent Shape Evolution of Patterned Polymer Films Studied

Article pubs.acs.org/Macromolecules

Size-Dependent Shape Evolution of Patterned Polymer Films Studied in Situ by Phase-Retrieval-Based Small-Angle X-ray Scattering Kim Nygård,*,†,‡ Sean P. Delcambre,§ Dillip K. Satapathy,† Oliver Bunk,† Paul F. Nealey,§ and J. Friso van der Veen†,⊥ †

Research Department of Synchrotron Radiation and Nanotechnology, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland Department of Chemistry and Molecular Biology, University of Gothenburg, SE-41296 Gothenburg, Sweden § Department of Chemical and Biological Engineering, University of WisconsinMadison, Madison, Wisconsin 53706, United States ⊥ ETH Zürich, CH-8093 Zürich, Switzerland ‡

ABSTRACT: Patterned polymer films are known to exhibit shape evolution when annealed at temperatures close to or above the glass transition temperature. Here, we employ small-angle X-ray scattering to address the size-dependent shape evolution of poly(methyl methacrylate) (PMMA) gratings obtained by thermal nanoimprint lithography. Using an iterative phase-retrieval scheme, we reconstruct the height profile of the grating in situ in a model-independent manner during a heating ramp through the glass transition. This allows us to directly observe the evolution from a trapezoidal shape, via a sinusoidal-like one, into a flat film, in agreement with ex-situ atomic force microscopy experiments. Moreover, we find the onset temperature of shape evolution to decrease monotonically with decreasing pattern size, the difference being ∼4 °C between gratings with periods of 240 and 80 nm. We primarily attribute the size-dependent shape evolution to a reduction in viscosity with decreasing pattern size, which is induced by either free-surface effects or surfacetension-driven non-Newtonian flow.

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INTRODUCTION Confinement at the nanometer scale is known to strongly influence material properties, such as the melting temperature Tm and the glass transition temperature Tg.1 An illustrative example is given by thin polymer films, in which there is ample evidence for a large change in Tg of up to tens of °C, once the thickness is decreased below a critical value of a few tens of nanometers.2 The sign of the change in Tg depends on the confining geometry; in general, free-standing polymer films exhibit a depression in Tg compared to the bulk value, while the opposite is true for polymer films on solid substrates exhibiting strongly attractive polymer−substrate interfacial interactions.3,4 Moreover, the Tg has been found to vary locally with distance from the interface,5 highlighting the difficulty in addressing confinement effects already for this simplest possible confining geometry. To date, the mechanisms underlying the thicknessdependent Tg in thin polymer films remain an active topic of research.6 In the case of more complex confining geometries, in particular technologically relevant patterned polymer films, studies on the size-dependent Tg are scarce.7 Instead, significant effort has been put into studies of a closely related phenomenon: the shape evolution or “melting” of patterned polymer films when annealed at temperatures close to or above Tg. These studies are important both from a fundamental point of view, i.e., to understand the mechanisms behind the © 2012 American Chemical Society

phenomenon, and from a technological point of view, i.e., to quantify the stability of nanopatterned polymer films. Experimentally, the research on this topic has followed two different paths. First, the shape evolution has been addressed using atomic force microscopy (AFM).8−10 Within this approach, it is possible to both follow the shape evolution in real space and probe the kinetics of the phenomenon as a function of feature size, although with a rather limited temporal resolution. Second, the shape evolution has been studied by insitu scattering from periodically patterned polymer films using either visible light or X-rays.11−18 These experiments have a much improved temporal resolution compared to AFM experiments, although at the expense of obtaining data in reciprocal rather than in real space. Nonetheless, by simplified modeling of the full scattering pattern, one can obtain insight into the temporal evolution of different structural parameters during the annealing process.13,18 In this article, we reconcile the aforementioned real-spacebased AFM and reciprocal-space-based scattering techniques. More specifically, we address the issue of size-dependent shape evolution of patterned polymer films near Tg by means of insitu small-angle X-ray scattering (SAXS) experiments on Received: April 1, 2012 Revised: June 21, 2012 Published: June 29, 2012 5798

dx.doi.org/10.1021/ma300662s | Macromolecules 2012, 45, 5798−5805

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poly(methyl methacrylate) (PMMA) gratings obtained by thermal nanoimprint lithography (NIL). The novelty of our approach is the use of an iterative phase-retrieval scheme, which allows us to reconstruct the average grating height profile as a function of temperature during a temperature ramp in a modelindependent manner. This approach allows us to identify a sequence of grating shapesfrom a trapezoidal shape, via a sinusoidal-like one, into a flat filmin agreement with ex-situ AFM experiments. Moreover, we observe a monotonic decrease in the onset temperature of shape evolution with decreasing pattern size, the difference being ∼4 °C between the largest (240 nm) and the smallest (80 nm) period gratings of the present study. This phenomenon can primarily be attributed to a reduced viscosity with decreasing grating period, induced by either free-surface effects or surface-tension-driven non-Newtonian flow.

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Figure 1. Initial patterned PMMA film on a silicon substrate as observed by cross-sectional SEM. The pattern height is 100 nm, the period is 160 nm, and the residual layer is ∼20 nm.

MATERIALS AND METHODS

Materials. Poly(methyl methacrylate) [PMMA, Mn = 75 kg/mol, Mw/Mn = 1.05, Tg = 121 ± 1 °C by differential scanning calorimetry (DSC)] was purchased from Polymer Source, Inc. Anisole and acetone were purchased from Fisher Scientific. All materials were used as received without further purification. Bare 2.5 in. diameter, 200 μm thick Si ⟨100⟩ wafers were purchased from Virginia Semiconductor, Inc. Thermal Nanoimprint Lithography. PMMA was dissolved in anisole at a concentration of 6 wt % and spin-coated onto 200 μm thick bare Si wafers. The wafers were ultrasonically cleaned at room temperature for 300 s in acetone and dried prior to coating. After spincoating, the samples were baked on a hot plate at 160 °C for 120 s in air to evaporate residual anisole. The films were ∼120 nm thick, as measured by profilometry (AlphaStep) and ellipsometry (Rudolph Instruments). The thin films were patterned by thermal NIL using an Obducat 2.5 NIL instrument. The Si master pattern used for imprinting was obtained from Obducat AB and consisted of several fields of dense 1:1 line:space grating structures with periods of P = 80, 120, 160, and 240 nm. In comparison to the polymer’s radius of gyration, Rg = (0.096Mw0.98)1/2 ≈ 78 Å as estimated following ref 12, the nominal line widths correspond to roughly 5Rg, 8Rg, 10Rg, and 15Rg. The height of topography in all master pattern fields was 100 nm, and each patterned field measured 1 × 1 mm2 in area. The master was treated with a fluorinated trichlorosilane coating to prevent adhesion of the polymer to the master surface. The patterning conditions involved heating the samples and nanoimprint master to 160 °C while in contact and applying 40 bar of pressure for 300 s before cooling to room temperature and separating the master from the patterned polymer film. The initial pattern height (∼100 nm) and residual layer thickness (∼20 nm) were verified by cross-sectional scanning electron microscopy (SEM) using a LEO 1550VP field emission SEM (see Figure 1). The initial patterned polymer films as observed by AFM (see details below) are shown in Figure 2. In-Situ Small-Angle X-ray Scattering. The SAXS experiment was carried out at the cSAXS beamline of the Swiss Light Source. The incident X-ray beam impinged normal to the patterned polymer films and the scattered X-rays were collected in transmission geometry 7.15 m behind the sample using the single-photon-counting PILATUS 2M pixel detector.19 The incident X-ray beam had an energy of ℏω = 12.4 keV (wavelength λ = 0.10 nm), a beam size of approximately 200 × 200 μm2 at the sample position, and it was focused onto the detector plane in order to maximize the angular resolution. We used a 7 m long evacuated flight tube between the sample and the detector in order to reduce parasitic scattering. The use of a semitransparent central beamstop (3.5 mm thick Si, transmission ∼0.9 × 10−6 at 12.4 keV20) downstream of the sample allowed monitoring the intensity of the direct beam, which in turn made possible the model-independent reconstruction of the grating’s height profile using an iterative phaseretrieval scheme. Throughout the experiment, the sample temperature

Figure 2. Initial patterned PMMA films as observed by AFM for grating periods P of (a) 80, (b) 120, (c) 160, and (d) 240 nm. was increased from ambient up to a maximum of 160 °C at a rate of 10 °C/min, and X-ray scattering data were collected in continuous mode in the temperature range T = 80−160 °C using an exposure time of 1 s. In the remainder of this paper we have summed the scattering data into 3 s bins in order to improve the statistical accuracy; however, the height-profile reconstructions obtained using 1 and 3 s data bins are practically indistinguishable. For analysis of the SAXS data, we made use of an iterative phaseretrieval scheme,21 which has previously been applied for studies on the ordering of colloidal suspensions confined in diffraction gratings.22−24 This approach allowed us to reconstruct the average height profile of the grating as a function of temperature in a modelindependent manner. For temperatures T ≤ 130 °C, we could reliably determine the diffracted intensities up to M = 12 and 20 diffraction orders for grating periods of P = 160 and 240 nm, respectively, leading to a real-space sampling interval of Δx = P/(2M + 1) ≈ 6 nm in both cases. In order to facilitate comparison, we used the same sampling interval also at larger temperatures, although high-order diffraction peaks could not be resolved. Ex-Situ Atomic Force Microscopy. A series of samples containing fields of nanoimprinted PMMA gratings were placed onto a calibrated, PID-controlled hot plate at room temperature. The temperature of the hot plate was increased at a rate of 10 °C/min, and samples were systematically removed from the hot plate and quenched to room temperature at regular intervals with increasing hot plate temperature. AFM data were acquired at room temperature using a Veeco Nanoscope IV Multimode AFM instrument in tapping mode, 5799


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using single-crystal diamond probes (nominally 7 nm radius of curvature and 20° tip cone angle) purchased from MikroMasch. Each grating field was measured over a 1 × 1 μm2 area. Differential Scanning Calorimetry. Solid specimens of PMMA were prepared via solvent casting. PMMA was dissolved in anisole at a total polymer concentration of 25 wt %. The solutions were transferred into aluminum weigh pans and dried to remove residual anisole. The samples were slowly ramped to 160 °C over the course of 3 days in a vacuum oven at ambient pressure with a continually refreshed headspace atmosphere. The samples remained in the annealing chamber for 3 days. Thermogravimetric analysis (TA Instruments Q500) was performed to ensure that all residual anisole had been removed from the samples. Portions of the solid specimen weighing 5−10 mg were removed and analyzed by DSC. The samples were thermally cycled from 20 to 160 °C and back to 20 °C at a ramp rate of 10 °C/min four times to ensure adequate thermal contact with the sample stage before data was collected. The Tg of each specimen was measured from the inflection point of a step change in the heat flow versus temperature curve as the sample was heated through the glass transition. Five specimens were measured for the PMMA sample studied in this work.

observed, indicating a large-scale shape evolution of the patterned films into flat ones. By Fourier transforming the diffraction pattern, we obtain the autocorrelation function A(x) of the grating profile, A(x) ∝ h(x) ⊗ h(−x), with h(x) denoting the height profile of the grating and ⊗ the convolution operator.25 Although A(x) does not provide the height profile as a function of temperature directly, it does provide a model-free real-space representation of the diffraction data in a straightforward manner. To demonstration this, we present in Figure 4 the autocorrelation

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RESULTS AND DISCUSSION During the SAXS experiment, we monitored the scattering pattern in transmission mode as the temperature of the sample was increased from room temperature up to 160 °C at a rate of 10 °C/min. This is exemplified in Figure 3, which shows the Figure 4. Autocorrelation function A(x) as a function of temperature for a PMMA grating with the period P = 160 nm.

function with increasing temperature obtained for a PMMA grating with a period of P = 160 nm. In this plot, the real-space sampling interval is ∼6 nm (see Materials and Methods). At low temperatures, a nearly rectangular (or trapezoidal) shape of h(x) leads to a slightly rounded, triangular shape of ΔA(x) = A(x) − 1. With increasing temperature, ΔA(x) becomes shallower and broader, implying a decrease in height and increase in width of h(x) as observed elsewhere.13 Finally, we observe a large-scale shape evolution of the nanoimprinted pattern into a flat film, as evidenced by the autocorrelation function becoming unity at elevated temperatures. The above analysis is also readily extended to smaller-period gratings, as shown in Figure 5 for a grating with P = 80 nm and using the diffracted intensities up to M = 6 diffraction orders. In order to obtain the height profile h(x) in a modelindependent manner from the SAXS data in situ during the temperature ramp, we make use of an iterative phase-retrieval scheme.21 The results are presented in Figure 6 for two gratings

Figure 3. SAXS pattern obtained from a PMMA grating with a period of P = 160 nm for selected temperatures (vertically offset for clarity). Diffraction orders m = 1−10 are shown.

scattered intensity I(q), as a function of the scattering vector modulus q, collected at selected temperatures from a PMMA grating with a period of P = 160 nm. Because of the periodicity in the imprinted polymer films, the SAXS pattern exhibits characteristic diffraction peaks at positions qm = 2πm/P in reciprocal space, with m denoting the mth diffraction order. At temperatures well below the bulk Tg, the total diffracted intensity Itot = ∑m≠0I(qm) is nearly invariant. However, as the temperature of the sample is increased above a perioddependent characteristic temperature, which is close to the bulk Tg of 121 ± 1 °C as determined by DSC, we observe a rapid decay of Itot. Moreover, we find the high diffraction orders, corresponding to high spatial frequencies, to decay faster than the low orders, in agreement with previous AFM studies.9 At the end of each heating ramp, i.e., at the temperature T = 160 °C, no diffraction pattern can be

Figure 5. As Figure 4, except for P = 80 nm. 5800


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Figure 6. Height profiles h(x) reconstructed from in-situ SAXS data for PMMA gratings with periods P = 240 nm (top) and 160 nm (bottom).

Figure 7. Height profiles h(x) of PMMA gratings with a period of P = 240 nm at selected temperatures as determined by in-situ SAXS (top, geometrically convoluted with the nominal AFM tip shape to facilitate comparison) and ex-situ AFM (bottom).

with periods of 160 and 240 nm at selected temperatures. Again, the real-space sampling interval is ∼6 nm in both cases (see Materials and Methods). In this plot, the reference height at each temperature is given by the maximum height of the pattern. For both grating periods, the functional form of the height profile h(x) is found to evolve from a trapezoidal to a sinusoidal grating and further into a flat film. This sequence of grating shapes also provides the motivation for employing the present iterative phase-retrieval scheme instead of a simpler, model-dependent approach; any model-dependent analysis, such as the previously used assumption of a trapezoidal shape,13 would provide a correct description of the grating’s shape evolution only in a limited temperature range. We have verified the shape evolution of the 240 nm period polymer grating with increasing temperature using ex-situ AFM, as shown in Figure 7. In order to facilitate comparison, we have geometrically convoluted the SAXS-based height profiles in Figure 7 using the nominal AFM tip shape. In general, the agreement between SAXS and AFM profiles is good, thereby reconciling the real-space data obtained by AFM and the reciprocal-space data provided by SAXS. However, three differences need to be mentioned. (i) The onset temperature for shape evolution is found to be a few °C lower in the SAXS data compared to the AFM data, an effect which can primarily be attributed to radiation damage in the former case (see last paragraph of this section).26 (ii) The trench widths obtained by AFM are slightly narrower than the corresponding ones obtained by SAXS, the full width at half-maximum being ∼60 and 75 nm, respectively, for the T = 120 °C data. Given the good agreement between the SEM data of Figure 1 and the 160 nm period SAXS profile at T = 120 °C in Figure 6, the difference in trench widths obtained by SAXS and AFM may

imply inaccuracies in the adopted nominal tip shape. Importantly, for periods smaller than 240 nm we could not reach the bottom of the grating trench with the AFM tip, demonstrating the potential of the present phase-retrieval-based SAXS approach for studies on high-aspect-ratio patterns. (iii) The AFM data confirm that the initial grating height was about 100 nm, in contrast to ∼85 nm as determined by SAXS. The initial grating height of ∼100 nm was also verified by crosssectional SEM. We emphasize that the adopted phase-retrieval algorithm is known to provide quantitative reconstructions of density profiles from diffraction patterns (see, e.g., ref 27). At the moment, the reason for this discrepancy cannot be unambiguously determined. First, we have verified the initial grating height obtained by SAXS for two separate 240 nm period gratings, ruling out the possibility of a misalignment of the grating during the SAXS experiment. Second, one may speculate whether the discrepancy could be explained by previously observed capillary instabilities in nanoimprinted polymer films.28,29 However, we found no evidence of such instabilities in our AFM experiments (see Figure 2). Finally, a possible remaining explanation could be systematic defects in the 240 nm period PMMA gratings; since the SAXS experiment probed the height profile averaged over an area 40 000 times larger than the area measured with AFM (cf. Figure 2), defects in the PMMA grating would show up as effectively shallower grating trenches in the SAXS compared to the AFM profiles. While the sequence of grating shapes presented in Figure 6 does not depend on the grating period, the onset temperature for shape evolution is found to decrease with decreasing period. In order to quantify this effect, we can monitor the diffraction data as follows. Within the kinematic theory of diffraction and 5801


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for transmission geometry, the mth-order diffracted intensity Im is given by Im ∝ |am|2, with am denoting the mth Fourier amplitude of the grating shape.25 To a first approximation, the grating height is given by the principal Fourier component, m = 1. Consequently, by monitoring a1(T), we are in effect monitoring the height of the grating during the temperature ramp. This is presented in the top panel of Figure 8 for a set of

the data is a monotonic decrease in the characteristic temperature with decreasing pattern size, the difference in Tc between the largest (P = 240 nm) and the smallest (P = 80 nm) period gratings studied here being ΔTc ≈ 4 °C. Similar trends have previously been observed using ex-situ AFM.10 In order to semiquantitatively explain the data, we adopt a simple model of surface-tension-driven viscous flow by Hamdorf and Johannsmann.11 This model has also previously been discussed in studies on shape evolution of NIL-based, high-aspect-ratio polymer gratings.13−15 In the simplest approximation, the shape evolution of the grating is governed by the balance of two terms. First, the curvature of the polymer−air interface gives rise to a Laplace pressure across the interface, the value of which is inversely proportional to the local radius of curvature and which drives the shape evolution toward a flat film. The height profiles h(x) of Figure 6 support this hypothesis, with the initial shape evolution being most strongly manifest in the sharp corners of the gratings. Second, the resistance to viscous flow is described by the viscosity η of the material. Considering a shallow grating structure on a polymer surface and assuming an ideal Newtonian fluid, Hamdorf and Johannsmann derived a simple relationship between the viscosity and the time dependence of the grating height.11 For nonsinusoidal grating profiles, as in the present study, the grating height profile can be Fourier decomposed.8 Using our notation, the temperature dependence of the Fourier amplitudes am is then given by q cγ(T ) dam(T ) =− m am(T ) dT 2η(T )

(1)

with am(T) denoting the mth-order Fourier amplitude at temperature T and γ(T) the surface tension. The constant c, which is defined by dam/dT = cȧm, with ȧm denoting the derivative of am with respect to time, takes into account the present temperature ramp with a constant temperature gradient. It should be noted, however, that our problem is more complex because of the following reasons. (i) The residual layer (∼20 nm) is small compared to the grating dimensions. As a consequence, we may expect an influence of the solid substrate. In order to address this issue, one would need to carry out experiments as a function of residual-layer thickness. (ii) There have been reports of residual solvent in thin spin-coated homopolymer films, with the residual solvent residing predominantly at the polymer−substrate interface.31 (iii) The present PMMA sample is entangled, with the average molar mass, Mn = 75 kg/mol, being larger than the critical molecular weight of entanglement for PMMA, Mc ≈ 15 kg/ mol.32 Consequently, we may expect residual stress in our PMMA gratings induced by the NIL process, which has previously been found to induce an initial, fast shape evolution of polymer gratings.13−15 (iv) Our PMMA sample is not necessarily behaving as an ideal Newtonian fluid. Nonetheless, within the model of eq 1, Tc is essentially determined from a large change in the viscosity η(T) close to the glass transition temperature, and we can therefore expect a close connection between Tc and Tg. To gain further insight into the size-dependent onset temperature for shape evolution, we determine an effective viscosity η(T) from a1(T) using eq 1. This is shown in Figure 9 for different grating periods, assuming a temperatureindependent surface tension γ ≈ 30 mN/m.12 For comparison, we also present the temperature-dependent viscosity above Tg in the bulk phase, as predicted using the Williams−Landel−

Figure 8. Top: Fourier amplitude modulus log[a1(T)/a1(TI)] as a function of temperature obtained for PMMA gratings with different periods P. The crossing point of the dashed lines depicts the characteristic temperature Tc for the onset of shape evolution, shown here for P = 240 nm. Bottom: characteristic temperature Tc(P) as determined from the top panel. The dashed line depicts the bulk Tg as determined by DSC.

PMMA gratings with periods between P = 80 and 240 nm. At sample temperatures well below the bulk Tg, a1(T) is nearly invariant with increasing temperature. At temperatures near the bulk Tg, a1(T) starts decaying exponentially and eventually reaches zero as the polymer film becomes flat. It should be noted that such a rapid drop of a1(T) [or, equivalently, the total diffracted intensity Itot(T)] close to the bulk Tg is not limited to NIL-based structures but has also been observed for PMMA gratings obtained using EUV lithography.30 Moreover, the shape evolution into flat films has also been observed for F8BT gratings obtained by spin-coating on prepatterned silicon masters.18 Finally, we define a characteristic temperature Tc(P) for the onset of shape evolution from the crossing point of linear fits to the log[a1(T)/a1(TI)] data below and above the onset of the rapid decay, with TI = 80 °C being the initial temperature (see top panel of Figure 8 for the case of P = 240 nm). The characteristic temperature Tc(P) is presented in the bottom panel of Figure 8. For comparison, we also show the bulk Tg as determined by DSC. The most prominent feature in 5802


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measurements of polymer viscosities in the bulk phase.35 Finally, for even larger temperatures there are hints of a decrease in η(T) with increasing temperature, although the diffracted amplitudes are too weak to allow drawing definite conclusions. What is the driving force behind the size-dependent onset temperature for shape evolution as reported here? In principle, one may think of several possible explanations: (i) There have been reports of a reduced viscosity in thin polymer films with decreasing film thickness, induced by a mobile surface layer with a characteristic size comparable to the polymer’s radius of gyration, ∼Rg (see, e.g., ref 36 and references therein). Since the fraction of free surface increases with decreasing grating period, a possible explanation for the size dependence of Tc(P) is simply a reduction in the effective viscosity with decreasing grating period due to such free-surface effects. (ii) One may also expect increasing residual stress in the NIL-based patterned polymer films with decreasing feature size, which, in turn, would induce a reduction in Tc(P) with decreasing grating period. In order to estimate the importance of residual stress, we can determine the bulk terminal relaxation time, which reflects the longest time needed for the polymer to relax entanglement constraints, as τ0 = η0J0e with J0e denoting the steady-state compliance.10,15 Inserting the WLF value η0 ≈ 3 × 106 Pa s and estimating J0e ≈ 4 × 10−6 Pa−1 using the parameters of ref 32, we obtain τ0 ≈ 12 s at the NIL imprinting temperature (T = 160 °C). This estimate of τ0 is significantly smaller than the NIL imprinting time (300 s), implying that residual stress is not a dominant factor in the present case. (iii) A third possible explanation is spatial confinement of the polymer coils. It has previously been observed that spatial confinement of polymer chains to dimensions smaller than or comparable to Rg induces an entropic force which drives the shape evolution.10 However, since the nominal line widths are relatively large in the present study, between 5Rg and 15Rg, this mechanism can be ruled out. (iv) One may question whether there was residual solvent in our polymer films and, if so, whether it plays a role in the observed shape evolution. Indeed, recent studies have brought into evidence an enhanced layer of residual solvent at the polymer−substrate interface in thin homopolymer films.31 Given the relatively short annealing time of the present polymer films, we cannot directly rule out the effect of residual solvent. However, we note that similar shape evolution as reported here has also been observed in polymer films annealed under vacuum for up to 12 h.12 (v) Finally, Peng et al. reported surface-tension-induced reduction of the viscosity, akin to “shear thinning”, in patterned polymer films.10 Following their reasoning, we estimate the initial surface-tension-induced stress in our patterned PMMA films to increase from 0.5 to 4.6 MPa upon reducing the grating period from 240 to 80 nm. These values are larger than the critical shear stress for the onset of non-Newtonian flow, σc ∼ 1/J0e ≈ 0.25 MPa, and although we do not have simple shear stress in the present case, we can expect a decrease in viscosity induced by the large surface-tension-induced stress. On the basis of the above considerations, we predominantly attribute the observed size-dependent onset temperature for shape evolution to a reduction in viscosity, induced by either free-surface effects or surface-tension-driven non-Newtonian flow. Finally, we briefly address the effect of radiation damage induced by the X-ray beam during the in-situ SAXS experiment. X-ray irradiation causes chain scissioning along the backbone of PMMA, thereby decreasing the average molecular weight of the

Figure 9. Effective viscosities η(T) for different grating periods as determined from the data of Figure 8 (top panel) using eq 1. The data are vertically offset for clarity. The statistical error bars are smaller than the symbol size for temperatures above 109, 111, 112, and 118 °C for grating periods of 80, 120, 160, and 240 nm, respectively. The solid lines depict the zero shear rate viscosity η0(T) as estimated using the Williams−Landel−Ferry equation (see text for details), while the dashed lines are obtained from linear fits to the data of Figure 8 for T ≫ Tg.

Ferry (WLF) equation:33 η0(T) = η0(T0) exp[−C1(T − T0)/ (C2 + (T − T0))], with η0 being the zero shear rate viscosity, C1 and C2 empirical parameters, and T0 a reference temperature. For the WLF data presented in Figure 9, we have used the parameters C1 = 8.9, C2 = 176 °C, and T0 = 190 °C following ref 32, while we have estimated η0(T0) = 4.6 × 105 Pa s from the literature value η0(T0) = 1.04 × 106 Pa s for Mw = 100 kg/ mol34 using the scaling law η0 ∝ Mw3.4. Since the parameters adopted here (C1 and C2) have been determined for a slightly different molecular weight polymer (Mn = 100 kg/mol) and for larger temperatures (T = 150−260 °C), the WLF data should be considered merely a semiquantitative estimate of η0(T). All the effective viscosities η(T) presented in Figure 9 exhibit a qualitatively similar behavior, irrespective of grating period. For T ∼ Tg, we observe a rapid decrease in η(T). For temperatures a few degrees above Tg, there is a transition from a highly temperature-dependent to a temperature-independent η(T), and the size-dependent temperature at which this transition occurs essentially defines the onset temperature for shape evolution, Tc(P). The values of η(T) in this temperature regime show only a weak size dependence: η = (3.5 ± 0.3) × 107, (2.3 ± 0.3) × 107, (1.9 ± 0.3) × 107, and (1.6 ± 0.3) × 107 Pa s for P = 80, 120, 160, and 240 nm, respectively, as determined from the dashed lines in Figure 9. While the observed shift in Tc to smaller temperatures with decreasing grating period is clear, indicating a decrease in η with decreasing P for T ∼ Tg, we cannot conclude whether the weak size dependence of η in the constant-η regime is a real phenomenon or induced by effects neglected in the simple model of eq 1. The rapid drop in η(T) followed by a constant plateau differs qualitatively from the monotonic decrease observed both in the WLF data of Figure 9 and direct 5803


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polymer and increasing its polydispersity. This decrease in average molecular weight, in turn, leads to a decrease in the onset temperature of shape evolution, as evidenced by recent SAXS experiments on PMMA gratings as a function of absorbed dose.30 For thin films, either patterned or flat, the absorbed dose can be estimated as D ≃ N0(μen/ρ)ℏωρ, with N0 denoting the integrated flux density on the sample, (μen/ρ) the mass energy absorption coefficient, which takes into account the amount of energy absorbed in the material,37 ℏω the incident X-ray energy, and ρ the density of the material. By estimating N0 ≈ 2.5 × 1014 photons/mm2 from the diffraction data and using (μen/ρ) = 1.7 g/cm2 for PMMA, we obtain an absorbed dose of D ≈ 250 mJ/mm3 for each sample at the bulk Tg. Importantly, although this dose is expected to induce a minor shift in Tc to smaller temperatures (we estimate ΔTc ≃ −3 °C from ref 30), the dose was identical for all samples in the present study and cannot therefore explain the size-dependent effects we report here.

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CONCLUSIONS In summary, we report in-situ SAXS studies on NIL-based PMMA gratings in order to address the size-dependent shape evolution of patterned polymer films near the glass transition temperature. First, we have determined the height profile of the grating as a function of temperature in a model-independent manner, thereby identifying a sequence of profile shapes from a trapezoidal, via a sinusoidal-like profile, into a flat film, in agreement with ex-situ AFM experiments. Second, we have observed a monotonic decrease in the onset temperature of shape evolution with decreasing pattern size, an effect which we primarily attribute to a reduction in viscosity with decreasing grating dimensions, induced by either free-surface effects or surface-tension-driven non-Newtonian flow. As demonstrated in this study, SAXS provides a direct means to probe the shape evolution of high-aspect-ratio patterned polymer films in situ during annealing. A future application of this technique could be to study the effect of adding smallmolecule diluents,38,39 either plasticizers or antiplasticizers, on the size-dependent onset temperature for shape evolution as observed here.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The SAXS experiment was carried out at the cSAXS beamline of the Swiss Light Source, Paul Scherrer Institut, Switzerland. REFERENCES

(1) Alcoutlabi, M.; McKenna, G. B. J. Phys.: Condens. Matter 2005, 17, R461−R524. (2) Keddie, J. L.; Jones, R. A. L.; Cory, R. A. Europhys. Lett. 1994, 27, 59−64. (3) Torres, J. A.; Nealey, P. F.; de Pablo, J. J. Phys. Rev. Lett. 2000, 85, 3221−3224. (4) Fryer, D. S.; Peters, R. D.; Kim, E. J.; Tomaszewski, J. E.; de Pablo, J. J.; Nealey, P. F.; White, C. C.; Wu, W.-L. Macromolecules 2001, 34, 5627−5634. (5) Ellison, C. J.; Torkelson, J. M. Nat. Mater. 2003, 2, 695−700. (6) Pye, J. E.; Roth, C. B. Phys. Rev. Lett. 2011, 107, 235701. 5804


Macromolecules

Article

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Size-Dependent Shape Evolution of Patterned Polymer Films Studied

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