Self-Organized Swelling of a Metal-Capped Polymer Thin Bilayer

Feb 24, 2007 - Self-Organized Swelling of a Metal-Capped Polymer Thin Bilayer ... for the metal films on the ridge and groove of the corrugated patter...
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4404

J. Phys. Chem. C 2007, 111, 4404-4411

Self-Organized Swelling of a Metal-Capped Polymer Thin Bilayer S. Joon Kwon* and Jae-Gwan Park Materials Science and Technology DiVision, Korea Institute of Science and Technology (KIST), P.O. Box 131, Cheongryang, Seoul 130-650, Korea ReceiVed: NoVember 21, 2006; In Final Form: January 19, 2007

We report on the formation of self-organized surface patterns on a thin metal film capped polymer bilayer on a substrate by swelling. The self-organization is directed by a periodically corrugated elastomeric mold which exerts a nodal effect that confines the intrinsic swelling wave, and the resulting self-organized patterns are anisotropic and quite periodic. The corrugated pattern confined by the elastomeric mold was observed from the earlier stages of swelling while the small wrinkles (the first self-organized pattern) were formed in the later stages of the swelling. The temporal evolution of the first self-organized pattern was analyzed theoretically on the basis of the wave interaction relationship between the intrinsic swelling wave and the periodic corrugation formed in the earlier stages, and the experimental data were well-matched with the results of the analysis. The maximum value of the harmonic number for the wave number of the corrugated pattern was also analyzed. The strain in the metal thin film increases with increasing swelling time and arrives at a state of mechanical equilibrium (strain growth rate ∼0). The growth rate and moment of arrival of the strain at the state of mechanical equilibrium were different for the metal films on the ridge and groove of the corrugated pattern. In the case of the self-organized swelling directed by a periodically corrugated elastomeric mold with a relatively large line width, irregular wrinkles or twisted patterns (the second self-organized pattern) were observed which were easily distinguished from the corrugated patterns by the pattern replication and the first selforganized swelling patterns.

I. Introduction Pattern formation on a thin film is an interesting subject because of its significance in science and industry.1-11 In a thin film, patterns result from thin film instabilities, such as wrinkling,1-5 dewetting,6-8 and rupture.9-11 These patterns are intrinsic, in that they form spontaneously. The use of external confinement to control the direction in which the intrinsic patterns are formed on the thin film can have interesting effects on micro- and nanosize patterning. The main idea behind the application of external confinement is that the characteristic length of the intrinsic surface pattern can interact with the period of the external pattern.1,2,4,6,8-11 This interaction is readily observable when the order of magnitude of the characteristic length scale of the intrinsic surface pattern is similar to that of the external pattern.1,2,4,8,9 Of the multitude of surface patterns, wrinkling is of particular interest because of its isotropic nature over the whole surface of the film, although it has a certain dominant wavelength associated with it.1-5 In the case of a metal-capped polymer thin bilayer, wrinkling occurs because of the relaxation of the plane stress in the film which is produced by annealing above the glass transition temperature (Tg) of the polymer (buckling)1-4 or through saturation in the solvent vapor (swelling).5 Recent studies on the wrinkling of a metal-polymer bilayer showed that the wrinkles produced by buckling can be controlled so as to form anisotropic and regular microscale periodic patterns.1,2,4 In the case of wrinkles induced by swelling, however, there have been no notable studies involving the controlling of the intrinsic patterns. In the present study, we * To whom correspondence should be addressed. Phone: +82-2-9585504. Fax: +82-2-958-5489. E-mail: [email protected].

report on the formation of swelling-induced self-organized surface patterns in a metal-capped polymer thin bilayer on a substrate. The formation of the swelling-induced self-organized pattern is a consequence of the external confinement of the bilayer. This confinement produces a nodal effect which originates from the strong conformal contact made between the elastomeric mold with its periodic micro-size patterns and the underlying bilayer. This conformal contact is caused by the good wetting property of the elastomeric mold which is placed on the surface of the metal film. The good wetting property is attributed to elasticity and low surface tension of the elastomeric mold. The periodicity of the self-organized swelling wave depends on the geometry of the elastomeric mold and the wavelength of the intrinsic swelling wave. The morphological dynamics of the selforganized swelling pattern is also dictated by the dynamics of the intrinsic swelling wave. In this study, a theoretical analysis was conducted to elucidate the experimentally observed behaviors of the self-organized swelling wave. II. Experimental Section The bilayer dealt with in the present study was composed of aluminum (Al)-capped novolak (NV) epoxy resin (Toppan Printing Co., Japan) with a curing agent of hexamethylenetetramine (HMTA, Kangnam Hwasung Co., Korea) as a hardener. The cured NV resin (600 < MW < 700, 85 °C < Tg < 105 °C) was not delaminated or cracked by annealing even at 130 °C. The NV resin was mixed with the curing agent rigorously, and the mixture was dissolved in ethanol (Aldrich, U.S.A.). The bilayer was prepared by the spin coating of the NV resin mixed with the curing agent in the ethanol solution onto a cleaned flat Si substrate followed by the thermal evaporation of the Al on

10.1021/jp067746p CCC: $37.00 © 2007 American Chemical Society Published on Web 02/24/2007

Metal-Capped Polymer Thin Bilayer

J. Phys. Chem. C, Vol. 111, No. 11, 2007 4405

the as-coated polymer layer. The polymer layer was isothermally annealed at 60 °C (under Tg of the cured NV resin) for 30 min in a constant temperature oven prior to the thermal evaporation of the metal film in order to remove the residual solvent in the film. The as-prepared bilayer was placed on a flat pedestal in a Teflon sealed reactor whose atmosphere was saturated with ethanol vapor at room temperature.5 Prior to the sealing of the reactor, a poly(dimethylsiloxane) (PDMS, Sylgard 184, Dow Corning, U.S.A.) negative replica (mold) of a bas-relief structure fabricated by photolithography was prepared and placed on the surface of the metal film. During the placement of the PDMS mold, no additional pressure was imposed on the bilayer or the mold. The thickness of the polymer layer was measured using an ellipsometer (Uvisel, Horiba Jobin Yvon, Japan). The resulting surface patterns were examined with an atomic force microscope (AFM, Dimension 3100, Digital Instruments, U.S.A.) in the contact mode. The schematic experimental procedure is illustrated in Figure 1a,b. III. Results and Discussion 3.1. Pattern Replication and the First Self-Organized Swelling Patterns. As is apparent from the top AFM image in Figure 1c, a wrinkled surface morphology without the PDMS mold is observable, which results from the relaxation of the stress during the duration of swelling. This wrinkled morphology can be considered intrinsic since it is formed without external confinements or perturbations. The intrinsic swelling wave pattern lacking directional periodicity could be transformed into anisotropic wave patterns. These anisotropic swelling patterns had clear directionality and periodicity, since they were directed by the strong conformal contact of the upper corrugated PDMS mold and could be directed into two-dimensional (2D, lower right image of Figure 1c) as well as into one-dimensional (1D) patterns (lower left image of Figure 1c). In particular, the replication giving rise to the 1D anisotropic pattern forms according to two sequential processes in the course of the swelling, as shown in Figure 2. Prior to the self-organization, corrugated patterns form in the earlier times of the swelling. The periodic corrugated pattern had the same periodicity as that with the PDMS mold, although the shape of the corrugation in the earlier times of the swelling is not exactly rectangular, as is the corrugation with the PDMS mold, but is almost sinusoidal. The formation of the corrugated pattern resulting from the effect of the PDMS mold is very similar to that observed in the case where capillary force lithography is used for the patterning of a polymer thin film.12 Interestingly, such a corrugated pattern has also been observed in the self-organized buckling of a metalcapped polymer thin bilayer.2 After the earlier times of swelling, small wrinkles form (denoted as the first self-organization). These wrinkles have considerable regularity and periodicity and form on the ridge of the corrugated pattern made by the pattern replication. The wave vector of the wrinkles was perpendicular to that of the corrugated pattern, and their wavelength was smaller than the line width of the corrugation. These characteristics of the first self-organized pattern (small wrinkles) are similar to those of the wave interaction-driven buckling pattern of a metal-polymer bilayer.4 As shown in Figure 3, the corrugated pattern without small wrinkles on its ridges was observed in the earlier times of swelling. It is noteworthy that the period of this corrugated pattern lacking wrinkles does not change until the state of dynamic equilibrium of the swelling is reached. During the duration of the corrugated pattern formation, the protruding part of the corrugated PDMS mold (particularly the edges) causes

Figure 1. Schematic illustration of the experimental procedure: swelling of a metal-capped polymer thin bilayer takes place when the reactor is saturated with solvent vapor (a), and an isotropic swelling wave forms due to the relaxation of the in plane stress in the bilayer (b). The intrinsic swelling wave in the aluminum (Al) (hm ) 20 nm)capped NV (hp ) 73 nm) thin film on the Si substrate saturated with ethanol vapor at room temperature after 48 h (in the state of dynamic equilibrium) with the dominant wavelength of λm(te) ) λe ) 684 nm (upper three-dimensional (3D) AFM image and its FFT image (4 × 4 µm2)) can be transformed into 1D (lower left 3D AFM image and its FFT image (50 × 50 µm2)) or 2D periodic swelling patterns (lower right 3D AFM image and its FFT image (50 × 50 µm2)) by the placement of periodically corrugated PDMS molds on the underlying bilayer (c).

the nodal condition to be satisfied for the intrinsic swelling wave, since the height of the PDMS mold (1 µm) is much larger than the amplitude of the intrinsic swelling wave ( ∼ several tens of nanometers), to be able to accommodate the replicated wave pattern within it. Considering the slow rate of the wave vector of the intrinsic swelling wave (time for arrival at the state of dynamic equilibrium ∼ several tens of hours in the present case), we find it interesting that the nodal effect produced by the elastomeric mold does not disappear or weaken during the duration of swelling but is sustained, thus dictating the formation of the corrugated pattern. As shown in Figure 3, the wavelength of the small wrinkles on the ridge of the corrugated pattern decreased with increasing swelling time and stopped decreasing when the swelling arrived at its state of dynamic equilibrium. On the groove of the corrugated pattern, no distinctive intensities were observed corresponding to the wrinkles, although the value

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Kwon and Park

Figure 2. 3D AFM images (20 × 20 µm2) of the swelling patterns on the Al (hm ) 20 nm)-capped NV (hp ) 73 nm) thin film on the Si substrate saturated with ethanol vapor at room temperature in the earlier (t ) 1 h; for a, c, and e) and later (t ) 48 h; for b, d, and f) times of the swelling directed by the corrugated PDMS molds with line widths (L ) 1.0 µm for a and b, L ) 1.5 µm for c and d, and L ) 2.0 µm for e and f). Throughout the whole process of the swelling, a corrugated pattern was observed, while small wrinkles on the ridge of the corrugated pattern (denoted as the first self-organization) were observed to be formed after the earlier times of swelling.

of the surface roughness was not completely zero. The absence of wrinkles on the groove of the corrugated pattern contrasts with the case of self-organized buckling.4 In contrast to the behavior of the wavelength of the wrinkle, the surface roughness represented by the root mean square (rms) roughness on the ridge and groove of the corrugated pattern increased with increasing swelling time. Additionally, the height of the corrugated pattern (distance between the groove and the ridge) also increased with increasing swelling time. This increase in the height of the corrugation might be due to an increase in the mobility of the swollen polymer layer, and the complete kinetics for the increase in the corrugation height can be elucidated using modified capillary kinetics (not given in the present study) which is distinctive from the capillary kinetics for the formation of polymer corrugation.12 The conventional capillary kinetics is not relevant for the present case because the polymer layer is not directly in contact with the PDMS mold. A detailed discussion is out of the range of this study but will be given in another study in the near future by us. Rather, we concentrated on the morphological dynamics of the first self-organized patterns on the ridge. To obtain a profound understanding of

Figure 3. 3D AFM images (20 × 20 µm2) showing the morphological evolution of the first self-organized swelling patterns (small wrinkles) on the Al (hm ) 20 nm)-capped NV (hp ) 73 nm) thin film on the Si substrate saturated with ethanol vapor at room temperature directed by corrugated PDMS molds with line width of L ) 1.5 µm (a at t ) 1 h, b at t ) 3 h, c at t ) 10 h, d at t ) 20 h, and e at the time for the state of dynamic equilibrium, t ) te ) 48 h). On the right of each 3D AFM image are cross-sectional profiles of the surface patterns on the ridge (A, top most) and groove (B, middle) of the self-organized wrinkles and over the corrugation (C, lower most).

the formation of the first self-organized swelling patterns in a metal-capped polymer thin bilayer, the morphological evolution of the first self-organized pattern is discussed in the following section.

Metal-Capped Polymer Thin Bilayer 3.2. Dynamics of the First Self-Organized Swelling Patterns. The wave number of the intrinsic swelling wave can be obtained by considering the stress relaxation in the metal and polymer layers. The stress which occurred in the metal thin film is caused by a difference in the responsibility of each film to the solvent vapor. First, the free energy of the deformed thin cross-linked polymer film, q, can be calculated by introducing the vertical deflection profile in conjunction with the amplitude  and the wave number k in the x direction, such that W(x) )  cos(kx). The value of q at the interface between the substrate and the cross-linked polymer layer with σp ) 1/3 can be expressed as q ≈ 2〈Ep〉k cos(kx)/κ3, λ ) 2π/k,5,13 where 〈Ep〉 ) (1/te)∫t0eEp(t)dt is the average Young’s modulus of the crosslinked polymer layer over the whole swelling time (te), where te is the time for the state of dynamic equilibrium of the swelling. κ is the product of k and the thickness of the polymer layer, hp, and λ is the wavelength of the surface wave. For the analysis of the deformation of the bilayer, the following von Karman equation was employed:14,15

Emhm3 ∂4W ∂2W + B + q ) 0, A ) , ∂x4 ∂x2 12(1 - σm2) Emφ(t)hm (1) B) 3(1 - σm)(1 - φ(t))

A

where A is the flexural rigidity of the metal layer including Young’s modulus, Em, the Poisson’s ratio, σm, and the thickness of the metal layer, hm, and B is the force acting per unit length in the plane of the polymer which can be written with the timedependent volume fraction of the absorbed solvent in the polymer layer, φ(t), assuming that the linear strain is equivalent in each dimension.5,15 Once the solvent begins to swell the bilayer, φ(t) grows continuously, and the strain also increases correspondingly until it reaches the dynamic equilibrium value of the volume fraction, φe, which is equal to that of the saturated state. In consideration of q, we assumed that the temporal change of Young’s modulus of the polymer layer is not significant, since the polymer layer is a cross-linked resin and the process temperature is much lower than Tg of the cross-linked resin. Therefore, for the sake of simplicity, we employed an approximation of the average Young’s modulus, 〈Ep〉, instead of a precise temporal profile of Ep during the duration of swelling. In the case of swelling of a metal-capped polymer bilayer, in which the polymer layer is sufficiently soft (i.e., non-cross-linked materials or the process temperature is above Tg) to give a significant temporal change in viscoelastic property, a more precise consideration of the time dependence of the elastic modulus should be accompanied in the analysis. A more rigorous analysis is required to analyze the morphological dynamics of an elastic film on a viscoelastic substrate16 (or noncross-linked polymer) in conjunction with the process temperature which is above Tg of the viscoelastic substrate (polymer). The dominant wave number of the intrinsic swelling wave, km(t), can be determined using q and eq 1 as km ≈ {[4〈Ep〉(1 φ(t))]/[Emhmhp3φ(t)]}1/4.5 As the swelling progresses, φ(t) increases and therefore λm(t) increases, and the order of magnitude of λm(t) and the confinement periodicity have the same value prior to the arrival of the swelling at the state of dynamic equilibrium. The rate of φ(t) is written in terms of the displacement along the z direction of the chain of the polymer layer from its state of dynamic equilibrium, Uz(t), such that φ(t) ) Uz(t)/(hp + Uz(t)). Uz(t) satisfies the collective diffusion kinetics of the polymer network relative to the solvent and,

J. Phys. Chem. C, Vol. 111, No. 11, 2007 4407 therefore, is expressed as Uz(t) ∼ (Det)1/2, where De is the effective diffusion constant of the polymer network.5 By differentiating km(t) with respect to t and making use of the expression for φ(t), one can find that km(t) continuously decreases with increasing swelling time until it reaches the state of dynamic equilibrium satisfying the relationship km(t) ) ke(te/t)1/8, where ke is the wave number in the state of dynamic equilibrium of the swelling (km(te) ) ke). Because km(t) decreases with t, the time-dependent wave vector of the wrinkles on the ridge of the corrugated pattern, kW(t), can be determined using the wave interaction relationship:4,8

kW(t)2 ) |kC2 - km(t)2|

(2)

where kC is the harmonic wave vector with the harmonic number nh such that kC ) (2nh + 1)π/L and nh ) 0, 1, 2, ...4 which satisfies the nodal condition given by the corrugation. In the case of the wave interaction-driven self-organized buckling of the metal-capped polymer corrugated bilayer (the formation of the rectangular corrugated bilayer occurred prior to the wrinkling),4 nh ) 0. The smaller the value of nh, the higher the probability of the emergence of the harmonic wave profile for the formation of the wave profile (probability ∝ 1/(2nh + 1)2),2 and therefore, the wave interaction relationship is kW(t)2 ) km(t)2 - kC2.4 In contrast to the former case, in this case, the pattern replication accompanies the spontaneous formation of the corrugation (the corrugation did not occur prior to the wrinkling); nh need not be zero, and km(t) decreases with increasing swelling time. Therefore, the wave-interaction relationship in eq 2 should be kW(t)2 ) kC2 - km(t)2 for the first self-organized swelling. Interestingly, a value of nh larger than zero does not induce the variation of the periodicity of the corrugated pattern made by the pattern replication. The corrugated pattern without the variation of the periodicity is clearly distinguished from that observed in the case of the buckling of the metal-polymer bilayer directed by the corrugated PDMS mold,2 in which harmonic single (nh ) 0), double (nh ) 1), triple (nh ) 2), and so forth self-organized corrugated wave patterns are formed. Therefore, it is necessary to determine what kind of effect on the wrinkles on the ridge of the corrugated pattern is produced by the nonzero value of nh in the first selforganization. Using the wave-interaction relationship given in eq 2, we find that the dominant wavelength of the wrinkle on the ridge, λW(t) ) 2π/kW(t), can be expressed as follows:

λW(t) )

2L ((2nh + 1) - (2L/λe)2(te/t)1/4)1/2 2

(3)

where λe ) λm(te) ) 2π/ke is the wavelength of the intrinsic swelling wave at a state of dynamic equilibrium (t ) te). Because of the condition which needs to be satisfied for the existence of λW(t) when t ) te and 2nh + 1 > 2L/λe in the denominator of the right-hand term of eq 3, nh can be written as follows:

nh ) [(L/λe) - (1/2)] + na

(4)

where the brackets around the term on the right-hand side indicate the greatest integer function (Gauss’s notation) and na is an additional positive integer used for the determination of the minimum value of nh. To prevent the possibility of confusion, the brackets were used only for Gauss’s notation in the equation presented in our study. From the description of nh as a step function of L/λe in eq 4, λe can be written as the following inequalities (2nh - 2na + 3)2 e (2L/λe)2 ) (2nh + 1)2 - (2L/λW(te))2 < (2nh - 2na + 5)2. Solving these inequali-

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Figure 4. Relationship between the ratio of the line width of the mold corrugation (L) to λe, L/λe, and the critical swelling time for the formation of the first self-organized pattern, tC (a). The inset shows the relationship between L/λe and the harmonic number for the wave number of the periodic corrugation, nh. Relationship between t-1/4 and (2L/λW(t))2, where λW(t) is the wavelength of the first self-organized swelling wave on the ridge of the corrugated pattern, for the morphological evolutions of the first self-organized swelling patterns on the ridge of the corrugated pattern of the Al (hm ) 20 nm)-capped NV (hp ) 73 nm) thin film on the Si substrate saturated with ethanol vapor at room temperature (b). In this case, the corrugated patterns by the pattern replication in the earlier times of swelling were directed by corrugated PDMS molds with line widths (L ) 1.0 µm with filled square symbol, L ) 1.5 µm with filled circle symbol, and L ) 2.0 µm with filled delta symbol). The dotted lines denote the state of dynamic equilibrium of the swelling. Each set of experimental data was fitted with solid linear lines. Each L/λe data point was determined by measuring the wavelength of the wrinkle formed on the 40 ridges of the 5 corrugated reference samples (8 ridges for each corrugated reference sample) for L ) 1.0 µm, 25 ridges of the 5 corrugated reference samples (5 ridges for each corrugated reference sample) for L ) 1.5 µm, and 15 ridges of the 5 corrugated reference samples (3 ridges for each corrugated reference sample) for L ) 2.0 µm with an area of 20 × 20 µm2. The error bars in each data point indicate the standard deviations.

ties, one can find that na should be larger than 1, and therefore, the minimum value of na is 2. In the inset of Figure 4a, the relationship between L/λe and nh is presented. Using the expression for nh as a function of L/λe, we could also explain the experimental observation that there are no wrinkles on the ridge of the corrugated pattern in the earlier times of swelling. For instance, no wrinkles were observed on the ridge of the corrugated pattern when t ) 1 h in the cases of the selforganized swelling directed by the PDMS molds with L ) 1.5 µm (refer to Figures 2c and 3a) and with L ) 2.0 µm (refer to Figure 2e). The critical swelling time for the spontaneous formation of wrinkles on the ridge of the corrugated pattern by the first self-organization, tC, can be expressed such that tC )

Kwon and Park te(2L/(λe(2nh + 1)))8 by using the expression of λW(t) given in eq 3. When t e tC, there are no wrinkles on the ridge. In the cases of the self-organized swelling directed by the PDMS molds with L ) 1.5 µm and L ) 2.0 µm, the calculated values of tC are 1.15 h and 1.53 h, respectively, and therefore, no wrinkles were found when t ) 1 h, since t < tC. In contrast to the former two cases, indications of wrinkles were found on the ridge when t ) 1 h in the case of the self-organized swelling directed by the PDMS molds with L ) 1.0 µm (refer to Figure 2a). Appearance of these indications when t ) 1 h can be explained by the calculated value of tC ) 0.66 h. As was plotted in Figure 4a, an increase in the value of L/λe leads to a discontinuous increase in tC. This discontinuity in L/λe is due to the discontinuousness of nh as a step function of L/λe. One notable finding here is that tC is relatively short (shorter than 1/2 min) when the value of L/λe is smaller than 1/2, while tC is quite long (maximum value of tC ∼ half the day when L/λe is nearly equal to 11/2 (tC ) te(11/13)8)). This means that the first selforganization can easily be prevented from forming in the earlier times of the swelling by controlling L. The reason why the maximum value of tC is limited will be discussed in the last section. Therefore, the time-dependent formation of the first selforganized wrinkles can be controlled by manipulating the line width of the corrugation of the mold. In order to examine the validity of the wave-interaction relationship used for determining the morphological dynamics of the first self-organized wrinkles on the ridge of the corrugated pattern, the theoretical expectation was compared with the experimental observation for three different values of L. For this comparison, eq 3 was changed into a relationship between 2L/λW(t) and t-1/4 such that (2L/λW(t))2 ) (2nh + 1)2 - (2L/ λe)2(te)1/4te-1/4. Experimentally, λe ) 684 nm when t ) te ) 48 h in the Al-capped (hm ) 20 nm) NV (hp ) 73 nm) bilayer on the Si substrate saturated with ethanol vapor at room temperature. As is apparent from Figure 4b, the linear fitting lines are well-matched with the experimental data for the different values of L. From the slopes and y intercepts of the fitting lines, the values of nh and te can be determined. In the cases of the first self-organization directed by the PDMS molds with L ) 1.0 µm, L ) 1.5 µm, and L ) 2.0 µm, the calculated values of nh obtained from the linear fittings were 1.95 ( 0.088, 2.95 ( 0.072, and 3.96 ( 0.11, respectively. These values of nh are very well-matched with the theoretically predicted values of nh such as nh ) 2, nh ) 3, and nh ) 4, respectively. The experimentally determined values of te (te ) 43.7 ( 1.28 h for L ) 1.0 µm, te ) 44.9 ( 0.82 h for L ) 1.5 µm, and te ) 50.1 ( 1.76 h for L ) 2.0 µm) also showed good agreements with the experimentally observed value of te ) 48 h. These agreements lead us to conclude that the validity of the waveinteraction relationship suggested in the present study is sufficient to capture the critical properties of the dynamic behavior of the first self-organized pattern on the ridge of the corrugated pattern. One notable finding is the temporal variation of the strain of the metal layer during the duration of the swelling. The direct measurement of the strain of the thin metal film on the structured polymer layer was very difficult, and therefore, the indirect calculation of the strain by adapting the AFM measurement was employed. For the indirect measurement of the strain, the rms roughness of the wrinkled metal thin film on the ridge and groove of the corrugated pattern was measured instead of the surface area of the wrinkled metal layer, since the values of the rms roughness were different in the cases of the wrinkles on the ridge and groove. The time-dependent strain of a metal thin

Metal-Capped Polymer Thin Bilayer

J. Phys. Chem. C, Vol. 111, No. 11, 2007 4409

Figure 5. Strain rate of the metal (Al) film (hm ) 20 nm) on the corrugated polymer (NV) layer (hp ) 73 nm) on the Si substrate saturated with ethanol vapor at room temperature during the duration of the first self-organized swelling directed by the corrugated PDMS molds with line widths (L ) 1.0 µm with filled and open square symbols, L ) 1.5 µm with filled and open circle symbols, and L ) 2.0 µm with filled and open triangle symbols). Filled and open square symbols represent the strains of the metal film on the ridge and groove of the corrugated pattern, respectively. Each horizontal solid and dotted line indicates the state of mechanical equilibrium of the strain rate in each case. Each strain data point was determined by measuring the rms surface roughness of the 40 ridges and grooves of the 5 corrugated reference samples (8 ridges and grooves for each corrugated reference sample) for L ) 1.0 µm, 25 ridges and grooves of the 5 corrugated reference samples (5 ridges and grooves for each corrugated reference sample) for L ) 1.5 µm, and 15 ridges and grooves of the 5 corrugated reference samples (3 ridges and grooves for each corrugated reference sample) for L ) 2.0 µm with the area of 20 × 20 µm2. The error bars in each data point indicate the standard deviations.

film with a wave profile of (t) cos(2πx/λW(t)), u(t), can be obtained as follows:

∫02π/λ (t) (1 + (2π(t) sin(2πx/λW(t))/λW(t))2)1/2 dx W

u(t) )

-

λW(t) 1≈

4((t)2 + (λW(t)2/16))1/2 λW(t)

- 1 ≈ 8((t)/λW(t))2 (5)

where one should note that the condition (t) , λW(t) for the profile of the wrinkles on the ridge and groove of the corrugated polymer structure was used in eq 5. Indeed, the experimentally observed value of λW(t) exceeds that of (t) by two or three orders of magnitude. The value of the rms roughness, rms(t), was calculated by using the measured value of (t) with the 2 1/2 ) (t)/x2, and relationship rms(t) ) ((t)2/(2π)∫2π 0 sin x dx) therefore, the approximate value of u(t) can be calculated by using eq 5 and the relationship u(t) ≈ (4rms(t)/λW(t))2. In Figure 5, the temporal changes of the calculated values of the strain in the metal thin film on the ridge and groove of the corrugated pattern during the duration of the swelling are shown. The strain of the metal thin film on the ridge at first increases with increasing swelling time and then becomes constant. This type of temporal behavior of the strain can be observed in the case of the creep and relaxation loading of the polymer.17 The increasing rate of the strain is nearly constant and becomes zero at nearly the same moment prior to the achievement of the state of dynamic equilibrium of the swelling (t ) 18.7 ( 0.38 h) for the three different values of L. This increasing rate of the strain represented by the slope of the line is dependent only on the

properties of the materials.3 The increasing rates of the strain of the metal thin film on the groove are different but become zero near the state of dynamic equilibrium of the swelling (t ) 45.6 ( 0.21 h compared with te ) 48 h) for the three different values of L. The variation in the growth rate of the strain of the metal film on the groove with the value of L could be due to the difference in the extent of conformal contact of the PDMS mold on the underlying metal thin film. The wrinkle on the groove formed during the first self-organization is gradually in direct contact with the protruding part of the PDMS mold. Therefore, the stretching of the metal film on the groove is suppressed by the PDMS mold. The extent of this suppression of the wrinkles can differ because of the difference in the geometry (L) and the contact area of the edges of the protruding parts of the PDMS molds. It is interesting to note that the growth rate of the strain of the metal film on the ridge is much larger (by one order of magnitude) than that of the metal film on the groove and becomes nearly zero prior to te. Since the strain of the metal film on the ridge becomes constant earlier than that of the metal film on the groove, the stress relaxation starts to occur in the polymer layer under the ridge ahead of that in the polymer layer under the groove of the corrugation. The stretching of the metal film on the ridge is more weakly suppressed by the PDMS mold than that of the metal film on the groove. Therefore, (t) of the wrinkles of the metal film on the ridge is larger than that on the groove. Additionally, the growth rate of the strain of the metal film on the ridge is also larger than that on the groove, since the state of mechanical equilibrium needs not be dependent on the state of dynamic equilibrium of the swelling. In the case of the strain of the metal film on the groove, the suppression can be considered to be sufficiently strong to direct the state of mechanical equilibrium so as to be nearly the state of dynamic equilibrium. Unfortunately, the effect of the dynamic equilibrium in determining the strain rate of a metal film on the corrugated pattern could not be found. Further study is required into these differences in the temporal behaviors of the strain of the metal film on the corrugated pattern. 3.3. Second Self-Organized Swelling Patterns. In the case of the self-organization in the swelling directed by the PDMS mold incorporated with a relatively larger value of L, other kinds of patterns were observed. As shown in Figure 6, the selforganized swelling directed by the PDMS mold with relatively larger values of L produced zigzag-like wrinkles (Figure 6a for L ) 5.0 µm) or twisted patterns (Figure 6b for L ) 10.0 µm and 6c for L ) 15.0 µm), although the corrugated patterns remain throughout the whole process of the swelling, as is the case in the context of Figures 2 and 3. In particular, the twisted patterns are similar to the microfolding pattern observed in the buckling of a metal-polymer bilayer annealed at a temperature sufficiently higher than Tg of the polymer layer.18 There is a distinct difference between these patterns and the wrinkles formed in the first self-organization directed by the PDMS molds with L e 2.0 µm, in that the wave vectors of the former patterns are not perpendicular to the corrugated pattern. Although it seems that each pattern presented in Figure 6 has its own dominant wavelength, as was shown in the AFM cross-sectional images (line denoted as A) and fast Fourier transform (FFT) images, the propagation direction and the dominant periodicity of the patterns were not clear enough to be determined. Therefore, the pattern observed in the case of the swelling directed by the PDMS molds with the relatively larger value of the line width can be referred to as the second self-organized swelling pattern; the replicated corrugated pattern, first, and

4410 J. Phys. Chem. C, Vol. 111, No. 11, 2007

Kwon and Park

Figure 6. 3D AFM images and their FFT images (50 × 50 µm2) of the second self-organized swelling patterns in the Al (hm ) 20 nm)-capped NV (hp ) 73 nm) thin film on the Si substrate saturated with ethanol vapor at room temperature in the state of dynamic equilibrium (t ) te ) 48 h) of the swelling directed by the corrugated PDMS molds with line widths of L ) 5.0 µm for a, L ) 10.0 µm for b, and L ) 15.0 µm for c. Lower images are the AFM cross sectional images in the y (A) and x directions (B).

second self-organized swelling patterns should be clearly differentiated. However, we could not elucidate why the relatively larger value of L of the corrugated pattern leads to the formation of the second self-organized swelling patterns, such as the off-perpendicular wave-like swelling patterns, and could not elucidate what kind of wave interaction relationship governs their formation. One possible explanation for the first problem is as follows. An increase in the value of nh due to an increase in the value of L/λe in the relationship nh ) [(L/λe) (1/2)] + 2 will lead to an increase in the mechanical free energy required to wrinkle the metal layer (strain energy) and will lead to an increase in the surface free energy of the wrinkled bilayer because of the increase in the surface area; these increases in the free energy will produce a maximum value of nh, denoted as nhC, which limits the increase in the value of nh. The value of nhC determines whether the second self-organized swelling pattern is governed by the wave-interaction relationship given in eq 3 (with L satisfying an inequality of 2nhC + 1 > 2L/λe, perpendicular to the direction of the corrugation) or it is not (with L satisfying a inequality of 2nhC + 1 < 2L/λe, offperpendicular to the direction of the corrugation). Although the value of nhC could not be calculated theoretically, it can be conjectured. On the basis of the experimental observations, we found that nhC could not be larger than 6, since 2nhC + 1 < 10/0.684. However, we could not determine whether the value of nhC is 5 or 6 and why 6 is the largest value of nh in the second self-organization. In order to obtain a more profound understanding of nhC, a deeper investigation in conjunction with different cases of the swelling of a metal-polymer bilayer is required. IV. Summary In summary, the self-organization in swelling of a metalcapped polymer thin bilayer on a substrate saturated with solvent vapor was reported and analyzed. By the placement of a periodically corrugated elastomeric mold on the underlying bilayer, the intrinsic swelling wave pattern was directed into a corrugated pattern which is a replication of the elastomeric mold and was subsequently self-organized into two kinds of patterns.

The periodically corrugated pattern replicated in the earlier stages of the swelling has the same wavelength as that of the mold throughout the whole process of the swelling. The first self-organized pattern, which was observed after the earlier times of the swelling, was small wrinkles perpendicular to the corrugated pattern, whose wavelength was smaller than the line width of the corrugated pattern formed in the earlier stages. A decrease in the wavelength of the first self-organized small wrinkles on the ridge of the corrugated pattern was observed during the duration of swelling, and this temporal evolution of the wrinkle could be predicted well by theoretical analysis based on the wave interaction relationship between the intrinsic swelling wave and the corrugated pattern. The strains in the metal thin film on the ridge and groove of the corrugated polymer layer increase with increasing swelling time during the course of the swelling and become constant at the state of mechanical equilibrium. The growth rate of the strain of the metal film on the groove is smaller than that of the metal film on the ridge and becomes almost zero near the state of dynamic equilibrium of the swelling. In the case of the strain rate of the metal film on the ridge, the state of mechanical equilibrium is achieved prior to that of the dynamic equilibrium of the swelling. The self-organization directed by the elastomeric mold with a relatively larger line width produced irregular wrinkles or twisted patterns (the second self-organization), and the absence of the first self-organization indicates that the maximum value of the harmonic number determining the wave number of the corrugated pattern is limited to a certain value. References and Notes (1) Yoo, P. J.; Park, S. Y.; Suh, K. Y.; Lee, H. H. AdV. Mater. 2002. 14, 1383. (2) Yoo, P. J.; Park, S. Y.; Kwon, S. J.; Suh, K. Y.; Lee, H. H. Appl. Phys. Lett. 2003, 83, 4444. (3) Yoo, P. J.; Lee, H. H. Phys. ReV. Lett. 2003, 91, 154502. (4) Kwon, S. J.; Yoo, P. J.; Lee, H. H. Appl. Phys. Lett. 2004, 84, 4487. (5) Kwon, S. J.; Park, J. G.; Lee, S. H. J. Chem. Phys. 2005, 122, 031101. (6) Reiter, G. Phys. ReV. Lett. 1992, 68, 75. (7) Kargupta, K.; Sharma, A. Phys. ReV. Lett. 2001, 86, 4526.

Metal-Capped Polymer Thin Bilayer (8) Kwon, S. J. J. Appl. Phys. 2006, 99, 063503. (9) Suh, K. Y.; Lee, H. H. J. Chem. Phys. 2001, 115, 8204. Suh, K. Y.; Park, J. H.; Lee, H. H. J. Chem. Phys. 2002, 116, 7714. (10) Seeman, R.; Brinkmann, M.; Kramer, E. J.; Lange, F. F.; Lipowsky, R. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 1848. (11) Gonuguntla, M.; Sharma, A.; Subramanian, S. A. Macromolecules 2006, 39, 3365. Gonuguntla, M.; Sharma, A.; Mukherjee, R.; Subramanian, S. A. Langmuir 2006, 22, 7066. (12) Suh, K. Y.; Kim, Y. S.; Lee, H. H. AdV. Mater. 2001, 113, 1386.

J. Phys. Chem. C, Vol. 111, No. 11, 2007 4411 (13) Fredrickson, G. H.; Ajdari, A.; Leibler, L.; Carton, J. Macromolecules 1992, 25, 2882. (14) Landau, L. D.; Lifshitz, E. M. Theory of Elasticity, 3rd ed.; Pergamon: Oxford, U.K., 1986. (15) Sharp, J. S.; Jones, R. A. L. Phys. ReV. E: Stat., Nonlinear, Soft Matter Phys. 2002, 66, 011801. (16) Huang, R. J. Mech. Phys. Solids 2005, 53, 63. (17) Wiseman, A. S.; Rajagopal, K. R. Mechanical Response of Polymers; Cambridge: New York, 2000. (18) Kwon, S. J. J. Phys.: Condens. Matter 2006, 18, 9403.