Polymer film rupturing in comparison with leveling and dewetting

Surface Science 594 (2005) 192–202 www.elsevier.com/locate/susc

Polymer film rupturing in comparison with leveling and dewetting Ioannis Karapanagiotis b

a,*

, William W. Gerberich

b

a ‘‘ORMYLIA’’ Art Diagnosis Centre, Ormylia, Chalkidiki 63071, Greece Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA

Received 3 June 2005; accepted for publication 9 July 2005 Available online 11 August 2005

Abstract The break up of a thin polystyrene (PS) film applied on silicon (Si) upon heating above the bulk glass transition temperature (Tg) of the polymer is studied using atomic force microscopy (AFM). In a 17-nm thick PS film rupturing occurs with the formation of indent-like surface disturbances pointing toward the Si substrate and leads to the standard nucleated dewetting process. Indent growth toward the substrate is accompanied by an increase of the indent radius at the level of the free, unperturbed, PS surface and a decrease of the radius of curvature at the indent bottom. The two radii are comparable and are 1–3 orders of magnitude larger than the film thickness. The area induced in the system upon indent formation was measured for several indents and found to be almost negligible comparing to the total area of the system. Rupturing (growing indents) is discussed with respect to the opposing leveling (healing indents) process of artificially induced indents. Also, a comparison of the indent growth rate toward the substrate, calculated using previously published data, with the dewetting rate of an expanded dry patch along the substrate is provided, which suggests that the former is about 2–3 orders of magnitude lower than the latter.
2005 Elsevier B.V. All rights reserved. Keywords: Wetting; Surface energy; Surface defects; Surface relaxation and reconstruction; Surface roughening; Silicon; Atomic force microscopy

1. Introduction

* Corresponding author. Tel.: +30 23710 98400; fax: +30 23710 98402. E-mail address: [email protected] (I. Karapanagiotis).

In the last two decades, dewetting of thin organic films from hard substrates has received significant attention, as polymer films are extensively used in several applications. These are primarily in the micro-electronics industry but also in printing technology, cultural heritage protection and

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2005 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2005.07.023

I. Karapanagiotis, W.W. Gerberich / Surface Science 594 (2005) 192–202

conservation and membrane technology. Several reports contributed to the clarification of many aspects of the dewetting phenomenon. Early investigations focused mainly on the film rupturing mechanisms that lead to dewetting. The result of this research was that depending on the film thickness either nucleation and growth or spinodal decomposition can be the rupturing mechanism [1–10]. In either case, however, film thickness, h, has to be h < 100 nm. In thicker films dewetting is initiated only under the influence of extrinsic defects [6,11,12]. Other studies examined the growth of holes (dry patches) on substrates [13–23]. This growth regime follows the break up of the film. Recently, many investigations focused on potential strategies to prevent dewetting [24–30] and on exploiting dewetting to fabricate ordered polymer and biomolecule arrays at the micrometer scale [31–37]. The present study focuses on the film rupturing process. Detailed description of the latter is crucial to understand, prevent or exploit the dewetting phenomenon, as it is the initial stage from which dewetting is initiated. However, very few reports have provided experimental evidence regarding the 3-D morphology and dynamics developed during film break up [6,38,39]. The rupturing process of a polystyrene (PS) film on a silicon (Si) surface upon heating above the bulk glass transition temperature (Tg) of PS is presented. Polymer films are 17-nm thick and rupture via a nucleation and growth process which is recorded by atomic force microscopy (AFM). Film break up occurs via indent-like surface disturbances which grow toward the substrate, upon continuous heating above Tg. AFM is employed to perform a detailed characterization of the indent evolution, by measuring several topographical features during local film thinning. The spontaneous indent growing process is then compared with an opposing indent healing process, studied in detail elsewhere [40,41] on the basis of similar (comparable) topographical features evolved in both processes. Film break up is followed by the formation of dry patches which grow then laterally uncovering thus the substrate. An effort to compare the rates of the two consecutive processes (the indent growth rate with the dewetting rate) is finally performed.

193

2. Experimental section Monodisperse (Mw/Mn = 1.02, Polymer Labs, UK) low molecular weight (Mw = 10,900 g/mol) PS was dissolved in spectroscopic grade toluene. Solutions of 1.0 wt.% and 5.0 wt.% were spin cast onto several 50 mm diameter, polished, Si wafers resulted in films with thicknesses of 17 nm (thin films) and 120 nm (thick films) respectively. Wafers were used as they were received from the manufacturer (Virginia Semiconductor, Fredericksburg, VA). The h1 0 0i oriented Si wafers were covered by a native oxide film. The thickness of this film was measured by ellipsometry and found to be 1.8 nm. Ellipsometry was also used to measure the thicknesses of the PS films. Spin coating was performed in a class 10 clean room, to minimize airborne particle effects. For the same reason solutions were filtered with 0.2 lm Teflon filters prior to spin coating. Thin and thick films were then annealed at 60 C and 100 C respectively, overnight in vacuum to remove residual solvent (Tg = 91 C, for Mw = 10,900 g/mol [42]). The free surfaces of the resulting films appeared to be featureless, according to optical microscopy micrographs and atomically smooth according to AFM images. The latter, however, revealed the presence of some (scarce) airborne particles, collected on the free surfaces of the PS films. Thin films were then heated at 140 C > Tg to initiate dewetting. Optical microscopy recorded the standard dewetting process, while AFM was used to record, in detail, the topographical features of the surface instabilities, acted as nucleation sites for dewetting onset. A Nanoscope III SPM (Digital Instruments, Santa Barbara, CA) operated in contact mode and mounted with a standard silicon nitride tip, was utilized as an AFM. Forces in the range of 1–10 nN were applied from the 200 lm cantilever to the polymer surface. For all image acquisitions the same probe was used with a nominal tip radius of 20–60 nm. On the free surface of the thick films (120 nm) nanoindents were induced using a Hysitron Triboscope (Hysitron Inc., Minneapolis, MN) apparatus mounted with a standard three sided pyramid (Berkovich) diamond tip. The depths of the residual indents were lower than the film thickness. Samples were then heated at 110 C

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and AFM was employed to record the leveling (healing) process of the nanoindents. On another set of Si wafers 5 wt.% solutions of monodisperse PS (Mw/Mn = 1.09, Polymer Labs, UK) with Mw = 29,300 g/mol were spin cast, similarly to the previously described procedure. Samples were annealed at 100 C overnight in vacuum to remove residual solvent. The thickness of the resulting films was 108 nm. Large indents, which penetrated the organic films, were induced on the films by Hysitron Triboscope. Upon heating at 140 C (>Tg) indents grew laterally and expanded to circular dry patches (dewetting). Dewetting rates were measured using AFM.

3. Results and discussion 3.1. Nucleated dewetting process Fig. 1 shows the standard nucleated dewetting process of a thin PS film from a Si surface. The initially flat film ruptures either spontaneously or under the influence of extrinsic defects, such as airborne particles [6,12,38], resulting in the formation of holes, at random sites (Fig. 1a). Substrate is thus exposed to the air. The holes then grow laterally (Fig. 1b) and coalesce (Fig. 1c) resulting in polymer ridges which disintegrate to spherical droplets (Fig. 1d). Dewetting therefore tends to

Fig. 1. Dewetting process of PS on Si, upon heating above the Tg. (a) The film ruptures to tiny dry patches that expose Si substrate to the air. (b) Dry patches expand laterally and (c) coalesce. (d) The polymer mass is accumulated in ridges which result in droplets. PS film thickness is h = 17 nm.

I. Karapanagiotis, W.W. Gerberich / Surface Science 594 (2005) 192–202

minimize the film/substrate interface. The prerequisites for dewetting onset can be summarized as follows: (i) The initial (unperturbed) film thickness (h) has to be below the critical thickness (hc) of a large sessile drop flattened by gravity (h < hc) [43]. In the case of spontaneous dewetting, the film has to be ultra-thin and in particular, h < 100 nm. (ii) In general, the temperature must be above the Tg of the polymer (T > Tg) i.e., the polymer must be able to flow. Otherwise, the kinetic barrier, raised by the augmented viscosity of the polymer prevents dewetting onset. In some cases, however, dewetting of thin polymer films was recorded under conditions at which the polymer could not flow as a simple liquid. In these systems dewetting was linked to plastic deformation, occurred because of internal tension [44–46]. (iii) The substrate surface has to be non-wettable by the polymer. Consequently the equilibrium contact angle, he, between the film and the substrate has to be he > 0 and not equal to zero which corresponds to the complete wetting case. Therefore the spreading coefficient, S, of the bilayer coating/ substrate, defined by Eq. (1), is negative S < 0 [11,47] S ¼ cs  cfs  cf ¼ cf ðcos he  1Þ

ð1Þ

195

where cs and cf are the surface energy of the substrate and the film respectively andcfs is the film/ substrate interfacial energy. In the system of Fig. 1, all the above conditions are fulfilled as follows: Initial film thickness was 17 nm (<100 nm), the system was heated at 140 C (>Tg = 91 C) and typically he for PS on a Si surface is on the order of 20 > 0 [11]. 3.2. Spontaneous break up of the film We now focus on the nucleation stage of the spontaneous dewetting process, occurred prior to the formation of the holes (Fig. 1a). The latter are formed by indent-like disturbances developed at random sites of the free polymer surface. These instabilities point toward the substrate. They grow with time, reach the substrate and form holes, according to Fig. 1a [6,38]. Fig. 2 shows spontaneously formed surface disturbances, captured by AFM. Four indents are visible, as ‘‘dark areas’’. A cross section of the image that includes three of them is shown, indicating that indent depths are lower than the film thickness (h = 17 nm). This was verified by meticulous AFM measurements at which each indent was scanned separately to increase image resolution. Indent formation and growth is accompanied by the removal of the

Fig. 2. (a) PS film surface exhibiting four disturbances, developed spontaneously at random sites, upon heating above Tg. (b) A cross section of the image including indents 1, 2 and 3 is shown. Indent depths are lower than the film thickness, h = 17 nm.

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Stange et al. [6]. In this study h = 22 nm, M = 22,000 g/mol, annealing temperature was 144 C and therefore Rg = 4.2 nm [42] which result in Rg/h = 0.19, close to the corresponding value of our system (0.18). AFM images of this study did not reveal distinguishable rims around the spontaneous depressions [6]. The absence of distinguishable rims around spontaneous indents is also pronounced in Fig. 3a which presents AFM cross sections of five surface depressions. Point A corresponds to the maximum indent depth, yA and it is shown for the deepest indent 5 of the figure. Cross sections are presented in the same plot to visualize indent evolution toward the substrate. Although cross sections correspond

5

0

-5 y (nm)

polymer chains, initially located between the indent bottom and the substrate. Depending on the film thickness, this results in the formation of a rim around the indent which is distinguishable from the unperturbed polymer surface [39,48,49]. Masson and Green [39] made meticulous observations associated to the evolution of spontaneous indents developed at the free surface of PS (M = 130 kg/mol) on Si, upon annealing at 170 C. In this report it was shown that indents evolve toward the substrate by a two stage process: Initially (stage FI) a rim is formed around the depression which is afterwards dissipated (stage FII) inside the film. Based on this scenario three cases were reported: For films with 74 nm < h < 104 nm it was shown that formation stage FII (no rim) is the longest one (case A). For films with 29 nm < h < 74 nm stage FI (distinguishable rim) is dominant as stage FII narrows substantially (case B). For h < 29 nm only formation stage FI was recorded in the evolution of a spontaneous depression (case C). The absence of distinguishable rims around the spontaneous depressions of Fig. 2 can be explained if the system of our study falls in case A and assuming that for low molecular weight PS (M = 10,900 g/mol) stage FI is extremely short i.e., rim relaxes so fast that was not captured in our case. In the following, we attempt to compare our observation (absence of the rim) with the conditions suggested by Masson et al., by normalizing the molecular size with respect to film thickness. For M = 130 kg/mol and 170 C we calculate the radius of gyration, Rg, to be 10.4 nm [42]. Therefore, cases A, B and C correspond to 0.14 > Rg/h > 0.10, 0.36 > Rg/h > 0.14 and Rg/h > 0.36 respectively. For the system of our study, M = 10,900 g/mol, Rg = 3 nm at 140 C [42] and h = 17 nm which result in Rg/h = 0.18. This falls within the range of case B, but it is very close to the 0.14 border of cases A and B and of course far away from the condition of case C. Errors, raised by the differences in h, M and annealing temperature of our system with the one studied by Masson et al., might affect substantially the attempt presented above. Finally, we compare Fig. 2 with another experimental investigation in which a similar PS/Si bilayer was used as a model to characterize spontaneously formed indents by

y

Indent 1 Indent 2 Indent 3 Indent 4 Indent 5

-10

A

R at y=15nm

-15

x

A -20 -1.5

-1

-0.5

(a)

0 x (micron)

0.5

1

1.5

2 Indent 5

1.5 R x (micron)

196

1

0.5 y

A

0

(b)

0

5

10 y (nm)

15

20

Fig. 3. (a) AFM cross sections of five spontaneous indents. Point A corresponds to the maximum indent depth, yA. The indent (lateral) radius at y = 15 nm, Rxjy=15 nm is shown for indent 5. (b) Rx as a function of depth y for indent 5. Rx is zero at the indent bottom, y = yA, and maximizes at the level of the free unperturbed film surface, y = 0.

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to different indents, the indent growth scenario described by Fig. 3a appears to be similar to the evolution of a single spontaneous indent, described in a previous study [6]. As the indent grows toward the substrate (and yA increases) the lateral indent radius, Rx, at a specific y position increases. Rx is defined in Fig. 3a for indent 5 and y = 15 nm. Fig. 3b provides Rx measurements for indent 5, as a function of indent depth. At the level of the free unperturbed film surface (y = 0) Rx takes its maximum value. For larger y values, the indent gradually narrows resulting in smaller Rx which finally decays to 0 at the maximum indent depth, yA . Although Rx is very useful to describe the indent evolution process at the free polymer surface (y = 0) it cannot be used to monitor the topography at the indent bottom (point A) because RxjA = 0. At yA, another radius, the radius of curvature RcjA is more appropriate to record the local topography. The procedure, followed to measure RcjA using AFM images, is described in Appendix A. Fig. 4 presents RcjA measurements as a function of indent depth, yA. In the same plot corresponding measurements of Rxjy=0 are provided. Power law curve fits suggest that Rc jA  y 2 A and Rx jy¼0  5

10

Rc at y=y

A

Rc at y=yA & Rx at y=0 (nm)

Rx at y=0 4

10

3

10

Direction of indent evolution (Growing) 2

10

4

6

8

10

12

14

16

18

y (nm) A

Fig. 4. Indent radius at the free film surface Rxjy=0 and radius of curvature at the indent bottom RcjA as a function of indent depth. Power law curve fits are provided: Rc jA  y 2 and A For yA < 11.1 nm RcjA > Rxjy=0 and for Rx jy¼0  y 0:8 A . yA > 11.1 nm RcjA < Rxjy=0. Thickness of the initially unperturbed film is h = 17 nm.

197

y 0:8 A , indicating that structural changes during indent evolution are more severe at the bottom i.e., RcjA depends stronger by the indent depth. Fig. 4 shows that the two radii are comparable and vary within a length range of 0.5–16.7 lm, which is significantly higher than the initial unperturbed film thickness (h = 17 nm). The measured radii are also considerably higher than the radius of curvature of the AFM probe, which is typically on the order of 0.04 lm and therefore the data of Fig. 4 are not affected substantially by tip size effects. As the indent grows toward the substrate, it ‘‘expands’’ laterally (Rxjy=0 increases) and it becomes steeper at the bottom (RcjA decreases). At some point, corresponding to yA = 11.1 nm the two radii become equal. Rxjy=0 increase induces a reduction in the local curvature. On the contrary, RcjA decrease during indent evolution gives rise to the Laplace penalty which opposes indent growth. However, the indent grows due to destabilizing long-range intermolecular forces [1,2]. The next topographical feature that we discuss in the following is the surface area, created with indent formation [11]. Considering the cross section of indent 5 in Fig. 3a it is obvious that a length equal to Ly = 2yA is the result of indent formation. This is essentially the length ‘‘created’’ in the perpendicular direction y, which in the absence of the indent becomes Ly = 0. According to this concept, in three dimensions an extra area, Aextra, is created, because of indent presence. This area can be measured by AFM following a procedure which is described in detail elsewhere, for indents induced artificially by nanoindentation [11]. The same procedure was followed here to measure Aextra associated with the spontaneously formed indents and the results are presented in Fig. 5, as a function of indent depth. For comparison the lateral area, Ax, defined by the indent radius, Ax = p(Rxjy=0)2, is shown. Ax is the (lateral) area ‘‘occupied’’ by an indent at the level of the free unperturbed surface. As it was expected, the trend of the data show that both Aextra and Ax increase as an indent grows toward the substrate i.e., as yA increases. It is interesting, however, to notice that Ax Aextra. The % area increase because of indent presence, defined as 100Aextra/(Aextra + Ax) is calculated to be 0.3%, on average. Apparently,

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10

Aextra & Ax (nm2)

6

10

A extra Ax 5

10

4

10

1000 4

6

8

10

12

14

16

18

y (nm) A

Fig. 5. Extra surface area induced in the system upon indent formation, Aextra, as a function of indent depth, yA. For comparison the area, defined by the indent radius at the free film surface is shown, Ax = p(Rxjy=0)2. Lines showing the data trends are provided.

the total area increase of the system because of indent formation is substantially less than that and it is determined by the number of indents per unit area i.e., the indent density. Consequently, film rupturing induces a small, new surface comparing to the total surface of the system. This is because the indent radius Rxjy=0 is on the order of a lm (Fig. 4) which is substantially larger than the thickness of the unperturbed film (h = 17 nm).

nace, quenching the sample and imaging at room temperature. Fig. 6 shows the leveling process of an indent imposed by nanoindentation on a 120nm thick PS (Mw = 10,900 g/mol) upon heating at 110 C. In contrast to the spontaneously formed growing indents, here a rim of accumulated polymer mass around the indent is present and relaxes during indent leveling. It has been observed that the rim relaxation rate is higher than the healing rate of the indent bottom [41]. Fig. 7 presents Rxjy=0 and RcjA measurements as a function of indent depth, yA for a leveling indent. As an indent heals (yA decreases) both radii, Rxjy=0 and RcjA, increase. Consequently the corresponding radii of curvature decrease. Leveling is driven by the Laplace pressure which tends to flatten the film. Similarly, in the opposing process of Fig. 4 Rxjy=0 increases as the indent grows toward the substrate resulting thus in a decrease of the corresponding radius of curvature. As it has been noticed, however, RcjA decreases during indent growth (yA increase) and therefore the induced local Laplace pressure increases. This is balanced by a simultaneous increase of the destabilizing long-range intermolecular interactions (driving forces for the break up of the film) between the film 10 0 -10

3.3. Crowing (spontaneous break up) versus leveling y (nm)

-20

In this paragraph film break up (i.e., the growth process of spontaneously formed indents) is compared with the opposing, indent healing (leveling) process. The latter is associated with the relaxation of indents, induced artificially by nanoindentation and has been studied in detail elsewhere [40,41]. Here a comparison with the break up of the film is presented on the basis of similar topographical features. We note that the film break up was studied using thin PS films (h = 17 nm) while the leveling process of the artificial indents was recorded using thick PS films (h = 120 nm). By using thick films we were able to capture the evolution (leveling) process of a single indent, by following a cyclic procedure of heating the sample in a fur-

-30 t

1

-40

t

-50

t

2 3

t

4

-60 -70 -4

-3

-2

-1

1 0 x (micron)

2

3

4

Fig. 6. AFM cross sections of a nanoindentation induced healing (leveling) indent. Indent profiles after heating at 110 C, for t1 = 2.6, t2 = 7.9, t3 = 14.6 and t4 = 21.8 min are shown. Film thickness in this case is, h = 120 nm. The healing process shown here is opposing to the indent growing process described in Fig. 3a.

I. Karapanagiotis, W.W. Gerberich / Surface Science 594 (2005) 192–202

Rc at y=y

5

10

A

Rc at y=yA & Rx at y=0 (nm)

Rx at y=0

4

10

Direction of indent evolution (Leveling)

3

10

2

10

0

20

40

60 y (nm)

80

100

120

A

Fig. 7. Indent radius at the free film surface Rxjy=0 and radius of curvature at the indent bottom RcjA as a function of indent depth. Indent was induced by nanoindentation. Thickness of the initially unperturbed film is h = 120 nm.

free surface at point A and the substrate, as the separation distance h  yA decreases (i.e., yA increases). Finally, we note that the minimum value of RcjA 100 nm in Fig. 7 should be affected by tip size effects, considering that the typical radius of curvature of the AFM probe is around 40 nm. The minimum value of RcjA is included in Fig. 7 to illustrate the trend of the data. 3.4. Film break up versus dewetting Dewetting is initiated by the break up of the film, which is followed by the growth of the formed dry patches on the substrate (Fig. 1a and b). As dewetting is exploited in many applications as a micro-pattern process, a comparison of the rates of the two consecutive processes (film break up and hole growth) is of great interest. The dynamics

199

of the rupturing of PS films on Si has been studied by Stange et al. [6]. The depths of seven spontaneous indents were measured as a function of annealing time at conditions shown in Table 1 (system I). Exponential curve fits described the trend of the data. Using the results of this report we calculate the minimum growth rate to be 0.04 nm/min (at the beginning of the film break up) and the maximum 0.2 nm/min (at later annealing stages). To compare the calculated indent growth rates with corresponding dewetting rates we measured the radii of advancing dry patches as a function of annealing time. The conditions of the experiment are shown in Table 1 and are indicated as system II. For a direct comparison with system I, similar annealing temperature and PS with comparable molecular size were chosen. The large difference in the film thicknesses of system I and II does not affect the final conclusion, as shown below. In system II holes were induced by nanoindentation. Fig. 8 shows AFM measurements of the radii of growing dry patches, Rdp , as a function of annealing time, t. An unentangled polymer film, such the one of system II, has an extrapolation length, b, on the order of the molecular size, shown in Table 1 and therefore h = 108 nm b. Consequently the polymer should flow like a usual liquid and the dewetting velocity, dRdp/dt, should be constant i.e., in this case PS is a non-slipping film [14,15]. Fig. 8 suggests that dRdp/dt = 0.08 lm/min. For unentangled PS it has been shown that the dewetting rate is independent of the film thickness [50]. Consequently, thinner films (22 nm) should dewet from the substrate with the same rate measured for films with h = 108 nm. As a result, we finally conclude that the process of the break up of the film is slower than the subsequent dewetting process. Indents grow toward the substrate with a rate

Table 1 Dynamic measurements of indent growth—film thinning (system I) and dry patch growth—dewetting (system II) for PS on Si System

Growth type

Mw (g/mol)

h (nm)

T (C)

Rate (nm/min)

REE (nm)

I II

Indent growth Dry patch growth

22,000 29,300

22 108

144 140

0.04–0.2* 0.08 · 103

10.4 12.0

Molecular weight (Mw) and corresponding end-to-end molecular sizes (REE), unperturbed film thicknesses (h) and annealing temperatures (T) are provided. REE was calculated for the temperatures indicated [42]. * Calculated from the data of Ref. [6].

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y = 1.64 + 0.08x R2= 1 y = 3.04 + 0.08x R2= 1

9

y = 2.24 + 0.08x R2= 1 Rdp (micron)

8 7 6 5 4 3 0

10

20

30

40

50

60

70

80

t (min)

Fig. 8. Radius of dry patch, Rdp , as a function of time, t. Measurements of three holes are shown. Annealing temperature is 140 C, h = 108 nm and PS 29,300 g/mol (system II of Table 1).

of 2–3 orders of magnitude lower than the rate by which a dry patch (hole) grows on the substrate. We note that if we apply the slip condition on the system of our study the final conclusion (film dewets faster than it breaks) will be even more pronounced as the estimated dRdp/dt for h = 22 nm will be higher for two reasons: (i) ‘‘slip’’ dewetting velocity is higher than the ‘‘non-slip’’ [20] and (ii) also dRdp/dt  h0.5 [51].

Rxjy=0 increases. On the contrary, the curvature at the indent bottom RcjA decreases, giving rise to the Laplace pressure which opposes indent growth. The two radii were found to be comparable and one to three orders of magnitude larger than the film thickness. No rims (crests) were found around the spontaneously formed surface depressions. In the opposing indent healing process a similar lateral ‘‘expansion’’ was reported accompanied by a Rxjy=0 increase. In contrast to growing, healing results in a RcjA increase until the surface becomes flat. Spontaneous formation of indent-like surface disturbances results in an increase of the total area of the system, which however, is negligible (<0.3%) comparing to the total surface of the system. Dynamic measurements, combined with previously reported data, suggest that the film break up is a slower process than the subsequent lateral dry patch growth.

Acknowledgement Prior support by the Center for Interfacial Engineering (CIE), a National Science Foundation Engineering Research Center at the University of Minnesota is gratefully acknowledged.

Appendix A 4. Conclusions Measurements associated with the topographical changes, which occur at the initiation stage (break up of the film) of the standard nucleated dewetting process were presented. The morphology of spontaneous indents, formed at PS films (h = 17 nm) on Si upon heating above Tg, was recorded with AFM elucidating the indent growth process that leads to dewetting onset. Several indents with depths, yA, lower than the film thickness (yA < h) were captured. The top view shape of a spontaneous indent can be considered as circular, described by a radius Rxjy=0. The indent narrows, however, as it points toward the substrate resulting in RxjA = 0. During indent growth, the indent ‘‘expands’’ laterally and consequently

The mean radius of curvature at the indent bottom indicated by point A, RcjA, is defined as follows:   1 1 1 1 ¼ þ ð2Þ Rc jA 2 Rc1 jA Rc2 jA where Rc1jA and Rc2jA are the minimal and the maximal values of the curvature radius RcjA, of a section normal to the surface at point A. At a point A(xA, yA) with y = f(x), Rc1jA is defined as 1 jf 00 ðxA Þj ¼ 3=2 Rc1 jA 1 þ f 0 ðxA Þ2

ð3Þ

Rc2jA can be defined similarly, according to the above. Using Eqs. (2) and (3), RcjA was measured as follows: Using AFM images of spontaneous

I. Karapanagiotis, W.W. Gerberich / Surface Science 594 (2005) 192–202 -10 -11

y (nm)

-12 -13 -14 -15 -16 -1 7 -0.1

-0.05

0 x (micron)

0.05

0.1

Fig. 9. AFM cross section of indent bottom. Data points are shown along with fourth order polynomial fit: y = f(x) = M0 + M1x + M2x2 + M3x3 + M4x4.

indents, cross sections at several directions were taken. These were fit with a fourth order polynomial function as shown in Fig. 9. Using Eq. (3) minimal, Rc1jA and maximal, Rc2jA radii of curvature were measured, which then were used to calculate RcjA using Eq. (2).

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