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Solid-state dewetting of thin iron films on sapphire substrates controlled by grain boundary diffusion
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Acta Materialia 61 (2013) 3148–3156 www.elsevier.com/locate/actamat
Solid-state dewetting of thin iron films on sapphire substrates controlled by grain boundary diffusion O. Kovalenko a, J.R. Greer b, E. Rabkin a,⇑ a
Department of Materials Science and Engineering, Technion–Israel Institute of Technology, 32000 Haifa, Israel b Materials Science, California Institute of Technology, Pasadena, CA 91125, USA Received 14 October 2012; accepted 28 January 2013 Available online 16 March 2013
Abstract The initial stages of solid-state dewetting of 25 nm-thick Fe films on basal plane-oriented sapphire substrates were found to occur via nucleation and growth of through-thickness craters within the film. The rims along these voids were not elevated, in contrast to commonly observed void growth mechanisms. Instead, the material that was consumed during the crater expansion was absorbed by several isolated grains in its vicinity but not adjacent to it. These grains transformed into faceted hillocks that protruded above the original film surface at later stages. A thin film dewetting model is proposed, in which the self-diffusion of Fe atoms along the grain boundaries transports the mass from the expanding cavities to the hillocks and determines the kinetics of this dilation. The grain boundary self-diffusion coefficients of Fe that were estimated based on the experimentally determined crater expansion rates and the proposed model agreed well with the literature. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Grain boundary diffusion; Surface diffusion; Theory; Thin films; Capillary phenomena
1. Introduction Thin metal films deposited on ceramic substrates have been reported to be thermodynamically metastable and to evolve into arrays of isolated particles at temperatures that are sufficiently high to activate solid-state diffusion [1]. The driving force for this process is the decrease in the total energy of all surfaces and interfaces in the “thin film–substrate” system. The term “dewetting”, borrowed from the science of thin fluid films [2], is also widely used for describing the agglomeration of thin solid films. In the past, thin film dewetting was considered a harmful process that limited the thermal stability of microsystems. It also has some benefits: controlled dewetting is being increasingly employed for producing ordered nanoparticle arrays for optical/magnetic applications and for catalytic growth of nanowires and nanotubes [1]. This increasing technological importance of ⇑ Corresponding author. Tel.: +972 4 829 4579; fax: +972 4 829 5677.
E-mail address: [email protected] (E. Rabkin).
thin film dewetting drives the need for fundamental studies of the underlying physical mechanisms and kinetics responsible for it [3–5]. The dewetting process usually begins with a nucleation of the through-the-thickness craters within the film, which continue to expand, exposing the native substrate surfaces to the ambient. The solid film material consumed by the growing hole accumulates in the top rim, which forms an elevated ridge surrounded by a depression. The development of this “ridge-depression” topography on the surface of a receding thin film is described well by the classical surface diffusion equation, derived under the assumption that the gradient of surface curvature is the sole driving force for surface diffusion [6,7]. Once the depression reaches the substrate, the rim disconnects from the rest of the film and undergoes the process of fragmentation similar to Rayleigh instability [6,8]. The formation of ridges at the rim of the growing holes has been experimentally observed in a number of experimental studies of solid-state dewetting of both polycrystalline [1,9] and single-crystalline [10,11] thin films. High
1359-6454/$36.00 Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2013.01.062
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surface anisotropy of thin film material may lead to the formation of atomically flat facets in the rim region and to a change in the mechanism of solid-state dewetting [12]. It is generally believed that the formation of ridges is a characteristic “signature” of solid-state dewetting [1]. We have observed the solid-state dewetting process in 25-nm-thick polycrystalline iron films deposited on sapphire substrates to consist of the nucleation and growth of craters within the film, whose outer rims were at the same elevation as the rest of the film. We postulate that the solid material at the outer edges of the crater diffused away from it and formed vertically oriented hillocks, or elevated individual grains. These hillocks were found to serve as the embryonic phases of the future microparticles, similar to the kind reported in Au [13,14]. 2. Experimental Twenty-five-nanometer-thick Fe films were magnetron sputtered on a (0 0 0 1)-oriented, polished single crystalline sapphire substrate that had been ultrasonically cleaned with acetone, ethanol and deionized water before deposition. The deposition was performed in an radio-frequency magnetron sputtering chamber (Von Ardenne GmbH) from a 99.9 wt.% pure Fe target (Kurt J. Lesker). The base pressure in the system was 3 107 torr and the Ar sputtering pressure was 9 103 torr. The deposition rate ˚ s1 and the Ar flow was 20 sccm. was maintained at 0.09 A After the deposition, the film was patterned by microindentation marks created by a Vickers microhardness indenter
Fig. 2. The dependence of the fractional exposed area of the substrate, f, on the cumulative annealing time.
to identify the same area after consecutive heat treatments (interrupted annealing technique). The thermal treatments at 750 °C were performed in a tube furnace with a constant flow of Ar + 10%H2 ultrahigh-purity gas to prevent the oxidation of Fe and to reduce the thin surface oxide layer, which was likely formed when the samples were manipulated in air. The samples were placed in the quartz boat and introduced to the hot zone of the furnace by a manipulator. The heating time of the boat with the sample from room temperature to 750 °C was 5 min, followed by an isothermal anneal at 750 °C for additional 15 min. After each treatment, the film
Fig. 1. The AFM micrographs of Area 1 acquired after annealing at 750 °C for (a) 15 min, (b) 30 min, (c) 45 min and (d) 60 min. Cumulative annealing times are given.
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Fig. 3. The dependencies of the areas of individual holes (see Fig. 1) on the cumulative annealing time for (a) Area 1 and (b) Area 2.
Fig. 5. (a) The three-dimensional AFM image of a typical hole with a neighboring elevated grain and (b) a corresponding line topography profile taken along the blue line. The cumulative annealing time is 45 min. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
to the pre-patterned microindentation marks is shown in the optical micrograph, Fig. S1, in the Supplementary material. After the last treatment, the sample was imaged in a scanning electron microscope (SEM; Zeiss Ultra-Plus FEG-SEM) and electron backscattering diffraction (EBSD) analysis of crystallographic orientations of selected individual grains was performed in environmental SEM (FEI, Quanta 200). 3. Results
Fig. 4. The dependence of the roughness of the residual Fe film on the cumulative annealing time.
surface topography was measured by atomic force microscopy (AFM) using an XE-70 atomic force microscope (Park Systems Corp.). The topography evolution of two different areas of the film (“Area 1” and “Area 2”) was continuously tracked. The location of these areas with respect
Fig. 1 presents four AFM images of Area 1 taken immediately after each consecutive heat treatment. The topographical changes in Area 2 were similar to those of Area 1 and are summarized in Fig. S2 in the Supplementary material. After the first treatment, only three individual craters nucleated in Area 1 (total area of 10 10 lm2), with additional ones nucleating after each additional heat treatment. All craters expanded with cumulative annealing time and eventually coalesced, which rendered measuring
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Fig. 6. Height histograms of the AFM images for different cumulative annealing times for (a) Area 1 and (b) Area 2. The main and secondary peaks correspond to the surface of the residual Fe film and to the holes exposing the substrate, respectively.
the geometrical parameters of individual craters impossible. The AFM images in Fig. 1 also demonstrate that the craters did not generally contain any ridges along their perimeters, and that both the grain size and the surface roughness of the Fe film increased with annealing time (see Table S1 in the Supplementary material). In what follows we will quantify these qualitative observations in more detail.
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The dependence of the exposed fractional area of the film, f, defined as a ratio of the exposed area from all the craters, Ac, and the total area of the image, Ai, on the cumulative annealing time, is shown in Fig. 2. f was found to be linearly correlated with the cumulative annealing time between the incipient crater nucleation and the total agglomeration of the film into an array of isolated islands for each observed area of the sample. Fig. 3 shows the concurrent nearly linear dependence of the exposed area within the individual craters that nucleated as a result of the first annealing on the cumulative annealing time. The aerial growth rates of the craters obtained employing the least square fitting are also shown in this figure. The overall Fe film roughness, expressed as Rq (root mean square) roughness, was amplified with cumulative annealing time, as shown in Fig. 4. This was expected because of the thermal grooving at the grain boundaries (GBs) [15,16]. A typical GB thermal groove grows by solid-state diffusion and commonly has two parallel ridges in the vicinity of the groove root, with the height of the ridges and the depth of the root increasing with time. In addition to the GB grooving, some of the grains exhibited a significant increase in their average height relative to the surrounding film (Fig. 5a). The term “hillock” is often employed to describe such elevated individual grains, which protrude substantially above the average thickness
Fig. 7. AFM images of a growing hole and a neighboring hillock after annealing for (a) 45 min and (b) 60 min. (c) A three-dimensional AFM image of the same area, emphasizing the normal growth of hillocks. (d) Line topography profile quantifying the hole and hillock growth.
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pole figure with the crystallographic orientations of 78 individual hillocks measured by EBSD analysis. This pole figure is very similar to that obtained from the analysis of isolated Fe microparticles formed after full dewetting of the film [18]. This suggests that the hillocks, which developed during the incipient stages of solid-state dewetting of the Fe film, likely served as nuclei for the future microparticles. 4. Discussion
Fig. 8. FEG-SEM image of the Fe film after annealing for 60 min showing the holes and several isolated faceted hillocks.
of the polycrystalline thin film [17]. The most intriguing observation in this study is that the craters did not have elevated rims along their edges, and that the hillocks were laterally separated from the exposed substrates by several hundred nanometers, i.e. over the extent of several “regular” grains, which did not protrude above the average film height (Fig. 5b). The absence of the ridges around the expanding craters raises the question of where the consumed material was absorbed. The histograms of pixel height distributions obtained via AFM are shown in Fig. 6. The two peaks in each histogram correspond to the average height of the Fe film and the exposed sapphire substrate. The absolute values of heights in these images were chosen arbitrarily; we assigned a zero height to the coordinate of the Fe film and evaluated the relative difference between the two peaks. The distance between the two peaks increased with each subsequent heat treatment, which implies that the average thickness of the Fe film increased, likely as a result of its absorbing the Fe atoms removed from the crater perimeters. This mode of dewetting is very different from the classical mode, in which the rejected material typically accumulates around the growing cavity [1,9–12]. The distance between the two peaks increased by 5 nm after the fourth (longest) treatment. The width of the thin film peak also increased with the annealing time, which was likely caused by the increasing surface roughness associated with the higher discrepancies in heights among the individual grains. Well-developed, anisotropic hillocks were formed on the surface of the film in the same locations as the elevated grains after the fourth heat treatment, as shown in Fig. 7. The faceted, anisotropic topology of these hillocks (see Fig. S3 of the Supplementary material) is virtually identical to the shape of the isolated microparticles formed in the final stages of dewetting of thin Fe films [18]. A field emission gun (FEG)-SEM image of the film with the evolution of crater expansion and hillock formation after the fourth heat treatment is shown in Fig. 8. No ridges around the growing holes can be seen in this micrograph, but several faceted hillocks at some distance from the holes can be recognized. Fig. 9 shows the {0 1 1}
The overall dewetting behavior of the thin Fe film observed in the present work is similar to that in other systems reported in the literature [1,9,11,19]. A notable difference with respect to previous observations is the absence of ridges around the perimeter of the growing craters. The height histograms of the AFM images presented in Fig. 6 suggest that at least some of the material consumed by this process was more or less homogeneously absorbed by the remaining Fe film, which led to an increase in its thickness. Some of the material may also have evaporated during the heat treatments. Though the kinetics of metal evaporation under ambient pressure of a protective gas is rather slow, recent data on size evolution of Au nanoparticles on sapphire at temperatures close to the melting point of the metal have demonstrated that evaporation does play some role during heat treatment [20]. The ratio of the initial and final volumes of the Fe film, Vi/Vf, can be determined by: Vi hi ¼ V f ðhi þ DhÞð1 f Þ
ð1Þ
where hi and Dh are the thickness of the original Fe film and the final increase in the thickness of remaining Fe film, respectively, and f = Ac/Ai, as defined in Section 3. Employing Dh 5 nm (see Fig. 6) and f 0.21 and 0.17 (see Fig. 2) gave volumes ratios (Vi/Vf) of 1.05 for Area 1 and 1.01 for Area 2. This suggests that the Fe losses due to evaporation were minimal, and that essentially all of
Fig. 9. The polar figure of 78 individual hillocks formed in the Fe film after annealing for 60 min, determined with the aid of EBSD in SEM.
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the material consumed by the growing craters was redistributed elsewhere in the residual film. Some of the possible mechanisms for the redistribution of this material are surface diffusion, diffusion along the film–substrate (Fe–sapphire) interface, diffusion along the GBs and bulk diffusion in the film. It would be reasonable to assume that surface diffusion mechanisms similar to those discussed in detail in Refs. [6,7] operate here because the surface self-diffusion coefficient of Fe at 750 °C is Ds 1.8 1011 m2 s1 [21], which is sufficiently high. This may lead to rapid growth and subsequent coalescence of the ridges along the neighboring craters, which would be manifested in the overall thickness increase in the Fe film. The literature data on surface self-diffusion in Fe is consistent with this hypothesis; for example, the mass transfer surface diffusion coefficient of Fe at 750 °C as determined by Seebauerpand ffiffiffiffiffiffiffi Jung [21] results in an average diffusion distance of Ds t 250 lm, a value that grossly exceeds the distance between the neighboring craters of 25 lm (see Fig. 1). On the other hand, rapid surface diffusion would inhibit the formation of elevated grains and hillocks such as the ones observed here because any material flow normal to the substrate would be swiftly redistributed along the large surface area [22]. Further, the top surface shape of the grains which comprise the film would be expected to be nearly hemispherical because fast diffusion would level off any steep gradients of surface curvature. The AFM images of the film (Fig. 1) and the corresponding topography line profiles (Figs. 5b and 7d) clearly demonstrate that this is not the case, and the surface curvature in the vicinity of GB thermal grooves is much higher than it is at the center of the grains. These arguments suggest that it is unlikely that the fast surface diffusion is the governing mass transport mechanism in this study. Several factors may inhibit surface diffusion in favor of a slower-rate transport – for example, the surface segregation of residual impurities, which has been shown to “poison” the active diffusion sites [21], and the faceting of the surfaces, which impedes the nucleation of surface steps, a critical stage in mass transfer surface diffusion along the faceted surfaces [23,24]. The alternative routes for the mass transfer which may have enabled the crater expansion in the Fe films include GB diffusion and diffusion along the film–substrate interface. We propose a simple one-dimensional diffusion model of crater growth, which is schematically shown in Fig. 10. For a film with a columnar grain microstructure, diffusion along the GBs would not be expected to contribute to the expansion of the clusters; therefore it is feasible that the Fe atoms first diffuse downward from the surface toward the substrate along the vertical crater walls and then migrate along the film–substrate interface (Fig. 10). This interface serves as both a short-circuit diffusion path and a sink for the diffusing Fe atoms. The accretion of the material at the interface causes the elevation of the grains above those locales, which leads to the formation and growth of hillocks. Our observations indicated that the relative
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Fig. 10. A one-dimensional model of hillock growth controlled by diffusion along the film–substrate interface.
density of such isolated elevated grains and hillocks (see Figs. 5 and 7) was sparse, hence it is reasonable to model the case where a single perfect interface sink is available in the vicinity of a growing cavity at a distance L from its edge, and that this sink absorbs all of the material generated as a result of the expanding crater. Material accumulation may also occur at the tilted GBs beneath the growing hillock [22]. In the model we further assumed that the vertical edges were atomically flat and faceted, and we employed the concept of a weighted mean curvature to describe their motion [25,26]. The surface diffusion flux along the vertical facet, js, and the edge retraction velocity, v, can be determined from the following equations: js ¼
Ds ds @l ; kT @y
v¼
@js Ds d s @ 2 l ¼ @y kT @y 2
ð2Þ
where Ds and ds are the surface self-diffusion coefficient along the facet and the surface diffusion width, respectively, and kT has its usual thermodynamic meaning. The self-similarity of the vertical facet motion in combination with the second part of Eq. (2) suggests that l is a parabolic function of y [25,26], and hence three independent boundary conditions are required. Two of them are related to the surface diffusion flux at the vertical facet termini: js ðy ¼ 0Þ ¼ 0 js ðy ¼ hÞ
Di di lðy ¼ hÞ L kT
ð3aÞ ð3bÞ
Eq. (3a) signifies a negligible contribution of the diffusion along the film surface parallel to the substrate to the overall transport. Eq. (3b) reflects that the Fe–sapphire interface beneath the growing hillock is a perfect sink for the diffusing Fe atoms, and that the excess chemical potential there is zero. The right-hand side of Eq. (3b) describes the diffusion flux along the Fe–sapphire interface, with Di and di being the interface self-diffusion coefficient of Fe atoms and the interface diffusion width, respectively. The third condition that is necessary for determining the function l(y) can be derived by applying an infinitesimal displacement to the edge of the film to calculate the average : excess chemical potential on the vertical facet, l ¼ l
Dc X h
ð3cÞ
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with Dc = cFe + ci cs, where cFe, ci and cs are the surface energy of the upper surface of the Fe film, the energy of the Fe–sapphire interface and the relevant surface energy of sapphire, respectively, and X is the atomic volume of Fe. In fact, Dc represents the thermodynamic driving force for thin film dewetting. The solution of Eq. (2) with the boundary conditions (3) is: v¼
D s ds DcX kT h2 13 h þ Ld
ð4Þ
where d = Dsds/Didi. For 3Ld h, Eq. (4) can be simplified such that the edge retraction is clearly controlled by the interface diffusion: v
Di di DcX kT h2 L
ð5Þ
In the present work, L 1 lm and h = 25 nm, so that the condition 3Ld h is fulfilled even for d 1. Therefore, Eq. (5) can be used to calculate the edge retraction velocity. Eq. (5) can be derived more simply by assuming a linear distribution of the excess chemical potential at the interface from the film edge, given by Eq. (3c), to the bottom of the hillock, where it vanishes. We utilize this approach to analyze a more realistic two-dimensional case, in which the material rejected by the growing craters can flow concurrently along the Fe–sapphire interface and along the columnar GBs in the film (Fig. 11). In the two-dimensional case, Eq. (3c) for the average chemical potential of the atoms on the vertical facet should be modified to include an additional energy change associated with the GBs, i.e. when the edge is displaced, the area of the GBs changes, too. In the simplest approximation of a circular opening within a film with identical grains of width w and with the GBs radially extending along the circle, the average chemical potential would amount to: Dc cb ¼ l þ X ð6Þ h w where cb is the energy of the GB. It is plausible that the diffusion flux in the film proceeds within the region of width u, which is the average width among the openings and the hillocks (Fig. 11), and that the relevant effective diffusivity in the film, Deff, can be represented as a weighted average of GB and Fe–sapphire interface diffusivities:
Fig. 11. A two-dimensional model of hillock growth controlled by selfdiffusion along the GBs.
Deff ¼
Db wh þ Di h þ1 w
ð7Þ
where Db is the self-diffusion coefficient along the GBs in Fe. We assume that the diffusion width of the GB is the same as that of the interface, di. Then, employing the same simplified arguments that justified Eq. (5), we arrive at the following expression for the rate of area change in the individual crater, dA/dt: h Db w þ Di di u Dc þ wh cb X dA ¼ ð8Þ dt kTh2 L Eq. (8) demonstrates that the rate of increase in the exposed area is approximately constant, at least until the crater and the hillock radii are substantially smaller than the distance L between them. This is in agreement with the experimental data (Fig. 3). At the later stages of growth, the rate of area increase should accelerate with time because the concomitant reduction in L becomes significant. It is possible that the hillocks are “attracting” the growing cavity until they are absorbed by the moving crater edge. Several such absorbed hillocks are visible in the AFM image of the film after the longest annealing time of 60 min (Fig. 1). A quantitative estimate of the crater growth rate based on Eq. (8) is difficult because no reliable data on the metal self-diffusion along the metal–ceramic interfaces is available in the literature. We checked whether the material transport by the GB diffusion alone (i.e. Di Db) cold result in hole growth rates comparable to those observed in the experiment. The following values were employed in the calculations: L 1 lm, T = 1023 K, X = 1.12 1029 m3 at1, Dc 2.5 J m2 [27–29], cb 1 J m2, w 120 nm, di = 0.5 nm and u 600 nm. With the experimentally observed crater growth rates (Fig. 3), Eq. (8) yields the following range of the product between the GB width and GB diffusivity: 2.42 1021 m3 s1 < Dbdi < 5.08 1021 m3 s1. This is in good agreement with the GB self-diffusion coefficients in a-Fe at 750 °C reported by Divinski et al. [30] (from 2.6 to 2.8 1021 m3 s1, depending on material purity) and by Ha¨nsel et al. [31] (3.3 1021 m3 s1). The results of this analysis suggest that the GB self-diffusion in Fe film is sufficiently rapid to transport the material rejected by the growing cavity to the base of the hillock, which grows at the expense of the opening. No definite conclusion on the possible contribution of the diffusion along the Fe–sapphire interface to the crater expansion can be reached based on this data. Analogously, if bulk diffusion in the Fe film were the sole mass transport mechanism, the calculated craters expansion rates would be by two to three orders of magnitude lower than the ones observed experimentally. This quantitative analysis supports the proposed hypothesis that material is being transported from the moving edges of an expanding crater to the remote hillocks along the GBs, which drives the dewetting in thin polycrystalline films when surface diffusion is suppressed. Such a mechanism bears some similarity to the growth of nanowhiskers during physical vapor deposition of thin metal
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films discussed by Schamel et al. [32]. It was suggested that the nanowhiskers nucleated in the regions of the substrate where metal–substrate adhesion was substantial. The isolated adatoms, which were condensed on the regions with a high metal–substrate interface energy, diffused along the surface until they were absorbed at the bottom of a growing whisker. In both cases, the material for growing structures (hillocks or whiskers) is supplied by diffusion driven by the chemical potential gradient, and material accretion occurs at their root. In this work, the gradient in the chemical potential of Fe atoms, which drives them towards the hillocks, is related to the capillary effects because of the excess chemical potential of the solid–vapor boundary (Eqs. (3c) and (6)). In the nanowiskers [32], the excess in chemical potential is associated with the two-dimensional random distribution of adatoms on the substrate. The dewetting mechanism uncovered in this work may be operating in parallel with the classical mechanism via surface diffusion parallel to the substrate [6,7]. Under such circumstances, the growth of hillocks at some distance away from the crater would occur simultaneously with the formation of a ridge along the perimeter of the opening. For example, even a marginal amount of surface diffusion has been observed to cause ridge formation during the dewetting of thin polycrystalline Au films [33]. Finally, we would like address the question of why a limited number of grains were particularly efficient at first absorbing the material, then growing upward and transforming into hillocks. The incoming material can be absorbed by a remote grain by material accretion either at the tilted GBs or at the film–substrate interface. In the former case, the grains which were separated from their neighbors by the tilted GBs would absorb the incoming material and transform into hillocks [22]. In the latter case, where material accumulates at the Fe–sapphire interface, some special misorientation relationship between the Fe grain and the underlying sapphire may result in an increased sink efficiency of the interface, which would lead to the particles with these specific misorientation relationships surviving in the fully dewetted film. The sharpening of the texture of the dewetted Fe film observed in our recent work is consistent with this mechanism [18]. In any case, the nucleation and growth of isolated hillocks in thin films is a well-known phenomenon, discussed in a number of publications (e.g. Refs. [22,34]), and its full analysis is beyond the scopes of the present work. 5. Conclusions 1. We employed an interrupted annealing technique to study the microstructure evolution of a region of thin polycrystalline Fe film deposited on a basal-plane-oriented sapphire substrate. We found that, during annealing at a temperature of 750 °C, the film agglomerated by the nucleation and growth of through-the-thickness craters. After nucleation, the areas of these craters increased linearly with annealing time.
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2. The craters did not form elevated rims along their edges, a commonly observed morphology at this stage of dewetting in thin metal films. Instead, both the surface roughness and the average thickness of the Fe film increased with annealing time. We demonstrated that the material loss due to growing holes was approximately balanced by the material gain due to the thickening of the remaining film, i.e. no material was lost to evaporation. 3. We demonstrated that the concurrent increase in roughness and in the average thickness of the Fe film was associated with the growth of selected grains normal to the substrate. These elevated grains later transformed into faceted hillocks protruding far above the rest of the film. In most cases, the growing hillocks were separated from the craters by several “normal” grains. 4. We proposed a dewetting mechanism of thin polycrystalline films: the excess chemical potential of the Fe atoms at the edges of the craters drives these atoms towards the sinks at the bottom of the grains, which subsequently transform into hillocks. This model suggests that the material transport occurred along the GBs in the film. The GB self-diffusion coefficients of Fe estimated from experimentally determined cavity expansion rates and the proposed model agree well with the literature.
Acknowledgements This work was supported by the US–Israel Binational Science Foundation, Grant No. 2010148, and by the Russell Berry Nanotechnology Institute at the Technion. The helpful advice and assistance of Dr. L. Klinger, Mr. M. Kazakevich, Mr. D. Amram and Ms. L. Popilevsky are heartily acknowledged. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.actamat.2013.01.062. References [1] Thompson CV. Annu Rev Mater Res 2012;42:399. [2] Samid-Merzel N, Lipson SG, Tannhauser DS. Phys Rev E 1998;57:2906. [3] Klinger L, Rabkin E. Acta Mater 2012;60:6065. [4] Leroy F, Cheynis F, Passanante T, Mu¨ller P. Phys Rev B 2012;85:195414. [5] Jiang W, Bao W, Thompson CV, Srolovitz DJ. Acta Mater 2012;60:5578. [6] Srolovitz DJ, Safran SA. J Appl Phys 1986;60:255. [7] Wong H, Voorhees PW, Miksis MJ, Davis SH. Acta Mater 2000;48:1719. [8] Kan W, Wong H. J Appl Phys 2005;97:043515. [9] Mu¨ller CM, Spolenak R. Acta Mater 2010;58:6035. [10] Ye J, Thompson CV. Phys Rev B 2010;82:193408.
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Acta Materialia 61 (2013) 3148–3156 www.elsevier.com/locate/actamat
Solid-state dewetting of thin iron films on sapphire substrates controlled by grain boundary diffusion O. Kovalenko a, J.R. Greer b, E. Rabkin a,⇑ a
Department of Materials Science and Engineering, Technion–Israel Institute of Technology, 32000 Haifa, Israel b Materials Science, California Institute of Technology, Pasadena, CA 91125, USA Received 14 October 2012; accepted 28 January 2013 Available online 16 March 2013
Abstract The initial stages of solid-state dewetting of 25 nm-thick Fe films on basal plane-oriented sapphire substrates were found to occur via nucleation and growth of through-thickness craters within the film. The rims along these voids were not elevated, in contrast to commonly observed void growth mechanisms. Instead, the material that was consumed during the crater expansion was absorbed by several isolated grains in its vicinity but not adjacent to it. These grains transformed into faceted hillocks that protruded above the original film surface at later stages. A thin film dewetting model is proposed, in which the self-diffusion of Fe atoms along the grain boundaries transports the mass from the expanding cavities to the hillocks and determines the kinetics of this dilation. The grain boundary self-diffusion coefficients of Fe that were estimated based on the experimentally determined crater expansion rates and the proposed model agreed well with the literature. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Grain boundary diffusion; Surface diffusion; Theory; Thin films; Capillary phenomena
1. Introduction Thin metal films deposited on ceramic substrates have been reported to be thermodynamically metastable and to evolve into arrays of isolated particles at temperatures that are sufficiently high to activate solid-state diffusion [1]. The driving force for this process is the decrease in the total energy of all surfaces and interfaces in the “thin film–substrate” system. The term “dewetting”, borrowed from the science of thin fluid films [2], is also widely used for describing the agglomeration of thin solid films. In the past, thin film dewetting was considered a harmful process that limited the thermal stability of microsystems. It also has some benefits: controlled dewetting is being increasingly employed for producing ordered nanoparticle arrays for optical/magnetic applications and for catalytic growth of nanowires and nanotubes [1]. This increasing technological importance of ⇑ Corresponding author. Tel.: +972 4 829 4579; fax: +972 4 829 5677.
E-mail address: [email protected] (E. Rabkin).
thin film dewetting drives the need for fundamental studies of the underlying physical mechanisms and kinetics responsible for it [3–5]. The dewetting process usually begins with a nucleation of the through-the-thickness craters within the film, which continue to expand, exposing the native substrate surfaces to the ambient. The solid film material consumed by the growing hole accumulates in the top rim, which forms an elevated ridge surrounded by a depression. The development of this “ridge-depression” topography on the surface of a receding thin film is described well by the classical surface diffusion equation, derived under the assumption that the gradient of surface curvature is the sole driving force for surface diffusion [6,7]. Once the depression reaches the substrate, the rim disconnects from the rest of the film and undergoes the process of fragmentation similar to Rayleigh instability [6,8]. The formation of ridges at the rim of the growing holes has been experimentally observed in a number of experimental studies of solid-state dewetting of both polycrystalline [1,9] and single-crystalline [10,11] thin films. High
1359-6454/$36.00 Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2013.01.062
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surface anisotropy of thin film material may lead to the formation of atomically flat facets in the rim region and to a change in the mechanism of solid-state dewetting [12]. It is generally believed that the formation of ridges is a characteristic “signature” of solid-state dewetting [1]. We have observed the solid-state dewetting process in 25-nm-thick polycrystalline iron films deposited on sapphire substrates to consist of the nucleation and growth of craters within the film, whose outer rims were at the same elevation as the rest of the film. We postulate that the solid material at the outer edges of the crater diffused away from it and formed vertically oriented hillocks, or elevated individual grains. These hillocks were found to serve as the embryonic phases of the future microparticles, similar to the kind reported in Au [13,14]. 2. Experimental Twenty-five-nanometer-thick Fe films were magnetron sputtered on a (0 0 0 1)-oriented, polished single crystalline sapphire substrate that had been ultrasonically cleaned with acetone, ethanol and deionized water before deposition. The deposition was performed in an radio-frequency magnetron sputtering chamber (Von Ardenne GmbH) from a 99.9 wt.% pure Fe target (Kurt J. Lesker). The base pressure in the system was 3 107 torr and the Ar sputtering pressure was 9 103 torr. The deposition rate ˚ s1 and the Ar flow was 20 sccm. was maintained at 0.09 A After the deposition, the film was patterned by microindentation marks created by a Vickers microhardness indenter
Fig. 2. The dependence of the fractional exposed area of the substrate, f, on the cumulative annealing time.
to identify the same area after consecutive heat treatments (interrupted annealing technique). The thermal treatments at 750 °C were performed in a tube furnace with a constant flow of Ar + 10%H2 ultrahigh-purity gas to prevent the oxidation of Fe and to reduce the thin surface oxide layer, which was likely formed when the samples were manipulated in air. The samples were placed in the quartz boat and introduced to the hot zone of the furnace by a manipulator. The heating time of the boat with the sample from room temperature to 750 °C was 5 min, followed by an isothermal anneal at 750 °C for additional 15 min. After each treatment, the film
Fig. 1. The AFM micrographs of Area 1 acquired after annealing at 750 °C for (a) 15 min, (b) 30 min, (c) 45 min and (d) 60 min. Cumulative annealing times are given.
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Fig. 3. The dependencies of the areas of individual holes (see Fig. 1) on the cumulative annealing time for (a) Area 1 and (b) Area 2.
Fig. 5. (a) The three-dimensional AFM image of a typical hole with a neighboring elevated grain and (b) a corresponding line topography profile taken along the blue line. The cumulative annealing time is 45 min. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
to the pre-patterned microindentation marks is shown in the optical micrograph, Fig. S1, in the Supplementary material. After the last treatment, the sample was imaged in a scanning electron microscope (SEM; Zeiss Ultra-Plus FEG-SEM) and electron backscattering diffraction (EBSD) analysis of crystallographic orientations of selected individual grains was performed in environmental SEM (FEI, Quanta 200). 3. Results
Fig. 4. The dependence of the roughness of the residual Fe film on the cumulative annealing time.
surface topography was measured by atomic force microscopy (AFM) using an XE-70 atomic force microscope (Park Systems Corp.). The topography evolution of two different areas of the film (“Area 1” and “Area 2”) was continuously tracked. The location of these areas with respect
Fig. 1 presents four AFM images of Area 1 taken immediately after each consecutive heat treatment. The topographical changes in Area 2 were similar to those of Area 1 and are summarized in Fig. S2 in the Supplementary material. After the first treatment, only three individual craters nucleated in Area 1 (total area of 10 10 lm2), with additional ones nucleating after each additional heat treatment. All craters expanded with cumulative annealing time and eventually coalesced, which rendered measuring
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Fig. 6. Height histograms of the AFM images for different cumulative annealing times for (a) Area 1 and (b) Area 2. The main and secondary peaks correspond to the surface of the residual Fe film and to the holes exposing the substrate, respectively.
the geometrical parameters of individual craters impossible. The AFM images in Fig. 1 also demonstrate that the craters did not generally contain any ridges along their perimeters, and that both the grain size and the surface roughness of the Fe film increased with annealing time (see Table S1 in the Supplementary material). In what follows we will quantify these qualitative observations in more detail.
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The dependence of the exposed fractional area of the film, f, defined as a ratio of the exposed area from all the craters, Ac, and the total area of the image, Ai, on the cumulative annealing time, is shown in Fig. 2. f was found to be linearly correlated with the cumulative annealing time between the incipient crater nucleation and the total agglomeration of the film into an array of isolated islands for each observed area of the sample. Fig. 3 shows the concurrent nearly linear dependence of the exposed area within the individual craters that nucleated as a result of the first annealing on the cumulative annealing time. The aerial growth rates of the craters obtained employing the least square fitting are also shown in this figure. The overall Fe film roughness, expressed as Rq (root mean square) roughness, was amplified with cumulative annealing time, as shown in Fig. 4. This was expected because of the thermal grooving at the grain boundaries (GBs) [15,16]. A typical GB thermal groove grows by solid-state diffusion and commonly has two parallel ridges in the vicinity of the groove root, with the height of the ridges and the depth of the root increasing with time. In addition to the GB grooving, some of the grains exhibited a significant increase in their average height relative to the surrounding film (Fig. 5a). The term “hillock” is often employed to describe such elevated individual grains, which protrude substantially above the average thickness
Fig. 7. AFM images of a growing hole and a neighboring hillock after annealing for (a) 45 min and (b) 60 min. (c) A three-dimensional AFM image of the same area, emphasizing the normal growth of hillocks. (d) Line topography profile quantifying the hole and hillock growth.
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pole figure with the crystallographic orientations of 78 individual hillocks measured by EBSD analysis. This pole figure is very similar to that obtained from the analysis of isolated Fe microparticles formed after full dewetting of the film [18]. This suggests that the hillocks, which developed during the incipient stages of solid-state dewetting of the Fe film, likely served as nuclei for the future microparticles. 4. Discussion
Fig. 8. FEG-SEM image of the Fe film after annealing for 60 min showing the holes and several isolated faceted hillocks.
of the polycrystalline thin film [17]. The most intriguing observation in this study is that the craters did not have elevated rims along their edges, and that the hillocks were laterally separated from the exposed substrates by several hundred nanometers, i.e. over the extent of several “regular” grains, which did not protrude above the average film height (Fig. 5b). The absence of the ridges around the expanding craters raises the question of where the consumed material was absorbed. The histograms of pixel height distributions obtained via AFM are shown in Fig. 6. The two peaks in each histogram correspond to the average height of the Fe film and the exposed sapphire substrate. The absolute values of heights in these images were chosen arbitrarily; we assigned a zero height to the coordinate of the Fe film and evaluated the relative difference between the two peaks. The distance between the two peaks increased with each subsequent heat treatment, which implies that the average thickness of the Fe film increased, likely as a result of its absorbing the Fe atoms removed from the crater perimeters. This mode of dewetting is very different from the classical mode, in which the rejected material typically accumulates around the growing cavity [1,9–12]. The distance between the two peaks increased by 5 nm after the fourth (longest) treatment. The width of the thin film peak also increased with the annealing time, which was likely caused by the increasing surface roughness associated with the higher discrepancies in heights among the individual grains. Well-developed, anisotropic hillocks were formed on the surface of the film in the same locations as the elevated grains after the fourth heat treatment, as shown in Fig. 7. The faceted, anisotropic topology of these hillocks (see Fig. S3 of the Supplementary material) is virtually identical to the shape of the isolated microparticles formed in the final stages of dewetting of thin Fe films [18]. A field emission gun (FEG)-SEM image of the film with the evolution of crater expansion and hillock formation after the fourth heat treatment is shown in Fig. 8. No ridges around the growing holes can be seen in this micrograph, but several faceted hillocks at some distance from the holes can be recognized. Fig. 9 shows the {0 1 1}
The overall dewetting behavior of the thin Fe film observed in the present work is similar to that in other systems reported in the literature [1,9,11,19]. A notable difference with respect to previous observations is the absence of ridges around the perimeter of the growing craters. The height histograms of the AFM images presented in Fig. 6 suggest that at least some of the material consumed by this process was more or less homogeneously absorbed by the remaining Fe film, which led to an increase in its thickness. Some of the material may also have evaporated during the heat treatments. Though the kinetics of metal evaporation under ambient pressure of a protective gas is rather slow, recent data on size evolution of Au nanoparticles on sapphire at temperatures close to the melting point of the metal have demonstrated that evaporation does play some role during heat treatment [20]. The ratio of the initial and final volumes of the Fe film, Vi/Vf, can be determined by: Vi hi ¼ V f ðhi þ DhÞð1 f Þ
ð1Þ
where hi and Dh are the thickness of the original Fe film and the final increase in the thickness of remaining Fe film, respectively, and f = Ac/Ai, as defined in Section 3. Employing Dh 5 nm (see Fig. 6) and f 0.21 and 0.17 (see Fig. 2) gave volumes ratios (Vi/Vf) of 1.05 for Area 1 and 1.01 for Area 2. This suggests that the Fe losses due to evaporation were minimal, and that essentially all of
Fig. 9. The polar figure of 78 individual hillocks formed in the Fe film after annealing for 60 min, determined with the aid of EBSD in SEM.
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the material consumed by the growing craters was redistributed elsewhere in the residual film. Some of the possible mechanisms for the redistribution of this material are surface diffusion, diffusion along the film–substrate (Fe–sapphire) interface, diffusion along the GBs and bulk diffusion in the film. It would be reasonable to assume that surface diffusion mechanisms similar to those discussed in detail in Refs. [6,7] operate here because the surface self-diffusion coefficient of Fe at 750 °C is Ds 1.8 1011 m2 s1 [21], which is sufficiently high. This may lead to rapid growth and subsequent coalescence of the ridges along the neighboring craters, which would be manifested in the overall thickness increase in the Fe film. The literature data on surface self-diffusion in Fe is consistent with this hypothesis; for example, the mass transfer surface diffusion coefficient of Fe at 750 °C as determined by Seebauerpand ffiffiffiffiffiffiffi Jung [21] results in an average diffusion distance of Ds t 250 lm, a value that grossly exceeds the distance between the neighboring craters of 25 lm (see Fig. 1). On the other hand, rapid surface diffusion would inhibit the formation of elevated grains and hillocks such as the ones observed here because any material flow normal to the substrate would be swiftly redistributed along the large surface area [22]. Further, the top surface shape of the grains which comprise the film would be expected to be nearly hemispherical because fast diffusion would level off any steep gradients of surface curvature. The AFM images of the film (Fig. 1) and the corresponding topography line profiles (Figs. 5b and 7d) clearly demonstrate that this is not the case, and the surface curvature in the vicinity of GB thermal grooves is much higher than it is at the center of the grains. These arguments suggest that it is unlikely that the fast surface diffusion is the governing mass transport mechanism in this study. Several factors may inhibit surface diffusion in favor of a slower-rate transport – for example, the surface segregation of residual impurities, which has been shown to “poison” the active diffusion sites [21], and the faceting of the surfaces, which impedes the nucleation of surface steps, a critical stage in mass transfer surface diffusion along the faceted surfaces [23,24]. The alternative routes for the mass transfer which may have enabled the crater expansion in the Fe films include GB diffusion and diffusion along the film–substrate interface. We propose a simple one-dimensional diffusion model of crater growth, which is schematically shown in Fig. 10. For a film with a columnar grain microstructure, diffusion along the GBs would not be expected to contribute to the expansion of the clusters; therefore it is feasible that the Fe atoms first diffuse downward from the surface toward the substrate along the vertical crater walls and then migrate along the film–substrate interface (Fig. 10). This interface serves as both a short-circuit diffusion path and a sink for the diffusing Fe atoms. The accretion of the material at the interface causes the elevation of the grains above those locales, which leads to the formation and growth of hillocks. Our observations indicated that the relative
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Fig. 10. A one-dimensional model of hillock growth controlled by diffusion along the film–substrate interface.
density of such isolated elevated grains and hillocks (see Figs. 5 and 7) was sparse, hence it is reasonable to model the case where a single perfect interface sink is available in the vicinity of a growing cavity at a distance L from its edge, and that this sink absorbs all of the material generated as a result of the expanding crater. Material accumulation may also occur at the tilted GBs beneath the growing hillock [22]. In the model we further assumed that the vertical edges were atomically flat and faceted, and we employed the concept of a weighted mean curvature to describe their motion [25,26]. The surface diffusion flux along the vertical facet, js, and the edge retraction velocity, v, can be determined from the following equations: js ¼
Ds ds @l ; kT @y
v¼
@js Ds d s @ 2 l ¼ @y kT @y 2
ð2Þ
where Ds and ds are the surface self-diffusion coefficient along the facet and the surface diffusion width, respectively, and kT has its usual thermodynamic meaning. The self-similarity of the vertical facet motion in combination with the second part of Eq. (2) suggests that l is a parabolic function of y [25,26], and hence three independent boundary conditions are required. Two of them are related to the surface diffusion flux at the vertical facet termini: js ðy ¼ 0Þ ¼ 0 js ðy ¼ hÞ
Di di lðy ¼ hÞ L kT
ð3aÞ ð3bÞ
Eq. (3a) signifies a negligible contribution of the diffusion along the film surface parallel to the substrate to the overall transport. Eq. (3b) reflects that the Fe–sapphire interface beneath the growing hillock is a perfect sink for the diffusing Fe atoms, and that the excess chemical potential there is zero. The right-hand side of Eq. (3b) describes the diffusion flux along the Fe–sapphire interface, with Di and di being the interface self-diffusion coefficient of Fe atoms and the interface diffusion width, respectively. The third condition that is necessary for determining the function l(y) can be derived by applying an infinitesimal displacement to the edge of the film to calculate the average : excess chemical potential on the vertical facet, l ¼ l
Dc X h
ð3cÞ
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with Dc = cFe + ci cs, where cFe, ci and cs are the surface energy of the upper surface of the Fe film, the energy of the Fe–sapphire interface and the relevant surface energy of sapphire, respectively, and X is the atomic volume of Fe. In fact, Dc represents the thermodynamic driving force for thin film dewetting. The solution of Eq. (2) with the boundary conditions (3) is: v¼
D s ds DcX kT h2 13 h þ Ld
ð4Þ
where d = Dsds/Didi. For 3Ld h, Eq. (4) can be simplified such that the edge retraction is clearly controlled by the interface diffusion: v
Di di DcX kT h2 L
ð5Þ
In the present work, L 1 lm and h = 25 nm, so that the condition 3Ld h is fulfilled even for d 1. Therefore, Eq. (5) can be used to calculate the edge retraction velocity. Eq. (5) can be derived more simply by assuming a linear distribution of the excess chemical potential at the interface from the film edge, given by Eq. (3c), to the bottom of the hillock, where it vanishes. We utilize this approach to analyze a more realistic two-dimensional case, in which the material rejected by the growing craters can flow concurrently along the Fe–sapphire interface and along the columnar GBs in the film (Fig. 11). In the two-dimensional case, Eq. (3c) for the average chemical potential of the atoms on the vertical facet should be modified to include an additional energy change associated with the GBs, i.e. when the edge is displaced, the area of the GBs changes, too. In the simplest approximation of a circular opening within a film with identical grains of width w and with the GBs radially extending along the circle, the average chemical potential would amount to: Dc cb ¼ l þ X ð6Þ h w where cb is the energy of the GB. It is plausible that the diffusion flux in the film proceeds within the region of width u, which is the average width among the openings and the hillocks (Fig. 11), and that the relevant effective diffusivity in the film, Deff, can be represented as a weighted average of GB and Fe–sapphire interface diffusivities:
Fig. 11. A two-dimensional model of hillock growth controlled by selfdiffusion along the GBs.
Deff ¼
Db wh þ Di h þ1 w
ð7Þ
where Db is the self-diffusion coefficient along the GBs in Fe. We assume that the diffusion width of the GB is the same as that of the interface, di. Then, employing the same simplified arguments that justified Eq. (5), we arrive at the following expression for the rate of area change in the individual crater, dA/dt: h Db w þ Di di u Dc þ wh cb X dA ¼ ð8Þ dt kTh2 L Eq. (8) demonstrates that the rate of increase in the exposed area is approximately constant, at least until the crater and the hillock radii are substantially smaller than the distance L between them. This is in agreement with the experimental data (Fig. 3). At the later stages of growth, the rate of area increase should accelerate with time because the concomitant reduction in L becomes significant. It is possible that the hillocks are “attracting” the growing cavity until they are absorbed by the moving crater edge. Several such absorbed hillocks are visible in the AFM image of the film after the longest annealing time of 60 min (Fig. 1). A quantitative estimate of the crater growth rate based on Eq. (8) is difficult because no reliable data on the metal self-diffusion along the metal–ceramic interfaces is available in the literature. We checked whether the material transport by the GB diffusion alone (i.e. Di Db) cold result in hole growth rates comparable to those observed in the experiment. The following values were employed in the calculations: L 1 lm, T = 1023 K, X = 1.12 1029 m3 at1, Dc 2.5 J m2 [27–29], cb 1 J m2, w 120 nm, di = 0.5 nm and u 600 nm. With the experimentally observed crater growth rates (Fig. 3), Eq. (8) yields the following range of the product between the GB width and GB diffusivity: 2.42 1021 m3 s1 < Dbdi < 5.08 1021 m3 s1. This is in good agreement with the GB self-diffusion coefficients in a-Fe at 750 °C reported by Divinski et al. [30] (from 2.6 to 2.8 1021 m3 s1, depending on material purity) and by Ha¨nsel et al. [31] (3.3 1021 m3 s1). The results of this analysis suggest that the GB self-diffusion in Fe film is sufficiently rapid to transport the material rejected by the growing cavity to the base of the hillock, which grows at the expense of the opening. No definite conclusion on the possible contribution of the diffusion along the Fe–sapphire interface to the crater expansion can be reached based on this data. Analogously, if bulk diffusion in the Fe film were the sole mass transport mechanism, the calculated craters expansion rates would be by two to three orders of magnitude lower than the ones observed experimentally. This quantitative analysis supports the proposed hypothesis that material is being transported from the moving edges of an expanding crater to the remote hillocks along the GBs, which drives the dewetting in thin polycrystalline films when surface diffusion is suppressed. Such a mechanism bears some similarity to the growth of nanowhiskers during physical vapor deposition of thin metal
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films discussed by Schamel et al. [32]. It was suggested that the nanowhiskers nucleated in the regions of the substrate where metal–substrate adhesion was substantial. The isolated adatoms, which were condensed on the regions with a high metal–substrate interface energy, diffused along the surface until they were absorbed at the bottom of a growing whisker. In both cases, the material for growing structures (hillocks or whiskers) is supplied by diffusion driven by the chemical potential gradient, and material accretion occurs at their root. In this work, the gradient in the chemical potential of Fe atoms, which drives them towards the hillocks, is related to the capillary effects because of the excess chemical potential of the solid–vapor boundary (Eqs. (3c) and (6)). In the nanowiskers [32], the excess in chemical potential is associated with the two-dimensional random distribution of adatoms on the substrate. The dewetting mechanism uncovered in this work may be operating in parallel with the classical mechanism via surface diffusion parallel to the substrate [6,7]. Under such circumstances, the growth of hillocks at some distance away from the crater would occur simultaneously with the formation of a ridge along the perimeter of the opening. For example, even a marginal amount of surface diffusion has been observed to cause ridge formation during the dewetting of thin polycrystalline Au films [33]. Finally, we would like address the question of why a limited number of grains were particularly efficient at first absorbing the material, then growing upward and transforming into hillocks. The incoming material can be absorbed by a remote grain by material accretion either at the tilted GBs or at the film–substrate interface. In the former case, the grains which were separated from their neighbors by the tilted GBs would absorb the incoming material and transform into hillocks [22]. In the latter case, where material accumulates at the Fe–sapphire interface, some special misorientation relationship between the Fe grain and the underlying sapphire may result in an increased sink efficiency of the interface, which would lead to the particles with these specific misorientation relationships surviving in the fully dewetted film. The sharpening of the texture of the dewetted Fe film observed in our recent work is consistent with this mechanism [18]. In any case, the nucleation and growth of isolated hillocks in thin films is a well-known phenomenon, discussed in a number of publications (e.g. Refs. [22,34]), and its full analysis is beyond the scopes of the present work. 5. Conclusions 1. We employed an interrupted annealing technique to study the microstructure evolution of a region of thin polycrystalline Fe film deposited on a basal-plane-oriented sapphire substrate. We found that, during annealing at a temperature of 750 °C, the film agglomerated by the nucleation and growth of through-the-thickness craters. After nucleation, the areas of these craters increased linearly with annealing time.
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2. The craters did not form elevated rims along their edges, a commonly observed morphology at this stage of dewetting in thin metal films. Instead, both the surface roughness and the average thickness of the Fe film increased with annealing time. We demonstrated that the material loss due to growing holes was approximately balanced by the material gain due to the thickening of the remaining film, i.e. no material was lost to evaporation. 3. We demonstrated that the concurrent increase in roughness and in the average thickness of the Fe film was associated with the growth of selected grains normal to the substrate. These elevated grains later transformed into faceted hillocks protruding far above the rest of the film. In most cases, the growing hillocks were separated from the craters by several “normal” grains. 4. We proposed a dewetting mechanism of thin polycrystalline films: the excess chemical potential of the Fe atoms at the edges of the craters drives these atoms towards the sinks at the bottom of the grains, which subsequently transform into hillocks. This model suggests that the material transport occurred along the GBs in the film. The GB self-diffusion coefficients of Fe estimated from experimentally determined cavity expansion rates and the proposed model agree well with the literature.
Acknowledgements This work was supported by the US–Israel Binational Science Foundation, Grant No. 2010148, and by the Russell Berry Nanotechnology Institute at the Technion. The helpful advice and assistance of Dr. L. Klinger, Mr. M. Kazakevich, Mr. D. Amram and Ms. L. Popilevsky are heartily acknowledged. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.actamat.2013.01.062. References [1] Thompson CV. Annu Rev Mater Res 2012;42:399. [2] Samid-Merzel N, Lipson SG, Tannhauser DS. Phys Rev E 1998;57:2906. [3] Klinger L, Rabkin E. Acta Mater 2012;60:6065. [4] Leroy F, Cheynis F, Passanante T, Mu¨ller P. Phys Rev B 2012;85:195414. [5] Jiang W, Bao W, Thompson CV, Srolovitz DJ. Acta Mater 2012;60:5578. [6] Srolovitz DJ, Safran SA. J Appl Phys 1986;60:255. [7] Wong H, Voorhees PW, Miksis MJ, Davis SH. Acta Mater 2000;48:1719. [8] Kan W, Wong H. J Appl Phys 2005;97:043515. [9] Mu¨ller CM, Spolenak R. Acta Mater 2010;58:6035. [10] Ye J, Thompson CV. Phys Rev B 2010;82:193408.
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