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Capillarity-driven migration of a thin Ge wedge in contact with a bicrystalline Au film
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Acta Materialia 59 (2011) 2481–2490 www.elsevier.com/locate/actamat
Capillarity-driven migration of a thin Ge wedge in contact with a bicrystalline Au film T. Radetic a,1, A.M. Minor a,b, U. Dahmen a,⇑ a b
National Center for Electron Microscopy, Lawrence Berkeley National Lab, Berkeley, CA, USA Department of Materials Science and Engineering, University of California, Berkeley, CA, USA
Received 28 November 2010; received in revised form 25 December 2010; accepted 27 December 2010 Available online 25 January 2011
Abstract We have investigated the retraction of a single-crystalline Ge wedge in epitaxial contact with a bicrystalline Au film using in situ electron microscopy. The rate of retraction was close to that predicted for capillarity-driven surface diffusion, following kinetics proportional to tn, with n = 0.22–0.35, but crystal anisotropy caused migration to be significantly faster along h1 0 0i directions than along h1 1 0i. The bicrystalline Au substrate was not inert, but underwent abnormal grain growth in the area swept by the receding Ge wedge. Cross-sections made from plan-view transmission electron microscopy samples revealed that this was related to ridge formation during the retraction process. In situ observations of the process in an inclined orientation showed direct evidence of substrate grain boundaries being dragged by the receding Ge wedge. The results can be understood in the framework of capillarity models for isotropic solid-state wedges and reactive wetting in high-temperature liquid–solid experiments. Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Dewetting; Capillarity; Bicrystalline substrate; Wedge migration; TEM characterization
1. Introduction The thermodynamics and kinetics of wetting, including dynamic features such as spreading or retraction of a liquid droplet on an inert solid substrate are well understood in theory and clearly documented experimentally [1]. When the substrate is not inert, the liquid droplet interacts with the substrate, leading to new types of phenomena such as ridging and reactive wetting, which have been investigated more recently. Reactive wetting takes place when the interaction between the liquid droplet and the solid substrate results in the formation of a new compound at the interface [2,3]. Ridging occurs in response to the vertical component ⇑ Corresponding author. Address: NCEM, MS 72, Lawrence Berkeley National Lab, Berkeley, CA 94720, USA. Tel.: +1 510 486 4627; fax: +1 510 486 5888. E-mail address: [email protected] (U. Dahmen). 1 Present address: Faculty of Technology and Metallurgy, University of Belgrade, Belgrade, Serbia.
of a liquid droplet’s surface tension [4] on a deformable substrate. Reactive wetting and ridging have an important effect on the local microscopic and macroscopic contact angle, the evolution toward equilibrium, and the rate at which a liquid droplet spreads or retracts [4]. Wetting in the solid state exhibits similar phenomena, but the capillary behavior of solid particles on a solid substrate is far less developed. Winterbottom proposed a method similar to the Wulff construction to describe the equilibrium configuration of an anisotropic solid particle on a deformable surface [5]. Based on this method Taylor and Cahn predicted the optimum orientation of a crystalline nucleus on an isotropic substrate [6]. In an experimental observation of this effect, Marks and Ajayan used high-resolution electron microscopy to image small Au crystals partially submerged in an MgO substrate [7]. Similarly, the shape of solid particles partially wetting grain boundaries in solids was studied experimentally by Johnson et al. [8] and theoretically by Siem et al. [9], and the solid–liquid transition of such particles was observed directly by in situ electron microscopy [10]. These
1359-6454/$36.00 Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2010.12.051
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studies investigated the local equilibrium of a solid particle with a solid surface or interface. A simplified geometry to study the junction of a solid particle with a solid surface is offered by a wedge-shaped film on a substrate because it essentially reduces the problem to two dimensions. The morphological evolution of an isotropic wedge-shaped thin film on an inert substrate has been investigated theoretically by Wong et al. [11], who found that during thermal annealing, thin films with a non-equilibrium contact angle rearrange in order to attain local equilibrium. This configuration remains self-similar as it grows in scale via surface diffusion at a rate proportional to t1/4. However, no experimental studies of this effect have been reported, nor have there been any observations on the effect of spreading/retracting of liquid or solid particles on the microstructure and morphology of the substrate. In their present form, the models also do not account for anisotropy. Furthermore, if the substrate is sufficiently thin, its microstructure may become unstable. For example, a polycrystalline substrate in contact with a solid “droplet” can be subject to abnormal grain growth resulting from a difference in thermal expansion or anisotropy of surface, interface and strain energy [12,13]. In this paper we report an experimental study of the morphological evolution of a single-crystalline Ge wedge on a bicrystalline gold substrate. Our observations document the morphological development of the Ge wedge during thermal annealing, but also demonstrate a significant microstructural instability in the supporting bicrystalline film. We show that the observed phenomena are related to classical grain boundary grooving [14,15] and to the spreading/retraction of a liquid droplet on a deformable substrate [4]. Both processes are driven by capillarity and can be explained using the same phenomenological approach by accounting for the interaction between the wedge and the substrate during microstructural development. 2. Experimental procedure The specimen geometry of interest in this work, a wedge-shaped solid on a plane-parallel thin film, corresponds to a conventional plan-view specimen for transmission electron microscopy (TEM) prepared by dimpling and ion milling from the substrate side only (Fig. 1). To study the morphological evolution at the contact line during ther-
mal annealing we chose thin films of Au on a Ge substrate. However, in this study, as a consequence of the specimen geometry, the Au film takes on the role of the substrate while the Ge forms a thin wedge. This geometry is illustrated schematically in Fig. 1. Thin Au films were grown by physical vapor deposition on single-crystal {0 0 1} Ge substrates [16]. Before deposition, the substrate was submerged for 2 min in a 10% HF solution until the surface became hydrophobic. The thickness of the film was controlled by the mass of Au evaporated from a W boat. The evaporation apparatus was evacuated to a pressure below 2 107 mbar. Prior to deposition, the substrate was held at 280 °C for 45 min, followed by flash deposition. Subsequently, the film was annealed at 200 °C for 2 h in order to remove residual stresses. At 200 °C the mutual solubility of Ge and Au is negligible, thus minimizing the effect of interdiffusion [17]. The microstructure of the Au films was that of a mazed bicrystal, a structure similar to a polycrystal with only two allowed grain orientations that are related to each other by a 90° rotation about their common h1 1 0i surface normal [18]. The grains were strictly columnar with grain boundaries perpendicular to the substrate. Hence all grain boundaries were 90°h1 1 0i tilt boundaries. The Au–Ge phase diagram is a simple binary eutectic with no intermediate phases and a eutectic temperature of 361 °C. To avoid formation of eutectic or metastable phases during ion milling, the specimen holder was cooled by liquid nitrogen. Since the desired specimen geometry required ion milling from the Ge side only, any redeposition of Ge on the Au film was prevented by placing a glass slide on the film side of the holder. After ion milling, specimens were cleaned in a Fischione plasma cleaner. Although it was not possible to control the Ge wedge angle precisely during ion milling, a rough estimate of this angle could be obtained from an observation of interference fringes in an optical microscope. For the samples reported here the macroscopic wedge angle was in the range of 8–15°. The evolution of the morphology at the contact line (see Fig. 1) was studied during in situ annealing in JEOL 200CX and 3010 microscopes at 200 and 300 kV, respectively. Annealing temperatures in the range of 290–340 °C corresponded to homologous temperatures of HAu m ¼ 0:42 0:46 and HGe ¼ 0:47 0:51 and were below the Au– m Ge eutectic point of 361 °C [17]. Images were recorded on film as well as a TV-rate video camera.
contact line contact line Ge Au freestanding Au
Au/Ge
cross section
Fig. 1. Schematic of the sample geometry used to generate a Ge wedge on a Au substrate.
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To obtain 3-D information about the interface morphology and to evaluate contact angles at the triple line, a crosssection slice of the TEM specimen was cut by a focussed ion beam (FIB) (Fig. 1) after determining the exact position of the Au–Au/Ge junction and coating the region of interest with Pt in order to preserve the local morphology and contact angles. The selected region was sliced with a Ga+ ion beam, lifted out, attached to a Cu grid and thinned to electron transparency. Due to the complexity of this procedure only two states were characterized, the initial state prior to annealing and the equilibrated state after annealing for 60 min at 330 °C. Conventional and high-resolution imaging as well as energy-dispersive X-ray spectroscopy (EDS) characterization of these specimens was carried out in a Philips CM200 microscope. 3. Experimental results The morphological evolution of the contact line at the tip of the Ge wedge during in situ annealing in plan view is illustrated in Fig. 2. This contact line can be traced from moire´ fringes in plan-view specimens, since moire´ patterns are due to interference between two overlapping lattices (Fig. 3). The line of contact at the tip of the Ge wedge coincides with the edge of the moire´ pattern. As the Ge wedge retracts, the contact line migrates, as indicated by the receding moire´ fringes. In the initial state prior to the annealing, the “coastline” of this Ge wedge is irregular. During annealing, this initially almost circular junction (outlined in Fig. 2a) migrated over a distance of about 2 lm and transformed into the faceted shape seen in Fig. 2b. These facets are either parallel or perpendicular to the moire´ fringes, i.e. aligned with the h1 1 0i directions of the Ge substrate (Figs. 2b and 3). The migration of the Ge wedge is clearly accompanied by anisotropic and abnormal grain growth in the Au film (Fig. 2b). In the area swept by the receding wedge, Au
Fig. 3. Contact line between freestanding Au and Ge on the Au substrate as delineated by moire´ fringe contrast. In the case of {0 0 1}Ge on a {1 1 0}Au bicrystal, a moire´ pattern is generated by the interference between diffracted beams from {2 2 0}Ge and {0 0 2}Au planes, which are parallel in the epitaxial relationship. The moire´ fringe spacing is dmoire´ = 1/(gGe220–gAu002) = 10.5 nm and the pattern is thus easily resolved under diffraction contrast conditions.
grains are about an order of magnitude larger than elsewhere. The reason for this abnormal grain growth becomes apparent from detailed in situ experiments during annealing, as shown in Fig. 4. Initially, all grains are strictly columnar, but with the onset of wedge migration, grain boundaries attached to the contact line tend to change inclination. While in the rest of the film grains grow at a rate slower than expected for curvature driven grain growth, the migration of the contact line induces grain growth at a much faster rate. Initially, the contact line recedes very fast, but the rate of retraction slows down as the interface aligns parallel to Ge {1 1 0} until the migration effectively comes to a halt.
Fig. 2. Contact line of a circular Ge wedge on a Au film with mazed bicrystal structure. Due to diffraction contrast, the two grain orientations in the Au film appear either black or white. (a) Prior to annealing, the contact line is nearly circular. (b) During annealing for 1 h at 320 °C, the Ge wedge retracts anisotropically, and the contact line displays facets parallel to the {1 1 0} traces of Ge. (c) Evolution of the area swept by migration of the wedge. Different shades of gray correspond to different annealing times.
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Fig. 4. Sequence of images illustrating the attachment of grain boundaries in the Au film to the contact line with the Ge wedge (outlined) moving toward the right. The two grain orientations are seen in light and dark contrast, respectively. The Ge is visible via moire´ fringes, best seen in (d). Grains are columnar and hence grain boundaries are seen edge-on in this plan view. However, where the grain boundaries are attached to the contact line, they change inclination. This is clearly apparent from the abrupt change in projected width of the grain boundary where it meets the Ge junction (A). When a grain boundary detaches from the contact line, it returns to its original columnar orientation (narrow projected width (B)).
In order to characterize the sample geometry in the vicinity of the contact line between the Au film and Ge wedge after the retraction, a cross-section slice was cut by FIB from the plan-view specimen annealed for 60 min at 330 °C (Fig. 5a). For that particular specimen the migration of the Ge wedge slowed and eventually ceased during in situ annealing. The thickness profile of the cross-section is presented in Fig. 5b. At the contact line the Ge wedge ends as a sharp, faceted 35 nm thick step. This is accompanied by formation of a corresponding ridge in the Au film, which covers the blunted tip of the receding Ge wedge. A magnified cross-sectional view of the contact line in Fig. 5c shows the blunted Ge tip to exhibit {1 1 1}, {3 1 1} and {1 0 0} facets. The cross-section shown in Fig. 5 was cut from a planview sample after the Ge wedge had retracted by about 1.75–2.0 lm. From the tracing of the profile thickness in Fig. 5a it is apparent that over this distance, the top surface of the Au film is smoother than the surface that was not swept by the migrating wedge during annealing. By comparison to the cross-section of the annealed sample shown in Fig. 5, the morphology of a cross-section prior to annealing is characterized by a gradual decrease in thickness and the absence of a step at the line of contact. The phenomena described in the preceding section were studied in the temperature range of 290–340 °C, where the
process was sufficiently rapid to cover more than 1 lm in 1 h (see Fig. 2). Migration of the interface was also observed at temperatures as low as 225 °C, albeit with significantly slower kinetics. 4. Discussion To understand the solid-state dewetting observed in this study we use the isotropic model [11] as a framework. The model predicts that a linear wedge retracts at a rate that is controlled by surface diffusion in the early stage and by volume diffusion in the later stage of dewetting. In our case, the wedge geometry has axial symmetry, the interface energies and migration rates are strongly anisotropic, and the substrate is a bicrystal with columnar grain boundaries. These factors lead to a number of additional features that affect the kinetics and mechanisms of the process. The effect of crystalline anisotropy is clearly apparent from Fig. 2c, which shows how the wedge evolves from an initially circular shape toward a strongly anisotropic faceted shape. The alignment of facets parallel to h1 1 0iGe is consistent with the reported tendency of Ge monolayer domain growth in (0 0 1)Ge orientation to form step and island edges parallel to the h1 1 0iGe direction [19,20]. In situ observations of the contact line migration at higher magnification, as manifested by the disappear-
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Fig. 5. (a) Collage of 30 individual micrographs outlining a cross-section of the annealed plan-view sample. Under these imaging conditions, the Au substrate appears black and the Ge wedge white. The curvature of the Au substrate is due to residual stresses. Note how the blunted tip of the Ge wedge is covered by Au, as illustrated in the contracted profile tracing in (b). Note that the change in profile thickness appears exaggerated on the plot, since the vertical scale is expanded by an order of magnitude compared to the horizontal scale. (c) Cross-section view of the Ge wedge and supporting Au film in the vicinity of the contact line (DF image, g = {2 2 0}Ge).
ance of the moire´ fringes, were found to display the same anisotropy on a local scale. By measuring the relative rates of motion in different crystallographic directions, the h1 0 0iGe direction is found to move about 1.3–1.7 times faster than the h1 1 0iGe direction. This means that at steady state no intermediate orientations would be stable, and all junction lines would align along h1 1 0i directions. On the microscopic level, the Ge wedge does not retract monotonically. Fig. 2c shows a superposition of outlines of the area swept by the contact line from images recorded during in situ observation at 320 °C, with gray levels corresponding to the different annealing times. This superposition clearly shows that portions of the contact line are temporarily halted, but when the line becomes unpinned, it triggers a cascade-like motion in its vicinity. Similar effects were reported in other capillarity-driven phenomena such as grain boundaries detaching from thermal grooves [15,21] or the motion of a liquid droplet on a deformable substrate [4]. An example of such a sudden motion in the wedge retraction is seen in the image sequence in Fig. 4. On the macroscopic level, the retraction of the Ge wedge is characterized by initially rapid kinetics, which slow down with time until the motion effectively stops. The mass transport mechanisms that are expected to control the kinetics of the interface migration in the temperature range of this study (0.4–0.5 Tm), are expected to follow a power law with exponents n = 1/4 and n = 1/2 for surface and volume
diffusion, respectively [11]. Experimental observations on individual segments of the contact line showed a large variation in the measured rates of motion, due to anisotropy, local pinning and thickness variations resulting from ion beam thinning. To obtain a more accurate measure of the rate of motion, we evaluated the area swept by the interface rather than the distance traversed by individual segments. This approach averages out local variations and yields a more reliable measure of the rate of wedge migration. Fig. 6 shows a typical series of measurements and their analysis. A superposition of tracings from images recorded during in situ observation at 320 °C is shown in Fig. 6a, with gray levels indicating sequential positions of the contact line. The area swept was measured from the traces of the contact line on images recorded during in situ observations in the temperature range 290–340 °C. The corresponding plot of area A swept between successive frames vs. time t is shown in Fig. 6b. To obtain the best powerlaw fit to these data, we plotted the coefficient of determination R2 of a least-squares fit of A / tn to the measured data as a function of exponent n (Fig. 6c). The corresponding curves exhibited steep maxima, resulting in the experimentally determined exponents being highly accurate. Fig. 7 shows that the value of the exponent increases from 0.22 to 0.35 in the temperature range from 290 °C to 340 °C. The error bars illustrate that the rate of migration varied among different specimens from the same bulk sample, even for identical heat treatments. However, it is
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Fig. 6. (a) Traces of the area swept by the receding contact line. Lighter shades correspond to longer annealing times. (b) Plot of migration kinetics. (c) Plot of the coefficient of determination R2 as a function of the exponent n.
Fig. 7. Plot of the experimentally determined values of the power law exponent n for a range of temperatures. Large standard deviations are a consequence of local variations in wedge angle.
clear that the exponent increases with temperature. At low temperature, the experimentally determined exponents are
close to the value predicted for surface diffusion (n = 1/ 4). The rise in the exponent with temperature can be attributed to an increased contribution of volume diffusion (n = 1/2) as the eutectic temperature of 361 °C is approached. However, it was not possible to determine the relative contribution of each diffusion mechanism to the retraction of the wedge because data for surface diffusion of Ge and Au are either unavailable or unreliable, varying by as much as an order of magnitude [22–24]. In addition, interface diffusion may play an increasing role in the later stages of the process as the Au ridge increases in size. Although diffusion data are not available for the Ge–Au interface in our experiment, the process is expected to be anisotropic due to the high crystallographic symmetry (mmm) of the epitaxial orientation relationship between the Ge and the two Au grains. According to the principle of symmetry-dictated extrema [25], the mirror planes and twofold rotation axes of the orientation relationship must be extrema in physical properties, including diffusion. Similarly, surface diffusion in Ge is anisotropic with fast diffusion paths along the h1 1 0i directions [26,27]. These
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anisotropies agree with the observation of anisotropic wedge retraction, which causes an initially circular geometry to develop into a square (Fig. 2). The sides of the square are aligned with symmetry elements of the orientation relationship as well as the direction of fast surface diffusion. The most prominent feature associated with the thin Ge wedge retraction was the abnormal grain growth in the supporting Au film. As seen in Fig. 2, the grains in the part of the film swept by the contact line are an order of magnitude larger than the grains elsewhere in the Au substrate. Since the abnormal grain growth accompanies disappearance of the thinnest sections of the Ge wedge, both processes might be due to the dissolution of Ge in the Au film. The solubility of Ge in Au is 1–2.5 at.% in the temperature range of interest [17]. The interdiffusion of the Ge into Au film could affect the grain boundary structure and enhance mobility. For example, a similar morphology of abnormal grain growth in Y- and Si-doped alumina was found to be due to diffusioninduced grain boundary migration (DIGM) [28]. However, if the incorporation of the Ge into the grain boundaries enhanced their mobility, grain growth should be faster wherever the Au film is in contact with the Ge. It is apparent from Fig. 2b that this is not observed experimentally. In addition, the effect was not restricted to the temperature range of measurable solubility of Ge in Au, but was observed as low as 180 °C, where the solubility is negligible [17]. Furthermore, X-ray microanalysis of the area of the Au film swept by the receding Ge did not show any increase in Ge content relative to the rest of the film, and the morphology of the cross-section did not show evidence of metastable compound formation. Finally, the same phenomenon was also observed for Au films grown on Si substrates [29], although in this temperature range, the Au–Si phase diagram [30] shows no mutual solubility. These experimental findings are clear evidence against DIGM as the underlying cause of the observed phenomenon. Instead, our observations show abnormal grain growth in the Au substrate to be solely associated with the migration of the contact line under the influence of capillary forces. Capillary forces cause retraction of the Ge wedge over large distances in order to establish macroscopic equilibrium, and lead to rearrangements at the wedge tip in order to establish microscopic equilibrium at the contact line. Prior to annealing, the surface geometry at the contact line is not at equilibrium, but is imposed by the geometry of the sample preparation. During annealing, the Ge wedge and Au film undergo significant morphological changes in the vicinity of the contact line. From cross-section samples, we found that in the very initial stages of wedge retraction, a ridge is formed in the Au substrate (Fig. 5), which may lead to establishment of local equilibrium at the junction similar to that observed for liquid droplets spreading/retracting on a deformable substrate [4]. Ridge formation at the triple junction is a consequence of the vertical component of the surface tension acting at the contact line. As in the case of a liquid droplet and grain boundary
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grooves, the shape of the ridge at the tip of the solid wedge is influenced by the mechanism of mass transport leading to the ridge formation. Grain boundary grooves growing under a diffusion-controlled mechanism are characterized by the formation of two humps [14,15], while in the case of a liquid droplet, ridge creation is accompanied by some undercutting below the surface of the substrate at the flanks of the ridge [4]. Our experimental results on the morphological evolution of the migrating solid wedge on the substrate clearly show the formation of a ridge in the supporting Au film, but the undercutting in the Au film is absent (Fig. 5). In the case of a liquid droplet on a deformable substrate, spreading/retracting is dominated by the ridge velocity and size, as the mass transport mechanism is the rate-controlling parameter. Our results show that in case of solids, the establishment of local equilibrium and the wedge retraction introduce microstructural changes in the substrate, which in turn can influence the kinetics of the contact line migration. The ridge formation at the migrating triple line affects the character and motion of grain boundaries in the Au film, which ultimately control the mechanism of the abnormal grain growth. This is illustrated in Fig. 8. When the Au ridge (Fig. 8b) associated with the retracting Ge wedge encounters one of the grain boundaries present in the bicrystalline substrate, the boundary could either extend through the ridge (Fig. 8c) or curve to follow the migrating contact line (Fig. 8d) while remaining pinned at the grain boundary groove at the bottom surface. In both cases, the length of the boundary increases. However, the curved boundary will pull free from its surface groove when it reaches a critical angle [15] and then straighten out to minimize its length (Fig. 8e). This process of grain boundary motion was experimentally observed, demonstrating directly that grain boundaries are dragged by the receding wedge, leading to abnormal grain growth in the Au film. Our observations show that during the initial stages, the grain boundaries in the Au substrate are not affected by the Ge retraction and the associated formation of the Au ridge. However, once the Au ridge has built up to a critical thickness, the boundaries follow the retracting wedge as outlined schematically in Fig. 8. To maintain the mass balance, Au diffuses in from other areas such as asperities on the surface or the edge of the thin foil. This process can be very rapid as demonstrated by observations of local thickness changes in freestanding thin films of Au using weak beam dark-field imaging at 300 °C. A rough estimate of the critical thickness can be obtained from a simple consideration of the total boundary length in a film of thickness T. If the boundary extends through the Au ridge (Fig. 8c) its length is T + DT. If the boundary is dragged to an inclination angle h by the receding Ge wedge, its length is approximately T/cos h. The critical thickness DT at which the boundary pulls free of the surface groove is then given by: DT =T ¼ ð1=cos hg 1Þ:
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a
b
c
d
e
Fig. 8. Model of the interaction of the grain boundary with the migrating contact line due to the ridge formation and subsequent drag of the grain boundary resulting in abnormal grain growth.
The groove angle hg is determined by the balance between surface and grain boundary energies as hg = sin1(cgb/2cs) [15]. From direct observation of cross-section specimens (Fig. 9a), the groove angle at some boundaries was found to be as large as hg 30°. The corresponding critical thickness is DT/T = 0.15. Experimental observations of wedge retraction during thermal annealing support this estimate. As illustrated in Fig. 9, the columnar grain structure of the bicrystal and the crystallographic alignment between the Ge wedge and the Au substrate lend themselves to a particularly useful
form of analysis that provides detailed 3-D information from a 2-D projection. Since the grain boundaries in the Au substrate are strictly normal to the surface, the local substrate thickness can be measured by tilting the sample away from the substrate normal and measuring the projected width of the inclined grain boundaries. This is seen in Fig. 9b) where the sample has been tilted about 24°. In addition, by choosing to tilt the sample around a common plane normal, it is possible to maintain a strong moire´ fringe pattern wherever Ge and Au overlap in projection, as seen at the bottom edge of the micrograph in Fig. 9b. Images in such an orientation clearly show the Ge wedge along with the position and width of the grain boundaries. By recording such images during in situ annealing of these structures it was possible to observe the mechanism of wedge retraction in detail. Fig. 9c and d show a tracing of the projected width of grain boundaries in the Au substrate during Ge wedge retraction at 280 °C. The position of the triple junction is marked by a dashed line. In Fig. 9c all grain boundaries have the same projected width W, given by W = T sin a, where a is the tilt angle used for observation. In Fig. 9d the Ge wedge has retracted toward the bottom of the image. In its wake the grain boundaries have become wider in projection, due to the thickening of the Au substrate as it forms a ridge. The measured boundary width W of about 65 nm at a tilt angle of 24° indicates a film thickness of about 160 nm. The increased width of the boundaries in the area swept by the Ge wedge is indicated by gray level shading in Fig. 9d. This is most apparent in the grain marked with the symbol (+), where the film thickness has increased by about 33 nm due to the Au ridge. This corresponds to the critical thickness since, below this grain, the receding Ge wedge has begun to drag the grain boundaries, as seen from the motion of the grain marked with the symbol (*). Note that below the triple line, the projected grain boundary width remains constant. From these figures it is also clear how the wedge migration causes anomalous grain growth. Many other observations of similar geometries confirm the same behavior as that outlined in Fig. 9. As a dewetting phenomenon, the retraction of the Ge wedge in this system is driven by the balance of surface and interface energies. Unfortunately, there are no data in the literature on the Au/Ge interface energy, and quantification is further impeded by the evident anisotropy of the system (e.g. Fig. 2). However, reports of experimentally observed phenomena related to wetting in the Au–Ge system are in line with our observations of the retracting Ge wedge and its partial coverage by a Au ridge. For example, partial wetting was also observed during metal-mediated crystallization of amorphous Ge on a Au substrate [31], where it was reported that crystalline Ge nucleates at grain boundary grooves in the Au substrate and has a tendency to be buried under a metal layer as Au migrates to the top surface to replace amorphous Ge. Likewise, a study [32] of the early stages of epitaxial growth of Au on [0 0 1] Ge showed that the Ge surface gets covered with a
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Fig. 9. Due to the tilt character of grain boundaries in mazed bicrystal Au films, the film thickness can be determined by measuring the projected grain boundary width of the tilted specimen in a TEM. By tilting around a common diffraction vector (g220Ge | g200Au of grain 1), the area of projected overlap between Ge and grain 1 is visible via moire´ fringes (b). Tracings of such micrographs are shown in (c and d). Wider boundaries, indicating an increased film thickness are denoted by darker shading in (d). The Au–Au/Ge interface is delineated by a dotted line. Comparison of the projected grain boundary width before (c) and after in situ annealing (d) provides information about film thickness changes due to formation of a Au ridge. The grain boundary segment marked by the symbol (+) increases in thickness without changing position. By comparison, the segment marked by the symbol () is dragged by the receding Ge wedge, thus changing position without changing thickness. This indicates the start of abnormal grain growth and shows that there is a critical increase in the film thickness required for grain boundary attachment to the interface and the start of abnormal grain growth.
reconstructed Au monolayer followed by formation of 3-D clusters of [1 1 0]-oriented Au. From our analysis, we can conclude that the formation of a Au ridge which grows in thickness as it continues to partially wet the receding Ge wedge is responsible for the anomalous grain growth associated with the wedge retraction. 5. Summary A detailed study of the morphological evolution of an anisotropic thin solid Ge wedge on a deformable Au substrate with bicrystalline structure has been conducted using in situ electron microscopy. The driving force for the
observed wedge retraction was due to capillarity acting on the contact line. On the global scale, shape evolution was controlled kinetically, with a growth exponent of 0.2 at low temperature, close to the value of 1/4 expected for surface diffusion control, and increasing to 0.35 at higher temperature. On the local scale, the process was highly anisotropic and associated with anomalous grain growth in the bicrystalline Au substrate. The key to this behavior was the formation of a Au ridge covering the front of the retracting Ge wedge, discovered by observation of crosssections from in situ reacted samples. Dynamic observations of plan-view samples during wedge retraction showed that beyond a critical thickness of about 30 nm this ridge began to drag the grain boundaries in the substrate.
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Acknowledgements This work was performed at the National Center for Electron Microscopy, Lawrence Berkeley National Laboratory, and was supported by the Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under Contract No. DE-AC02-05CH11231. References [1] Eustathopoulos N, Nicholas MG, Drevet B. Wettability at high temperatures. Oxford: Pergamon Press; 1999. [2] Saiz E, Tomsia AP, Cannon RM. Acta Mater 2000;48:4449. [3] Voytovych R, Robaut F, Eustathopoulos N. Acta Mater 2006;54:2205. [4] Saiz E, Tomsia AP, Cannon RM. Acta Mater 1998;46:2349. [5] Winterbottom WL. Acta Metall 1967;15:303. [6] Taylor JE, Cahn JW. J Electron Mater 1988;17:443. [7] Ajayan PM, Marks LD. Nature 1989;338:139. [8] Johnson E, Johansen A, Dahmen U, Chen S, Fuji T. Mater Sci Eng 2001;A304:187. [9] Siem EJ, Carter WC, Chatain D. Philos Mag 2004;84:991. [10] Dahmen U, Hagege S, Faudot F, Radetic T, Johnson E. Philos Mag 2004;84:2651. [11] Wong H, Miksis MJ, Voorhees PW, Davis SH. Acta Mater 1997;45:2477.
[12] Dannenberg R, Stach E, Groza JR, Dresser BJ. Thin Solid Films 2000;379:133. [13] Zhang JM, Xu KW, Ji V. Appl Surf Sci 2002;187:60. [14] Mullins WW. J Appl Phys 1957;28:333. [15] Mullins WW. Acta Metall 1958;6:414. [16] Westmacott KH, Hinderberger S, Dahmen U. Philos Mag A 2001;81:1547. [17] Okamoto H, Massalski TB. Bull of alloy phase diagrams 1984;5:601. [18] Dahmen U, Westmacott KH. Scr Metall 1988;22:1673. [19] Li M, Altman EI. Surf Sci 2003;526:L117. [20] Minoda H, Tanishiro Y, Yamamoto N, Yagi K. Surf Sci 1995;331– 333:913. [21] Dannenberg R, Stach EA, Groza JR, Dresser BJ. Thin Solid Films 2000;370:54. [22] Gobel H, Blanckenhagen PV. Surf Sci 1995;331–333:885. [23] Lin TS, Chung YW. Surf Sci 1989;207:539. [24] Blakeley JM. Introduction to the properties of crystal surfaces. Oxford: Pergamon Press; 1973. [25] Cahn JW, Kalonji G. J Phys Chem Solids 1994;55:1017. [26] Frisch T, Verga A. Phys Rev Lett 2005;94:226102. [27] Myslivecek J, Schelling C, Scha¨ffler F, Springholz G, Smilauer P, Krug J, et al. Surf Sci 2002;520:193. [28] Dillon SJ, Harmer MP. Acta Mater 2007;55:5247. [29] Radetic T, Dahmen U. Unpublished research. [30] Chevalier PY. Thermochem Acta 1989;141:217. [31] Bian B, Tanaka T, Ohkubo T, Hirotsu Y. Philos Mag A 1998;78:157. [32] Wang J, Li M, Altman EI. Surf Sci 2005;596:126.
Acta Materialia 59 (2011) 2481–2490 www.elsevier.com/locate/actamat
Capillarity-driven migration of a thin Ge wedge in contact with a bicrystalline Au film T. Radetic a,1, A.M. Minor a,b, U. Dahmen a,⇑ a b
National Center for Electron Microscopy, Lawrence Berkeley National Lab, Berkeley, CA, USA Department of Materials Science and Engineering, University of California, Berkeley, CA, USA
Received 28 November 2010; received in revised form 25 December 2010; accepted 27 December 2010 Available online 25 January 2011
Abstract We have investigated the retraction of a single-crystalline Ge wedge in epitaxial contact with a bicrystalline Au film using in situ electron microscopy. The rate of retraction was close to that predicted for capillarity-driven surface diffusion, following kinetics proportional to tn, with n = 0.22–0.35, but crystal anisotropy caused migration to be significantly faster along h1 0 0i directions than along h1 1 0i. The bicrystalline Au substrate was not inert, but underwent abnormal grain growth in the area swept by the receding Ge wedge. Cross-sections made from plan-view transmission electron microscopy samples revealed that this was related to ridge formation during the retraction process. In situ observations of the process in an inclined orientation showed direct evidence of substrate grain boundaries being dragged by the receding Ge wedge. The results can be understood in the framework of capillarity models for isotropic solid-state wedges and reactive wetting in high-temperature liquid–solid experiments. Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Dewetting; Capillarity; Bicrystalline substrate; Wedge migration; TEM characterization
1. Introduction The thermodynamics and kinetics of wetting, including dynamic features such as spreading or retraction of a liquid droplet on an inert solid substrate are well understood in theory and clearly documented experimentally [1]. When the substrate is not inert, the liquid droplet interacts with the substrate, leading to new types of phenomena such as ridging and reactive wetting, which have been investigated more recently. Reactive wetting takes place when the interaction between the liquid droplet and the solid substrate results in the formation of a new compound at the interface [2,3]. Ridging occurs in response to the vertical component ⇑ Corresponding author. Address: NCEM, MS 72, Lawrence Berkeley National Lab, Berkeley, CA 94720, USA. Tel.: +1 510 486 4627; fax: +1 510 486 5888. E-mail address: [email protected] (U. Dahmen). 1 Present address: Faculty of Technology and Metallurgy, University of Belgrade, Belgrade, Serbia.
of a liquid droplet’s surface tension [4] on a deformable substrate. Reactive wetting and ridging have an important effect on the local microscopic and macroscopic contact angle, the evolution toward equilibrium, and the rate at which a liquid droplet spreads or retracts [4]. Wetting in the solid state exhibits similar phenomena, but the capillary behavior of solid particles on a solid substrate is far less developed. Winterbottom proposed a method similar to the Wulff construction to describe the equilibrium configuration of an anisotropic solid particle on a deformable surface [5]. Based on this method Taylor and Cahn predicted the optimum orientation of a crystalline nucleus on an isotropic substrate [6]. In an experimental observation of this effect, Marks and Ajayan used high-resolution electron microscopy to image small Au crystals partially submerged in an MgO substrate [7]. Similarly, the shape of solid particles partially wetting grain boundaries in solids was studied experimentally by Johnson et al. [8] and theoretically by Siem et al. [9], and the solid–liquid transition of such particles was observed directly by in situ electron microscopy [10]. These
1359-6454/$36.00 Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2010.12.051
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studies investigated the local equilibrium of a solid particle with a solid surface or interface. A simplified geometry to study the junction of a solid particle with a solid surface is offered by a wedge-shaped film on a substrate because it essentially reduces the problem to two dimensions. The morphological evolution of an isotropic wedge-shaped thin film on an inert substrate has been investigated theoretically by Wong et al. [11], who found that during thermal annealing, thin films with a non-equilibrium contact angle rearrange in order to attain local equilibrium. This configuration remains self-similar as it grows in scale via surface diffusion at a rate proportional to t1/4. However, no experimental studies of this effect have been reported, nor have there been any observations on the effect of spreading/retracting of liquid or solid particles on the microstructure and morphology of the substrate. In their present form, the models also do not account for anisotropy. Furthermore, if the substrate is sufficiently thin, its microstructure may become unstable. For example, a polycrystalline substrate in contact with a solid “droplet” can be subject to abnormal grain growth resulting from a difference in thermal expansion or anisotropy of surface, interface and strain energy [12,13]. In this paper we report an experimental study of the morphological evolution of a single-crystalline Ge wedge on a bicrystalline gold substrate. Our observations document the morphological development of the Ge wedge during thermal annealing, but also demonstrate a significant microstructural instability in the supporting bicrystalline film. We show that the observed phenomena are related to classical grain boundary grooving [14,15] and to the spreading/retraction of a liquid droplet on a deformable substrate [4]. Both processes are driven by capillarity and can be explained using the same phenomenological approach by accounting for the interaction between the wedge and the substrate during microstructural development. 2. Experimental procedure The specimen geometry of interest in this work, a wedge-shaped solid on a plane-parallel thin film, corresponds to a conventional plan-view specimen for transmission electron microscopy (TEM) prepared by dimpling and ion milling from the substrate side only (Fig. 1). To study the morphological evolution at the contact line during ther-
mal annealing we chose thin films of Au on a Ge substrate. However, in this study, as a consequence of the specimen geometry, the Au film takes on the role of the substrate while the Ge forms a thin wedge. This geometry is illustrated schematically in Fig. 1. Thin Au films were grown by physical vapor deposition on single-crystal {0 0 1} Ge substrates [16]. Before deposition, the substrate was submerged for 2 min in a 10% HF solution until the surface became hydrophobic. The thickness of the film was controlled by the mass of Au evaporated from a W boat. The evaporation apparatus was evacuated to a pressure below 2 107 mbar. Prior to deposition, the substrate was held at 280 °C for 45 min, followed by flash deposition. Subsequently, the film was annealed at 200 °C for 2 h in order to remove residual stresses. At 200 °C the mutual solubility of Ge and Au is negligible, thus minimizing the effect of interdiffusion [17]. The microstructure of the Au films was that of a mazed bicrystal, a structure similar to a polycrystal with only two allowed grain orientations that are related to each other by a 90° rotation about their common h1 1 0i surface normal [18]. The grains were strictly columnar with grain boundaries perpendicular to the substrate. Hence all grain boundaries were 90°h1 1 0i tilt boundaries. The Au–Ge phase diagram is a simple binary eutectic with no intermediate phases and a eutectic temperature of 361 °C. To avoid formation of eutectic or metastable phases during ion milling, the specimen holder was cooled by liquid nitrogen. Since the desired specimen geometry required ion milling from the Ge side only, any redeposition of Ge on the Au film was prevented by placing a glass slide on the film side of the holder. After ion milling, specimens were cleaned in a Fischione plasma cleaner. Although it was not possible to control the Ge wedge angle precisely during ion milling, a rough estimate of this angle could be obtained from an observation of interference fringes in an optical microscope. For the samples reported here the macroscopic wedge angle was in the range of 8–15°. The evolution of the morphology at the contact line (see Fig. 1) was studied during in situ annealing in JEOL 200CX and 3010 microscopes at 200 and 300 kV, respectively. Annealing temperatures in the range of 290–340 °C corresponded to homologous temperatures of HAu m ¼ 0:42 0:46 and HGe ¼ 0:47 0:51 and were below the Au– m Ge eutectic point of 361 °C [17]. Images were recorded on film as well as a TV-rate video camera.
contact line contact line Ge Au freestanding Au
Au/Ge
cross section
Fig. 1. Schematic of the sample geometry used to generate a Ge wedge on a Au substrate.
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To obtain 3-D information about the interface morphology and to evaluate contact angles at the triple line, a crosssection slice of the TEM specimen was cut by a focussed ion beam (FIB) (Fig. 1) after determining the exact position of the Au–Au/Ge junction and coating the region of interest with Pt in order to preserve the local morphology and contact angles. The selected region was sliced with a Ga+ ion beam, lifted out, attached to a Cu grid and thinned to electron transparency. Due to the complexity of this procedure only two states were characterized, the initial state prior to annealing and the equilibrated state after annealing for 60 min at 330 °C. Conventional and high-resolution imaging as well as energy-dispersive X-ray spectroscopy (EDS) characterization of these specimens was carried out in a Philips CM200 microscope. 3. Experimental results The morphological evolution of the contact line at the tip of the Ge wedge during in situ annealing in plan view is illustrated in Fig. 2. This contact line can be traced from moire´ fringes in plan-view specimens, since moire´ patterns are due to interference between two overlapping lattices (Fig. 3). The line of contact at the tip of the Ge wedge coincides with the edge of the moire´ pattern. As the Ge wedge retracts, the contact line migrates, as indicated by the receding moire´ fringes. In the initial state prior to the annealing, the “coastline” of this Ge wedge is irregular. During annealing, this initially almost circular junction (outlined in Fig. 2a) migrated over a distance of about 2 lm and transformed into the faceted shape seen in Fig. 2b. These facets are either parallel or perpendicular to the moire´ fringes, i.e. aligned with the h1 1 0i directions of the Ge substrate (Figs. 2b and 3). The migration of the Ge wedge is clearly accompanied by anisotropic and abnormal grain growth in the Au film (Fig. 2b). In the area swept by the receding wedge, Au
Fig. 3. Contact line between freestanding Au and Ge on the Au substrate as delineated by moire´ fringe contrast. In the case of {0 0 1}Ge on a {1 1 0}Au bicrystal, a moire´ pattern is generated by the interference between diffracted beams from {2 2 0}Ge and {0 0 2}Au planes, which are parallel in the epitaxial relationship. The moire´ fringe spacing is dmoire´ = 1/(gGe220–gAu002) = 10.5 nm and the pattern is thus easily resolved under diffraction contrast conditions.
grains are about an order of magnitude larger than elsewhere. The reason for this abnormal grain growth becomes apparent from detailed in situ experiments during annealing, as shown in Fig. 4. Initially, all grains are strictly columnar, but with the onset of wedge migration, grain boundaries attached to the contact line tend to change inclination. While in the rest of the film grains grow at a rate slower than expected for curvature driven grain growth, the migration of the contact line induces grain growth at a much faster rate. Initially, the contact line recedes very fast, but the rate of retraction slows down as the interface aligns parallel to Ge {1 1 0} until the migration effectively comes to a halt.
Fig. 2. Contact line of a circular Ge wedge on a Au film with mazed bicrystal structure. Due to diffraction contrast, the two grain orientations in the Au film appear either black or white. (a) Prior to annealing, the contact line is nearly circular. (b) During annealing for 1 h at 320 °C, the Ge wedge retracts anisotropically, and the contact line displays facets parallel to the {1 1 0} traces of Ge. (c) Evolution of the area swept by migration of the wedge. Different shades of gray correspond to different annealing times.
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Fig. 4. Sequence of images illustrating the attachment of grain boundaries in the Au film to the contact line with the Ge wedge (outlined) moving toward the right. The two grain orientations are seen in light and dark contrast, respectively. The Ge is visible via moire´ fringes, best seen in (d). Grains are columnar and hence grain boundaries are seen edge-on in this plan view. However, where the grain boundaries are attached to the contact line, they change inclination. This is clearly apparent from the abrupt change in projected width of the grain boundary where it meets the Ge junction (A). When a grain boundary detaches from the contact line, it returns to its original columnar orientation (narrow projected width (B)).
In order to characterize the sample geometry in the vicinity of the contact line between the Au film and Ge wedge after the retraction, a cross-section slice was cut by FIB from the plan-view specimen annealed for 60 min at 330 °C (Fig. 5a). For that particular specimen the migration of the Ge wedge slowed and eventually ceased during in situ annealing. The thickness profile of the cross-section is presented in Fig. 5b. At the contact line the Ge wedge ends as a sharp, faceted 35 nm thick step. This is accompanied by formation of a corresponding ridge in the Au film, which covers the blunted tip of the receding Ge wedge. A magnified cross-sectional view of the contact line in Fig. 5c shows the blunted Ge tip to exhibit {1 1 1}, {3 1 1} and {1 0 0} facets. The cross-section shown in Fig. 5 was cut from a planview sample after the Ge wedge had retracted by about 1.75–2.0 lm. From the tracing of the profile thickness in Fig. 5a it is apparent that over this distance, the top surface of the Au film is smoother than the surface that was not swept by the migrating wedge during annealing. By comparison to the cross-section of the annealed sample shown in Fig. 5, the morphology of a cross-section prior to annealing is characterized by a gradual decrease in thickness and the absence of a step at the line of contact. The phenomena described in the preceding section were studied in the temperature range of 290–340 °C, where the
process was sufficiently rapid to cover more than 1 lm in 1 h (see Fig. 2). Migration of the interface was also observed at temperatures as low as 225 °C, albeit with significantly slower kinetics. 4. Discussion To understand the solid-state dewetting observed in this study we use the isotropic model [11] as a framework. The model predicts that a linear wedge retracts at a rate that is controlled by surface diffusion in the early stage and by volume diffusion in the later stage of dewetting. In our case, the wedge geometry has axial symmetry, the interface energies and migration rates are strongly anisotropic, and the substrate is a bicrystal with columnar grain boundaries. These factors lead to a number of additional features that affect the kinetics and mechanisms of the process. The effect of crystalline anisotropy is clearly apparent from Fig. 2c, which shows how the wedge evolves from an initially circular shape toward a strongly anisotropic faceted shape. The alignment of facets parallel to h1 1 0iGe is consistent with the reported tendency of Ge monolayer domain growth in (0 0 1)Ge orientation to form step and island edges parallel to the h1 1 0iGe direction [19,20]. In situ observations of the contact line migration at higher magnification, as manifested by the disappear-
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Fig. 5. (a) Collage of 30 individual micrographs outlining a cross-section of the annealed plan-view sample. Under these imaging conditions, the Au substrate appears black and the Ge wedge white. The curvature of the Au substrate is due to residual stresses. Note how the blunted tip of the Ge wedge is covered by Au, as illustrated in the contracted profile tracing in (b). Note that the change in profile thickness appears exaggerated on the plot, since the vertical scale is expanded by an order of magnitude compared to the horizontal scale. (c) Cross-section view of the Ge wedge and supporting Au film in the vicinity of the contact line (DF image, g = {2 2 0}Ge).
ance of the moire´ fringes, were found to display the same anisotropy on a local scale. By measuring the relative rates of motion in different crystallographic directions, the h1 0 0iGe direction is found to move about 1.3–1.7 times faster than the h1 1 0iGe direction. This means that at steady state no intermediate orientations would be stable, and all junction lines would align along h1 1 0i directions. On the microscopic level, the Ge wedge does not retract monotonically. Fig. 2c shows a superposition of outlines of the area swept by the contact line from images recorded during in situ observation at 320 °C, with gray levels corresponding to the different annealing times. This superposition clearly shows that portions of the contact line are temporarily halted, but when the line becomes unpinned, it triggers a cascade-like motion in its vicinity. Similar effects were reported in other capillarity-driven phenomena such as grain boundaries detaching from thermal grooves [15,21] or the motion of a liquid droplet on a deformable substrate [4]. An example of such a sudden motion in the wedge retraction is seen in the image sequence in Fig. 4. On the macroscopic level, the retraction of the Ge wedge is characterized by initially rapid kinetics, which slow down with time until the motion effectively stops. The mass transport mechanisms that are expected to control the kinetics of the interface migration in the temperature range of this study (0.4–0.5 Tm), are expected to follow a power law with exponents n = 1/4 and n = 1/2 for surface and volume
diffusion, respectively [11]. Experimental observations on individual segments of the contact line showed a large variation in the measured rates of motion, due to anisotropy, local pinning and thickness variations resulting from ion beam thinning. To obtain a more accurate measure of the rate of motion, we evaluated the area swept by the interface rather than the distance traversed by individual segments. This approach averages out local variations and yields a more reliable measure of the rate of wedge migration. Fig. 6 shows a typical series of measurements and their analysis. A superposition of tracings from images recorded during in situ observation at 320 °C is shown in Fig. 6a, with gray levels indicating sequential positions of the contact line. The area swept was measured from the traces of the contact line on images recorded during in situ observations in the temperature range 290–340 °C. The corresponding plot of area A swept between successive frames vs. time t is shown in Fig. 6b. To obtain the best powerlaw fit to these data, we plotted the coefficient of determination R2 of a least-squares fit of A / tn to the measured data as a function of exponent n (Fig. 6c). The corresponding curves exhibited steep maxima, resulting in the experimentally determined exponents being highly accurate. Fig. 7 shows that the value of the exponent increases from 0.22 to 0.35 in the temperature range from 290 °C to 340 °C. The error bars illustrate that the rate of migration varied among different specimens from the same bulk sample, even for identical heat treatments. However, it is
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Fig. 6. (a) Traces of the area swept by the receding contact line. Lighter shades correspond to longer annealing times. (b) Plot of migration kinetics. (c) Plot of the coefficient of determination R2 as a function of the exponent n.
Fig. 7. Plot of the experimentally determined values of the power law exponent n for a range of temperatures. Large standard deviations are a consequence of local variations in wedge angle.
clear that the exponent increases with temperature. At low temperature, the experimentally determined exponents are
close to the value predicted for surface diffusion (n = 1/ 4). The rise in the exponent with temperature can be attributed to an increased contribution of volume diffusion (n = 1/2) as the eutectic temperature of 361 °C is approached. However, it was not possible to determine the relative contribution of each diffusion mechanism to the retraction of the wedge because data for surface diffusion of Ge and Au are either unavailable or unreliable, varying by as much as an order of magnitude [22–24]. In addition, interface diffusion may play an increasing role in the later stages of the process as the Au ridge increases in size. Although diffusion data are not available for the Ge–Au interface in our experiment, the process is expected to be anisotropic due to the high crystallographic symmetry (mmm) of the epitaxial orientation relationship between the Ge and the two Au grains. According to the principle of symmetry-dictated extrema [25], the mirror planes and twofold rotation axes of the orientation relationship must be extrema in physical properties, including diffusion. Similarly, surface diffusion in Ge is anisotropic with fast diffusion paths along the h1 1 0i directions [26,27]. These
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anisotropies agree with the observation of anisotropic wedge retraction, which causes an initially circular geometry to develop into a square (Fig. 2). The sides of the square are aligned with symmetry elements of the orientation relationship as well as the direction of fast surface diffusion. The most prominent feature associated with the thin Ge wedge retraction was the abnormal grain growth in the supporting Au film. As seen in Fig. 2, the grains in the part of the film swept by the contact line are an order of magnitude larger than the grains elsewhere in the Au substrate. Since the abnormal grain growth accompanies disappearance of the thinnest sections of the Ge wedge, both processes might be due to the dissolution of Ge in the Au film. The solubility of Ge in Au is 1–2.5 at.% in the temperature range of interest [17]. The interdiffusion of the Ge into Au film could affect the grain boundary structure and enhance mobility. For example, a similar morphology of abnormal grain growth in Y- and Si-doped alumina was found to be due to diffusioninduced grain boundary migration (DIGM) [28]. However, if the incorporation of the Ge into the grain boundaries enhanced their mobility, grain growth should be faster wherever the Au film is in contact with the Ge. It is apparent from Fig. 2b that this is not observed experimentally. In addition, the effect was not restricted to the temperature range of measurable solubility of Ge in Au, but was observed as low as 180 °C, where the solubility is negligible [17]. Furthermore, X-ray microanalysis of the area of the Au film swept by the receding Ge did not show any increase in Ge content relative to the rest of the film, and the morphology of the cross-section did not show evidence of metastable compound formation. Finally, the same phenomenon was also observed for Au films grown on Si substrates [29], although in this temperature range, the Au–Si phase diagram [30] shows no mutual solubility. These experimental findings are clear evidence against DIGM as the underlying cause of the observed phenomenon. Instead, our observations show abnormal grain growth in the Au substrate to be solely associated with the migration of the contact line under the influence of capillary forces. Capillary forces cause retraction of the Ge wedge over large distances in order to establish macroscopic equilibrium, and lead to rearrangements at the wedge tip in order to establish microscopic equilibrium at the contact line. Prior to annealing, the surface geometry at the contact line is not at equilibrium, but is imposed by the geometry of the sample preparation. During annealing, the Ge wedge and Au film undergo significant morphological changes in the vicinity of the contact line. From cross-section samples, we found that in the very initial stages of wedge retraction, a ridge is formed in the Au substrate (Fig. 5), which may lead to establishment of local equilibrium at the junction similar to that observed for liquid droplets spreading/retracting on a deformable substrate [4]. Ridge formation at the triple junction is a consequence of the vertical component of the surface tension acting at the contact line. As in the case of a liquid droplet and grain boundary
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grooves, the shape of the ridge at the tip of the solid wedge is influenced by the mechanism of mass transport leading to the ridge formation. Grain boundary grooves growing under a diffusion-controlled mechanism are characterized by the formation of two humps [14,15], while in the case of a liquid droplet, ridge creation is accompanied by some undercutting below the surface of the substrate at the flanks of the ridge [4]. Our experimental results on the morphological evolution of the migrating solid wedge on the substrate clearly show the formation of a ridge in the supporting Au film, but the undercutting in the Au film is absent (Fig. 5). In the case of a liquid droplet on a deformable substrate, spreading/retracting is dominated by the ridge velocity and size, as the mass transport mechanism is the rate-controlling parameter. Our results show that in case of solids, the establishment of local equilibrium and the wedge retraction introduce microstructural changes in the substrate, which in turn can influence the kinetics of the contact line migration. The ridge formation at the migrating triple line affects the character and motion of grain boundaries in the Au film, which ultimately control the mechanism of the abnormal grain growth. This is illustrated in Fig. 8. When the Au ridge (Fig. 8b) associated with the retracting Ge wedge encounters one of the grain boundaries present in the bicrystalline substrate, the boundary could either extend through the ridge (Fig. 8c) or curve to follow the migrating contact line (Fig. 8d) while remaining pinned at the grain boundary groove at the bottom surface. In both cases, the length of the boundary increases. However, the curved boundary will pull free from its surface groove when it reaches a critical angle [15] and then straighten out to minimize its length (Fig. 8e). This process of grain boundary motion was experimentally observed, demonstrating directly that grain boundaries are dragged by the receding wedge, leading to abnormal grain growth in the Au film. Our observations show that during the initial stages, the grain boundaries in the Au substrate are not affected by the Ge retraction and the associated formation of the Au ridge. However, once the Au ridge has built up to a critical thickness, the boundaries follow the retracting wedge as outlined schematically in Fig. 8. To maintain the mass balance, Au diffuses in from other areas such as asperities on the surface or the edge of the thin foil. This process can be very rapid as demonstrated by observations of local thickness changes in freestanding thin films of Au using weak beam dark-field imaging at 300 °C. A rough estimate of the critical thickness can be obtained from a simple consideration of the total boundary length in a film of thickness T. If the boundary extends through the Au ridge (Fig. 8c) its length is T + DT. If the boundary is dragged to an inclination angle h by the receding Ge wedge, its length is approximately T/cos h. The critical thickness DT at which the boundary pulls free of the surface groove is then given by: DT =T ¼ ð1=cos hg 1Þ:
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a
b
c
d
e
Fig. 8. Model of the interaction of the grain boundary with the migrating contact line due to the ridge formation and subsequent drag of the grain boundary resulting in abnormal grain growth.
The groove angle hg is determined by the balance between surface and grain boundary energies as hg = sin1(cgb/2cs) [15]. From direct observation of cross-section specimens (Fig. 9a), the groove angle at some boundaries was found to be as large as hg 30°. The corresponding critical thickness is DT/T = 0.15. Experimental observations of wedge retraction during thermal annealing support this estimate. As illustrated in Fig. 9, the columnar grain structure of the bicrystal and the crystallographic alignment between the Ge wedge and the Au substrate lend themselves to a particularly useful
form of analysis that provides detailed 3-D information from a 2-D projection. Since the grain boundaries in the Au substrate are strictly normal to the surface, the local substrate thickness can be measured by tilting the sample away from the substrate normal and measuring the projected width of the inclined grain boundaries. This is seen in Fig. 9b) where the sample has been tilted about 24°. In addition, by choosing to tilt the sample around a common plane normal, it is possible to maintain a strong moire´ fringe pattern wherever Ge and Au overlap in projection, as seen at the bottom edge of the micrograph in Fig. 9b. Images in such an orientation clearly show the Ge wedge along with the position and width of the grain boundaries. By recording such images during in situ annealing of these structures it was possible to observe the mechanism of wedge retraction in detail. Fig. 9c and d show a tracing of the projected width of grain boundaries in the Au substrate during Ge wedge retraction at 280 °C. The position of the triple junction is marked by a dashed line. In Fig. 9c all grain boundaries have the same projected width W, given by W = T sin a, where a is the tilt angle used for observation. In Fig. 9d the Ge wedge has retracted toward the bottom of the image. In its wake the grain boundaries have become wider in projection, due to the thickening of the Au substrate as it forms a ridge. The measured boundary width W of about 65 nm at a tilt angle of 24° indicates a film thickness of about 160 nm. The increased width of the boundaries in the area swept by the Ge wedge is indicated by gray level shading in Fig. 9d. This is most apparent in the grain marked with the symbol (+), where the film thickness has increased by about 33 nm due to the Au ridge. This corresponds to the critical thickness since, below this grain, the receding Ge wedge has begun to drag the grain boundaries, as seen from the motion of the grain marked with the symbol (*). Note that below the triple line, the projected grain boundary width remains constant. From these figures it is also clear how the wedge migration causes anomalous grain growth. Many other observations of similar geometries confirm the same behavior as that outlined in Fig. 9. As a dewetting phenomenon, the retraction of the Ge wedge in this system is driven by the balance of surface and interface energies. Unfortunately, there are no data in the literature on the Au/Ge interface energy, and quantification is further impeded by the evident anisotropy of the system (e.g. Fig. 2). However, reports of experimentally observed phenomena related to wetting in the Au–Ge system are in line with our observations of the retracting Ge wedge and its partial coverage by a Au ridge. For example, partial wetting was also observed during metal-mediated crystallization of amorphous Ge on a Au substrate [31], where it was reported that crystalline Ge nucleates at grain boundary grooves in the Au substrate and has a tendency to be buried under a metal layer as Au migrates to the top surface to replace amorphous Ge. Likewise, a study [32] of the early stages of epitaxial growth of Au on [0 0 1] Ge showed that the Ge surface gets covered with a
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Fig. 9. Due to the tilt character of grain boundaries in mazed bicrystal Au films, the film thickness can be determined by measuring the projected grain boundary width of the tilted specimen in a TEM. By tilting around a common diffraction vector (g220Ge | g200Au of grain 1), the area of projected overlap between Ge and grain 1 is visible via moire´ fringes (b). Tracings of such micrographs are shown in (c and d). Wider boundaries, indicating an increased film thickness are denoted by darker shading in (d). The Au–Au/Ge interface is delineated by a dotted line. Comparison of the projected grain boundary width before (c) and after in situ annealing (d) provides information about film thickness changes due to formation of a Au ridge. The grain boundary segment marked by the symbol (+) increases in thickness without changing position. By comparison, the segment marked by the symbol () is dragged by the receding Ge wedge, thus changing position without changing thickness. This indicates the start of abnormal grain growth and shows that there is a critical increase in the film thickness required for grain boundary attachment to the interface and the start of abnormal grain growth.
reconstructed Au monolayer followed by formation of 3-D clusters of [1 1 0]-oriented Au. From our analysis, we can conclude that the formation of a Au ridge which grows in thickness as it continues to partially wet the receding Ge wedge is responsible for the anomalous grain growth associated with the wedge retraction. 5. Summary A detailed study of the morphological evolution of an anisotropic thin solid Ge wedge on a deformable Au substrate with bicrystalline structure has been conducted using in situ electron microscopy. The driving force for the
observed wedge retraction was due to capillarity acting on the contact line. On the global scale, shape evolution was controlled kinetically, with a growth exponent of 0.2 at low temperature, close to the value of 1/4 expected for surface diffusion control, and increasing to 0.35 at higher temperature. On the local scale, the process was highly anisotropic and associated with anomalous grain growth in the bicrystalline Au substrate. The key to this behavior was the formation of a Au ridge covering the front of the retracting Ge wedge, discovered by observation of crosssections from in situ reacted samples. Dynamic observations of plan-view samples during wedge retraction showed that beyond a critical thickness of about 30 nm this ridge began to drag the grain boundaries in the substrate.
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