Thin Solid Films 527 (2013) Contents lists available at SciVerse ScienceDirect. Thin Solid Films

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1 Thin Solid Films 527 (2013) Contents lists available at SciVerse ScienceDirect Thin Solid Films journal homepage: Structure zone model for extreme shadowing conditions S. Mukherjee, D. Gall Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA article info abstract Article history: Received 17 July 2012 Received in revised form 15 October 2012 Accepted 7 November 2012 Available online 15 November 2012 Keywords: Structure zone model Physical vapor deposition Glancing angle deposition Atomic shadowing Surface diffusion Whisker Previously reported data on the microstructure of glancing angle deposited (GLAD) metal layers is used to extend the qualitative arguments of the structure zone model for physical vapor deposition to growth conditions with exacerbated atomic shadowing. At low growth temperatures T s relative to the melting point T m, the microstructural development is governed by atomic shadowing for both normal deposition and GLAD, resulting in fibrous grains with voided boundaries (Zone I). As the homologous growth temperature θ=t s /T m is raised above approximately 0.3, GLAD layers continue to exhibit well separated columns while conventional thin films show dense columnar microstructures (Zone II). θ>0.5 leads to equiaxed grains independent of deposition angle (Zone III). Therefore, strong shadowing during GLAD suppresses Zone II microstructures, causing a direct transition from Zone I to Zone III. GLAD microstructures can be divided into four distinct zones: rods, columns, protrusions, and equiaxed grains: separated self-affine rods form for θbθ c =0.24±0.2, while considerably broader columns develop at θ>θ c, due to exacerbated self-shadowing associated with an increased growth front roughness, causing larger growth exponents. Above θ 0.35, protrusions develop on top of some columns as they capture an overproportionate amount of deposition flux and grow much higher than the surrounding layer. At θ>0.5, diffusion processes dominate over atomic shadowing, leading to faceted rough layers with equiaxed grains. In addition, the large mass transport facilitates the formation of whiskers that form for many metal GLAD layers at θ> Elsevier B.V. All rights reserved. 1. Introduction The microstructure of films deposited by physical vapor deposition (PVD) depends on the processing parameters such as substrate temperature T s [1 5], gas pressure [1,4,6 9], ion bombardment [9 11], impurities [5], deposition geometry [11,12], substrate roughness [13] and substrate rotation [14]. The systematic analysis of the microstructure of films grown by a normal deposition flux led to the development of the structure zone model (SZM) [1,4,15,16], which qualitatively explains the morphology development as a function of adatom mobility controlled by the process parameters. The fundamental physical processes at play during growth are shadowing and surface diffusion [2]. Shadowing depends on the deposition angle and causes preferential deposition on mounds, leading to the formation of a rough, porous, columnar microstructure. On the other hand, diffusion leads to a reduction in porosity and a smoothening of the film surface. It is controlled by T s, ion bombardment, impurities and the material system [1]. The initial SZM and the later revisions explain morphological changes in terms of the interplay between the competing phenomena of shadowing and diffusion, and classify the different film morphologies into zones (I, T, II and III) [1,4,5,15,16] as a function of increasing adatom mobility, while keeping the degree of shadowing constant. Corresponding author. Tel.: ; fax: address: galld@rpi.edu (D. Gall). In contrast, glancing angle deposition (GLAD) [17,18] is a PVD technique where the shadowing effect is purposely exacerbated by a grazing incident angle α>80 of the deposition flux. This leads to the formation of self-affine [19] isolated columnar nanorod structures with a high level of porosity [20] and surface roughness [21] in a wide range of material systems [16,22] including metals [23] and covalently bonded materials [24]. Most research on GLAD is done at low temperatures, so that surface diffusion is kinetically limited and the dominance of atomic shadowing can be exploited to create arrays of nanostructures including straight and slanted pillars [18], springs [25], spirals[26], tubes[27] and branched [28,29] or multi-component nanorods [30,31].The rod width w broadens with height h [28], which is attributed to growth competition [32,33] and is described by a power law scaling relationship [19,34] w h p ; where p is the growth exponent [23,24,35,36] which depends on process parameters including the angle of incidence [21,23,37], the substrate rotation [38 40], substrate patterning [18,32,39,41,42], the material system under consideration [36] and T s [43 45]. Recent studies on the microstructural evolution of GLAD layers at elevated temperatures [46 54] provide a motivation to revisit the fundamental competition between atomic shadowing and surface diffusion. The SZM cannot correctly describe GLAD microstructures because it assumes limited shadowing conditions which do not account for large deposition angles. Conversely, models that describe GLAD microstructural ð1þ /$ see front matter 2012 Elsevier B.V. All rights reserved.

2 S. Mukherjee, D. Gall / Thin Solid Films 527 (2013) features including layer porosity [55,56] and column tilt [57,58] and broadening [19,34] assume negligible or limited surface diffusion and therefore do not account for temperatures that exceed ~1/3 of the melting point. The question arises regarding what layer microstructure is expected at both a high growth temperature and a large deposition angle, that is, for large surface diffusion and strong atomic shadowing. In this article, we review recent experimental work on the temperature dependence of the microstructure of GLAD layers and discuss it within the framework of the SZM. For this purpose, the growth temperature is normalized by the melting point T m of the deposited material, to yield the homologous growth temperature θ=t s /T m.atlowtemperature, GLAD layers consist of high-aspect-ratio rods. Increasing θ leads to a continuous increase in their width. This is exacerbated by anomalous broadening at θ>~0.24, resulting in relatively broad columns. Growth competition at θ>~0.35 yields protrusions that extend above the surface of the surrounding film. At θ>~0.5, considerable mass transport results in approximately equiaxed grains and, for many metals, in the formation of whiskers. In contrast to the structure zone model for normal deposition, GLAD results in highly underdense microstructures up to θ~0.5. That is, there is a direct transition from a Zone I to a Zone III microstructure, while Zone II is suppressed due to the large shadowing length scale that limits the densification through surface diffusion for θ= Experimental data In this section, we summarize and discuss previously reported microstructural data of GLAD layers as a function of T s. The temperature dependence of GLAD microstructures has only relatively recently gained interest. Thus, most data that is discussed in this section has been reported within the last five years and stems primarily from four different research groups, including our own. It includes GLAD layers deposited by sputtering and by evaporation from angles α 80, with typically a continuously rotating substrate such that the net nanostructure growth direction is perpendicular to the substrate surface. The primary focus of this discussion is to understand the impact of increasing surface diffusion, facilitated by increasing θ, on the microstructural development of layers deposited by GLAD. Other deposition parameters, including the angular distribution of the deposition flux as well as growth rate and substrate rotation rate may also affect the microstructure but are, for clarity purposes, not discussed here. Instead, our particular interest is in temperature-induced qualitative changes in the microstructure which are observable for various material systems and scale with the homologous deposition temperature. They are all a direct result of the competition between atomic shadowing and surface diffusion. High temperature GLAD was pioneered by Suzuki et al., [47,48] who reported Al layer microstructures which exhibit rough surfaces, approximately equiaxed grains, and whiskers. They attribute the microstructural evolution to diffusion at elevated temperatures [47] which suppresses the formation of separated columns typical for low-temperature GLAD. Similarly, the formation of whiskers is also facilitated by considerable diffusion [48], and is reported for various other metals including Cu, Ag, Au, Mn, Fe, Co, Ni and Zn deposited at 390 C [49,50]. Comparing the reported micrographs for Al as a function of temperature indicates a transition from a microstructure that is dominated by separated columns at T s =85 C to a continuous layer with whiskers at T s =290 C [48]. This indicates a transition from a shadowing dominated to a diffusion-dominated microstructural development. At an intermediate temperature of T s =180 C, Al layers are porous and exhibit a columnar microstructure. However, their surface is very rough and the columns are of irregular shape, with some columns extending well above the column tips of their neighbors [48], a microstructural feature that we refer to as protrusions [33]. These results are summarized in Fig. 1, which is a plot that includes the microstructural information from all temperature dependent GLAD data discussed in this section. For the case of aluminum deposited by Suzuki et al., the columns and protrusions at T s =85 and 180 C are indicated by symbols c and p at θ=0.38 and 0.49, respectively, while T s 290 C leads to dense layers with equiaxed grains and whiskers, indicatedbyoverlayingsymbols e and w. Due to the relatively low melting point T m =933 K of Al, none of the reported Al GLAD microstructures is described as rods r. The low-temperature rod-microstructure is characterized by vertical rods which are narrower and exhibit a smaller broadening rate than the columns. The transition from rods to columns is due to a transition from a 2D to a 3D island growth mode, as discussed in more detail below. Suzuki et al. also reported the microstructure of Fe deposited by GLAD as a function of T s [50]. They found conventional GLAD columns at T s 300 C and irregular microstructures with protrusions for T s 330 C. In addition, whiskers start to develop above 330 C, indicating that surface diffusion is sufficient for whisker formation at 330 C (θ=0.33), while the columnar microstructure with protrusions suggests that atomic shadowing dominates over surface diffusion in determining the overall microstructural development up to θ~0.44 for Fe [49,50], as indicated in Fig. 1 for the Fe melting point of 1811 K. Deniz et al. [51] studied the microstructure of various metals and oxides deposited by GLAD as a function of T s. They introduced the interesting concept of a threshold temperature Θ T above which no nanostructuring occurs. The deposited layers are considered nanostructured if they consist of nanostructures that are separated by >2 nm and exhibit a height-to-width aspect ratio of ~10 or more. This is a good definition from a practical perspective, as it provides the useful temperature regime over which arrays of distinct GLAD nanostructure arrays can be deposited. In the context of the current discussion, microstructures characterized by rods or columns are considered to be nanostructured,astheyconsistof well-separated structures that exhibit a large height-to-width aspect ratio. In contrast, protrusions and equiaxed grains do not satisfy the nanostructuring definition by Deniz et al., since the width of the protrusions can approach their height, and equiaxed grains have an aspect ratio of ~1 and also exhibit no gap between them. Thus, within the sequence of microstructures with increasing temperature from r to c to p Fig. 1. High-temperature GLAD microstructural data from Refs. [23,32,33,43 54,59] for metallic and non-metallic systems classified into four zones: rods r, columns c, protrusions p, and equiaxed e grains. Microstructures that exhibit whiskers w are also labeled. The y-axis corresponds to the melting point T m and the x-axis shows the homologous deposition temperature θ=t s /T m. Each row of data points is labeled on the right, indicating the material as well as the relevant references. Italic symbols indicate non-metallic systems.

3 160 S. Mukherjee, D. Gall / Thin Solid Films 527 (2013) to e, the threshold temperature Θ T lies at the boundary between c and p. Fig. 1 includes data from Deniz et al. [51] for various metals, Sn, Al, Au, Ru, and W, as well as oxides RuO 2,SnO 2,andWO 3.ForSnandAl, room temperature deposition is already above Θ T, leading to e and p microstructures, respectively. In contrast, room temperature corresponds to θ=0.11 and 0.08 for Ru and W, yielding rods for both of these high-melting point metals. Au was studied as a function of T s. It exhibits columns up to θ=0.32, protrusions from θ= , and equiaxed grains for θ RuO 2, which has a melting point of 1473 K, shows a sequence from r to c to p to e for θ=0.35 to 0.43 to 0.50 to That is, Θ T is between θ= , which is considerably higher than for metals, with Θ T ~0.33. This is attributed to the covalent bonding and the related surface reconstruction, which yields a higher homologous activation energy for surface diffusion (E m /kt m ) [43], and is also consistent with the data for WO 3 and SnO 2, which show columns for all reported temperatures T s 866 K [51], indicating Θ T >0.50 and>0.45, respectively. Fig. 1 shows overlaying c and p symbols for these oxides, as the published micrographs do not clearly indicate if some columns exhibit protrusions. Also, italic symbols are used for these covalently bonded materials, in order to distinguish the data from the majority of metals presented in Fig. 1. Khare et al. has reported GLAD microstructures of Ag and Ge deposited at K [52 54]. Room temperature deposition of Ag, which corresponds to θ=0.24, leads to a columnar microstructure. In contrast, deposition at 573 and 623 K, corresponding to θ=0.46 and 0.50, respectively, results in equiaxed grains with approximately semi-spherical shapes, indicating considerable mass transport and a tendency for dewetting on the higher-surface-energy Si substrate. Such deposition at high temperature also leads to the formation of whiskers, which are preferentially formed when the deposition flux is collimated, likely due to the related higher average deposition angle and/or lower deposition rate. Khare et al. also found that the column width at low temperature can be increased by initial substrate pattering. The effect of patterning prior to GLAD has been studied by various researchers [53,59], and has been found to affect the broadening rate due to the initially lower intercolumnar competition [32,33]. This makes a distinction between r and c microstructures typically less obvious. The micrographs of Ge layers reported by Khare et al. indicate columns for θ= , protrusions for θ=0.47, and equiaxed grains at θ=0.51 [54]. This suggests that Ge exhibits a microstructural trend similar to the metals discussed above, despite the transition from an amorphous to a crystalline microstructure with increasing θ. In addition, they also report an increasing probability for column merging with increasing θ, consistent with previous work from our group on Ta columns which show an increase in the probability for merging from negligible at 473 K to 20% at 973 K [33]. Related work by Patzig et al. on Si shows that the nanostructure width increases from 115 to 140 nm with T s increasing from room temperature to 633 K [46]. The broadening is found to be qualitatively similar for GLAD columns, spirals, and screws, suggesting that an understanding of the temperature effects for GLAD rods/columns can likely be extended to include more complex GLAD nanostructure shapes. This work by Patzig et al. is consistent with data by Karabacak et al., who found an r microstructure and a growth exponent p=0.32 for Si growth at room temperature [23]. This data as well as room temperature data for Cu, Co, and W from the same Ref. [23] are also included in Fig. 1. Our own work on the temperature effects during GLAD has primarily focused on statistically analyzing the nanostructure width distribution for metal layers including Al, Cr, Nb, and Ta [43 45] as well as on growth competition [32,33] and probabilities for column branching and merging [18,29,33,60]. Fig. 2 shows micrographs of typical GLAD nanostructures deposited from an angle of 84 onto continuously rotating Si(001) substrates. The microstructures are comparable to those described and discussed in detail in Refs. [44,45]. Here, they are primarily shown to illustrate the characteristic r, c, p and w microstructural features with increasing θ. The Ta rods in Fig. 2(a) were deposited at room temperature, corresponding to θ=0.09. They have a total height of 500 nm and their width increases with height, following a power law with p=0.43, reaching a width of 100 nm near the top. Increasing T s results in an increase in the width at a given height [43] and a decrease in the broadening rate [44], which is due to a reduction in the growth front roughness and hence a reduced self-shadowing of the nanorods with increasing adatom mobility [45]. However,for metallic systems there exists a critical homologous temperature θ c at which the surface roughness of the growth front increases due to a change from a 2D to a 3D island growth mode. This leads to a discontinuity in the p vs θ curve, that is, p increases steeply at the transition temperature θ c [44,45]. Within the context of this paper, the transition from r to c microstructures is defined by this transition of the growth mode. Accordingly, Fig. 1 includes the data from Cr, Nb, and Ta layers from Ref. [45] for a large range of θ values. Based on the plot, the transition from r to c occurs between θ=0.20 and 0.26 for most metals, which is in good agreement with previously published values for the critical temperature of θ c =0.20±0.03 from Ref. [43] and θ c =0.24±0.02 from Ref. [45]. We note here that the distinction between r and c is in principle rigorous, based on statistical analyses of the nanostructure width vs height data. However, for many studies included in Fig. 1, such detailed data in not available and the classification into r or c microstructures includes considerable uncertainty, as it is based on the observed nanostructure width and apparent broadening rate from published micrographs. Fig. 2(b) shows an example of a c microstructure, from Cr deposited at T s =350 C corresponding to θ=0.29. The columns have a maximum height of 860 nm. They are 2.6 times wider than the Ta rods in Fig. 2(a), at a fixed height of 500 nm. The Cr columns also exhibit stronger broadening, with p=0.53. Based on the argument above, this large p value is attributed to θ>θ c. Increasing the homologous temperature further results in an increasing mass transport on the growth front which causes secondary shadowing instabilities. In particular, a nanostructure may develop a height that is sufficiently above those of its neighbors such that it captures an overproportional fraction of the deposition flux, resulting in exacerbated growth both perpendicular and parallel to the substrate surface. This leads to the development of protrusions which develop on top of columns and may be considerably wider and taller than the columns themselves. For example, we reported a p microstructure for Ta growth at T s =900 C (θ=0.36), where the protrusions are twice as wide and three times as tall as the surrounding columns [33]. The micrograph in Fig. 2(c) shows comparable protrusions, for the case of Nb deposition at T s =850 C, corresponding to θ=0.41. The overall microstructure is columnar, however, with a very rough surface and columns of irregular shape. In particular, the micrograph shows various regular grains that are nm wide and nm tall, but also a few grains with a ten times larger volume and a width and height of 600 and 1000 nm, respectively, exhibiting pointed sharp tops. We refer to these grains as protrusions, as they extend well above the surrounding layer. Similar to the reports by Suzuki et al. discussed above and summarized in Fig. 1, we have also observed the development of a microstructure with equiaxed grains and whiskers for growth temperatures larger than approximately half the melting point. Fig. 2(d) is an example of an e and w microstructure, showing an Al GLAD layer deposited at T s =250 C, corresponding to θ =0.56. This layer has a thickness of 1.2 μm, but shows 1 2 μm wide rod-shaped whiskers that extend 3 10 μm above the layer. The surface is rough with facets that approach the size of the layer thickness, indicating a microstructure with equiaxed grains. 3. Discussion of the structure zone model Fig. 3(a) shows the SZM initially proposed by Movchan and Demchishin (MD) [15] and later revised by Thornton [1] for metallic layers grown by PVD as a function of increasing homologous temperature

4 S. Mukherjee, D. Gall / Thin Solid Films 527 (2013) Fig. 2. Cross-sectional SEM micrographs from Ta, Cr, Nb, and Al GLAD layers deposited with continuous substrate rotation at homologous temperatures θ=t s /T m =0.09, 0.29, 0.41, and 0.56, showing typical microstructural features including (a) rods, (b) columns, (c) protrusions, and (d) equiaxed grains with whiskers. θ=t s /T m. Increasing temperature (or in some cases ion bombardment) causes an increase in the diffusion length scale which results, in turn, in changing microstructures that are divided into 3 Zones I, II and III [15]. Each zone has its unique texture, porosity and range of process parameters [2]. Shadowing controls the film microstructure and texture in Zone I, and the film is columnar with tapered voids between columns [2]. The structure in Zone I has been further classified into Zone Ia, Ib and Ic in an extended SZM [5]. Zone Ia is characterized by ballistic Fig. 3. (a) Structure zone model for thin films deposited by physical vapor deposition with a normal deposition flux [2,15]. The x-axis shows the homologous deposition temperature θ=t s /T m. (b) Corresponding schematic for layers deposited by glancing angle deposition with continuous substrate rotation, showing rods r, columns c, protrusions p, equiaxed grains e, andwhiskers w. growth with a low adatom mobility at low T s that leads to the formation of columnar structures. Zone Ib occurs at low T s but in the presence of ion bombardment, which increases the adatom mobility and leads to densification of the columnar structure. Zone Ic occurs at slightly higher T s, sufficient to cause adatom motion and the formation of crystalline islands. This leads to faceted columnar structures with facets being planes with the lowest crystallographic growth rate [5]. In Zone II, surface diffusion is the leading process that controls morphological evolution, and the film consists of columnar grains with defined dense grain boundaries, faceted top surfaces, and an increased grain width. In Zone III, the microstructure is governed by bulk diffusion, and the microstructure exhibits equiaxed grains. The relative position of the zones in the SZM varies with the deposition parameters and material system under consideration [5]. Thornton, extended the initial MD model by adding the deposition pressure as a parameter to describe the effect of adatom mobility induced by energetic particle bombardment in a sputtering system [2]. In Thornton's model, an additional transition zone T between Zones I and II is included. Films in Zone T exhibit a fibrous texture, as in Zone I, however, they show no voids and domes, due to the additional adatom transport associated with energetic bombardment. Fig. 3(b) is a corresponding schematic, illustrating qualitative changes with increasing homologous deposition temperatures θ of the microstructure of GLAD layers deposited with substrate rotation. It is based on the experimental observations summarized above, which show distinct microstructural features, in particular rods, columns, protrusions, equiaxed grains, and whiskers. At low temperatures, the microstructure is characterized by well separated rods. The rods are self-affine structures with an average width that follows a power law relation with the height as described in Eq. (1) [23,45]. At the zero-temperature limit (θ=0), the growth exponent p tends to an analytical value of 0.5, which is an average of the two in-plane orthogonal exponents during GLAD with a stationery substrate [23]. Also, in the absence of surface diffusion at θ=0, the morphology is material independent and is governed by geometric shadowing alone [43], comparable to Zone Ia in the SZM. Fig. 3(b) also shows some rods that are shorter than their neighbors. Their growth was terminated prematurely due to intercolumnar shadowing competition which has been

5 162 S. Mukherjee, D. Gall / Thin Solid Films 527 (2013) reported to cause rod extinction [32,33], and provides space for broadening of the neighboring rods, i.e. p>0. Increasing θ increases the diffusion length-scale and results in a faceted columnar structure with a high level of porosity, resembling the Zone I structure with a normal incident deposition flux. The higher adatom mobility at higher θ also increases the width of the rods at a given height [43], similar to the increasing columnar width in the SZM. The broadening rate or p decreases with increasing θ, due to a reduction in growth front roughness of individual rods which, in turn, reduces rod self-shadowing. At a critical homologous temperature θ c =0.24±0.02 for metallic systems [45], a change from 2D to 3D island growth mode occurs as the adatoms overcome the Ehrlich Schwoebel barrier [61,62], leading to an increase in the roughness of the nanorod growth fronts. This dramatically increases the self-shadowing and consequently the nanostructure broadening rate, such that we refer to microstructures grown above θ c as columns. The easy observable difference between rods and columns is the width, which is larger for the columns. However, the fundamental difference is their broadening rate with increasing height. This rate is quantified by p, which is 0.39 and 0.80 just below and above θ c for rods and columns, respectively [44,45]. Increasing θ (>θ c ) results in a gradual decrease of p from the anomalous high value at θ c. This is attributed to a decreasing roughness of the growth front with increasing diffusion length. That is, for θ>θ c, the column broadening rate decreases with increasing θ, while the column width at a constant h increases with increasing θ. Increasing θ further to ~0.35 results in the development of protrusions. Protrusions are microstructural features that extend a column above the tips of the neighboring columns. They are typically considerably wider than the columns and exhibit irregular shapes with strong broadening. We attribute the formation of protrusions to the larger diffusion length which causes an increase in the lateral length scale of surface mounds on the growth front of individual columns. This, in turn, leads to a chaotic instability where the surface mound on one column extends vertically and captures an over-proportional fraction of the deposition flux in comparison to the neighboring columns. Consequently, this column will grow at a higher rate than its neighbors and, once its height is clearly above its neighbors, it will exhibit a strong lateral growth rate, leading to strong broadening and the formation of irregularly shaped protrusions. The onset temperature for the formation of protrusions coincides with the threshold temperature for nanostructuring, that has been introduced by Deniz et al. [51]. According to their study and also evident from Fig. 1, the transition from columns to protrusions occurs at θ= for various metals. In contrast, ceramics including RuO 2,WO 3 and SnO 2 exhibit higher threshold temperatures of Θ T = As discussed above, this is related to the ratio of the activation energy for surface diffusion over the melting temperature, which is typically higher for covalently bonded materials than for metals, and is also typically higher for compounds than for pure elements. As θ is increased above 0.5, the surface and/or bulk diffusion length becomes comparable or greater than the length scale for shadowing interactions for any realistic layer thickness. Thus, diffusion starts to dominate the microstructural evolution, causing a transition from a Zone I to a Zone III microstructure, as illustrated in Fig. 3(b). At approximately the same temperature, many metals also form whiskers. Whiskers may nucleate at a crystalline defect or impurity and form due to a not-well-understood strong preferential growth along certain crystalline orientations. While their formation is not well understood, it is clear that they only occur if there is considerable surface and/or bulk mass transport. This is consistent with the observation, also evident in Fig. 1, that they only form at relatively large θ>0.4. Also, based on Refs. [47,48], a large deposition angle is required for their formation. We attribute this to two possible mechanisms: (i) the large surface roughness associated with strong shadowing conditions results in a considerably higher probability for the nucleation of whiskers; or (ii) the growth of whiskers is facilitated by the over-proportionally large fraction of the glancing deposition flux that impinges on whiskers rather than onto the vertical surface. Comparing Fig. 3(a) and (b) indicates that the microstructure for normal deposition [Fig. 3(a)] is similar to that for oblique deposition angles [Fig. 3(b)], for both the low and high temperature limits, but the microstructures qualitatively differ in the intermediate temperature range. We attribute the resemblance at low θ to a dominance of atomic shadowing, irrespective of deposition angle. Therefore, GLAD microstructures at low θ qualitatively resemble a Zone I microstructure, which is underdense and exhibits separated columns, with the quantitative difference being the degree of porosity, which is considerably larger for GLAD. Similarly, we attribute the resemblance at high θ to a dominance of atomic diffusion, irrespective of deposition angle. Consequently, GLAD layers deposited at θ>0.5 show an equiaxed grain structure, similar to a Zone III microstructure, with a noteworthy distinction that GLAD layers have a higher tendency for whisker formation. At intermediate deposition temperatures of approximately 0.3bθb0.5, the deposition angle strongly affects the competition between diffusion and shadowing processes. This leads to qualitatively different microstructures in Fig. 3(a) and (b): for normal deposition, surface diffusion processes densify grain boundaries, leading to a dense columnar Zone II microstructure. In contrast, GLAD causes strong atomic shadowing effects, resulting in underdense microstructures with well separated columns and, particularly at high θ, irregular protrusions. That is, GLAD layers resemble underdense Zone I microstructures for θ up to ~0.5, above which there is a direct transition to a Zone III microstructure. In the context of discussing the competition between shadowing and surface diffusion, we note a fundamental difference in the length scale of these two competing processes: the surface diffusion length is primarily determined by θ. That is, it is constant for given deposition conditions and a given material system. In contrast, atomic shadowing is purely geometric and therefore scales with the length scale of the surface morphological features. Thus, with increasing layer thickness, when both the vertical and lateral length scales of the surface roughness increase, the length scale of atomic shadowing also increases and ultimately dominates over surface diffusion, which has a constant length scale. Therefore, for any given θ, there is a critical layer thickness above which the length scale of atomic shadowing will be larger than that for surface diffusion, leading to a shadowing dominated microstructure. This argument is independent of the deposition angle and suggests that shadowing always wins, as long as the deposition flux has an oblique component and the thickness is sufficiently large. Therefore, the structure zone model in Fig. 3 is, in principle, dependent on the thickness of the deposited layer. However, the realistic layer thicknesses over which a discussion of microstructural development is reasonably useful is also limited by practical aspects. In particular, thin films that are thinner than ~30 nm have a microstructure that is primarily determined by nucleation processes which are not described by the SZM. On the other hand, the range of achievable PVD deposition rates also limits the maximum thickness, with many applications having thicknesses in the ~1 μm range, and almost all thin films being thinner than 100 μm. Thus,thestructurezonemodelinFig. 3 should be considered applicable for thin films with thickness from ~100 nm to ~10 μm, since all data discussed in this manuscript are for layers in that thickness range. A considerable increase in thickness yields, in principle, a shift of transitiontemperatures to smaller θ values. 4. Conclusions The morphology evolution of GLAD layers as a function of increasing substrate temperature is described by four distinct zones: rods, columns, protrusions and equiaxed grains with whiskers. Well separated, selfaffine columnar rods with high aspect ratio grow under conditions of limited surface diffusion. The self-affinity of the rods is manifested by

6 S. Mukherjee, D. Gall / Thin Solid Films 527 (2013) their broadening as a function of their height and is characterized by the growth exponent p. The growth exponent decreases with increasing surface diffusion due to reduction in growth front roughness. At a critical homologous growth temperature θ c =0.24±0.2, the morphology changes from rods to columns, characterized by a higher column width and a discrete increase in p. This transition is driven by an increased growth front roughness at higher θ, leading to exacerbated self-shadowing. Beyond θ=θ T (~0.35 for metals), the morphology exhibits protrusions, which are characterized by their higher column width and low aspect ratio compared to columns. This is attributed to a diffusion-assisted chaotic instability for self-shadowing such that some rods capture an overproportional flux and grow much higher than the surrounding film. The value of Θ T increases for covalently bonded systems to , due to associated higher homologous activation energies for surface diffusion (E m /kt m ). Beyond θ=0.5, surface and bulk diffusion overcome the shadowing length scale, resulting in continuous films with equiaxed grains which also exhibit a high probability for the formation of whiskers. This last morphological transition is equivalent to a direct transition from Zone I to Zone III of the SZM for films deposited from a normal angle. Thus, the development of a Zone II structure, characterized by a dense columnar microstructure and facilitated by considerable surface diffusion, is suppressed during GLAD. Acknowledgments This research was supported by the National Science Foundation, under grant nos and References [1] J.A. Thornton, J. Vac. Sci. Technol. A 11 (1974) 666. [2] J.A. Thornton, Ann. Rev. Mater. Sci. 7 (1977) 239. [3] J.A. Thornton, J. Vac. Sci. Technol. A 4 (1986) [4] R. Messier, A.P. Giri, R.A. Roy, J. Vac. Sci. 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