Islands on TiO2 Nanorod

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Solid-state Dewetting of Gold Aggregates/islands on TiO2 Nanorod Structures Grown by Oblique Angle Deposition Shizhao Liu, and Joel Plawsky Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b03259 • Publication Date (Web): 17 Nov 2017 Downloaded from http://pubs.acs.org on November 21, 2017

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Solid-state Dewetting of Gold Aggregates/islands on TiO2 Nanorod Structures Grown by Oblique Angle Deposition Shizhao Liu and Joel L. Plawsky* The Howard P. Isermann Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, United States

Abstract: A composite film made of a stable, gold nanoparticle (NP) array with well-controlled separation and size atop a TiO2 nanorod film was fabricated via the oblique angle deposition technique (OAD). The fabrication of the nanoparticle array is based on controlled, Rayleigh-instability-induced, solid-state dewetting of as-deposited gold aggregates on the TiO2 nanorods. It was found that the initial spacing between as-deposited gold aggregates along the vapor flux direction should be greater than the TiO2 inter-rod spacing created by 80° OAD in order to control the dewetting and produce NP arrays. A numerical investigation of the process was conducted using a phase-field modeling approach. Simulation results showed coalescence between neighboring gold aggregates is likely to have caused the uncontrolled dewetting in the 80° deposition and this could be circumvented if the initial spacing between gold aggregates is larger than a critical value smin. We also found that TiO2 nanorod tips affect dewetting dynamics differently than planar TiO2. The topology of the tips can induce contact line pinning and an increase in the contact angle along the vapor flux direction to the supported gold aggregates. These two effects are beneficial for the fabrications of monodisperse NPs based on Rayleigh-instability-governed self-assembly of materials, as they help to circumvent the undesired coalescence and facilitate the instability growth on the supported material. The findings uncover the application potential of OAD as a new method to fabricate structured films as template substrates to mediate dewetting. The reported composite films would have uses as optical coatings and photocatalytic systems taking advantage of the ability to combine plasmonic nanostructures within a nanostructured, dielectric film. Key words: oblique angle deposition, phase-field method, solid-state dewetting, Rayleigh instability

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1. Introduction Oblique angle deposition (OAD) is a fabrication technique used in physical vapor depositions (PVD) to engineer thin films composed of spatially-distributed nanocolumnar structures 1, 2, 3. OAD can be conducted in PVD systems such as electron-beam evaporation 4, 5, thermal evaporation 6, 7 and sputtering 8 by tilting the substrate to make the incident vapor flux arrive at oblique angles. The phenomenon enabling OAD, the shadowing effect, is triggered in this way to create voids between initial film nuclei which later grow into separated, nanocolumnar structures 4. The growth of separated nanocolumns is only successful when the deposited atoms have limited mobility 9, 10, 11. This is because unlimited surface diffusion of ad-atoms on the substrate will result in a complete loss of surface area as the film attempts to reduce its free energy. Therefore, nanostructured noble metal films are more challenging to produce than oxides as noble metals generally have high surface diffusivities even at room temperature while oxides have low diffusivities even at elevated temperatures 12, 13 . OAD of noble metals requires strict control of the deposition conditions to suppress surface diffusion 14, and post-deposition treatments which suppress dewetting and sustain the columnar morphology are also necessary 15, 16. For these reasons, very few OAD films with sophisticated nanostructures have been produced using noble metals compared to oxides. Reports of multi-layer stacks of metal and oxide/metal OAD films are even more limited. In contrast, multi-layer oxide OAD films have been extensively reported. Vertical nanorods 17, slanted nanorods 18, zig-zag nanospirals 19, helical nanospirals 20 and many other forms of OAD nanocolumns were easily made from oxides and assembled in a bottom-up manner in a single run of OAD 21, 22, 23. We are motivated to drive the growth of stable, noble metal OAD nanostructures, and combine them with dielectrics in multi-layer stacks. Multi-layer stacks may exhibit unique properties as opposed to individual layers. For example, silver nanoparticle arrays will exhibit much stronger absorption when they are deposited in the vicinity of a continuous silver layer 24 and TiO2 OAD films show a higher photocatalytic activity when they are deposited onto WO3 25. Noble metal nanoparticles (NP) would enhance the local electric field intensity at their resonant frequency 26 and oxide nanocolumnar OAD films are known for their high photocatalytic activity 27. OAD growth of a stable noble metal NP array with well-controlled separation and size on the oxide nanocolumnar OAD films may produce structures with enhanced photocatalytic activity and enhanced, absorptive and reflective, optical properties. 2


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As discussed above, due to the high surface diffusion, the noble metal deposits tend to form large aggregates on the substrate during OAD and those aggregates deform and grow, so we would expect that a properly mediated process for the controlled dewetting of the as-deposited aggregates could be employed to produce a thermodynamically stable NP array on the oxide nanocolumns. A capillary phenomenon appropriate for NP array fabrication, the Rayleigh instability 28, could occur whether the film is in a liquid or solid state. Arising from infinitesimal perturbations developed on the structure’s surface, Rayleigh instability can fragment the structure into a chain of spherical particles spaced with the characteristic wavelength of the fastest growing perturbation. It is known that substrates that support the dewetting materials strongly affect the dynamics of dewetting 29, 30. Failing to dominate the dewetting via a Rayleigh instability mechanism results in large, irregularly-shaped islands instead of periodically distributed spherical NPs 15, 16. The tips of the oxide nanocolumns provide a mechanism for controlled dewetting as they are generally of nanometers in width and quasi-periodic 31 in space. Understanding how these characteristics affect dewetting is critical to the successful fabrication of noble metal NP arrays on OAD nanocolumns. More importantly, the knowledge can be extended to a more general class of template-mediated dewetting, where substrates with periodic surface heterogeneities mediate the dewetting by imposing additional periodic constraints or perturbations besides the characteristic wavelength of the instability 32.OAD has great potential for fabricating such template substrates, as a great variety of structured films with controllable and well-defined column width, periodicity and lattice arrangement have been produced by OAD when combined with pre-deposition seeding 33, 34, 35. However, attention was rarely paid to the interfacial phenomena at the surface of OAD films. OAD fabrication of multi-layered, oxide/metal film stacks, could be broken down into the fabrication of a sequential series of two-layer oxide/metal stacks. Figure 1 shows how we scaled up a two-layer, oxide/metal, stack to a nine-layer stack. The overall film consists of five layers of slanted TiO2 nanorod films interspersed with four layers of gold NP arrays. In this work, we report on the OAD fabrication of a two-layer film stack consisting of a nanometer-sized array of gold NPs with controlled separation and size atop a slanted TiO2 nanorod film. The fabrication was realized by using OAD to grow the TiO2 nanorod substrate and supported gold aggregates as primary structures, followed by rapid thermal annealing (RTA) at high temperatures to accelerate the dewetting and the growth of the Rayleigh instability to fragment the gold aggregates and produce NP arrays. We considered varying levels of initial spacing between gold aggregates (inter-aggregate spacing) in the OAD by controlling the deposition angle. It was observed that for a 20-nm thick gold deposit, 3


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gold NP arrays could be produced using the reported method when the initial inter-aggregate spacing was larger than the spacing created by 80˚ deposition, otherwise irregularly-shaped gold islands with hundreds of nanometers in diameter were formed. To illustrate how the initial inter-aggregate spacing decides the dewetting outcome and to reveal the possible connection between the nanorod tip’s topology and dewetting dynamics, we used phase-field modeling to demonstrate and compare the dynamics of solid-state gold aggregates dewetting on TiO2 nanorod tips versus TiO2 planes. Modeling results show that there exists a critical value of the initial inter-aggregate spacing below which the dewetting aggregates coalesce and suppress the Rayleigh instability, and this spacing threshold is increased when TiO2 nanorods are supporting the gold. Detailed analysis of the modeling results reveals TiO2 nanorod tips affect the dewetting by inducing contact line pinning and increasing contact angle along the vapor flux direction. Contact line pinning helps to circumvent the coalescence and increasing contact angle would increase the growth rate of the instability and also reduce the geometrical threshold for instability onset.

Figure 1. Cross-sectional SEM image of a multi-layer film grown by OAD. The film consists of 9 alternating layers of slanted TiO2 nanorods and gold NP arrays. The scale bar represents 100 nm.

2. Experimental details All films were made in an electron-beam evaporation system (Temescal) using the OAD technique. The chamber was cooled by water to maintain a constant temperature. The evaporation sources of TiO2 and gold were located at the bottom of the chamber, about 30 cm below the substrate. All the films were deposited on silicon 4


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(100) wafers. When OAD is conducted at large deposition angles (the angle between the substrate normal and the incident vapor flux higher than ~80˚), the shadowing effect creates the largest separation between the deposited nanostructures 4. We deposited films at 80°, 85°, 87° and 89°. First, the bottom layer consisting of 180-nm thick, slanted TiO2 nanorods was deposited and then the evaporation source was switched to deposit 20-nm thick gold aggregates onto the tips of the TiO2 nanorods. The deposition rate was kept at ~0.8 nm/s for both the TiO2 and gold depositions. The chamber pressure was in the low 10-5 Torr range for TiO2 deposition and low 10-7 Torr range for gold deposition. No special temperature control was applied to the Si wafer. After the deposition, parts of the samples were cut from the wafer and immediately transferred to the rapid thermal annealer (AG Associates, Heatpulse 610) for thermal treatment at 600°C for 3 minutes under nitrogen. Then, the as-deposited and annealed samples were imaged using a scanning electron microscope (Carl Zeiss, Supra).

3. Results and discussion 3.1. Morphology of the as-deposited and annealed samples Figure 2 shows top-down SEM views of as-deposited (Figure 2a, 2c, 2e and 2g) and annealed (Figure 2b, 2d, 2f and 2h) samples. Gold regions at the top layer, are brighter in color. For the as-deposited samples, spatially-distributed, slanted TiO2 nanorods were formed on the Si wafer, and irregularly-shaped gold aggregates are present on the tips of the nanorods. The slanted TiO2 nanorods are tilted towards the direction of the incident flux and the flux direction is denoted by the arrows in the figures. The shadowing effect led to structured TiO2 nanorods as expected, but due to the anisotropic behavior of the shadowing effect, the spacing between the TiO2 nanorods is significantly higher along the rod tilt direction than perpendicular to it. This could be observed in the SEM images in Figure S1 (see Supporting Information) that show the as-deposited, TiO2 nanorods grew in the form of clusters: a bunch of TiO2 nanorods coalesce perpendicular to the rod tilt direction and form an elongated nanorod chain. This growth phenomenon was referred to as the bundling effect in related studies for OAD growth of different dielectrics and metals 36, 37, 38, 39. An analysis of Figure S1 (see Supporting Information) has shown that the average diameter of TiO2 nanorod is about 15 nm, and the nanorod cluster span hundreds of nanometers in the direction perpendicular to the rod tilt direction. Along the tilt direction of the TiO2 nanorods, the spacing between nanorods, i.e. nanorod clusters, increased as the deposition angle was increased from 80° (Figure 2a) to 89° (Figure 2g) due to the increasingly strong shadowing effect. The shadowing effect was much 5


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less effective for gold. In Figure 2a, 2c, 2e and 2g, the gold exhibits the morphologies associated with diffusion-unlimited OAD 19, 20: the gold ad-atoms formed irregularly-shaped aggregates that covered the elongated top-surface of each TiO2 nanorod cluster. By continuing the gold depositions at the same oblique angles, the as-deposited gold aggregates became separated with spacings nearly equal to those between the TiO2 nanorod clusters underneath. After the RTA treatment, a morphology change occurs. The elongated gold aggregates in the 85° (Figure 2d), 87° (Figure 2f) and 89° (Figure 2h) samples disappear after the RTA treatment. Instead, chains of separated gold NPs are formed on the top-surface of TiO2 nanorod clusters. These nanoparticles are predominantly spherical with some scattered ellipsoidal ones. Globally, a quasi-periodic gold NP array is formed in these three samples. In comparison, in the annealed 80° sample (Figure 2b), irregularly-shaped gold islands up to hundreds of nanometers in diameter are formed, spanning numerous TiO2 nanorod clusters. Neither local, nor global formation of a gold NP array was observed in the 80° sample.

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Figure 2. Top-down view SEM images of the as-deposited (a, c, e, g) and annealed (b, d, f, h) samples. The deposition angle for the samples in image a-b, c-d, e-f and g-h is 80°, 85°, 87°, and 89°, respectively. The arrows denote the tilt direction of TiO2 nanorods (the vapor flux 7


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direction). All scale bars represent 100 nm.

3.2. Phase-field modeling The experimental results show that gold nanoparticle formation is related to the initial spacing between large gold aggregates, such that large gaps between aggregates favor the production of gold NP arrays and small gaps seem to have caused the formation of the large gold islands. A key characteristic of TiO2 nanorod clusters that may also affect the dewetting process is the extent of their top-surface. To clarify the spacing issue, we used the phase-field method to model and compare the dynamics of solid-state gold aggregates evolving on TiO2 nanorod clusters and on continuous TiO2 planes. Large and small initial gaps were imposed between aggregates. Within the framework of the phase-field model, the dewetting dynamics of gold was studied in terms of the morphological evolution of a mixture of gold and air driven by the minimization of the mixture’s total free energy.

3.2.1. Geometrical model of gold aggregates deposited on TiO2 substrates SEM images, like those of Figure 2 show the as-deposited gold aggregates coat the top-surface of TiO2 nanorod clusters. These aggregates appear to meander across the surface but their largest dimension lies along a line perpendicular to the rod tilt direction. In the model, we generalized these features and treated the TiO2 nanorod clusters as a 1D-periodic structure in their tip region. The geometry consists of semi-infinite, tabular TiO2 cuboids periodically separated by air along the rod tilt direction. Exaggerating the dimension of the TiO2 nanorod clusters perpendicular to the tilt direction and neglecting their separation along this direction do not affect the simulation results, as it will be shown in Section 3.3. The geometrical simplification is shown schematically in Figure S2 in Supporting Information. Accordingly, the gold aggregates were simplified as finite cuboids resting on the top-surface of the TiO2 cuboids. In the control study where continuous, planar TiO2 serves as the supporting substrate, only the supporting substrate was replaced and the configuration of the gold cuboids was kept constant. The schematics of the simulation domains are shown in Figure 3. The simulation object is a gold aggregate supported by TiO2. The x-axis and y-axis define the plane formed by the TiO2 supporting layer. In correspondence to Figure S2, the y-axis represents the tilt direction of the TiO2 nanorods and the direction of periodicity, and 8


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x-axis represents the direction along which the TiO2 cuboids are stretching effectively to infinity. The simulation was performed on a unit cell of the periodic structure, which is a quarter segment of a single TiO2-supported gold aggregate. As shown in Figure 3, four boundary planes with symmetric boundary conditions (BCs) imposed, define the simulation domain along x- and y-direction; and along z-direction, the surface of the tip of TiO2 cuboid (or the surface of the TiO2 plane) bounds the domain from the bottom and a hypothetical plane bounds the domain from the top to represent the semi-infinite domain of air above the system.

Figure 3. Three-dimensional schematics illustrating the simulation domain for the system composed of periodic (a) TiO2 nanorod cluster-supported gold aggregates and (b) continuous, planar TiO2 -supported gold aggregates. Symmetric BCs are denoted at boundary planes of application.

The width of the TiO2 cuboid along the x-axis was set to be the nanorod’s diameter, d, which was measured from SEM images. The dimensions of the gold cuboid along the x-, y- and z-axes are described by the aggregate's length L, width W, and height H, where H is the gold film thickness. Though the sharp corners of initial state of the gold is a bit unphysical, we will show later in Section 3.3.1 that within 1 dimensionless time step, the square corners associated with cuboidal gold will transform into rounded cuboids due to the wetting BC imposed at the TiO2 supporting substrates. The separation between the gold cuboids along y-axis is defined by the spacing, s, whose magnitude increases as one changes from the 80˚ deposited substrate to the 89˚ substrate. We created different shaped gold aggregates by varying the length L.

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3.2.2. Model formulation The phase-field model treats the interface as a “diffuse” entity such that it has a finite thickness and so is more appropriately, an “interfacial region”. We defined the order parameter, φ, to distinguish between the air and the gold where φ = 1 denotes pure air, φ = –1 denotes pure gold and –1 < φ < 1 represents the air-gold interface. The motion of the air-gold interface then describes the morphological evolution of the gold aggregates. System components are mixed in the interfacial region and generate free energy. Free energy generated by the mixing between gold and air, gold and TiO2, and air and TiO2 is stored in the interfacial region. We used the Ginzburg-Landau functional to describe the free energy of the mixture per unit volume, F(φ), in this region: F (ϕ ) =

λ  1 2 2  f (ϕ ) + ε ∇ϕ  , 2 ε2  

(1)

where λ is the mixing energy density (J/m), ε is the capillary width (m) indicative of the interfacial thickness, f(φ) represents the bulk energy of the gold and the air, and the second term in Eqn. (1) represents the interface energy. We used a double-well potential form for f(φ): f (ϕ ) =

(

)

2 1 2 ϕ −1 4 .

(2)

The form of f(φ) indicates that φ lies between –1 and 1, the system will tend to separate into regions of pure -1 (gold) and 1(air) about the interfacial region. The term λ/ε2 has the unit of energy per unit volume and its magnitude indicates the volumetric thermal energy at a certain temperature in the interfacial region. If we neglect the thermal energy due to the air molecules, then λ/ε2 is equal to the molar thermal energy of gold, RT, divided by its molar volume, Vm. The mixing energy density, λ, and the capillary width, ε, are also related to the gold surface energy, σ (J/m2), by 40:

σ=

2 2 λ ⋅ 3 ε .

(3)

By solving Eqn. (2) & (3), we obtained the magnitude of ε to be:

ε=

3 2 2

⋅

σVm RT

.

(4)

Taking the first variation of F(φ) with respect to φ gives the chemical potential, µ, of the system. 10


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µ (ϕ ) =

δF (ϕ ) λ = 2 [(ϕ 2 - 1)ϕ − ε 2 ∇ 2ϕ ] δϕ ε .

(5)

Assuming that the diffusion of φ is driven by the gradient of the chemical potential, ▽µ, we arrive at the Cahn-Hilliard equation which describes the minimization of the total free energy of the system: ∂ϕ  γ (ϕ )λ  + ∇ ⋅ − ⋅ ∇ (ϕ 2 - 1)ϕ − ε 2 ∇ 2ϕ  = 0 2 ∂t ε   ,

[

]

(6)

where γ(φ) is the mobility parameter. In the absence of a bulk flow, the flux of φ has no convection contribution. For clarity, we introduced the mobility, M(φ), defined as M(φ) = γ(φ) λ/ε2, and rewrote Eqn. (6) as ∂ϕ + ∇ ⋅ − M (ϕ ) ⋅ ∇ ϕ 2 - 1 ϕ − ε 2 ∇ 2ϕ = 0 . ∂t

{

[(

]}

)

(7)

M(φ) has the unit of area per time so it is a diffusion coefficient in nature, and its magnitude will be a measure of the how quickly gold surface atoms can diffuse at a certain temperature, as well as the phase separation velocity in the phase-field modeling point of view. M(φ) could be chosen from various formulations, but studies 41

have shown an inappropriate choice of M(φ) could change the driving force for the

motion of the interface. In this study, the annealing temperature was well below the melting point of gold, so gold aggregates would remain in the solid-state and the morphology evolution and the interface motion would occur via the surface diffusion of gold atoms only, with no contribution from the bulk diffusion of gold or air. With these concerns, we chose a biquadratic mobility to eliminate any contribution from bulk diffusion 41:

(

)

M (ϕ ) = D s ϕ 2 - 1 , 2

(8)

Here Ds is the surface diffusion coefficient of gold at the system temperature. The physical meaning of M(φ) is apparent: M(φ) vanishes in the bulk gold (φ = –1) and in the air (φ = 1) and is only finite within the interfacial region (–1 < φ < 1). The magnitude of Ds strongly depends on the material and the temperature, and it could be calculated using an Arrhenius representation 12, 42. Increasing the temperature will give a larger Ds and thereby a faster dewetting process. It will take a shorter amount of time for the dewetting to reach the steady state. We supplemented the governing equation by two sets of boundary conditions (BCs). To ensure that the total mass is conserved in the computational domain and that the contact angle of gold on TiO2 always obeys Young’s equation, we imposed a zero-flux BC and a wetting BC at all non-symmetric boundary planes: 11


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n ⋅ ∇µ = 0

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,

(9)

λ n ⋅ ∇ϕ + f w ' (ϕ ) = 0 ,

(10)

Here n is the unit normal vector at the boundary planes pointing inwards the computation domain and fw(φ) is the wall energy function. fw (φ) determines the phase equilibrium at the boundary planes and it would affect the dynamic evolution of contact lines and may lead to undesired wall-layer formation 43. Here we chose a linear-form for fw(φ) since the gold-TiO2 contact angle is very close to π/2 radians 43. f w (ϕ ) = -ωϕ ,

(11)

ω is a constant related to the contact angle at the boundary planes defined by Young’s equation. We defined a characteristic length scale for this surface diffusion process using the thickness of the gold film, H. This choice leads to a characteristic diffusion time scale of H2/Ds. With this choice, we defined the following dimensionless variables and operators: r M (ϕ ) t ~ ~ ~ r = , ∇ = Lc ∇ , τ = 2 , M (ϕ ) = , Lc Ds Lc Ds where r is the position vector and Lc is the characteristic length scale. The dimensional parameters of the gold aggregate, initial inter-aggregate spacing, and width of TiO2 nanorod clusters were also made dimensionless via:

~ d ~ s ~ H ~ L ~ W H = , L= , W = , d = , s = . Lc Lc Lc Lc Lc

Eqn. (7) then becomes:

∂ϕ~ ( r~,τ ) ~  + ∇ ⋅ − 1 − ϕ 2 ∂τ 

(

)

2

ε ~ ⋅ ∇  ϕ 2 - 1 ϕ −    Lc

(

)

2  ~ 2    ∇ ϕ   = 0 .   

(12)

It is readily seen that in the transformed equation, a dimensionless parameter ε/Lc emerges. This is the Cahn number, Cn, and measures the relative magnitude of the interfacial thickness over the characteristic length scale of the system. As the magnitude of ε is known by Eqn. (4), the variation in the magnitude of Cn would reflect the actual dimension of gold aggregates. Substituting Cn into Eqn. (12) and dropping all the tildes gives final 12


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dimensionless governing equation:

{

]}

[

2 ∂ϕ ( r ,τ ) 2 + ∇ ⋅ − (1 − ϕ 2 ) ⋅ ∇ (ϕ 2 - 1)ϕ − C n ∇ 2ϕ = 0 . ∂τ

(13)

3.2.3. Simulation parameters Values of the parameters used in the simulation are given in Table 1. The simulations were performed using finite element methods with a time-dependent, adaptive mesh refinement applied to closely track and resolve the interface motion and composition. Due to the slower dewetting rate of gold aggregates on continuous, planar TiO2 compared to that on nanorod clusters, we set the total computation time to be 650 and 500 dimensionless steps for the planar TiO2 substrates and nanorod cluster substrates, respectively. Table 1. Phase-field modeling parameters

Parameter

Value Physical parameters and constants

Vm, molar volume of gold

1.000*10-5 m3mol-1 44

R, gas constant

8.314 JK-1mol-1

σ, surface energy of gold

1.280 Jm-2 45

Ds, surface self-diffusion coefficient of gold at 873K

4.26*10-16 m2s-1 42

θ, gold-TiO2 contact angle

1.791 rad 45

Experiment parameters and derived values T, absolute annealing temperature

873 K

ε, capillary width

1.875 nm

λ/ε , volumetric thermal energy

7.258*108 Jm-3

Cn, Cahn number (ε/H)

0.094

H, gold aggregate height (gold film thickness)

20 nm

W, gold aggregate width

20 nm

L, gold aggregate length

40 – 280 nm

d, TiO2 nanorod diameter

15 nm

2

3.3. Modeling results and discussion In this section, we present the results of the dewetting simulations. We started the simulation with a large value of the initial inter-aggregate spacing along Y-axis, s, and then gradually reduced s until simulation results indicate aggregate coalescence. We 13


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find there exists a critical value of s above which each gold aggregate will dewet independently to form spaced NPs, and below which the aggregates will coalesce and merge along Y-axis during dewetting. We defined this critical value of s as smin, where the subscript indicates a minimum initial spacing is required to prevent the coalescence.

3.3.1. Dewetting under the initial condition of s > smin The temporal evolution of the morphology of solid-state, cuboid-shaped gold aggregates when s > smin, is shown in Figure 4 and 5 for a TiO2 nanorod cluster substrate and for planar TiO2 substrate, respectively. Results at representative stages are shown. The profile of the gold particles is generated by a contour surface at φ= 0.

Figure 4. Temporal morphology evolution of a TiO2 nanorod cluster-supported gold aggregate 1, 1 and different lengths: (a) = 6, (b) = 9.64 with the initial dimension of and (c) = 14. The tip region of TiO2 nanorod clusters and gold particle surface have been profiled by grey and golden colors respectively. Mirroring the results about YZ-plane at X = 0 and about XZ-plane at Y = 0 gives the full picture of each dewetting scenario.

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Figure 5. Temporal morphology evolution of a gold aggregate supported on continuous, 1, 1 and different lengths: (a) = 6, (b) planar TiO2 with the initial dimension of = 9.86 and (c) = 14. The TiO2 plane and gold NP surface have been profiled by grey and

golden colors respectively. Mirroring the results about YZ-plane at X = 0 and about XZ-plane at Y = 0 gives the full picture of each dewetting scenario.

First, by comparing the results in Figure 4 and 5, we could see when each gold aggregate undergoes dewetting independently to form isolated NPs, the pathway by which the gold rearranges on the surface and the outcome of that rearrangement show a strong dependence on the initial geometry regardless of substrate. There exists a critical value of such that the gold aggregate will only be fragmented into a chain of spherical NPs by the instability if is no smaller than this value (Figure 4a, 4b, 5a and 5b), otherwise the aggregate spheroidizes and a single spherical NP forms at the center of the substrate at X = 0 (Figure 4c and 5c). The magnitude of this critical value is 9.64 for nanorod cluster substrate and 9.86 for planar substrate. The source of perturbations or instability, and the initial-length criterion for the onset of fragmentation are both the result of the “end effect” in finite-length structures 46

, which is not encountered in infinite-length structures. For all structures shown in Figure 4 and 5, we could observe that immediately after the dewetting starts, all the cuboid-shaped gold aggregates imposed with an initial contact angle of

radians

begin to evolve towards the equilibrium contact angle θ and become cylinder-shaped at τ = 1. Subsequently, as the surface atoms at the ends of the cylindrical gold 15


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aggregate are of higher chemical potential compared to those at the center at X= 0, they will migrate from the ends towards the center, making the gold aggregate bulge at its ends and retract towards X = 0. End bulging gives rise to axisymmetric perturbations along X-axis, making the center of the aggregates shorten in radius and form a necking region that connects the bulging ends. However, the simultaneous length retraction eliminates the possibility for perturbations of certain wavelengths to exist. For finite-length, cylinder-shaped structures imposed by axisymmetric perturbations, only perturbation modes of wavelength no smaller than 2πL/kc (L = length scale of the cylinder and kc = cut-off wave number) can grow 47, so a minimum length equal to this critical value must be sustained along X-axis until the growing perturbation modes amplify enough to reduce the radius of the necking region to zero and fragment the aggregate at X = 0. Geometries shorter than the critical value initially retract too fast to meet this condition, so the bulging ends rejoin each other eventually and only one single NP forms at X = 0 (Figure 4c and 5c); whereas longer geometries are able to sustain the required length long enough and yield two spherical NPs from the bulging ends (Figure 4a, 4b, 5a and 5b). We term the fragmented geometries as Rayleigh-unstable, and other geometries as Rayleigh-stable. The simulated dewetting pathways and outcomes in Figure 4 explain the experimental observations in Figure 2d, 2f and 2h, in which a large value of s was experimentally imposed by conducting the depositions at angles higher than 80˚. It was observed in the SEM images that the spaced spherical NPs composing the chains span only the top-surface of individual nanorod clusters. Due to the distributed sizes of the as-deposited gold aggregates, these spherical NPs are likely to be produced from the dewetting of as-deposited gold aggregates free from inter-aggregate coalescence, either via the Rayleigh instability-controlled fragmentation process or the spheroidization process, depending on the initial geometry. Results in Figure 4 and 5 indicate that the topology of the tip of nanorod clusters affects the dewetting dynamics by reducing the critical value, and beyond that, Figure 4a, 4b, 5a and 5b also show that the tip accelerates the rate at which the instability grows in Rayleigh-unstable aggregates. When gold aggregates are dewetting on TiO2 nanorod clusters, instability growth that leads to the fragmentation of the gold progresses much more rapidly. We extract the time of fragmentation event, τf, from all the Rayleigh-unstable gold aggregates and plot the results in Figure 6. It shows for all the Rayleigh-unstable gold aggregates, the dynamics of the instability are accelerated on the TiO2 nanorod cluster substrate, and the acceleration is 12.09%, 15.59% and 20.70% as varies from 14 to 10. 16


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Figure 6. Fragmentation time τf as a function of the initial length of gold aggregates for planar substrate and for nanorod cluster substrate.

These results suggest the tip of TiO2 nanorod cluster destabilizes the supported gold aggregate. When a nanorod cluster is used as the substrate, the destabilizing effect exerted by the tip reduces the geometrical threshold for fragmentation onset and accelerates the fragmentation dynamics. To investigate the tip effect in detail, we analyze and compare the temporal evolution of the TiO2-gold-air contact line along Y-axis for the Rayleigh-unstable gold aggregate with = 14 on different substrates, and plot the results in Figure 7. Contact lines are measured in the planes where the growing perturbation and the resultant spherical NPs are centered. Dynamic contact angles, θd, are also measured from Figure 7 and the results are plotted in Figure 8.

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Figure 7. Temporal migration of the TiO2-gold-air contact line on TiO2 nanorod cluster in the plane of (a) X = 0 and (b) X = 2.92; and on continuous, planar TiO2 in the plane of (c) X = 0 and (d) X = 2.93. Initial aggregate length = 14. Contact lines in (b) at τ = 348 and 349 (fragment) and in (d) at τ = 396 and 397 (fragment) overlap.

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Figure 8. Temporal evolution of the contact angle on continuous, planar TiO2 in the plane of X = 0 and X = 2.93 and on TiO2 nanorod cluster in the plane of X = 0 and X = 2.92. Contact angles are plotted from τ = 1.

Figure 7c and 7d depict the temporal migration of contact line on a featureless planar TiO2 substrate. The contact line migrates towards +Y-direction at X = 2.93 and -Y-direction at X = 0 as dewetting proceeds. Dynamic contact angle θd at X = 2.93 and X = 0 agrees reasonably well with the equilibrium contact angle θ over time, except that θd at X = 0 drops below θ near fragmentation time (see Figure 8). In contrast, Figure 7a and 7b show a different scenario: when the migrating contact line reach the edge of the cluster tip, it is pinned on the edge, generating a θd larger than θ (see Figure 8). The increased contact angle is due to the topology of the tip region of TiO2 nanorod clusters. For the modeled tip in this work, its extent is finite along Y-axis and the edge angle is

radians. According to Gibbs criterion 48, the edge of

the top-surface along X-axis can inhibit the spreading of the gold aggregates along Y-axis by contact line pinning: the contact line will remain pinned for all contact

angles between θ and θ + . Though the actual nanorod tips are unlikely to be sharp

at edges, curved edges obey Gibbs criterion as well 49. In related studies, the effect of increased contact angles on the Rayleigh instability development was studied for infinite-length, cylindrical liquid 50. It was demonstrated by linear stability analysis that the growth rate of the instability will be accelerated if the contact angle is increased. For comparison, we plot the temporal evolution of the contact line in the plane of Y = 0 and focus on dynamics in the necking region at X = 0 in Figure 9. By comparing the speed of radial retraction at X = 0 in the plane of Y = 0 between Figure 9a and Figure 9b, we could find the growth rate of the instability at X = 0 is clearly 19


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accelerated in Figure 9b, which agrees with the results in 50. In summary, we conclude that the topology of the TiO2 nanorod tips could affect the dewetting dynamics. The topology could increase the contact angle of supported material by contact line pinning, which facilitates the growth of Rayleigh instability. Contact lines at additional time steps are shown in Figure S3 of the Supporting Information.

Figure 9. Temporal migration of TiO2-gold-air contact line on (a) continuous, planar TiO2 and (b) TiO2 nanorod cluster. Figures are shown at the plane of Y = 0. Initial aggregate length: = 14.

3.3.2. Dewetting under the initial condition of s = smin When the initial spacing between gold aggregates, s, is reduced to smin, the dewetting dynamics change significantly: coalescence and merging between gold aggregates take place during dewetting and overrides the results from either a growing or decaying Rayleigh instability. This is shown, in Figure 10 and 11, by the sequence 20


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of events leading to the coalescence and merging between neighboring gold aggregates for different substrates and for both stable and unstable gold aggregates. Two stages could be identified in these coalescing cases: independent dewetting and coalescence/merging. The first stage is depicted in Figure 10 by the events at τ = 0 479 (nanorod cluster substrate) and τ = 0 - 554 (planar substrate), and in Figure 11 by the events at τ = 0 - 194 (nanorod cluster substrate) and τ = 0 - 203 (planar substrate). In the first stage, each gold aggregate would evolve independently: they would either fragment (Figure 10) or rearrange to a spheroid (Figure 11) depending on their initial length. At the end of the first stage, the gold aggregates have accomplished initial contact angle equilibrium and intermediate Rayleigh instability development, and are in the process of becoming spheroids as they reach their final equilibrium structures. While the gold particles are evolving towards the final equilibrium structure, they will spread along Y-axis. The first stage of the process ends when spreading particles come into contact with their neighbors along Y-axis The second stage begins with coalescence between neighboring particles, then quickly progresses to merging, and finally to the evolution towards an equilibrium morphology, which is demonstrated to be an infinite cylindrical structure.

Figure 10. Sequence of events leading to the coalescence and merging between (a) TiO2 nanorod cluster-supported and (b) continuous, planar TiO2 -supported gold aggregates with 1, 1 and aggregate length, = 14. smin is 0.900 in (a) and the initial dimension of 0.125 in (b). Mirroring the results about YZ-plane at X = 0 and about XZ-plane at Y = 0 gives the full picture of each dewetting scenario.

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Figure 11. Sequence of events leading to the coalescence and merging between (a) TiO2 nanorod cluster-supported and (b) continuous, planar TiO2-supported gold aggregates with the 1, 1 and aggregate length, = 6. smin is 0.860 in (a) and initial dimension of 1.050 in (b). Mirroring the results about YZ-plane at X = 0 and about XZ-plane at Y = 0 gives the full picture of each dewetting scenario

By comparing the dewetting pathways and outcomes simulated under s = smin with the experimental observation in Figure 2b, where the smallest initial spacing along the vapor flux direction (Y-axis) was created for gold aggregates by conducting the deposition at 80˚, we believe that the coalescence along Y-axis is one of the main mechanisms that results in the formation of the large, irregularly-shaped gold islands after RTA treatment in Figure 2b, in which it is shown that gold islands span hundreds of nanometers and cover numerous TiO2 nanorod clusters. Simulation results in Figure 10 and 11 shows in all the coalescing cases, the final, equilibrium structures are infinite, truncated gold cylinders that span the entire top-surface of both substrates. Though the simplifications we applied for TiO2 nanorod clusters and gold aggregates in model development have caused some deviation between the actual and the simulated dewetted structures, the simulated structures have captured the major characteristics of the large, irregular-shaped islands in Figure 2b. Having shown there is a minimum spacing, smin, that determines the dewetting pathways and outcomes, we show the connection between smin and the constraining effect exerted by the nanorod’s tip. We extract smin for gold aggregates with different initial lengths and substrate types, and plot the results in Figure 12. First, it can be seen that for both substrates, the dependence of smin on is similar. Three regions were identified in the plot: smin first increases with increasing until it reaches a local maximum at = 8; smin decreases with increasing until it reaches a local 22


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minimum at = 10; smin resumes its positive dependence on . This trend could be explained by using the critical initial length to divide the curve into two regions. When is smaller than the critical value, Rayleigh instability decays and a single particle is formed at some point. As larger particles would require a larger s to evolve independently, the smin will increase with increasing volume (length). When reaches the critical value, fragmentation takes place and divides the total volume into halves, which is characterized by a dip in the plot near the critical value. As keeps increasing, smin will again increase with increasing volume (length). Then, by comparing the magnitude of smin between different substrates, we find that given a certain initial length , gold aggregates supported by TiO2 nanorod clusters will always require a shorter initial spacing to prevent coalescence than its counterpart supported by planar TiO2. smin is reduced by about 20% for all simulated geometries. The pinning effect discussed in the previous section could be used to explained the reduction in smin: gold particles produced in the first stage are also subject to the constraining effect exerted by the tip of nanorod cluster, so their spreading along Y-axis is inhibited and smaller smin is needed to prevent the coalescence. From the above results, we conclude that the pinning effect exerted by the TiO2 nanorod tips prevents the inter-particle coalescence to a certain extent, and is therefore beneficial to the fabrication of ordered NP arrays.

Figure 12. Minimum spacing required to prohibit coalescence, smin, as a function of the initial length of gold NP aggregates for the planar substrate and nanorod cluster substrate.

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4. Conclusion In summary, we realized the OAD fabrication of a two-layer film stack for potential optical and sensing applications. The film consists of nanometer-sized gold NP arrays with controlled separation and size at the top and slanted TiO2 nanorods at the bottom. The fabrication is based on controlled, Rayleigh-instability-induced, solid-state dewetting of as-deposited gold aggregates. We demonstrated both experimentally and numerically that the initial spacing between as-deposited gold aggregates along the vapor flux direction determines the fabrication outcome, such that NP arrays can only be produced if the initial spacing between as-deposited gold aggregates is higher than a critical spacing, otherwise inter-aggregate coalescence and merging set in, producing large, irregularly-shaped gold islands. We focused the numerical analysis on the effect of nanorod tip topology on the dewetting dynamics of supported materials, and evaluated the effect by comparing the results with the dewetting dynamics on featureless, planar TiO2. We showed that TiO2 nanorod tips can exert two effects on the supported gold aggregates along the vapor flux direction: contact line pinning and an increase in the contact angle, both of which are beneficial to the fabrication of NP arrays based on controlled, Rayleigh-instability-induced, solid-state dewetting. The former circumvents the undesired coalescence by inhibiting the spreading of the dewetting gold aggregates, which is manifested by a reduction in the critical spacing by about 20% compared to planar TiO2. The latter effect reduces the geometrical threshold for instability onset and accelerates the instability dynamics, though it plays a better role when the inter-aggregate coalescence is not present. It is worth pointing out that, in this paper, the TiO2 nanorod films were fabricated using a basic form of OAD without any templating, so the arrangement of the nanorod films and the uniformity of the nanorod shapes are uncontrolled, and the initial inter-aggregate spacing can be no greater than the spacing produced by 89˚ deposition. However, since pre-deposition seeding can free OAD from these limitations, the results in this work would provide new insights into using OAD films and template substrates to mediating dewetting and achieve desired structures.

Associated Content Supporting Information Additional figures showing the SEM images of as-deposited slanted TiO2 nanorod films grown at different angles and geometry simplifications used in the phase-field 24


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model are given in the Supporting Information.

Author Information Corresponding Author *Email: [email protected]. Notes The authors declare no competing financial interest.

Acknowledgements The authors acknowledge the support by National Science Foundation (grant number: ECCS-1127731).

References 1. Robbie, K.; Brett, M. J. Sculptured thin films and glancing angle deposition: Growth mechanics and applications. Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films 1997, 15 (3), 1460-1465. 2. Robbie, K.; Sit, J. C.; Brett, M. J. Advanced techniques for glancing angle deposition. Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena 1998, 16 (3), 1115-1122. 3. Zhao, Y.; Ye, D.; Wang, G.-C.; Lu, T.-M. In Designing nanostructures by glancing angle deposition, 2003, pp 59-73. 4. Poxson, D. J.; Mont, F. W.; Schubert, M. F.; Kim, J. K.; Schubert, E. F. Quantification of porosity and deposition rate of nanoporous films grown by oblique-angle deposition. Applied Physics Letters 2008, 93 (10), 101914. 5. Colgan, M. J.; Brett, M. J. Field emission from carbon and silicon films with pillar microstructure. Thin Solid Films 2001, 389 (1–2), 1-4. 6. Robbie, K.; Brett, M. J.; Lakhtakia, A. First thin film realization of a helicoidal bianisotropic medium. Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films 1995, 13 (6), 2991-2993. 7. Jen, Y.-J.; Yu, C.-W. Metal and dielectric duality for an aligned Al nanorod array. Applied Physics Letters 2007, 91 (2), 021109. 8. Karabacak, T.; Wang, G.-C.; Lu, T.-M. Physical self-assembly and the nucleation of three-dimensional nanostructures by oblique angle deposition. Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films 2004, 22 (4), 1778-1784. 9. Deniz, D.; Lad, R. J. Temperature threshold for nanorod structuring of metal and oxide films grown by glancing angle deposition. Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films 2011, 29 (1), 011020. 10. Thornton, J. A. High rate thick film growth. Annual review of materials science 1977, 7 (1), 239-260. 11. Thornton, J. A. Influence of apparatus geometry and deposition conditions on the 25


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

structure and topography of thick sputtered coatings. Journal of Vacuum Science and Technology 1974, 11 (4), 666-670. 12. Drechsler, M.; Blackford, B.; Putnam, A.; Jericho, M. A measurement of a surface self-diffusion coefficient by scanning tunneling microscopy. Le Journal de Physique Colloques 1989, 50 (C8), C8-223-C8-228. 13. Nanko, M.; Ishizaki, K. Surface self-diffusivity of TiO 2 under high-pressure gas. Physical Review B 1997, 56 (11), 6965. 14. Barabási, A. L.; Stanley, H. E. Fractal Concepts in Surface Growth; Cambridge University Press: Cambridge, 1995. 15. Ma, L.; Huang, Y.; Hou, M.; Xie, Z.; Zhang, Z. Silver Nanorods Wrapped with Ultrathin Al2O3 Layers Exhibiting Excellent SERS Sensitivity and Outstanding SERS Stability. Scientific Reports 2015, 5, 12890. 16. Bachenheimer, L.; Elliott, P.; Stagon, S.; Huang, H. Enhanced thermal stability of Ag nanorods through capping. Applied Physics Letters 2014, 105 (21), 213104. 17. Horprathum, M.; Eiamchai, P.; Kaewkhao, J.; Chananonnawathorn, C.; Patthanasettakul, V.; Limwichean, S.; Nuntawong, N.; Chindaudom, P. Fabrication of nanostructure by physical vapor deposition with glancing angle deposition technique and its applications. AIP Conference Proceedings 2014, 1617 (1), 7-11. 18. Álvarez, R.; González-García, L.; Romero-Gómez, P.; Rico, V.; Cotrino, J.; González-Elipe, A. R.; Palmero, A. Theoretical and experimental characterization of TiO2 thin films deposited at oblique angles. Journal of Physics D: Applied Physics 2011, 44 (38), 385302. 19. Jiménez-Piqué, E.; González-García, L.; Rico, V. J.; González-Elipe, A. R. Nanoindentation of nanocolumnar TiO2 thin films with single and stacked zig-zag layers. Thin Solid Films 2014, 550, 444-449. 20. van Popta, A. C.; Sit, J. C.; Brett, M. J. Optical properties of porous helical thin films. Appl. Opt. 2004, 43 (18), 3632-3639. 21. Xi, J. Q.; Schubert, M. F.; Kim, J. K.; Schubert, E. F.; Chen, M.; Lin, S.-Y.; LiuW; Smart, J. A. Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection. Nat Photon 2007, 1 (3), 176-179. 22. Sobahan, K. M. A.; Yong Jun, P.; Jin Joo, K.; You Suk, S.; Ji Bum, K.; Chang Kwon, H. Nanostructured optical thin films fabricated by oblique angle deposition. Advances in Natural Sciences: Nanoscience and Nanotechnology 2010, 1 (4), 045005. 23. Park, Y. J.; Sobahan, K. M. A.; Kim, J. J.; Hwangbo, C. K. Linear polarization-discriminatory state inverter fabricated by oblique angle deposition. Opt. Express 2009, 17 (13), 10535-10541. 24. Leitner, A.; Zhao, Z.; Brunner, H.; Aussenegg, F. R.; Wokaun, A. Optical properties of a metal island film close to a smooth metal surface. Appl. Opt. 1993, 32 (1), 102-110. 25. Smith, W.; Zhao, Y. Enhanced Photocatalytic Activity by Aligned WO3/TiO2 Two-Layer Nanorod Arrays. The Journal of Physical Chemistry C 2008, 112 (49), 19635-19641. 26. Hutter, E.; Fendler, J. H. Exploitation of Localized Surface Plasmon Resonance. Advanced Materials 2004, 16 (19), 1685-1706. 26


Page 26 of 29

Page 27 of 29

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27. Riley, M.; Wu, V.; Liu, S.; Gill, W.; Lu, T.-M.; Plawsky, J. Surface area and porosity in obliquely grown photocatalytic titanium dioxide for air purification. Journal of Applied Physics 2014, 115 (17), 174907. 28. Rayleigh, L. On the Stability, or Instability, of certain Fluid Motions. Proceedings of the London Mathematical Society 1879, s1-11 (1), 57-72. 29. Hany, A. E.-S.; Hebert, M. M.; Viola, I. B. The impact of fabrication conditions on the quality of Au nanoparticle arrays on dimpled Ta templates. Nanotechnology 2012, 23 (43), 435602. 30. Sharma, A.; Reiter, G. Instability of Thin Polymer Films on Coated Substrates: Rupture, Dewetting, and Drop Formation. Journal of Colloid and Interface Science 1996, 178 (2), 383-399. 31. Karabacak, T.; Wang, G.-C.; Lu, T.-M. Quasi-periodic nanostructures grown by oblique angle deposition. Journal of Applied Physics 2003, 94 (12), 7723-7728. 32. Altomare, M.; Nguyen, N. T.; Schmuki, P. Templated dewetting: designing entirely self-organized platforms for photocatalysis. Chemical Science 2016, 7 (12), 6865-6886. 33. Ye, D. X.; Karabacak, T.; Lim, B. K.; Wang, G. C.; Lu, T. M. Growth of uniformly aligned nanorod arrays by oblique angle deposition with two-phase substrate rotation. Nanotechnology 2004, 15 (7), 817. 34. Goel, P.; Singh, K.; Singh, J. P. Polarization dependent diffraction from anisotropic Ag nanorods grown on DVD grating templates by oblique angle deposition. RSC Advances 2014, 4 (22), 11130-11135. 35. Huang, Z.; Bai, F. Wafer-scale, three-dimensional helical porous thin films deposited at a glancing angle. Nanoscale 2014, 6 (16), 9401-9409. 36. Kikuo Itoh, F. I., Yoshinori Takahashi, Kei Tsutsumi, Yoshie Noguchi, Kunito Okamoto, Tetsuji Uchiyama and Ienari Iguchi. Columnar Grain Structure in Cobalt Films Evaporated Obliquely at Low Substrate Temperatures. Japanese Journal of Applied Physics 2006, 45, 2534-2538. 37. Brown, T.; Robbie, K. Observations of self-assembled microscale triangular-shaped spikes in copper and silver thin films. Thin Solid Films 2013, 531, 103-112. 38. Kamiya, M.; Hara, K.; Itoh, K.; Okamoto, K.; Hashimoto, T.; Fujiwara, H. Magnetic analysis of the stress in nickel films obliquely deposited by sputtering. Journal of Magnetism and Magnetic Materials 1992, 117 (1), 232-238. 39. Abelmann, L.; Lodder, C. Oblique evaporation and surface diffusion. Thin Solid Films 1997, 305 (1), 1-21. 40. Yue, P.; Feng, J. J.; Liu, C.; Shen, J. I. E. A diffuse-interface method for simulating two-phase flows of complex fluids. Journal of Fluid Mechanics 2004, 515, 293-317. 41. Lee, A. A.; Münch, A.; Süli, E. Sharp-Interface Limits of the Cahn--Hilliard Equation with Degenerate Mobility. SIAM Journal on Applied Mathematics 2016, 76 (2), 433-456. 42. Okkerse, B. Self-Diffusion of Gold. Physical Review 1956, 103 (5), 1246-1249. 43. Huang, J.-J.; Huang, H.; Wang, X. Wetting boundary conditions in numerical simulation of binary fluids by using phase-field method: some comparative studies and 27


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new development. International Journal for Numerical Methods in Fluids 2015, 77 (3), 123-158. 44. Weast, R. C.; Astle, M. J.; Beyer, W. H. CRC handbook of chemistry and physics; CRC press Boca Raton, FL1988; Vol. 69. 45. Sivaramakrishnan, S. Interfacial properties of epitaxial gold nanocrystals supported on rutile titanium dioxide. University of Illinois at Urbana-Champaign2010. 46. Nichols, F. A. On the spheroidization of rod-shaped particles of finite length. Journal of Materials Science 1976, 11 (6), 1077-1082. 47. McCallum, M. S.; Voorhees, P. W.; Miksis, M. J.; Davis, S. H.; Wong, H. Capillary instabilities in solid thin films: Lines. Journal of Applied Physics 1996, 79 (10), 7604-7611. 48. Gibbs, J. W. The scientific papers of J. Willard Gibbs; Longmans, Green and Company1906; Vol. 1. 49. Extrand, C. W.; Moon, S. I. Contact Angles on Spherical Surfaces. Langmuir 2008, 24 (17), 9470-9473. 50. Raymond, L. S.; Eric, L. Capillary instability on a hydrophilic stripe. New Journal of Physics 2009, 11 (7), 075024.

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Islands on TiO2 Nanorod

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