Selective nucleation and self-organized crystallization

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ScienceDirect Progress in Crystal Growth and Characterization of Materials 62 (2016) 252–272 www.elsevier.com/locate/pcrysgrow

Review

Selective nucleation and self-organized crystallization Fei Jia, Di Zhao, Mu Wang * National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China Available online 29 June 2016

Abstract Nucleation is an important step in crystallization, and many self-organized patterns are determined in this process. In this study, after briefly reviewing the fundamentals of nucleation theory, we take a few examples to show the significance of concave-cornermediated nucleation in both self-organized formation of long-range-ordered patterns and in self-assembly of metallic nano wire array. We show that successive concave-corner-mediated nucleation on the growth front is an important mechanism leading to many long-range ordering effects in crystallization. This mechanism can also be applied in fabricating metallic nano wires with specific geometry, including straight metallic wire array with tunable line width and nanowires with periodic structures. © 2016 Elsevier Ltd. All rights reserved. Keywords: heterogeneous nucleation; corner-mediated nucleation; selective nucleation; mechanism of self-organized growth; pattern formation

1. Introduction It is well known that crystals are made of atoms/molecules possessing long-range order. Yet assembly and aggregation of these building blocks follow certain thermodynamic laws, which decide how a nucleus is formed and the crystal is developed. Historical record shows that Gibbs realized in later 1920s that the formation of a nucleus from the ambient phase requires the appearance of small clusters of building blocks from a supersaturated environment. Although the modeling was a bit oversimplified, it was a significant step toward the understanding of the transitions between different states of aggregation. Now we understand that when the embryo of the new phase is small, the surface-to-volume energy ratio turns out to be large compared with that of macroscopic entities. From this point of view, surface/interface plays a very important role in the early stage of crystallization. * Corresponding author. National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China. Tel.: +86 13813845490; fax: +86 25 8359 5535. E-mail address: [email protected] (M. Wang). http://dx.doi.org/10.1016/j.pcrysgrow.2016.04.013 0960-8974/© 2016 Elsevier Ltd. All rights reserved.

Thermodynamically to stimulate nucleation, a metastable (supersaturated) environment is required, and small fluctuations of density are necessary. Homogeneous nucleation occurs without the help of foreign substrate (surface) and is determined purely by the drop of free energy. Nucleation process is essentially a process of the first-order phase transformation, and the development of nucleus of the new phase should overcome an energy barrier. Only when the size of the embryo exceeds a certain critical size, the tendency to growth prevails. To form such clusters larger than the critical size, the system should overcome an activation barrier whose height is given by the work of formation of the critical nuclei. This nucleation process is usually called homogeneous nucleation. Comparing to homogeneous nucleation, heterogeneous nucleation, the nucleation process occurring on a foreign substrate, is much more common. Heterogeneous nucleation is typically faster than homogeneous nucleation. As that will be discussed in the next section, nucleation slows exponentially with the height of a free energy barrier ΔG*. This barrier comes from the free energy penalty of forming the surface of the growing nucleus. For homogeneous nucleation the nucleus is approximated by a sphere.

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However, droplets on surfaces are not complete spheres, hence the area of the interface between the droplet and the surrounding fluid is less than a sphere’s 4πr2. This reduction in surface area of the nucleus reduces the height of the barrier for nucleation and hence so speeds up nucleation process exponentially. Among heterogeneous nucleation, one interesting and important case is the concave-corner-mediated nucleation. The corner site provides a privileged location for nucleation comparing to the scenario of nucleating on a flat substrate. The corner-mediated nucleation plays an important role in lateral growth process. The basic picture of interfacial growth can be summarized as the formation of islands (nucleation) first, followed by a horizontal expansion of the islands on the substrate. Nascent islands can be compact, yet they can be ramified and fractal-like as well. As the compact islands or ramified branches develop on the substrate, the surface coverage increases and eventually a solid film is formed. Despite advances in the understanding of thin film growth, little attention has been paid to effects of interfacial tensions on the horizontal expansion of a crystalline island on a foreign substrate. An especially interesting scenario is that the lateral expansion occurs by repeated nucleation at the concave corner of the island and the substrate: if the material of the substrate is the same as that of the crystalline island, the embryo will follow the orientation of the crystalline island/substrate and the extension of the island is epitaxial growth; if, however, the crystalline island grows on a foreign substrate, thermodynamically the embryo occurring at the concave corner will experience unbalanced surface tensions on the two sides of the corner. Such situation will induce the effects such as wing-tilting in lateral growth GaN over the window shielding layer (usually SiC), and some other long-range ordering patterning. Herewith we will focus on how selective nucleation occurs in crystallization and hence leads to self-organized pattern formation. In later sections we will explain why the crystallographic orientation consecutively rotates in crystallization, resulting in a few long-range-ordering phenomena in lateral crystal growth. We will also show that selective nucleation at the concave-corner can be applied to interpret some peculiar growth behavior, and the effect can be applied to control the fabrication of nanostructures.

2. Fundamentals of nucleation: energy barrier and nucleation rate 2.1. Homogeneous nucleation Consider the case of formation of solid nuclei in a vapor phase. For simplicity we ignore the anisotropy of

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the solid phase and assume that the solid nuclei contain i atoms and possess radius r. The change of Gibbs free energy by forming a nucleus can be expressed as:

ΔG = i ⋅ Δμ + A (i ) ⋅ γ sv

(1)

where Δμ stands for the change of chemical potential for an atom to transfer from the vapor phase to the solid phase, γsv stands for the interfacial energy of the nucleus, and A(i) is the interfacial area of the nucleus, which depends on the geometrical shape of the nucleus and the number of atoms in the nucleus (i) as

A (i ) = η ⋅ i 2 3.

(2)

Suppose i atoms make a cube with edge length as a, and each atom has a volume Ωs. The volume of the cube v = iΩ s = a 3 , the interfacial area A(i) equals to 6a2. It follows that for cube we have η = 6Ω2s 3 . With the similar approach, we can obtain that for a spherical nucleus, 1 3 η = (36π ) Ω2s 3 . By taking Eq. (2) into Eq. (1), one may immediately obtain the relation between ΔG and i as:

ΔG = −i ⋅ Δμ + η ⋅ i 2 3γ sv.

(3)

∂ΔG = 0 , we may find that there is a critical size ∂i of the aggregate, Let

3

⎛ 2η ⋅ γ sv ⎞ i* = ⎜ . ⎝ 3Δμ ⎟⎠

(4)

Above this critical size i*, further increase of the cluster size will decrease Gibbs free energy of the system. In this way, nucleus grows up and a crystallite is formed. However, smaller than this critical size, any increase of the cluster will increase the Gibbs free energy. So in this case, the aggregate tends to disappear. Meanwhile fluctuation plays an important role to promote nucleation. To understand this better, we take a spherical aggregate with radius r. It follows that corresponding to i*, we have the critical radius of the cluster,

r* =

2γ sv ⋅ Ω s . Δμ

(5)

Corresponding to this critical cluster size, the drop of the Gibbs free energy is expressed as:

ΔG* =

4 ⋅ η3γ sv3 2 27 ( Δμ )

or ΔG* =

16π ⋅ Ω2s γ sv3 , 2 3 ( Δμ )

(6)

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Fig. 2. Consider nucleation on a flat substrate c, and the embryo s takes the shape of a spherical cap with diameter r. Fig. 1. The change of the Gibbs free energy as a function of cluster size.

which is the energy barrier for homogeneous nucleation. Only when the energy barrier is overcome, the aggregate survives and develops larger. We can plot the change of the Gibbs free energy as a function of cluster size r, as shown in Fig. 1. The crystallization process via homogeneous nucleation, in other words, is to overcome the nucleation barrier ΔG* and promote the transition from an aggregate to a crystallite. From Eq. (6) one may find that if the change of chemical potential Δμ is sufficiently large (the system is farther from equilibrium), or the interfacial energy of the nucleus γsv is sufficiently small, the energy barrier for nucleation will be small. 2.2. Heterogeneous nucleation In the scenario of homogeneous nucleation, atoms/ molecules aggregate and develop into a nucleus. In reality there will always be foreign subjects in the system, which may include impurity particles, crucible boundary, or the surface of another crystallite. These foreign objects play a very important role in promoting nucleation. In this section we focus on the role of a foreign subject (substrate) on nucleation. For simplicity, we consider the nucleation on a flat substrate c, the embryo s takes the shape of a spherical cap with diameter r, and the contact angle θ is defined as:

m = cosθ =

γ vc − γ sc , γ sv

(7)

where γsv stands for the interfacial energy of the nucleus and vapor environment, γvc stands for the interfacial energy of the vapor environment and the substrate, and γsc stands for the interfacial energy of the nucleus and the substrate. The volume of the embryo is Vs, the interfacial area of nucleus and the vapor phase is Asv, and the area of the interface of the embryo and the substrate is Asc, as shown in Fig. 2. From simple geometrical calculation

one may easily find that those interfacial areas and embryo volume can be expressed as

πr3 (2 + m ) (1 − m )2 3 Asv = 2π r 2 (1 − m ) . 2 2 Asc = π r (1 − m )

Vs =

(8)

It follows that the drop of Gibbs free energy by forming an embryo with the shape of spherical cap can be written as:

ΔG (r ) =

Vs Δμ + ( Asvγ sv + Ascγ sc − Ascγ cv ). Ωs

(9)

The first term is negative, which is contributed by the drop of free energy by forming the embryo from the ambient phase; the terms in the parentheses represent the contribution of interfacial energies. One may find that if the interfacial influence ( Asvγ sv + Ascγ sc − Ascγ cv ) is negative, then ΔG will be negative for sure. This means that spontaneous nucleation will occur. Taking Eq. (8) into Eq. (9), we get:

⎡ 4π r 3 ⎤ 2 ΔG (r ) = ⎢ Δμ + 4π r 2γ sv ⎥ (2 + m ) (1 − m ) Ω 3 ⎣ ⎦ s

4 . (10)

The maximum of ΔG(r) corresponds to the critical con∂ΔG (r ) ditions for the embryo. From = 0 we get the crit∂r ical size of the embryo r* and the energy barrier for heterogeneous nucleation ΔG* as:

r* =

2γ sv Ω s , Δμ

16πΩ2s γ sv3 (2 + m ) (1 − m ) ΔG* = 2 4 3 Δμ

2

(11)

Comparing Eqs. (11) and (6), one may find that the influence of a substrate on nucleation is reflected by the

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Fig. 4. There is a hole with cylindrical shape on a surface, the diameter is 2r. An embryo exists in the hole, with height h, and the contact angle between the embryo and the substrate is θ.

where m = cos θ, Vc stands for the volume of the embryo, Acv and Asc stand for interfacial areas of embryo-vapor phase and embryo-substrate, respectively. Note that Eq. (9) is universal, so by taking Eq. (12) into Eq. (9), one may get

Fig. 3. The plot of ƒ(m) as a function of m.

term f ( m ) =

(2 + m ) (1 − m )2

, where m represents the 4 wetting feature of the substrate. In Fig. 3 two scenarios are interesting: one is that m = −1, which corresponds to θ = 180° (the case of completely non-wetting). In this case the embryo touches the substrate by only one point, and the embryo essentially becomes a sphere. So in this case, the influence of substrate vanishes. Indeed, ƒ(−1) = 1, and heterogeneous nucleation energy barrier (Eq. (11)) degenerates to homogeneous nucleation energy barrier (Eq. (6)). The other situation is m = 1, which corresponds to m = 0°. In this scenario, the embryo essentially possesses the same surface energy as that of the substrate, so the contact angle between the embryo and the substrate is zero. Meanwhile, ƒ(1) = 0, indicating that the nucleation energy barrier vanishes. In most practical cases, the contact angle is in between zero and 180°, suggesting that 0 ≤ f(m) ≤ 1. This means that introducing substrate makes the nucleation energy barrier smaller. 2.3. The role of concave holes on a flat substrate on nucleation In preparation of flat substrate, it is difficult to avoid scratches and tiny pits on the surface. Here we take a cylindrical hole as an example to investigate the role of a hole on surface in nucleation. Suppose there is a hole in cylindrical shape, with diameter as 2r, the embryo has a height h, and the contact angle between the embryo and the substrate is θ, as shown in Fig. 4. Easily one may find that:

Vc = π r 2 h

(

Acv = 2π r 2 1 − 1 − m 2 Asc = 2π rh + π r 2

)

m 2,

(12)

ΔG (r , h ) =

π r 2h Δμ Ωs

(

⎡ + 2π rhγ sv ⎢r 1 − 1 − m 2 ⎣

)

r⎞⎤ ⎛ m2 − m ⎜ h + ⎟ ⎥ . ⎝ 2⎠ ⎦ (13)

Suppose r is a constant, we can investigate how ΔG varies with the depth of the hole h. From Eq. (13) one may find that the second term can be negative if the depth h is sufficiently deep. Meanwhile even though Δμ is positive, ΔG could remain negative; this means that the embryo in the hole may develop in unsaturated scenario. To guarantee the stable growth of the embryo, we should have:

∂ΔG (r , h ) < 0. ∂h

(14)

It follows that stable condition for an embryo is:

πr2 Δμ − 2π rmγ sv < 0, Ωs

(15)

2γ sv Ω s m . This means that smaller hole size favors Δμ the development of an embryo.

or r <

2.4. Nucleation at a concave-corner Here we consider nucleation mediated by a concave corner of the crystallite and the substrate. This scenario occurs mostly in lateral growth of a crystalline material on a foreign substrate. We suggest that there exist two scenarios for nucleating on the growth front, as schematically

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shown in Fig. 5. In one case, the crystallite initiates on the already existing crystallite via heterogeneous nucleation (scenario 1). In the other case, the crystallite nucleates at the concave corner of the already existing crystallite and the foreign substrate (glass surface) (scenario 2). Here we actually consider a case of electrocrystallization, where metal crystallites nucleate on the cathode. If electrocrystallization continues via scenario 1, then the crystallite will form an aggregate floating in the electrolyte. If, however, scenario 2 dominates, crystallite will coat the substrate (glass plate). In electrochemical deposition, the crystallographic orientation of the crystallites is normally random and the nucleus does not possess the same crystallographic orientation as the substrate. This situation is common when the growth is far from equilibrium and some impurities exist on the growing interface. Suppose the interfacial energy of crystallite and electrolyte is denoted as ϕ, and the interfacial energy of the crystallite nucleus and the crystallite substrate underneath is only a small fraction of ϕ. Define α as a small constant, which approaches zero only for epitaxial growth (i.e. the case where the orientation of the nucleus is the same as the substrate). Then the interfacial energy of the nucleus and the crystallite substrate underneath can be represented as αϕ. The contact angle of the nucleus and the deposit, θ, can be expressed as cos θ = 1 − α. It follows that the energy barrier for nucleation in scenario 1 can be written as:

ΔG1* =

φ 2Ω ⎡ arccos (1 − α ) − (1 − α ) 2α − α 2 ⎤⎦ ,, Δg ⎣

(16)

where Δg is the change of the free energy required for a metallic ion to become an atom in electrocrystallization, and Ω is the volume of the atom. For scenario 2, the substrate is asymmetric: one part of the substrate is copper, whereas the other part of the substrate is glass. Suppose the surface energy of the glass substrate and the electrolyte is ξ, and interfacial energy of the copper nucleus and the glass is γcs. We assume that γcs is only a fraction of ϕ, γcs = χϕ, where χ is a parameter less than unity. The radius of curvature of the nucleus is r. The energy barrier for nucleation at the concave corner (here for simplicity we take the concave corner as 90°) has the form

φ 2Ω ⎛ π ΔG2* = ⎜⎝ arccos (1 − α ) + arccos Θ − 2 Δg 2 − =

(

)

2α − α 2 − Θ (1 − α ) − ⎡⎣ 1 − Θ 2 + α − 1⎤⎦ Θ⎞ ⎠

φ 2Ω Λ , 2 Δg 2

(17)

Fig. 5. A schematic diagram to show the sites of nucleation on the growth front and the streamlines in front of the electrodeposit.

ξ − χ . The difference between these two φ energy barriers, δ, can be expressed as where Θ =

δ = ΔG2* − ΔG1* =

φ 2Ω ⎡ Λ ⎤ − arccos (1 − α ) + (1 − α ) 2α − α 2 ⎥ . Δg ⎢⎣ 2 ⎦

(18)

The sign of δ decides which site will be more energetically favorable for nucleation. Our calculations indicate that δ remains negative unless α and Θ are very small. Small α means that the electrodeposition of copper on copper aggregate is virtually an epitaxial process. The value Θ equates to the cosine of the wetting angle of copper on glass substrate. The fact that copper can be deposited on a glass surface indicates that Θ is not small. Instead, Θ should be close to unity. Therefore we conclude that δ should be negative for most cases, which means that nucleation at the concave corner (scenario 2) is thermodynamically favored in electrocrystallization. We need to point out, however, that whether an electrocrystallization can be experimentally observed depends on the nucleation rate, which is defined as the number of nuclei that may develop into crystallites in unit time and unit volume. The nucleation rate depends on both the energy barrier of nucleation ΔG and the probability that a nucleus catches the ions from the surrounding fluid. The steady state nucleation rate I can be expressed as:

I = ω *ΓZ1e

−

ΔG* kT

,

(19)

where Z1 is the concentration of cations near the electrodeposit, Γ is known in the literature as the Zeldovich factor, and ω∗ is the frequency with which the critical nucleus collects the cations [1]. It is known that when the electrocrystallization cell is thick, convection caused by the external fields will be strong and streamlines such as those shown in Fig. 5 are to be expected. At the same time, the middle part of the deposit faces the flux of cations, hence ω∗ is larger in this region. On the one hand, those

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parts at the concave corner of the copper deposit and the glass plate feel a flux moving away from the deposit, which implies that the nucleus will find it more difficult to catch cations, compared to scenario 1. Consequently, ω∗ becomes smaller at the concave corner. The difference between ω∗ at these two sites is related to the thickness of the electrodeposition cell. Thermodynamically, even though the nucleation barrier at the concave corner is lower, the local nucleation rate on the glass plate may not be high due to the smaller ω∗ at the concave corner in the thick cell. By decreasing the cell thickness, convection is strongly suppressed and the ion transfer is mainly driven by the electric migration and diffusion. In addition, ω∗ becomes more homogeneous over the whole deposit interface. Hence the thermodynamic effect may dominate the electrodeposition. Consequently, copper crystallites may coat the glass plate. From the above discussion, one may conclude that there are different approaches to depositing copper on a solid substrate. One way is to modify the surface energy of the glass plate and to decrease ΔG2* , which corresponds to that proposed by Fleury et al. [2,3]; an alternative way is to decrease the thickness of the electrolyte layer. Then, the nucleation rate on the glass plate can be increased as that shown in two studies [4,5]. 3. Concave-corner-mediated nucleation: origin of long-range ordering in lateral growth As we discussed in Section 2.4, when the thickness of growth system is large, nucleation corresponding to scenario 1 is preferred. This means that for a thickelectrolyte-film electrochemical growth, the polycrystalline electrodeposit will mostly develop with metallic crystallite itself as substrate. Meanwhile the electrodeposits will be suspended in the electrolyte and the growth pattern will be easily destroyed. This situation corresponds to that occurred in the very early stage of pattern formation studies in electro-crystallization [6,7]. In early 2000 we observed that once the thickness of the growth system becomes sufficiently small, nucleation at the concave-corner of metallic crystallite (electrodeposit) and the substrate becomes favorable. This corresponds to the scenario 2 in Section 2.4, and the crystallization occurs at the concave corner of the metallic crystallite and the substrate; the immediate advantage of this growth mode is that the electrodeposit can be taken out of the growth system without damaging the growth morphology, and all the metallic crystallites stick on the substrate. This is exactly the situation required in making nano-electrodes. Such an electrocrystallization was carried out in a cell made of two carefully cleaned, flat glass plates. There

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Fig. 6. (a) A schematic diagram of the experimental setup for the generation of ultrathin electrolyte film and for the electrodeposition. The cell for electrodeposition shown here has two parallel electrodes. (b) The details of the electrodeposition cell with the parallel-electrode design. (1) Top glass plate; (2) bottom glass plate; (3) cathode; (4) anode; (5) ice of electrolyte; (6) ultrathin electrolyte layer trapped between the ice of electrolyte and the glass substrate; (7) Peltier element used for stimulating nucleation in solidifying the electrolyte; (8) top cover of the thermostated chamber with a glass window; (9) rubber O ring for sealing; (10) thermostated chamber to keep a constant temperature for electrodeposition.

were two types of geometrical arrangements for the electrodes. In one scenario, the anode was a circular ring and the cathode was a graphite needle, which was inserted through a small hole at the center of the upper glass plate, perpendicular to the plane of the anode, and touching the electrolyte layer beneath. Meanwhile, the electric field was centripetal. For copper electrocrystallization, the ring anode was made of pure copper wire ~99.9% (Goodfellow, UK) and the ring radius was 10 mm. The diameter of the cathode was 0.5 mm. For the other scenario, two parallel, straight electrodes were 8.0 mm apart and fixed on the bottom glass plate [5]. The electrode materials were the same as those for the circular cell. A schematic diagram of the experimental setup is shown in Fig. 6. The aqueous solution of CuSO4(0.05 M, pH 4.5) (termed as electrolyte) was confined in the space between the upper and the lower glass plates and the electrodes. The salt solution (electrolyte) was prepared by analytical reagent CuSO4 and deionized, ultrapure water (electric resistivity 17.8 MΩ·cm). No special treatments such as coating with metal clusters [2,3] were made on the glass substrate

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surface except conventional cleaning. A Peltier element was placed beneath the electrodeposition cell to modify temperature. Both the deposition cell and the Peltier element were sealed in a thermostat chamber. Dry nitrogen flowed through the cell to prevent water condensation on the glass window, so in situ optical observation could be carried out. The temperature for electrodeposition was usually set to −4 °C for 0.05 M CuSO4 solution, below the freezing point of the electrolyte. To generate an ultrathin electrolyte layer for electrodeposition, the CuSO4 solution was solidified by decreasing temperature. To achieve a large, flat electrolytesolid interface, great care was taken in the beginning of solidification to keep only one or just a few ice nuclei in the system. Several melting–solidification cycles were repeated to fulfill this requirement. In our system, solidification started from the bottom glass plate. During solidification, CuSO4 was partially expelled from the solid and this effect was known as partitioning effect [8–11] in crystallization. As a result, the concentration of CuSO4 increased in front of the solid(electrolyte ice)–electrolyte interface. Meanwhile, very low solidification rate had to be applied to prevent the cellular interfacial morphology [10,11]. On the other hand, it is known that the temperature at which electrolyte solidifies (melting point/ solidification point) depends on the concentration of electrolyte. For the electrolyte of CuSO4, the solidification temperature decreases when the salt concentration is increased. Therefore, when the equilibrium was reached at a set temperature (−4 °C, for example), there existed an ultrathin layer of concentrated CuSO4 electrolyte between the ice of electrolyte and the glass substrate. In our experiments, electrodeposition was carried out in this ultrathin layer, where the CuSO4 concentration was expected not to exceed the saturated concentration of −4 °C (at −4 °C, the saturated concentration is about 0.7 M). The thickness of this ultrathin layer depended on the initial concentration of the electrolyte and the setting temperature. At −4 °C, this layer was around 200 nm in thickness (initial electrolyte concentration 0.05 M), which was based on the measurement of the thickness of copper electrodeposit with atomic force microscopy. As indicated in Fig. 6, the electrodes were in contact with the concentrated ultrathin electrolyte layer trapped between the ice of electrolyte and the glass substrate. To verify the existence of this ultrathin layer and to test whether it was indeed in contact with the electrodes, we measured the electric resistance between the electrodes. In one case, we immersed two electrodes in a cup of electrolyte and solidified the electrolyte into ice. Whereas in the other case, the measurement was carried out in the setup shown in Fig. 6. The separation of the electrodes, the initial

electrolyte concentration, and the temperature were the same for these two scenarios. It turned out that the resistance between the electrodes in the first case (bulk system) was several orders of magnitude higher than that in the second case. This suggests that for the electrocrystallization setup shown in Fig. 6, there existed a layer of concentrated electrolyte connecting the two electrodes. In this experiment, both potentiostatic and galvanostatic designs generated similar deposit morphology. In the potentiostatic experiment, the constant voltage across the electrodes was selected between 1.0 V and 5.0 V. Meanwhile, the electric current in electrodeposition was recorded as a function of time. In galvanostatic experiments, the constant current flowing through the deposition cell was in the range of 10 mA–100 mA and the voltage drop across the electrodes was recorded as a function of time. The typical copper deposit is shown in Fig. 7. Unlike previously reported random branching morphology [2,12], here the deposit branches are fingering and have smooth contour. The deposit is shiny and grows robustly on the glass substrate. Optical microscopy reveals that the fingering branch consists of “cellular structures” (Fig. 7(b) and (c)), and each is composed of long, narrow copper filaments. Although unbranched long filaments (more than 150 μm) can be found occasionally, bifurcation occurs to most of them. The overall density of the deposit and the average inter-filament separation do not change evidently, so the cellular pattern gradually increases in width. It can be seen from the tip region that the filaments are perpendicular to the contour of the fingering branches, which suggests that the metallic filaments develop along the local electric field. AFM reveals striking periodic corrugated structures on the filaments (Fig. 7(d)). It is noteworthy that the corrugations on the neighboring filaments correlate in position, which can be easily identified in the branch-splitting regions [Fig. 7(d)]. The coherence of these corrugations implies that they were generated simultaneously. The coherent, periodic growth of the filaments is associated with an evident oscillation of electric current. The period of these spatiotemporal oscillations depends on the voltage across the electrodes, the pH of the electrolyte, and the temperature, etc. The distinct difference between the electrodeposit shown here and those reported previously [2,3] is that here the branching rate has been significantly decreased, and the surface of the deposit becomes much smoother. It was suggested that strong electric migration versus slower diffusion was responsible for the formation of straight filaments [4]. To check the validity of this “migration vs. diffusion” argument, we recently carried out the replacement reaction in the ultrathin electrolyte layer of CuSO4 with zinc wires. Thin wires of zinc are placed

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in the positions of previous copper and carbon electrodes. The solidification procedure of the electrolyte is the same as before. Meanwhile, the zinc wire contacts the electrolyte between the ice and the glass plate, and no external voltage or current is applied. So there should be no electric migration on macroscopic scale. To our surprise, the deposit generated in this replacement reaction is less random and ramified, as shown in Fig. 8. AFM reveals that the surface of the deposit branches is very smooth. Whereas those generated in a much thicker electrolyte layer are very much random and ramified. These results strongly suggest that a strong electric migration may not be essential for the generation of straight, smooth filaments, and what we observed in the ultrathin layer electrocrystallization is a noise-reduce-effect. By reducing the layer thickness, convective noise in front of the growing interface (caused by both the natural convection and the electroconvection) is greatly suppressed, so the deposits become much more regular. It should be noted that in electrodeposition, the most front tips of electrodeposits are the “hottest points” for nucleation. According to the theory of Chazalviel [13], cation concentration behind the growing front virtually approaches zero. Once a nucleus appears and develops on the tip of the deposit filament, nucleation behind the tip becomes nearly impossible. All these factors ultimately lead to the electrodeposit filaments with a low branching rate. It is true that at low temperature and high electrolyte concentration, viscosity of the electrolyte increases considerably, which may change the deposit morphology. Could a higher viscosity contribute to the smooth and straight deposit filaments? This possibility has been checked by measuring the viscosity of CuSO4 electrolyte as a function of temperature and the corresponding variation of deposit morphology. By decreasing temperature from 30 °C to −5 °C, viscosity of the electrolyte changed from 0.855 × 10−3 Pa s to 2.135 × 10−3 Pa s. Corresponding to Fig. 7. (a) The macroscopic view of the electrodeposits of copper grown from a circular electrodeposition cell. The electrodeposit develops on the glass substrate with fingerlike branches. At the corners of the picture, the parts of the circular anode (pure copper wire) can be seen. The cathode is located in the center part of the deposit. (b) The electrodeposit generated in a cell with parallel electrodes. The black line at the bottom is the cathode. The fingerlike branches are similar to those formed in the circular cell. (c) Optical micrograph to show the detailed morphology of a fingerlike branch, in which long, narrow copper filaments can be identified. (d) The AFM view of the copper filaments. The periodic corrugated structures on neighboring filaments are correlated in position, as indicated by the dashed circles in the regions where the splitting of the filaments takes place. One may find that no scratches exist in front of the filament tips, as indicated by the arrows. This fact suggests that the filaments were not following the scratches on the glass surface during the growth.

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Fig. 8. The morphology of copper branches formed by replacement reaction from an ultrathin layer of CuSO4 with a zinc wire. The branches grow on the glass plate and initiate from a zinc wire that is in contact with the ultrathin layer of electrolyte. (a) The copper branches observed with optical microscope. The bar represents 50 μm. (b) AFM micrograph of the copper branches shown in (a). One may find that no essential differences can be identified between those generated by replacement reaction and those formed by electrochemical deposition with an external electric power supply.

this nearly triple increase of viscosity, the deposit morphology also changes. Fig. 9(a) illustrates the electrodeposits at 30 °C, and Fig. 9(b) shows the deposit grown at −5 °C in supercooled electrolyte solution. It should be emphasized that for both (a) and (b), the electrolyte remained in liquid state and the electrodeposition took place in the aqueous electrolyte layer sandwiched by glass plates, i.e., the electrodeposits floated in the electrolyte solution. The control parameters for the formation of the deposits shown in Fig. 9(a) and (b), such as the electrolyte

concentration, the electric current, and the geometric aspects of the electrodeposition cell, were kept the same except the temperature. It can be seen from Fig. 9(a) and (b) that with higher viscosity, the deposit branches were more condensed. The dendritic features became less evident at lower temperature. However, despite the difference on fine features, the patterns shown in both Fig. 9(a) and (b) were essentially dense-branching morphology. Fig. 9(c) shows the deposit grown on the surface of glass substrate at −3 °C in supercooled aqueous solution. Meanwhile, the thickness of the electrolyte was of the order of 300 mm. Fig. 9(d) shows the deposit of copper grown on the surface of glass plate at −3 °C in the ultrathin electrolyte solution film when the solidification of electrolyte had taken place. The major differences of growth conditions for those shown in Fig. 9(c) and (d) were the layer thickness of the electrolyte and the electrolyte concentration. Indeed electrolyte concentration affected the deposit morphology [14], yet on a microscopic scale the deposits were always ramified and randomly branching. In our experimental system, the electrolyte concentration does not tremendously change the microscopic morphology of the deposit. The reason is that we carried out control experiments under a microscope by changing electrolyte concentration from 0.008 M to 0.8 M. Although macroscopic pattern of the deposits varied, under optical microscope the deposit branches were always dense branching. Whereas for the patterns shown in Fig. 9(c) and (d), the difference of the exact electrolyte concentration in front of the electrodeposit should be less than 20 times [15]. It is therefore unlikely that such a difference in concentration may be responsible for the completely different morphologies shown in Fig. 9(c) and (d). So we conclude that the significant decrease of the branching rate and the increase of regularity of the deposit shown in Fig. 9(d) are mainly due to the geometrical restriction of the ultrathin electrolyte layer, which efficiently suppresses the noise in electrodeposition. The restriction of the thickness of electrolyte layer is also responsible for the periodic nanostructures on the filaments. The electrocrystallization of copper from the CuSO4 solution can be understood as follows: First, Cu2+ ions are driven by electric field to the cathode. Then they are reduced and diffused on the deposit surface. Nucleation of the adsorbed copper atoms, followed by limited growth, gives rise to a crystallite agglomerate. According to the Nernst equation, equilibrium electrode potential of Cu|Cu2+ increases when the concentration of Cu2+([Cu2+]) builds up. Whereas, the deposition of copper takes place only when the cathode potential is lower than this equilibrium value. The equilibrium electrode potential for Cu2O, however, is much higher than that for Cu.

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Fig. 9. The morphology of electrodeposits developed at different experimental conditions. (a) The copper electrodeposits grown at 30 °C in aqueous solution sandwiched by two glass plates; (b) the copper electrodeposits grown at −5 °C in supercooled aqueous solution sandwiched by two glass plates. The experimental conditions are the same for both (a) and (b) except for the temperature. (c) The copper electrodeposits grown on glass plate at −3 °C, just before the solidification of the electrolyte starts (i.e., in supercooled electrolyte solution). (d) The copper electrodeposits grown on glass plate at −3 °C when the electrolyte in the deposition cell has been solidified. The voltage across the electrodes is kept the same for both (c) and (d). We infer from (c) and (d) that the significant decrease of the thickness of the electrolyte layer plays a key role in decreasing the branching rate and the formation of much smoother electrodeposit filaments.

Therefore, for a wide range of the electrolyte concentration, Cu2O is deposited with priority. Suppose that [Cu2+] is initially high at the growing interface. As a result, the equilibrium potential for copper deposition is also high. By applying a sufficiently low electrode potential to the cathode, both Cu and Cu2O are deposited. It should be noted that the deposition rate of Cu2O is proportional to the product of both [Cu2+] and [OH−], whereas [OH−] is much lower than [Cu2+]. Therefore, the deposition rate of the semiconducting Cu2O is very low compared to that of copper. The electrodeposition consumes Cu2+, at the same time, the ion transport is confined by the geometrical restriction of the ultrathin electrodeposition system. Hence, [Cu2+] is lowered in front of the growing interface and it takes time for the Laplacian fields to compensate this descend. Meanwhile, the equilibrium electrode potential of Cu decreases and it may even become lower than the actual electrode potential. Once this occurs, the copper deposition stops, yet the deposition of Cu2O remains. Note that Cu2O deposits with a very low rate, which allows [Cu2+] in front of the growing interface being accumulated again. Consequently, the equilibrium electrode potential of Cu2+ resumes. When its value becomes higher than the actual electrode potential, copper deposition restarts. In this way copper filaments with

periodically modulated concentration of Cu2O, and hence periodic nanostructures are generated. It can be inferred that the periodicity of the compositional and topographic oscillations depends on the pH of the electrolyte, which has indeed been experimentally observed. 4. Selective nucleation in self-organizing 3D nano-trees Understanding the underlying formation mechanisms, controlling the morphologies, exploring their emergent properties, and exploiting their technological potentials are the central aspects of materials discovery of novel nanostructures [16–20]. As an important class of specific materials examples, ZnO semiconductor nanorods typically possess hexagonal cross sections, and can be exploited for development of a rich variety of nextgeneration optoelectronic devices. In particular, recent studies have shown that such nanorod materials can be used to develop polariton lasers [21–25] where the coupling of resonant modes and free excitons sensitively depends on the geometry of the cross sections. It is therefore essential to gain precise control of the nanostructural morphology. However, despite decades of enduring research efforts, the underlying microscopic mechanisms

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for the formation of such quasi-one-dimensional (quasi1D) nanostructures remain largely unexplored, especially with regard to quasi-1D hierarchical nanostructures. Most previous reports ascribe the formation of hierarchical nanostructures to the contributions of a given catalyst within the vapor–liquid–solid (VLS) mechanism [26,27]. In the VLS process, a catalytic liquid droplet on top of a nanowire adsorbs ambient vapor atoms, and subsequently nucleates crystals on liquid–solid interface. In nano-crystallization microscopic defects such as dislocations are usually absent [28]. On the other hand, it has been predicted decades ago that screw dislocations in an ultrathin crystalline rod may induce a torque, lead to an elastic twist of the crystalline lattice, and eventually form a chiral pattern if one end of the rod is free to rotate [29]. However, such an effect has not been experimentally observed until very recently, where a dislocation within the nanowire leads to a chiral hierarchical structure [30,31]. Stacking fault, a common twodimensional defect in semiconductor crystallization [32–34], has so far not been recognized to play any role in generating hierarchical nanostructures. In this section we demonstrate the remarkable contribution of stacking-fault-induced repeated polytypism on the formation of a unique hierarchical structure of ZnO nanorods, characterized by a hexagonal central trunk decorated with thin blades. The blades keep a fixed angle with respect to the central trunk, and resemble two sets of mutually intercalated propellers, each set possessing its own three-fold rotational symmetry and being rotated for 60° respect to each other. Our detailed structural analysis shows that the blades are epitaxially initiated through reentrant-corner-mediated nucleation. This finding demonstrates a previously unknown example of self-assembly process of hierarchical nanostructures controlled by polytypism, an intriguing new mechanism that may find broader applicability. We also explore the novel optical properties of such hierarchical nanostructures. The hierarchical structures of ZnO are fabricated on silicon (100) substrate by thermo-evaporation method. A horizontal tube furnace is used to grow ZnO nanostructure with ultrapure N2 as the carrier gas, where the zinc source is pure zinc powder (99.9%) without adding any catalysts. The system is heated to 550 °C at a rate of 25 °C/min and the temperature is kept at 550 °C during the growth process. Trace amount of ultrapure oxygen gas (3 sccm) is introduced into the furnace as the oxygen source. The substrate is placed 10 mm upstream of the zinc powder. To terminate the ZnO growth, the flux of O2 is cut off first, followed by blowing in large flux of ultrapure N2 (~5000 sccm) into the furnace and decreasing temperature afterward. A layer of the ZnO crystallites covers

the whole silicon substrate. The morphology and structures of the hierarchical ZnO structures were characterized with a field-emission scanning electron microscope (FESEM) and high-resolution transmission electron microscope (HRTEM). Cathodoluminescence (CL) spectroscopy was carried out at room temperature with Gatan MonoCL3+ associated with the FESEM. The micrographs of the ZnO microstructure with hexagonal central trunk decorated with flat paddle blades are shown in Fig. 10. Although the blades seem to possess a six-fold-symmetry with respect to the central trunk, they in fact belong to two sets of three-fold-symmetrical groups, each originates from different section on the hexagonal trunk and has been rotated by 60° with the central trunk as axis (Fig. 10(b)). From the same section of the trunk, only three blades develop outward, keeping a threefold symmetry to the trunk. The neighboring blade either nucleates on the same facet of the hexagonal trunk (and hence in parallel with the existing blade), or nucleates on an adjacent facet that has rotated by 60° around the central trunk. The blades keep a fixed angle with respect to the central trunk (Fig. 10), suggesting some intrinsic structural origins for the formation of the ZnO propellers. The HRTEM of the ZnO hierarchical pattern is shown in Fig. 11. It has been well established that in ambient conditions the hexagonal wurtzite (WZ) structure is the most stable polymorph of ZnO and is hence most commonly observed [35]. Yet ZnO may also crystallize into the cubic zinc–blende (ZB) structure [36–38]. Fig. 11(a) illustrates a TEM micrograph of the central trunk and propeller blades. It can be identified in Fig. 11(c) that both the trunk and the blade are in the WZ phase, whereas immediately adjacent the blade in the main trunk there is a defected ZB region. Region 1 (WZ) is in the sidebranching blade and is nearly defect-free; region 3 (WZ) is a part of the main trunk and contains visible stacking faults. Region 2 is a ZB slab with some stacking faults. The side-branching blade roots from the ZB slab in region 2 and develops outward. During the growth, both the blade and main trunk are simultaneously thickened, so a conical region (shoulder section) is generated (as marked by the red dashed lines in Fig. 11(b)). Since the WZ and ZB structures differ merely in stacking sequences of the closely packed atomic planes, the ZB {111} planes are parallel to the WZ {0001}, as indicated by the red lines in Fig. 11(c). In region 2, as marked by the bright yellow lines, the (0001) planes of the blade are approximately parallel to the (1) planes of the ZB phase. The angle between the growth direction of the blade and that of the trunk is measured as 104°, very close to the angle between two equivalent ZB {111}, 109.5°.

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Fig. 10. FESEM micrographs of ZnO hierarchical nanostructures composed of a hexagonal trunk decorated with two sets of mutually intercalated paddle blades, each set with its own threefold rotational symmetry, and being rotated for 60° with respect to each other. (a) Top, (b) side, and (c) bottom views, respectively. (d) High magnification image showing the flat hexagonal cross sections of the blades. The dashed lines in (d) serve as guides to the eye.

Microscopically, the WZ structure of ZnO is constructed with closely-packed Zn and O layers stacked along the [0001] direction in the sequence of ABABAB (Fig. 11(d)). Yet sequence ABCBABA or ABCABAB appears when a stacking fault is formed. If stacking fault occurs continuously, the local structure may change from the hexagonal WZ phase to the cubic ZB phase (Fig. 11(d)). For III–V and II–VI compounds, basal– plane stacking faults are frequently observed due to their very low formation energies [39,40]. A high concentration of stacking faults changes the structure from WZ to ZB [39]. It is noteworthy that for the scenario that a ZB segment is sandwiched by WZ-structured parts, there exist energetically identical yet crystallographically different stacking sequences, e.g., …ABABCABCAB… and …ABACBACBABAB…, where the underlined bold letters indicate the ZB segments. Topologically these two configurations differ by 60° with the [111] axis. As elucidated below, this feature determines the seemingly sixfold-symmetrical blades around the trunk. It can be determined from the HRTEM micrographs that the side surfaces of the WZ segments on the trunk are {10 10} . For the ZB structure, the {111} planes are the energetically preferred facets. Therefore, a ZB segment is modeled as a truncated {111} octahedron (Fig. 12(a)). We schematically plot three WZ and two ZB segments,

which mimic a section of the central trunk where a structural transformation takes place. The top and side surfaces of the WZ segments are {0001} and {10 10} facets, respectively, whereas the surfaces of the ZB structures are all {111}. Consequently a reentrant angle of 160.5° appears at the junction of the side surfaces of the WZ {10 10} and neighboring ZB {111} planes, where a sidebranching blade can be nucleated (Fig. 12(a)). The experimentally observed bumpy side surface of the central trunk (Fig. 10b) is consistent with this configuration. For both configurations of the ZB segment embedded in the WZ trunk, the ZB {111} planes epitaxially grow on WZ {0001}. Therefore, the ZB–WZ interface is atomically matched, and the orientation of ZB1 and ZB2 can be rotated by 60° along the [111] direction (Fig. 12(a)). At the interface of ZB and WZ segments, {111} of the ZB and {10 10} of the WZ phases form six reentrant corners. Due to electric neutralization requirement, each facet is alternatively terminated by O or Zn, as illustrated with different shade in Fig. 12(a). Among the six reentrant corners, only three possess Zn-terminated ZB {111}. It is well established that the reentrant corner site possesses a lower nucleation barrier and is energetically more favorable for nucleation [41]. It is also known that the fast growing facets of ZnO are the Zn-terminated ones [27]. Consequently, as the main trunk develops along the

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Fig. 11. Microstructural analysis of the ZnO propellers composed of a main trunk with layers of paddle blades. (a) Bright field TEM image, with the boxed region further enlarged in (b). (c) HRTEM image of the boxed region in (b). Regions 2 and 3 are on the main trunk and region 1 belongs to the sidebranching blade. (d) Fast Fourier transforms (FFTs) for different regions in (c); from top to bottom, the graphs represent the FFTs in regions 1, 2, and 3, respectively. Both the main trunk and the blades are assigned to the WZ structure, with the growth direction along the [0001] (the angle between them is 104°); the main trunk, however, is composed of ZB segments and stacking faults. (d) Atomic structure illustrating the WZ-ZB combination. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 12. Schematic illustrations of the crystallographic structure of the propellers. (a) The central trunk composed of alternating stacking of WZ and ZB slices. The side surfaces of the WZs are {10 10} facets, while those of the ZBs are {111} facets. ZB1 and ZB2 represent two ZB layers with different stacking sequences and are crystallographically rotated by 60° around the [111] axis. The white arrows indicate the reentrant sites (160.5°) formed by the ZB {111} and the underneath WZ {10 10} surfaces. Curved red arrows illustrate how a ZB segment is truncated from a {111} octahedron, where the Zn- and O-terminated surfaces (four for each type) are represented by darker and lighter hues, respectively. For ZnO the growth rate of the Znterminated facet is much higher. (b) Schematic for a hierarchical propeller structure generated by epitaxial growth of WZ branches on the Zn-terminated ZB faces from the reentrant sites. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

ZB [111] direction with a Zn-terminated facet, three sidebranching blades are nucleated at the reentrant corners with Zn-terminated ZB {111} and further develop downward to form a propeller pattern (Fig. 12(b)). It should be emphasized that the blade nucleates from the confined lamella of ZB {111}, so the cross section of the blade is strongly confined and hence has an elongated hexagon pattern (Fig. 10(d)). Geometrical calculations show that the angle between the blade and the main trunk should be 109.5° (Fig. 12(d)), consistent with our experimental observations of FESEM

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Fig. 13. SEM micrograph, CL spectra, and monochromic CL images of the ZnO hierarchical nanostructures. (a) Micrograph of a ZnO propeller. (b) CL spectra recorded at different locations (as schematically marked in (a)). The vertical dotted lines indicate the positions of wavelengths of 385 and 405 nm. Spectra from the hexagonal prism on top of the trunk (site 2) and on the blade (site 3) are enlarged by a factor of 2. Inset shows the Gaussian decomposition of the trunk emission peak at around 400 nm. (c) Monochromic CL images obtained with 405-nm emission. (d) The superimposed image of the SEM image. (c) Shows that the blades originate exactly from the intersections of the bright and dark emission bands, as marked by the arrows. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

(~104°) (Fig. 11(b)). It is noteworthy that on each segment of the ZB phase there are three Zn-terminated reentrant corners. On the neighboring ZB segments, such as ZB1 and ZB2, the sites with the same type of reentrant corners can be rotated by 60° with the WZ [0001] axis, which eventually leads to the seemingly six-fold-symmetry of the blades. To verify the above proposed mechanism, cathodoluminescence (CL) spectroscopy has been carried out on the ZnO hierarchical nanostructure. ZnO has intrinsic ultraviolet luminescence around 385 nm, which is conventionally attributed to the recombination of free excitons in the WZ structure [42]. In addition, defect-related blue to green band emissions have been reported [43]. Theoretical calculations of the energy band gap of the ZBtype ZnO indicate that it is approximately 0.1 eV lower than that of the WZ-type ZnO [40,44]. The narrower band gap means a red-shift of the primitive emission of the ZB-type ZnO with respect to that of the WZ-type. Accordingly, one would expect to observe luminescence of the ZB-type ZnO around 400–410 nm. Fig. 13 shows room temperature CL measurements on the ZnO hierarchical nanostructure. Based on the HRTEM observations, both the thin hexagonal prism on the foreside of

the thick central trunk and the flat blades aside of the main trunk are in the WZ phase (Fig. 11), and the thick central trunk possesses ZB lamella embedded in the WZ phase. As shown in Fig. 13(b), the blades and the thin perfect hexagonal prism on top of the central trunk are luminescent at 385 nm. On the main trunk, there is a distinct sharp peak centered at 405 nm, together with a minor shoulder at around 385 nm (Fig. 13(b)). With monochromatic imaging at 405 nm, bright strips appear on the trunk (Fig. 13(c)), which are expected to be the location of ZB lamella. The darker regions between the bright strips are in the WZ phase. Combining monochromatic imaging at 405 nm and the morphology, we conclude that the blades originate exactly from the intersections of the bright and dark emission bands (reentrant corner site), as marked by the arrows in Fig. 13(d). As an effort to explore the application potentials of the novel hierarchical nanostructures, the optical properties of the ZnO trunk decorated with periodically distributed, uniformly angled blades have been numerically studied. The normal incident light is z-polarized (inset of Fig. 14(a)). The electric field inside the trunk is calculated as a function of frequency of the incident light. A resonant electric field has been sensed inside the trunk

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by a z-polarized detector (Fig. 14(a)). The resonant frequency depends on the periodicity of the blades on the trunk. At the resonance the spatial distribution of electric field on the y–z cutting plane is plotted in Fig. 14(b), where two rows of circulating vortexes are aligned along the boundaries of the trunk. As illustrated in Fig. 14(b), perpendicular to the trunk, in the y-direction, one may identify a pair of oppositely circulating vortexes, which meet in the center of the trunk. Since the electric fields in these two vortexes are circulating in the opposite directions, the fields at the center of the trunk are parallel to each other. In the same row, the adjacent vortex is rotating in the opposite direction. In Fig. 14(b) two pairs of vortexes are illustrated in the blue box. At the time corresponding to phase difference ϕ = 0, in the center of the trunk the electric fields contributed by the neighboring vortex pairs are head-to-head; at ϕ = π, the field at the center of the trunk contributed by the neighboring vortex pairs are end-to-end. In this case the energy flux of the electromagnetic wave, characterized by the Poynting vector, is stronger near the boundaries of the trunk, as illustrated in Fig. 14(c). It should be pointed out that the integration of the Poynting vector across the x–y plane does not vanish, indicating that a portion of the incident energy is indeed zigzag transported in the z-direction near the trunk surface. Keeping the incident light z-polarized, a y-polarized detector inside the trunk also senses a resonant mode at a different frequency, as shown in Fig. 14(d). For this resonant mode, there exists a row of vortexes of electric field centered in the middle of the trunk, as illustrated in Fig. 14(e). At the time corresponding to ϕ = 0, the vortex of the electric field is rotating clockwise; at the time corresponding to ϕ = π, however, the vortex rotates counterclockwise. Meanwhile, the Poynting vector zigzag flows in the center of the trunk in the z-direction (Fig. 14(f)), and the integration of the Poynting vector across the x–y plane does not vanish, either. Fig. 14 indicates that for normal incidence of light, a portion of the incident energy is coupled into the trunk and is transported in the direction defined by the blades (-z). Off the resonant frequencies, no energy flux can be detected in the trunk. Comparing with previous ZnO nanowires without blades [45], the blades demonstrated here provide the essential boundary conditions for establishing resonance of electromagnetic waves in the trunk at the specific frequencies. In previous growth of hierarchical nanostructures of ZnO, catalysts were commonly introduced, the growth mechanism was normally attributed to the VLS process [26,27,46], and the morphology was featured by randomly positioned blades normal to the central trunk. In the VLS mechanism, coherent crystallographic relations

between the blades and the trunk do not exist. The hierarchical nanostructures presented in this Section, however, distinctly differ from the previous cases not only in geometrical morphologies, but more essentially in the underlying growth mechanisms. The accumulation of stacking faults along the [0001] direction of ZnO leads to the repeated polytypism of the WZ and ZB phases with intrinsic (in contrast to the extrinsic catalysts) concave corners across the interfaces of the WZ–ZB phases, which provide preferable sites for nucleation of the paddle blades. Since no catalyst is introduced in the present experiments, the formation of the propeller-like structure is a more inherent process. Furthermore, this discovery provides an example that in addition to dislocations [28,29], accumulation of stacking faults can also play an important role in assembling hierarchical structures. The unique hierarchical nanostructure self-assembled may act as a resonant waveguides for light transmission, and hence possess significant potential applications in photonics and energy harvesting. 5. Selective nucleation in making 2D metallic nanowire arrays Metallic microstructures are the essential building blocks in microelectronics as electric interconnections between different functioning parts [47]. In the blooming field of optoelectronics, metallic microstructures play a key role due to the surface-plasmon-polariton-related effects [48,49] and the applications in miniaturization of photonic circuits [50,51], near-field optics [52], and single-molecule optical sensing [53,54]. The electromagnetic resonance in the metallic structures may offer some unique properties that do not exist in conventional, naturally occurring materials, such as the negative refractive index [55,56]. In these researches, the metallic structures were usually fabricated by photolithography, which was time consuming and costly [57]. To achieve a desired metallic pattern more economically, we once developed a selective electrodeposition method, where the surface energy of substrate was modified by periodic stripes of lipid monolayers, hence local nucleation barrier for metal crystallization was reduced [58]. However, the width of the metallic wires in that case is limited by the width of the monolayer stripes. Here we show a new approach to fabricate the arrays of metallic microstructures with tunable line width. By imprinting polymer stripes on silicon surface, the concave corner of the polymer stripes and the silicon substrate provides a preferential nucleation site for electrodeposition. Hence metallic nanowires are formed by successive nucleation at the corner, and the width of the wires can be tuned by the parameters of electrodeposition. This method can also be

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Fig. 14. Electromagnetic resonances in the trunk with blades. (a) The resonance of Ez inside the trunk for z-polarized normal incidence. (b) The distribution of the electric field at the resonant frequency. When the phase difference φ = 0 and π, the electric fields in the neighboring regions in the center of the trunk are head-to-head and end-to-end, respectively, as illustrated in the box in (b). (c) At the resonance the Poynting vector is zigzag transported near the trunk surface. (d) The other resonance (Ey) detected in the trunk. (e) Plots of the electric field at the resonance on the y–z cross section. When the phase difference φ = 0 and π, the electric field is rotating clockwise and counterclockwise, respectively (see the marked box in (d)). (f) Corresponding to the resonance shown in (d) and (e), the Poynting vector zigzag flows along the central axis of the trunk. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

applied for fabricating more complicated structures rather than the straight line array only. Template-assisted electrodeposition is a very efficient way to fabricate nanostructures. Anodic aluminum oxide (AAO) [59–62] and polymeric membranes [63] are usually used as molds, and the size of the channels in these systems can be just a few nanometers [64]. However, the destructivity during removal from the template makes it difficult to preserve the spatial order among the nanowires [65,66], hence limiting their applications in optoelectronics. Instead of making three-dimensional

structures, two-dimensional arrays of metallic structures on silicon surface are easier to fabricate. For example, regular arrays of submicron-wide copper wires can be electrodeposited on a silicon substrate covered with stripes of Langmuir–Blodgett (LB) film [58]. The width of the copper wires generated by that method is, however, usually larger than the template underneath, and it is technically difficult to fabricate arrays of wires narrower than 100 nm over a large area. Another challenge in previous nanowire studies is to increase the length of the nanowires. It has seldom reported that the length of

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Fig. 15. (a) Schematic diagrams showing the procedures to prepare the PMMA-striped substrate. (b) SEM image of the PMMA-striped silicon substrate. The area with the dark contrast is covered with PMMA. The scale bar represents 4 μm. (c) Schematic diagrams of the electrodeposition setup with an ultrathin electrolyte layer by freezing the electrolyte solution. (1) Top glass plate; (2) bottom PMMA-striped silicon substrate; (3) cathode; (4) anode; (5) ice of electrolyte; (6) the ultrathin electrolyte layer trapped between the ice of electrolyte and the substrate; (7) Peltier element used for stimulating nucleation of electrolyte ice in freezing process; (8) top cover of the thermostated chamber with a glass window for optical observation; (9) rubber O-ring for sealing; (10) the thermostated chamber. (d) SEM image of the copper-wire array generated on the PMMAstriped substrate. The lines with the brighter contrast are the copper wires, the lines with the darker contrast are the PMMA stripes, and the area with the gray contrast is the silicon substrate. The scale bar represents 2 μm.

the nanowires in an array may exceed a few hundreds of micrometers free of defects. In this section we discuss a corner-mediated growth of ultra-narrow metallic wires assisted by polymer stripes embossed on silicon surface. To form the patterned substrate, a thin film of poly(methylmethacrylate) (PMMA) (mr-I 7030E molecular weight Mw = 75 kDa) is initially spin-coated on the silicon wafer. The film thickness is about 300 nm. The stripe patterns are introduced by nanoimprint lithography (NIL) [67,68]. The pressure applied on the mold and the temperature of embossing are carefully selected, so PMMA may flow into the cavities and reproduce the mold pattern. In our experiments, the pressure is 40 bars, and the embossing temperature is 170 °C. The entire system is thereafter cooled below the glass transition temperature (Tg) before demolding. After conformal molding, the residual polymer on the bottom of trench is removed by oxygen reactive ion etching (ORIE). In this way, periodic stripes of PMMA on the surface of silicon oxide are generated. The schematic diagram for the substrate preparation

is shown in Fig. 15(a). The generated striped substrate is shown in Fig. 15(b), where the darker stripe region is covered with PMMA, and the brighter area is the surface of silicon substrate. The height of the PMMA stripes is about 80 nm. With the PMMA-striped silicon substrate we carry out copper electrodeposition with our previously reported experimental system [4,69–71], in which the nanowires of copper are grown in an ultrathin electrolyte layer less than 300 nm thick. The schematic diagrams of the electrodeposition setup are shown in Fig. 15(c). The initial CuSO4 concentration is 0.05 M. We carry out electrodeposition with potentiostatic mode, and a constant voltage is applied across the electrodes, which is selected in the range of 0.2–1.5 V. We find that in the electrodeposition process, copper prefers to nucleate at the concave corner of the PMMA stripe and the silicon substrate. Successive nucleation of copper eventually forms an array of straight, homogeneous copper wires, as shown in Fig. 15(d).

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The width of copper wires depends on both the concentration of electrolyte CuSO4 and the electric voltage across the electrodes. Fig. 16(a)–(c) provide the morphology of the copper wires fabricated at different voltages, where the line width varies from 110 nm to 25 nm. The length of the copper wires in our experiments can easily reach 0.5 cm, which in fact simply depends on the separation of the electrodes. The longer wires can be achieved when the separation between the cathode and the anode becomes wider. Fig. 16(d) shows the dependence of the line width and the electric voltage across the electrodes. It indicates that to achieve a narrower copper wire, a lower voltage should be used. To verify the chemical purity of the metallic wires, mapping of energy dispersive spectrometry (EDS) has been applied, as shown in Fig. 17. In the selected scan region, the brighter (red) lines are the imaging of copper element (Fig. 17(b)), and the grey (green) background is the imaging for silicon element (Fig. 17(c)). The EDS data do not show any detectable concentration of oxygen along the wire, suggesting that the purity of the wires is high. The detailed topography at the concave corner of the PMMA stripe and the silicon substrate is shown in Fig. 18(a), where the tip of a grown copper wire can be clearly identified. Fig. 18(a) suggests that the copper nanowire is generated by successive nucleation at the concave corner of the PMMA stripe and the silicon substrate. The width of a copper nanowire depends on the voltage applied across the electrodes. The separation between the metallic nanowires is determined by the separation of the stripes and the width of PMMA stripe itself. The microscopic growth process of the copper wires can be understood as follows. As illustrated in Figs. 15(c) and 4(b), the electrolyte layer trapped between the substrate and the electrolyte ice is very thin, the nutrient transfer to the top surface of PMMA stripes is therefore confined. Consequently nucleation and crystallization of copper on the top surface of PMMA stripe is difficult. This feature distinguishes our current work with that in Ref. [59]. The growth mechanism of the copper wires can be understood by considering the energy barrier for nucleation on the side face of the PMMA stripe (scenario 1) and along the edge of the PMMA stripe and silicon substrate (scenario 2), respectively (Fig. 18(b)). Fig. 16. (a–c) SEM images of the copper-nanowire array generated at different applied voltages in electro-deposition. The scale bar represents 2 μm. (a) V = 0.6 V. (b) V = 0.4 V. (c) V = 0.3 V. (d) The dependence of the line width of the copper wires as a function of the applied voltage across the electrodes.

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Fig. 17. Mapping of the EDS was carried out in the selected area. The electric voltage to deposit this sample was 0.45 V and pH of electrolyte was 4.5. The bottom-left graph shows the imaging for copper element (brighter (red) lines); the bottom-right graph shows the imaging for silicon (grey (green)), where the areas covered with copper wires are darkened. The scale bar represents 2 μm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

For scenario 1 the embryo of nucleus initiates on the PMMA surface, and keeps its shape as a part of a sphere. For scenario 2, the substrate is asymmetric: one part of the substrate is PMMA stripe, whereas the other part of the substrate is the silicon covered with a very thin layer of oxide. From thermodynamics one may find that the energy barrier for nucleation in scenario 1 is:

ΔG1* =

8γ cf2 Ωc (θ1 − cosθ1 sin θ1 ) , Δg

where θ1 is the contact angle of the copper nucleus and the PMMA surface, Δg is the change of the free energy required for a copper ion to become an atom in electrocrystallization, and Ωc is the volume of an atom. The interfacial energy of the copper nucleus and electrolyte is denoted as γ cf . The energy barrier for nucleation in scenario 2 can be written as 8γ cf Ωc ΔG2* = [θ1 + θ 2 − π 2 − (sin θ1 − cosθ 2 ) cosθ1 Δg 2

− (sin θ 2 − cos θ1 ) cos θ 2 ] 2 ,

where θ 2 is the contact angle of the copper nucleus and the surface of silicon substrate. It follows that the

Fig. 18. (a) SEM image of the concave-corner region of the PMMA stripe and the silicon substrate. The tip of a copper nanowire can be clearly identified. The sample has been tilted 70° for imaging. The scale bar represents 200 nm. (b) Schematic diagram showing the possible sites of nucleation in electrodeposition. For Scenario 1, copper nucleus contacts the PMMA surface only. For Scenario 2, copper nucleus appears at the concave corner, and contacts both the PMMA stripe and the silicon substrate.

difference between these two energy barriers, δ, can be expressed as

δ = ΔG1* − ΔG2* =

8γ cf2 Ωc [π 4 − cosθ1 cosθ 2 + θ1 2 Δg − cosθ1 sin θ1 2 + sin θ 2 coosθ 2 2 − θ 2 2 ].

The sign of δ decides which site will be energetically favorable for nucleation. It has been experimentally observed that copper deposits easily on PMMA surface, while nucleation on the surface of silicon substrate is difficult [59,72]. This suggests that θ1 should be less than π π and θ2 is larger than , although we do not know 2 2 the exact value of these data. From the above expression of δ one may find that δ is positive in this regime. This means that nucleation at the concave corner (scenario 2) is indeed thermodynamically favorable in electrodeposition.

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process, forming some interesting regular patterns, it may also be applied in fabricating metallic nano wires with specific geometry, including straight metallic wire array with tunable line width and nanowires with periodic structures. By observation and understanding the concavecorner-mediated nucleation, we can learn from nature and create some structures that cannot occur spontaneously in nature. Such a fabrication approach could be faster, smarter and more effective than conventional methods, and demonstrate a new trend in next generation manufacturing. Fig. 19. In preparation of the arrays of PMMA strips (the dark stripes in the picture) on silicon substrate, some hemicycle defects are occasionally generated. This SEM image shows that the copper wires may follow the edge of the PMMA stripes in electrodeposition and develop into a more complicated pattern. The scale bar represents 2 μm.

The unique nucleation/crystallization behavior reported here demonstrates a simple and controllable way to fabricate arrays of straight copper nanowires on a solid substrate. According to the corner-mediated mechanism discussed above, this method can be applied to fabricate structures beyond straight line array when the patterned PMMA structures are used. In fact, in nanoimprinting process, some concave defects occasionally occur to the PMMA stripes. We find that copper nucleation may follow the edge of the PMMA stripe, sketch out the details of the out rims of the stripes, as shown in Fig. 19. This observation suggests that if the PMMA stripes possess a complicated topography, it is possible to fabricate irregular metallic structures that mimic the outline of the stripe edges. This growth behavior becomes especially interesting nowadays because of recent intensive studies on the interaction of electromagnetic waves with sub-wave-length metallic structures for the purpose of constructing metamaterials [55,56,73,74] in which both the electric permittivity and the magnetic permeability are simultaneously negative, hence the refractive index becomes also negative. Such metallic microstructures are normally fabricated by photolithography. Our results demonstrated here provide a possible alternative way to fabricate subwave-length metallic structures economically for applications in plasmonics and optoelectronics. 6. Concluding remarks Nucleation mediated by the concave corners plays a very important role in crystallization, and many selforganized patterns are determined by this process. Such mechanism occurs not only in natural crystallization

Acknowledgements Financial support from the State Key Program for Basic Research from MOST of China (Grant Nos. 2010CB630705 and 2012CB921502), and that from NSF of China (Grant Nos. 11204127, 11034005, 11328402 and 61077023) are greatly appreciated. References [1] I.V. Markov, Crystal Growth for Beginners: Fundamentals of Nucleation, Crystal Growth and Epitaxy, World Scientific, Singapore, 1995. [2] V. Fleury, D. Barkey, Europhys. Lett. 36 (1996) 253. [3] V. Fleury, W.A. Watters, L. Allam, T. Devers, Nature 416 (2002) 716. [4] M. Wang, S. Zhong, X.-B. Yin, J.-M. Zhou, R.W. Peng, Y. Wang, et al., Phys. Rev. Lett. 86 (2001) 3827. [5] S. Zhong, M. Wang, X.-B. Yin, J.-M. Zhuo, R.W. Peng, Y. Wang, et al., J. Phys. Soc. Jpn. 70 (2001) 1452. [6] (a) R.M. Brady, R.C. Ball, Nature 309 (1984) 225; (b) Y. Sawada, A. Dougherty, J.P. Gollub, Phys. Rev. Lett. 56 (1986) 1260. [7] M. Wang, N.B. Ming, Phys. Rev. A 45 (1992) 2493. [8] A.A. Chernov, Modern Crystallography III: Crystal Growth, Springer-Verlag, Berlin, 1984. [9] N.-B. Ming, Fundamentals of Crystal Growth Physics, Shanghai Science and Technology, Shanghai, 1982. [10] W. Kurz, D.J. Fisher, Fundamentals of Solidification, 4th ed., Enfield Publishing & Distribution Company, Enfield, NH, 2001. [11] A. Pimpinelli, J. Villain, Physics of Crystal Growth, Cambridge University Press, Cambridge, 1998. [12] T. Vicsek, Fractal Growth Phenomena, 2nd ed., World Scientific, Singapore, 1992 and references therein. [13] J.-N. Chazalviel, Phys. Rev. A 42 (1990) 7355. [14] F. Sagues, M.Q. Lopez-Salvans, J. Claret, Phys. Rep. 337 (2000) 97. [15] At −4 °C the saturated concentration of CuSO4 is about 0.7M, higher than this concentration crystallites of CuSO4 may nucleate. In our experiment, the initrial concentration of CuSO4 is 0.05 M. Therefore, the concentration difference for that in Fig. 9(c) and (d) should be around 14 times. Dissolution data of CuSO4 can be found in CRC Handbook of Chemistry and Physics, 78th Ed.(CRC-Press, 1997). [16] Z.W. Pan, Z.R. Dai, Z.L. Wang, Science 291 (2001) 1947.

272 [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]

F. Jia et al. / Progress in Crystal Growth and Characterization of Materials 62 (2016) 252–272 Z.L. Wang, J. Song, Science 312 (2006) 242. R. Yan, D. Gargas, P. Yang, Nat. Photonics 3 (2009) 569. R. Lal, S. Link, N.J. Halas, Nat. Photonics 1 (2007) 641. D.J. Shu, X. Xiong, Z.W. Wang, Z.Y. Zhang, M. Wang, N.B. Ming, J. Phys. Chem. C 115 (2011) 31. T. Nobis, E.M. Kaidashev, A. Rahm, M. Lorenz, M. Grundmann, Phys. Rev. Lett. 93 (2004) 103903. L.X. Sun, Z.H. Chen, Q.J. Ren, K. Yu, L.H. Bai, W.H. Zhou, et al., Phys. Rev. Lett. 100 (2008) 156403. M. Zamfirescu, A. Kavokin, B. Gil, G. Malpuech, M. Kaliteevski, Phys. Rev. B 65 (2002) 161205(R). G. Malpuech, A. Kavokin, A. Di Carlo, J.J. Baumberg, Phys. Rev. B 65 (2002) 153310. R. Johne, D.D. Solnyshkov, G. Malpuech, Appl. Phys. Lett. 93 (2008) 211105. M.H. Huang, Y.Y. Wu, H. Feick, N. Tran, E. Weber, P.D. Yang, Adv. Mater. 13 (2001) 113. P.X. Gao, Z.L. Wang, Appl. Phys. Lett. 84 (2004) 2883. R.L. Penn, J.F. Banfield, Science 281 (1998) 969. J.D. Eshelby, J. Appl. Phys. 24 (1953) 176. M.J. Bierman, Y.K.A. Lau, A.V. Kvit, A.L. Schmitt, S. Jin, Science 320 (2008) 1060. J. Zhu, H.L. Peng, A.F. Marshall, D.M. Bamett, W.D. Nix, Y. Cui, Nat. Nanotech. 3 (2008) 477. P. Caroff, K.A. Dick, J. Johansson, M.E. Messing, K. Deppert, L. Samuelson, Nat. Nanotech. 4 (2009) 50. H.J. Joyce, J. Wong-Leung, Q. Gao, H. Hoe Tan, C. Jagadish, Nano Lett. 10 (2010) 908. J. Johansson, K.A. Dick, P. Caroff, M.E. Messing, J. Bolinsson, K. Deppert, et al., J. Phys. Chem. C 114 (2010) 3837. U. Ozgur, Y.I. Alivov, C. Liu, A. Teke, M.A. Reshchikov, S. Dogan, et al., J. Appl. Phys. 98 (2005) 041301. Y. Ding, Z.L. Wang, T.J. Sun, J.S. Qiu, Appl. Phys. Lett. 90 (2007) 153510. A. Ashrafi, A. Ueta, A. Avramescu, H. Kumano, I. Suemune, Y.W. Ok, et al., Appl. Phys. Lett. 76 (2000) 550. L. Lazzarini, G. Salviati, F. Fabbri, M. Zha, D. Calestani, A. Zappettini, et al., ACS Nano 3 (2009) 3158. A.I. Persson, M.W. Larsson, S. Steinstrom, B.J. Ohlsson, L. Samuelson, L.R. Wallenberg, Nat. Mater. 3 (2004) 677. Y.F. Yan, G.M. Dalpian, M.M. Al-Jassim, S.-H. Wei, Phys. Rev. B 70 (2004) 193206. N.B. Ming, I. Sunagawa, J. Cryst. Growth 87 (1988) 13. M. Willander, O. Nur, Q.X. Zhao, L.L. Yang, M. Lorenz, B.Q. Cao, et al., Nanotechnology 20 (2009) 332001. H.B. Zeng, G.T. Duan, Y. Li, S.K. Yang, X.X. Xu, W.P. Cai, Adv. Funct. Mater. 20 (2010) 561. C.-Y. Yeh, S.-H. Wei, A. Zunger, Phys. Rev. B 50 (1994) 2715.

[45] T. Voss, G.T. Svacha, E. Mazur, S. Muller, C. Ronning, D. Konjhodzic, et al., Nano Lett. 7 (2007) 3675. [46] J.Y. Lao, J.G. Wen, Z.F. Ren, Nano Lett. 2 (2002) 1287. [47] S. Luryi, J. Xu, A. Zaslavsky, Future Trends in Microelectronics: The Nano Millennium, Wiley-Interscience, New York, 2002. [48] T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, Nature 391 (1998) 667. [49] J.B. Pendry, L. Martin-Moreno, F.J. Garcia-Vidal, Science 305 (2004) 847. [50] W.L. Barnes, A. Dereux, T.W. Ebbesen, Nature 424 (2003) 824. [51] E. Ozbay, Science 311 (2006) 189. [52] C. Girard, Rep. Prog. Phys. 68 (2005) 1883. [53] S.M. Nie, S.R. Emery, Science 275 (1997) 1102. [54] K. Kneipp, Y. Wang, H. Kneipp, L.T. Perelman, I. Itzkan, R.R. Dasari, et al., Phys. Rev. Lett. 78 (1997) 1667. [55] V.G. Veselago, Sov. Phys. Usp. 10 (1968) 509. [56] R.A. Shelby, D.R. Simth, S. Schultz, Science 293 (2001) 77. [57] B. Fay, Microelectron. Eng. 61 (2002) 11. [58] M.Z. Zhang, S. Lenhert, M. Wang, L.F. Chi, N. Lu, H. Fuchs, et al., Adv. Mater. 16 (2004) 409. [59] T.M. Whitney, J.S. Jiang, P.C. Searson, C.L. Chien, Science 261 (1993) 1316. [60] X.Y. Zhang, L.D. Zhang, G.W. Meng, G.H. Li, N.Y. Jin-Philipp, F. Philipp, Adv. Mater. 13 (2001) 1238. [61] Y.T. Pang, G.W. Meng, L.D. Zhang, Y. Qin, X.Y. Gao, A.W. Zhao, et al., Adv. Funct. Mater. 12 (2002) 719. [62] A.H. Liu, M. Ichihara, I. Honma, H.S. Zhou, Electrochem. Commun. 9 (2007) 1766. [63] C.R. Martin, Science 266 (1994) 1994. [64] B.H. Hong, S.C. Bae, C.W. Lee, S. Jeong, K.S. Kim, Science 294 (2001) 348. [65] Z. Zhang, D. Gekhtman, M.S. Dresselhaus, J.Y. Ying, Chem. Mater. 11 (1999) 1659. [66] W. Yoo, J. Lee, Adv. Mater. 16 (2004) 1097. [67] S.Y. Chou, P.R. Krauss, P.J. Renstrom, Appl. Phys. Lett. 67 (1995) 3114. [68] S.Y. Chou, P.R. Krauss, P.J. Renstrom, Science 272 (1996) 85. [69] S. Zhong, Y. Wang, M. Wang, M.Z. Zhang, X.B. Yin, R.W. Peng, et al., Phys. Rev. E 67 (2003) 061601. [70] Y. Wang, Y. Cao, M. Wang, S. Zhong, M.Z. Zhang, Y. Feng, et al., Phys. Rev. E 69 (2004) 021607. [71] T. Liu, S. Wang, Z.L. Shi, G.B. Ma, M. Wang, R.W. Peng, et al., Phys. Rev. E 75 (2007) 051606. [72] M.Z. Zhang, Y. Wang, G.W. Yu, M. Wang, R.W. Peng, N.B. Ming, J. Phys. Condens. Matter 16 (2004) 695. [73] D.R. Smith, J.B. Pendry, M.C.K. Wiltshire, Science 305 (2004) 788. [74] N. Fang, H. Lee, C. Sun, X. Zhang, Science 308 (2005) 534.