Structure, Growth Kinetics, and Ledge Flow during Vapor−Solid−Solid

pubs.acs.org/NanoLett

Structure, Growth Kinetics, and Ledge Flow during Vapor-Solid-Solid Growth of Copper-Catalyzed Silicon Nanowires C.-Y. Wen,† M. C. Reuter,‡ J. Tersoff,‡ E. A. Stach,† and F. M. Ross*,‡ † ‡

School of Materials Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, IBM T.J. Watson Research Center, Yorktown Heights, New York 10598 ABSTRACT We use real-time observations of the growth of copper-catalyzed silicon nanowires to determine the nanowire growth mechanism directly and to quantify the growth kinetics of individual wires. Nanowires were grown in a transmission electron microscope using chemical vapor deposition on a copper-coated Si substrate. We show that the initial reaction is the formation of a silicide, η′-Cu3Si, and that this solid silicide remains on the wire tips during growth so that growth is by the vapor-solid-solid mechanism. Individual wire directions and growth rates are related to the details of orientation relation and catalyst shape, leading to a rich morphology compared to vapor-liquid-solid grown nanowires. Furthermore, growth occurs by ledge propagation at the silicide/silicon interface, and the ledge propagation kinetics suggest that the solubility of precursor atoms in the catalyst is small, which is relevant to the fabrication of abrupt heterojunctions in nanowires. KEYWORDS Si nanowires, Cu3Si catalyst, vapor-solid-solid growth mechanism, in situ transmission electron microscopy

T

he vapor-liquid-solid (VLS) process using Au-Si liquid catalysts1,2 has become a routine method for fabricating one-dimensional self-assembled Si nanowires. Although Au is an excellent material for forming nanowires with controlled morphology, attention has recently focused on the use of alternative, solid catalyst materials3-8 for two different reasons. First, the catalyst material can be incorporated into the wire.9 Since Au is known to be a deep-level impurity in semiconductors, the electrical and optical properties of nanowires could in principle be improved using catalysts other than Au.10,11 Second, many nanowire applications could make use of heterostructure Si/Ge or Si/SiGe nanowires in which the composition changes along the length of the nanowires,12-14 preferably with compositionally abrupt and structurally perfect heterointerfaces.15,16 Formation of abrupt interfaces using the conventional Au-Si liquid catalyst, however, is thought to be fundamentally limited because of the high solubility of Si and Ge in the liquid, resulting in a “reservoir effect” that creates a composition gradient at the heterointerface.17,18 It has been suggested that solid catalysts may be advantageous in fabricating heterostructure nanowires due to the lower solubility of the growth species in the solid.3,4,19,20 It is therefore important to understand issues that arise during growth with solid catalysts in general. Copper has been investigated in some detail as a potential vapor-solid-solid (VSS) alternative to Au.5,21,22 Because Cu is not as electronically detrimental as Au, it has potential,

for example, for forming nanowires for photovoltaic applications.11,23 Furthermore, its eutectic temperature (TE) of 802 °C24 is relatively high. In principle, VSS growth should occur, rather than VLS, if the growth temperature is below the eutectic temperature of the semiconductor and the metallic starting material.5,21 This implies VSS growth for the Cu-Si system at around 500-600 °C. However, experimental and theoretical studies in several other materials25-28 suggest that liquid catalysts may exist far below TE, stabilized by size effects or by the supersaturation due to the growth process itself. In evaluation of a potential VSS material like Cu, direct evidence of the catalyst state during growth, determined through in situ observations, is therefore required. In this paper, we examine in situ the use of copper as a catalyzing material by carrying out wire growth in an ultrahigh vacuum transmission electron microscope (UHV-TEM). From the real-time observations we determine the catalyst structure during growth, confirming the VSS mechanism and the presence of Cu3Si catalysts. We find a variety of morphologies for copper-catalyzed Si wires and growth directions related to the catalyst orientation relation. We also measure the growth kinetics of individual wires. Two other VSS systems have been examined in situ, Au-Ge,25 where growth kinetics were determined, and Pd2Si-Si,29 where ledge flow was observed. Here, for Cu3Si-Si, we provide quantitative measurements of an unexpectedly complex ledge flow mechanism during growth. This process involves rigid rotation of the solid catalyst, as well as step nucleation, flow, and periodic pinning at the catalyst/wire interface. The kinetics of ledge flow imply a low Si solubility in the catalyst during VSS growth, supporting prior speculations3,4,19,20 that

* Corresponding author, [email protected]. Received for review: 10/8/2009 Published on Web: 12/30/2009 © 2010 American Chemical Society

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solid catalysts could be useful for the formation of abrupt heterointerfaces. The growth experiments were carried out in a Hitachi H-9000 UHV-TEM with a base pressure of 2 × 10-10 Torr and a maximum gas pressure during observations of 4 × 10-5 Torr.30 Observations were made in both plan-view geometry, which allowed studies of the catalyst formation and initial wire growth, and cross-sectional geometry, where the wire morphology, catalyst and interface structure, and wire growth rates could be determined. For plan-view observations, chemically etched Si(111) thin foils were used. For cross-sectional imaging, slices of n-type Si(111) wafers were used, mounted so that the electron beam was parallel to the substrate surface. Both types of substrate were chemically cleaned, loaded into a UHV side chamber, and flashed at 1250 °C to remove the surface oxide.31 A 0.1 nm coating of Cu was then thermally evaporated onto the growth surface at a pressure below 4 × 10-9 Torr. The substrate was transferred under UHV to the microscope polepiece and resistively heated to the growth temperature. Si nanowires started to grow after exposure to the chemical vapor deposition gas precursor disilane (20% diluted in helium), which flowed into the TEM polepiece gap through a capillary. Simultaneously, nanowire growth was recorded in bright or dark field imaging conditions onto videotape at a rate of 30 images per second. The growth temperature ranged between 470 and 550 °C and the disilane partial pressure between 1 × 10-7 and 8 × 10-6 Torr. The sample temperature was calibrated post-growth using an infrared pyrometer. Plan-view TEM observations provide information on the initial state and morphology evolution of the catalysts. Initial heating causes the Cu film to agglomerate (Figure 1a), and on reaching the growth temperature, e.g., 530 °C, larger islands form within a few minutes (Figure 1b-d). These islands have different orientations, as revealed in the variety of moire´ fringes formed due to overlap of the catalyst and Si lattices. Most islands are single-crystalline, but occasionally we observe defects such as grain boundaries (Figure 1c). After flowing disilane, nanowires start to grow from all islands, accompanied by a gradual catalyst shape change and appearance of sidewall facets (Figure 1e-h). We identify the structure of the islands as η′-Cu3Si by comparing electron diffraction patterns of the catalysts with those of the Cu3Si polymorphs.32 The polymorphs in the Cu3Si compounds differ in the stacking orders of the hightemperature hexagonal η-Cu3Si unit cell; for simplicity, we use the unit vectors of η-Cu3Si and we use “Cu3Si” to refer to the catalyst phase. Furthermore, the spacing of the moire´ fringes, for example in Figure 1d, is consistent with that resulting from an overlap of Cu3Si and Si(111) lattices. Figure 1 therefore shows that the evaporated Cu layer transforms to Cu3Si islands, which then catalyze the growth of Si nanowires. Figure 2a,b displays the morphology of the Si nanowires, recorded post-growth using scanning electron microscopy © 2010 American Chemical Society

FIGURE 1. Images captured from a video recorded in plan view. (a) The Si(111) substrate at 350 °C during initial heating of the sample. The dark contrast shows some of the Cu islands. (b-d) Morphology of Cu3Si on the substrate at 530 °C. The moire´ fringes in (d) are caused by an overlap of the Si and Cu3Si lattices. (e-h) Images of a typical catalyst before and after flowing disilane (1 × 10-6 Torr) at 530 °C for 1, 5, and 10 min, respectively. The radiating features in (h) are due to the formation of faceted nanowire sidewalls.

(SEM). Under these growth conditions, about 50% of the wires are kinked (and not analyzed further), 45% are straight and grow along the surface (wires labeled S in Figure 2b), and 5% are straight and grow up from the surface, mostly in 〈110〉 directions (wires labeled T). It is the T wires which show most clearly in TEM images such as Figure 2c and which are analyzed in detail here. The S wires also grow predominantly along 〈110〉, although their growth directions appear to depend on pressure to some extent (see Supporting Information). From cross-sectional TEM images recorded during growth (Figure 2c-e), we extract information on catalyst state, wire structure and growth kinetics for the wires that grow away from the substrate. As is clear from their faceted shape, the catalysts are in the solid state during wire growth, in agreement with the bulk eutectic temperature given above. We do not see measurable changes in catalyst sizes during growth, so in principle wire diameters should remain con515

DOI: 10.1021/nl903362y | Nano Lett. 2010, 10, 514-519

FIGURE 3. Growth rates measured for two wires at 530 °C as a function of disilane partial pressure. The insets show the catalyst morphology. The scale bar is 50 nm. The ratio of the catalyst surface area to wire cross-section of wire 1 is higher than that of wire 2. Error in the growth rate measurement is within (1.8 nm/min.

stant. The tapering observed is due to direct deposition of Si on the sidewalls. The growth direction of the wires in Figure 2c is consistent with 〈110〉 (shown as a dashed arrow), or with mirrored 〈110〉 after formation of a twin (dotted arrow). Detailed diffraction pattern analysis (see the inset in Figure 2d) shows that the epitaxial relation between the Cu3Si catalyst and silicon nanowire is Si(111¯)//Cu3Si(11¯01); Si[11¯0]//Cu3Si[112¯0]. Twin relations are frequently seen between wires; in such cases, the Si nanowires are mirror-symmetric in the [112¯] direction and the growth directions, catalyst orientations, and catalyst-nanowire contact angles are mirror-symmetric to each other. Occasionally we see wires with a different orientation relation, Si(111)// Cu3Si(11¯03) (Figure 2e), and in this case the growth direction is along Si[111]. These observations suggest that the wire growth direction is associated with the relative orientation of the catalyst and Si substrate. The primary growth direction, 〈110〉, is different from the most common growth direction, [111], for VLS Au-Si-catalyzed Si nanowires (e.g., ref 30) but is the same as has been observed in some other epitaxial nonAu-catalyzed nanowire growth on Si(111) substrates.6,7 We speculate that VSS growth has stricter requirements for reproducibility than VLS, since it requires control of wire and catalyst orientations, while reproducible VLS requires control only of wire orientation. In straight wires, we occasionally see extended defects such as stacking faults, but only in planes that are not parallel to the (111) growth plane. The existence of such defects does not appear to change the morphology of the wire. We did not observe multiple twinning or any hexagonal silicon phase as has been reported elsewhere for Cu-catalyzed Si nanowires.5,33 In Figure 3, wire axial growth rates measured in situ show an approximately linear relation with disilane partial pressure. This suggests that growth is limited by the arrival rate of Si from the vapor phase. Supply-limited growth is also consistent with the observation in Figure 3 that a wire with a higher ratio of catalyst surface area to wire cross section grows more quickly. In contrast, VLS Au-Si-catalyzed Si

FIGURE 2. (a, b) Scanning electron microscopy plan-view and grazing angle (10°) images of Cu3Si-catalyzed Si nanowires after 3 h of growth on Si(111) at 510 °C and 1 × 10-6 Torr Si2H6. S indicates wires that grow along the surface in 〈110〉 directions. T indicates wires growing off the surface, like those in (c), with growth directions also 〈110〉. (c) Bright-field transmission electron microscopy (TEM) image of nanowires (in projection over a ∼300 µm strip of substrate) recorded during growth at 530 °C and 1 × 10-6 Torr Si2H6. The dashed arrow indicates the projection of the vector in the [011] or [101] direction, and the dotted arrow indicates the mirror symmetric directions. (d) TEM image and electron diffraction pattern of a [101] wire. The growth plane of the wire is Si(111), which is labeled as A in the diffraction pattern, and the Cu3Si(0001) plane is labeled as B. The schematic illustration shows the electron diffraction patterns of Si[11¯0] and Cu3Si[112¯0] zone axes, open circles and solid circles, respectively, and the superposition of Si(111¯) and Cu3Si(11¯01) reflections, labeled O. Averaged over several wires, the Cu3Si[0001] direction is 8.3 ( 0.7° to Si[111] in the diffraction patterns, while the wire growth direction is 18.4 ( 0.7° off the Si[111] axis, as expected for a wire growing out of plane in the Si[011] or Si[101] direction. (e) TEM image and electron diffraction pattern showing a nanowire and catalyst with another orientation relation, Si(111)// Cu3Si(11¯03), labeled A and C, respectively. The growth direction is close to Si[111]. © 2010 American Chemical Society

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FIGURE 4. (a, b) Images extracted from a video recorded during growth of a nanowire at 520 °C and 1 × 10-6 Torr Si2H6. The video was recorded under dark field conditions by using a small objective aperture to block all the reflections except one from the Cu3Si structure. Thus, only the catalyst is visible, and its brightness fluctuates periodically during growth. (c) Bright field image of the catalyst and wire. The growth direction is Si[111].

nanowire growth shows diameter-independent growth rates over a similar pressure range; this is also supply limited, but there the droplet shapes are identical for each wire.34 An estimate of diffusion times within the catalyst suggests that wire growth should indeed be limited by disilane dissociation rather than by diffusion through the bulk of the catalyst. The activation energy of interdiffusion of Cu and Si in Cu3Si, 0.95 eV,35 is much lower than that of Si self-diffusion (>4 eV)36 and that of diffusion of Si at the interface between Cu3Si and Si (2.5 eV).37 As a result, mass transfer of Si and Cu should be dominated by interdiffusion within the catalyst. We extrapolate the data in ref 35 to obtain an interdiffusion coefficient of 2 × 10-7 cm2/s at the growth temperature (530 °C). Since the catalysts are below 100 nm in diameter, such a high diffusivity suggests that the equilibrium concentration of Si inside the catalyst should be established within milliseconds. In both cross-sectional and plan-view observations we consistently see changes in the appearance of the catalyst during growth. These changes provide clues to the growth mechanism. Dark field images of the catalyst, which are obtained by setting the objective aperture to form an image using electrons diffracted by the Cu3Si structure, can show dramatic oscillations in brightness during growth. Examples of strong and weak contrast are given in Figure 4 and the fluctuations are shown in Movie 1 in the Supporting Information. Dark field images are sensitive to small changes in crystal orientation, since the intensity scattered into the aperture depends dynamically on the interaction between the electron beam and the crystal. Thus, the contrast oscillation suggests that the particle is tilting back and forth repeatedly, with respect to the nanowire. We assume this is due to the propagation of individual ledges one at a time across the interface (see Supporting Information). Observing the interface directly, we can actually see ledge flow events in bright-field images, and an example is shown in Figure 5 and Movie 2 in the Supporting Information. The ledge shows as a small region of dark contrast (arrowed) due to lattice distortion around the ledge front. During wire growth, we find that successive ledges flow consistently in the same direction along the interface. By measuring in situ the axial growth rate of a single wire and the time between ledge © 2010 American Chemical Society

FIGURE 5. Images of a Si ledge moving along the interface during growth at 530 °C and 2.4 × 10-7 Torr Si2H6. The inset shows the region imaged and the direction of ledge flow. For clarity the ledge is marked by arrows. In (a), the interface is a complete Si(111) facet. In (b-d), a new ledge nucleates and propagates along the interface.

nucleation events, we determine that the wire grows on average 0.32 ( 0.03 nm per ledge. In other words, the height of the ledge is consistent with one Si(111) bilayer. From observations of ledge flow on several different wires, we find that two ledges seldom appear at the same time and that there is a short “incubation time” between the completion of one atomic plane and the nucleation of the next ledge. Multiple-ledge growth is only seen occasionally at high pressures. Because the ledge motion is unidirectional and there is an interval between ledge flow events, nanowire growth via spiral ledge motion around a screw dislocation is excluded. If we measure ledge propagation in detail (Figure 5c,d), we find that although a ledge may propagate at an overall speed of say 10 nm/s, there are points, spaced about 3 nm apart, at which the ledge is pinned, and ledges propagate between these points with jumps that are too fast to measure (>1000 nm/s) (Movie 2 in the Supporting Information). Referring back to Figure 1d, we suggest that the pinning is due to the periodicity of the interfacial dislocations that arise because of lattice mismatch between catalyst and nanowire. The Si ledge acts like an edge-type dislocation with Burgers vector normal to the interface, serving as a sink for Si during growth (climb). The strain field of interfacial dislocations can attract or repel such an edge dislocation so that its climb speed is expected to vary. Similar recurrent halting in ledge propagation, which may result from defects at the interface, was observed in Pd2Si-catalyzed Si nanowire growth.29 It is unlikely to happen in a system with a coherent interface, such as CoSi2/Si,38 or with a liquid catalyst. 517

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Real-time measurements of the ledge flow kinetics, such as those shown in Figure 5, indicate that the “incubation time” defined above is typically less than 20% of the time between consecutive ledge nucleation events, and the average ledge propagation speed is relatively slow (10 nm/s). In contrast, we have previously shown20 that VLS Au-Sicatalyzed Si nanowires grown at the same overall rate exhibit a long incubation time followed by ledge propagation at a rate too fast to measure (>1000 nm/s). During the incubation time, the concentration of Si atoms in the catalyst presumably increases, due to the incident flux, until it becomes favorable for a ledge to nucleate. The shorter incubation time for Cu3Si-catalyzed VSS wires compared to Au-Si-catalyzed VLS wires suggests that a smaller amount of excess Si in the catalyst can raise the chemical potential enough to nucleate a ledge. This implies a lower solubility of the precursor atom in the catalyst, as required to reduce the reservoir effect. Of course, this particular catalyst, being a silicide, is itself a Si reservoir and of less interest for heterostructure growth. Nonetheless, the demonstration of low solubility in this solid catalyst is encouraging for the use of other solid catalysts in heterostructure formation.

Finally, we also tested Cu-Si-catalyzed Si nanowire growth in the VLS mode above the eutectic temperature. As expected, droplets of a eutectic liquid formed and Si precipitated at the liquid/substrate interface, growing short wire “stubs”. However, the droplets disappeared within a few minutes to leave truncated Si cones (Figure 6). We assume this is due to fast diffusion of Cu atoms in or on Si. In conclusion, we have shown directly that the growth of silicon nanowires around 500-600 °C using Cu occurs via the VSS mechanism. We show that the catalyst is the η′-Cu3Si phase and the epitaxial growth direction is predominantly 〈110〉 but depends on the relative orientation of the catalyst and substrate. Real-time observations show that wire growth involves rigid rotations of the catalyst particles and is by repeated ledge nucleation and flow at the Cu3Si/Si interface, with the ledges propagating in a jumpy manner due to pinning by interfacial dislocations at the growth interface. In comparison with VLS growth, wires grown by VSS may require more stringent process control, because of the dependence of wire direction and growth rate on the details of the catalyst shape and orientation relation. On the other hand, this suggests the intriguing possibility that this VSS mode could provide a wider range of morphologies if the catalyst shape and orientation relationship could be controlled. The understanding of VSS growth in this and other systems is therefore an important goal in extending the possibilities of materials design using catalytic growth of nanowires. Acknowledgment. We acknowledge financial assistance from the NSF under Grants DMR-0606395 and DMR0907483. Supporting Information Available. Results of the effects of high disilane pressure on the growth of nanowires, TEM videos recorded during nanowire growth, and Movies 1 and 2. This material is available free of charge via the Internet at http://pubs.acs.org. REFERENCES AND NOTES (1) (2)

Wagner, R. S.; Ellis, W. C. Appl. Phys. Lett. 1964, 4, 89. Wagner, R. S., VLS mechanism of VLS growth. In Whisker Technology, Levitt, A. P., Ed.; Willey Interscience: New York, 1970; p 47. (3) Lensch-Falk, J. L.; Hemesath, E. R.; Perea, D. E.; Lauhon, L. J. J. Mater. Chem. 2009, 19, 849. (4) Wang, Y.; Schmidt, V.; Senz, S.; Go¨sele, U. Nat. Nanotechnol. 2006, 1, 186. (5) Arbiol, J.; Kalache, B.; Roca i Cabarrocas, P.; Morante, J. R.; Fontcuberta i Morral, A. Nanotechnology 2007, 18, 305606. (6) Kang, K.; Kim, D. A.; Lee, H.-S.; Kim, C.-J.; Yang, J.-E.; Jo, M.-H. Adv. Mater. 2008, 20, 4684. (7) Garnett, E. C.; Liang, W.; Yang, P. Adv. Mater. 2007, 19, 2946. (8) Kamins, T. I.; Williams, R. S.; Basile, D. P.; Hesjedal, T.; Harris, J. S. J. Appl. Phys. 2001, 89, 1008. (9) Allen, J. E.; Hemesath, E. R.; Perea, D. E.; Lensch-Falk, J. L.; Li, Z. Y.; Yin, F.; Gass, M. H.; Wang, P.; Bleloch, A. L.; Palmer, R. E.; Lauhon, L. J. Nat. Nanotechnol. 2008, 3, 168. (10) Gunawan, O.; Guha, S. Sol. Energy Mater. Sol. Cells 2009, 93, 1388. (11) Kayes, B. M.; Filler, M. A.; Putnam, M. C.; Kelzenberg, M. D.; Lewis, N. S.; Atwater, H. A. Appl. Phys. Lett. 2007, 91, 103110.

FIGURE 6. Images captured from an in situ video recorded during Cu-Si eutectic liquid catalyzed nanowire growth at 800 °C and 10-6 Torr Si2H6, after the times indicated. (a) The liquid Cu-Si catalyst, labeled L, and the base of a wire, B. The image is made by splicing together three frames in order to show the complete morphology. (b-d) A series of images of the central region of the wire showing shrinkage of the droplet. © 2010 American Chemical Society

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(12) Gudiksen, M. S.; Lauhon, L. J.; Wang, J.; Smith, D. C.; Lieber, C. M. Nature 2002, 415, 617. (13) Bjo¨rk, M. T.; Thelander, C.; Hansen, A. E.; Jensen, L. E.; Larsson, M. W.; Wallenberg, L. R.; Samuelson, L. Nano Lett. 2004, 4, 1621. (14) Yang, C.; Zhong, Z.; Lieber, C. M. Science 2005, 310, 1304. (15) Lieber, C. Nano Lett. 2002, 2, 81. (16) Samuelson, L.; Thelander, C.; Bjo¨rk, M. T.; Borgstro¨m, M.; Deppert, K.; Dick, K. A.; Hansen, A. E.; Mårtensson, T.; Panev, N.; Persson, A. I.; Seifert, W.; Sko¨ld, N.; Larsson, M. W.; Wallenberg, L. R. Physica E 2004, 25, 313. (17) Li, N.; Tan, T. Y.; Go¨sele, U. Appl. Phys. A: Mater. Sci. Process. 2008, 90, 591. (18) Clark, T. E.; Nimmatoori, P.; Lew, K.-K.; Pan, L.; Redwing, J. M.; Dickey, E. C. Nano Lett. 2008, 8, 1246. (19) Persson, A. I.; Larsson, M. W.; Stenstro¨m, S.; Ohlsson, B. J.; Samuelson, L.; Wallenberg, L. R. Nat. Mater. 2004, 3, 677. (20) Wen, C.-Y.; Reuter, M. C.; Bruley, J.; Tersoff, J.; Kodambaka, S.; Stach, E. A.; Ross, F. M. Science 2009, 326, 1247. (21) Yao, Y.; Fan, S. Mater. Lett. 2007, 61, 177. (22) Renard, V. T.; Jublot, M.; Gergaud, P.; Cherns, P.; Rouchon, D.; Chabli, A.; Jousseaume, V. Nat. Nanotechnol. 2009, 4, 654. (23) Davis, J. R.; Rohatgi, A.; Hopkins, R. H.; Blais, P. D.; RaiChoudhury, P.; McCormick, J. R.; Mollenkopf, H. C. IEEE Trans. Electron Devices 1980, 27, 677. (24) Binary Alloy Phase Diagram; Massalski, T. B., Ed.; American Society for Metals: Metals Park, OH, 1986.

© 2010 American Chemical Society

(25) Kodambaka, S.; Tersoff, J.; Reuter, M. C.; Ross, F. M. Science 2007, 316, 729. (26) Adhikari, H.; Marshall, A. F.; Goldthorpe, I. A.; Chidsey, C. E. D.; McIntyre, P. C. ACS Nano 2007, 1, 415. (27) Schwalbach, E. J.; Voorhees, P. W. Nano Lett. 2008, 8, 3739. (28) Wacaser, B. A.; Reuter, M. C.; Khayyat, M. M.; Wen, C.-Y.; Haight, R.; Guha, S.; Ross, F. M. Nano Lett. 2009, 9, 3296. (29) Hofmann, S.; Sharma, R.; Wirth, C. T.; Cervantes-Sodi, F.; Ducati, C.; Kasama, T.; Dunin-Borkowski, R. E.; Drucker, J.; Bennett, P.; Robertson, J. Nat. Mater. 2008, 7, 372. (30) Ross, F. M.; Tersoff, J.; Reuter, M. C. Phys. Rev. Lett. 2005, 95, 146104. (31) Stach, E. A.; Hull, R.; Tromp, R. M.; Reuter, M. C.; Copel, M.; LeGoues, F. K.; Bean, J. C. J. Appl. Phys. 1998, 83, 1931. (32) Wen, C.-Y.; Spaepen, F. Philos. Mag. 2007, 87, 5581. (33) Arbiol, J.; Fontcuberta i Morral, A.; Estrade´, S.; Peiró, F.; Kalache, B.; Roca i Cabarrocas, P.; Morante, J. R. J. Appl. Phys. 2008, 104, 064312. (34) Kodambaka, S.; Tersoff, J.; Reuter, M. C.; Ross, F. M. Phys. Rev. Lett. 2006, 96, 096105. (35) Hong, S. Q.; Comrie, C. M.; Russell, S. W.; Mayer, J. W. J. Appl. Phys. 1991, 70, 3655. (36) Ural, A.; Griffin, P. B.; Plummer, J. D. Phys. Rev. Lett. 1999, 83, 3454. (37) Solberg, J. K.; Nes, E. Philos. Mag. A 1978, 37, 465. (38) Chou, Y.-C.; Wu, W.-W.; Cheng, S.-L.; Yoo, B.-Y.; Myung, N.; Chen, L. J.; Tu, K. N. Nano Lett. 2008, 8, 2194.

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