New Mode of Vapor−Liquid−Solid Nanowire Growth - Nano Letters

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New Mode of Vapor-Liquid-Solid Nanowire Growth V. G. Dubrovskii,*,†,‡ G. E. Cirlin,†,‡ N. V. Sibirev,† F. Jabeen,§ J. C. Harmand,§ and P. Werner|| †

St. Petersburg Academic University, Khlopina 8/3, 194021 St. Petersburg, Russia Ioffe Physical Technical Institute of the Russian Academy of Sciences, Politekhnicheskaya 26, 194021 St. Petersburg, Russia § CNRS-LPN, Route de Nozay, 91460 Marcoussis, France Max-Planck Institut f€ur Mikrostrukturphysik, Weinberg 2, D-10620 Halle, Germany

)

‡

ABSTRACT: We report on the new mode of the vaporliquid-solid nanowire growth with a droplet wetting the sidewalls and surrounding the nanowire rather than resting on its top. It is shown theoretically that such an unusual configuration happens when the growth is catalyzed by a lower surface energy metal. A model of a nonspherical elongated droplet shape in the wetting case is developed. Theoretical predictions are compared to the experimental data on the Ga-catalyzed growth of GaAs nanowires by molecular beam epitaxy. In particular, it is demonstrated that the experimentally observed droplet shape is indeed nonspherical. The new VLS mode has a major impact on the crystal structure of GaAs nanowires, helping to avoid the uncontrolled zinc blende-wurtzite polytylism under optimized growth conditions. Since the triple phase line nucleation is suppressed on surface energetic grounds, all nanowires acquire pure zinc blende phase along the entire length, as demonstrated by the structural studies of our GaAs nanowires. KEYWORDS: Vapor-liquid-solid growth, droplet shape, zinc blende crystal structure

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anowires (NWs) of different semiconductor materials have recently drawn much attention due to their importance for nanoscale electronics, photonics, and sensing.1-6 These NWs are usually fabricated via the vapor-liquid-solid (VLS) mechanism7 developed long ago for micrometer scale “whiskers”.8,9 Using modern epitaxy techniques such as molecular organic chemical vapor deposition5,7,10 or molecular beam epitaxy (MBE),11,12 NWs with diameters of several tens of nanometers and lengths up to tens of micrometers can now be obtained. The fundamental principle underlying the VLS mechanism is the catalytic effect of a liquid metal particle assisting the NW growth from a supersaturated liquid alloy.8 For many reasons, Au is the most commonly used among other metal catalysts.5-12 However, Aucatalyzed VLS NWs may suffer from several drawbacks such as the unwanted Au contamination.13,14 In the case of III-V compounds, Au-assisted NWs often feature spontaneous zinc blende-wurtzite (ZB-WZ) polytypism15,16 and, despite recent progress in this field,17-21 the desired phase perfection is still difficult to achieve. During the VLS growth, two-dimensional (2D) NW monolayers (MLs) nucleate and extend laterally in a layer-by-layer fashion. Growth of small enough NWs is mononuclear.22,23 As stated, e.g., in ref 24, many experiments show that, in the Aucatalyzed growth, the droplet wets the growth front but not the sidewalls. The triple phase line (TPL) separating the vapor, liquid, and solid phases is therefore shifted upward upon the completion of each ML. Such a situation will be referred to as the r 2011 American Chemical Society

standard VLS growth. Nebol’sin and Shchetinin25 formulated an inequality for the surface energies under which the TPL position at the NW top is stable and, consequently, the standard VLS growth occurs. For a given semiconductor material, this requires high enough surface energy of liquid alloy in the droplet (determined by the catalyst metal and the alloy composition during growth). In the same paper,25 Nebol’sin and Shchetinin presented experimental data showing that the VLS growth of Si whiskers is indeed stable only when catalyzed by high surface energy metals. Later on, Glas and coauthors26 introduced a very important concept of the TPL nucleation and presented an inequality for the surface energies under which 2D islands emerge at the TPL rather than at the liquid-solid interface. Glas and coauthors26 also showed that, at a lower surface energy of WZ NW sidewalls,27-29 formation of WZ structure requires two conditions: (i) the TPL nucleation to gain the surface energy and (ii) high enough supersaturation of liquid alloy to overcome the stacking fault. This view has gained much support20,30,31 and is now widely used for tuning the crystal phase of Au-catalyzed III-V NWs.17-21,31,32 Recently, Dubrovskii33 noticed that the Nebol’sin-Shchetinin condition for the standard VLS growth25 is equivalent to the Glas condition for the TPL nucleation.26 Received: December 5, 2010 Revised: January 20, 2011 Published: February 23, 2011 1247

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Figure 1. Standard VLS growth involving surface energies described in the text: the TPL (shown by the black circles) at the outer periphery of top facet (a) and its stability under random horizontal (b) and vertical (c) shifts.

Figure 2. VLS growth in the wetting case: unstable configuration with intermediate y (a); system geometry at y = ymax (b) and the directions of surface forces after the droplet is torn apart (c). From geometrical considerations, the maximum of y in spherical geometry is given by y = -2R cotan βmax.

Therefore, in the mononuclear mode, 2D islands must nucleate preferentially at the TPL if the droplet does not wet the sidewalls. Whenever the Nebol’sin-Shchetinin inequality25 is broken, the droplet wets the sidewalls and the TPL position at the NW top becomes unstable. This is probably disadvantageous for the growth stability, but is definitely of a great relevance regarding the phase purity of III-V NWs. Indeed, the absence of TPL nucleation must retain the structure to pure ZB.26 Under optimized growth conditions yielding the wetting VLS behavior, the polytypism issue can thus be safely avoided. However, to the best of our knowledge, neither such unusual VLS scenario has been discussed theoretically nor any experimental evidence of it has been presented so far. From the above considerations, a transition from the standard to the novel VLS mode is anticipated when Au is changed to a lower surface energy catalyst. In ref 34, we presented Gacatalyzed, pure ZB GaAs NWs grown by MBE on Si(111) substrates. Research results of other groups35-37 also confirm that self-catalyzed III-V NWs adopt the ZB phase much more often than the Au-catalyzed NWs. While the WZ percentage in Ga-catalyzed GaAs NWs may depend on the growth conditions such as the As flux during MBE,37 100% pure ZB structure in GaAs NWs can never be obtained under otherwise identical conditions when catalyzed by Au. The change of growth catalyst can therefore suppress the formation of WZ phase on surface energetic grounds. In this work, we further develop this approach by considering the surface forces acting at different NW interfaces. We present a general analysis showing that, depending on the surface energies, there are only two preferred positions of the droplet at the NW top. The first one relates to the standard case and the second to the novel VLS mode where the droplet entirely surrounds the NW top. We develop a model for the droplet shape in the latter case and introduce the new VLS configuration that may hold for NWs whose growth can be catalyzed by a low surface energy metal. We present new experimental data demonstrating pure ZB phase of Ga-catalyzed GaAs NWs. We discuss the lateral extension of some of our NWs toward their tops, induced by the sidewall nucleation from the droplets surrounding the NWs. Most importantly, it is shown that our droplets have a nonspherical elongated shape (after growth), as predicted by theoretical model but impossible in the standard VLS configuration. The standard VLS growth in the nonwetting case is shown schematically in Figure 1a. We assume the NW as being a straight cylinder of a constant radius R and the droplet in the form of a spherical cup with the contact angle β0 > π/2. We will consider five surface energies shown in Figure 1: those of the horizontal solid-liquid interface γSL, the liquid-vapor interface γLV, the NW top facet in contact with the vapor γSV, the NW sidewalls in

contact with the vapor γWV, and the vertical solid-liquid interface γSLl. The contact angle is sometimes obtained from the balance of horizontal forces at the TPL: γSL = -γLV cos β0,24,25,33 yielding that the droplet is always more than a hemisphere. Let us first consider the stability of TPL position at the outer periphery of NW top. When the TPL is shifted horizontally toward the NW center (Figure 1b), the back surface force Fh = γSV - γLV cos β0 - γSL is positive in view of γSV > γSL and thus returns the TPL to the original position. When the TPL is randomly shifted downward (Figure 1c), the vertical force F0 = γLV sin β0þ γSLl - γWV is directed upward provided that γWV < γLV sin β0 þ γSL l

ð1Þ

This inequality, obtained here as the condition for stability of the TPL at the top NW periphery, is exactly identical to the Nebol’sin--Shchetinin condition for the standard VLS growth25 and also to the Glas condition for the TPL nucleation.26 It is noteworthy that eq 1 can be obtained from rather different considerations, i.e., by comparing the formation energies of a complete ML slice in an instantaneous nucleation process (at a constant “liquid plus ML” volume) in two positions: with the liquid surrounding the ML or being outset by the latter.25,26,30,33 Let us now see what happens if the inequality (1) is not satisfied, i.e., when γWV > γLV sin β0 þ γSL l

ð2Þ

Opposite to the previous case, whenever the TPL moves slightly downward, the surface force is also directed downward and tends to increase the part of NW y wetted by the liquid, as shown in Figure 2a. Under the constraint of fixed liquid volume Ω and radius R, the penetration of NW cylinder into the droplet leads to the increase of contact angle β. As β increases, the vertical force F = γWV - γLV sin β - γSLl > 0 can only increase. Therefore, any configuration with y between zero and y = -2R cotan βmax is unstable, and the droplet will continue sliding down until the cylinder hits the droplet surface (Figure 2b). Configuration shown in Figure 2b relates to the minimum surface energy of a spherical droplet under the condition given by eq 2. This is the consequence of the following theorem: The surface energy of the system incorporating the droplet and the NW of length L = constant G¼

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2πR 2 γ þ πR 2 γSL þ 2πRyγSL l þ 2πRðL - yÞγWV 1 þ cos β LV ð3Þ dx.doi.org/10.1021/nl104238d |Nano Lett. 2011, 11, 1247–1253

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Figure 3. Geometry of elongated droplet with H > D (a). Shape transformation of Ga droplet for the parameters described in the text (b).

under the condition of fixed liquid volume Ω¼

πR 3 ð1 - cos βÞ2 ð2 þ cos βÞ - πR 2 y ¼ constant sin3 β 3 ð4Þ

and at a constant R, has the minimum either at β = β0 (relating to y = 0) or at β = βmax(relating to y = ymax) when the inequality (1) is satisfied and only at β = βmax otherwise. To prove the theorem, we first express the height y in eq 3 through β by eq 4 and then differentiate the resulting G(β) with respect to β. The result is given by dG 2πR 2 ¼ ðγLV sin β þ γSL l - γWV Þ dβ ð1 þ cos βÞ2

ð5Þ

showing that the surface energy increases in the nonwetting case (1) and decreases otherwise. When G decreases at β = β0, it will continue decreasing at larger β, with the minimum being reached at y =ymax. When G increases at β = β0, the minimum energy is reached either in the standard VLS configuration with y = 0 or at y = ymax, depending on whether the value of G(β0) - G(βmax) is negative or positive. Surprisingly, the conventional Young’s equation, γWV = γLV sin β/ þ γSLl, in the geometry considered relates not to the minimum but to the maximum surface energy. This property follows directly from ! d2 G 2πR 2 γLV cos β/ ¼ π/2. The instability of Young’s configuration between y = 0 and y = ymax is physically explained by the constraint of fixed liquid volume, with any deviation of contact angle from β/ creating an uncompensated surface force. At βmax < β/, the standard VLS mode with y = 0 relates to the global energy minimum. Whenever βmax > β/, the two minima of surface energy are separated by the barrier G(β/). The stability of standard VLS growth discussed above is only local. Such case relates to possible fluctuation-induced transitions between the two states with y = 0 and y = ymax that will be studied elsewhere. The next step of system evolution could be the droplet torn apart, as shown in Figure 2c. Let us consider the directions of surface forces in this case. The vertical force acting at the top TPL on the NW sidewall, F1 = γWV - γLV sin βmax - γSLl, is always directed upward in view of eq 2 and βmax > β0. The horizontal

Figure 4. Dependences ΔG(Δβ) for Au-catalyzed NWs at β0 = 124, 117, and 110
and Ga-catalyzed NWs at β0 = 115, obtained from eqs 3 and 4. The circular dot represents the elongated droplet with minimum energy at Young’s contact angle β/ = 110
.

force acting upon the TPL resting on the top facet, Fh = γSV γLV cos βmax - γSL, returns the TPL back to the outer periphery provided that γSV > γSL - γLV cos βmax. This inequality gives the second condition for the stability of droplet at the NW top. However, as seen from Figure 2c, the force F1 acting upon the bottom TPL on the NW sidewall remains uncompensated and tends to decrease the contact angle βmax. Such force gives rise to further evolution of system morphology, with the droplet losing its spherical geometry. The new, stationary droplet shape should be obtained from the minimization of surface energy functional, which is not a simple problem in the general case. We now show that the nonspherical shape can be computed under the following reasonable assumptions (illustrated in Figure 3a): (i) constant Laplacian pressure along the droplet surface, yielding the constant curvature 1/R1 þ 1/R2 = constant, with R1 and R2 as the main radii of surface curvature; (ii) droplet surface given by a figure of rotation, r2 = f2(z); (iii) the Young’s condition for the equilibrium contact angle γWV = γLV sin β/ þ γSLl; (iv) small enough β/ such that -cotan β/ , 1; and (v) [f(z) - R]R , 1. It can be shown that, after the NW cylinder hits the droplet surface, the Young’s condition corresponds to the minimum surface energy at a fixed liquid volume, as in the standard 2D case. The parabolic equation describing the surface of droplet resting on the sidewalls can be written down as   z2 1 ð7Þ - C - z cotan β/ þ R f ðzÞ ¼ 4 R where C is the integration constant. The part of the droplet resting on the NW top should be spherical, of the radius Rd = 2/C, yielding 1249

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Figure 5. TEM image of the main part of a NW terminated by a Ga droplet (a). The selected area diffraction pattern, acquired from a region far removed from the droplet, shows the (110) ZB zone axis and demonstrates pure ZB structure. The scale in the insert is 5 nm-1. Panel b shows pure ZB phase of NW section just beneath the droplet, with few rotational twins. The scale bar in (b) represents 10 nm.

sin β0 = R/Rd = RC/2 for the top contact angle β0 . Together with the condition for the surface smoothness at the top corners, β0 = π - β/ (see Figure 3a), this gives C = (2 sin β/)/R, completing the unique determination of the curve given by eq 7. As seen from Figure 3, the stationary wetted part of the NW ys is larger than ymax. The height of parabolic droplet H is larger than its width D, which can never happen to a spherical droplet. To quantify our analysis, we consider the parameters approximately corresponding to the Au-catalyzed and Ga-catalyzed MBE growths of ZB, Æ111æ oriented GaAs NWs:26,29,30,34 γWV = 1.5 J/m2, γSLl = 0.75 J/m2, γLV = 1.0 J/m2 for Au-Ga liquid droplet and γLV = 0.8 J/m2 for Ga-As liquid droplet, with a typical radius of 40 nm. Spherical to parabolic shape transformation in the Ga-catalyzed case is shown in Figure 3b. Figure 4 presents the curves ΔG(β) = G(β) - G(β0), plotted against Δβ = β - β0 for the Au-catalyzed NWs (at three different β0) and for the Ga-catalyzed NWs at β0 = 115
. As is seen from the figure, typical parameters of Au-catalyzed growth relate to the standard VLS case with a positive derivative of energy at β = β0. However, the increase of β0 transforms the increasing ΔG(Δβ) curve to the curves having a maximum at β = β/. When catalyst metal is changed to Ga, the surface energy decreases in the entire range of contact angles, with the minimum energy of spherical droplet reached at βmax. The circular dot in Figure 4 represents the elongated droplet with the minimum energy at a constant Laplacian pressure, calculated for the surface geometry given by eq 7. The arrow represents the energetically favorable shape transformation shown in Figure 3b. It should be noted that the stationary state with the elongated droplet is not always possible. Indeed, at a very low γLV such that γWV > γLV þ γSLl, the Young’s equation on the sidewalls can never be satisfied. This situation corresponds to a complete wetting, with Ga atoms diffusing from the droplet and finally

forming a thin film on the sidewalls. Since the droplet disappears completely, the VLS growth can no longer proceed. Finally, the NW top surrounded by a supersaturated alloy can grow in radial direction due to the sidewall nucleation. The radial growth rate should however be slower than the vertical one, because the formation of a ring around the cylinder requires more surface area than that of a disk (of the same volume) on top of the cylinder. When such radial growth occurs, the resulting NW morphology would be a reverse conical, opposite to the case where the sidewall nucleation is enabled everywhere.38,39 We now present some new experimental data to confirm that the novel VLS mode occurs. As discussed, the first, indirect evidence is (almost) pure ZB phase of Ga-catalyzed GaAs NWs.34-36 Our GaAs NWs are grown by MBE on Si(111) substrates by a special procedure, involving the substrate anneal to form 70-100 nm diameter openings in the native oxide layer and the deposition of Ga which is collected in these openings. More growth details can be found in ref 34. The use of Si substrate enables producing Ga droplets of the required size and density. Otherwise, the influence of Si on the stationary NW growth far away from the substrate should not be crucial. The GaAs NWs presented in ref 34 were pure ZB remote from the droplet, with only a narrow section at the top exhibiting WZ-ZB transition followed by the WZ structure just beneath the droplet. In brief, the explanation of ZB to WZ transition at the end of the growth (opposite to the well-known WZ to ZB transition in the Au-catalyzed case16,26) is the following. After the Ga flux is turned off, there is still enough arsenic in the residual atmosphere to form stoichiometric solid GaAs at the expense of liquid Ga emptied from the droplet.40 This necessarily decreases the contact angle of the droplet and may lead to its breakdown. The remaining upper part of the droplet at the NW top may then enable the TPL nucleation producing the WZ structure. In later 1250

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Figure 6. Plan view SEM images of GaAs NWs grown after 15 min of growth (a) and (b), showing elongated droplet shape; scale bar represents 500 nm. Arrow in panel b points at the NW having lost a part of the droplet. Panel c shows the NW extending toward the top.

experiments, we took special care to preserve at most the stationary droplet configuration at the end of growth. The key growth modification involves periodical turn on the Ga source before or while the substrate is being cooled down. More details will be given elsewhere. For transmission electron microscopy (TEM) investigations of the crystal structure, the NWs are ultrasonically removed from the substrate, transferred to holey carbon films, and analyzed using a JEOL 4100 TEM operated at 200 kV. Conventional bright field TEM imaging of the NWs combined with selected area diffraction imaging is used to identify the crystal structure, Figure 5 showing typical TEM images. The TEM image of the main part of a NW in Figure 5a, with the corresponding selected area diffraction pattern (acquired from a region far removed from the droplet), demonstrates the general absence of stacking faults and mixed-phase regions. The dark bands are diffraction contrast features (bend contours) that are not associated with stacking disorder. Figure 5b shows the NW region just beneath the droplet, which, in contrast to the results of ref 34, also appears to be pure ZB, although featuring few rotational twins. Thus, the

use of turn on the Ga source at the end of growth enables to avoid the polytypism of the NW tip. Figure 6 shows typical scanning electron microscopy (SEM) images of Ga-catalyzed NWs. Plan views in panels a and b of Figure 6 clearly demonstrate the elongated shape of most droplets. Since such a shape is impossible if the droplet rests on the top facet, one must conclude that the droplet surrounds the NW as described by our theoretical model (although the buried tips of the NWs cannot be seen). The short NW highlighted in Figure 6b should have lost part of the Ga droplet catalyzing its growth. We have observed this effect in many samples. For example, a minor fraction of NWs presented in ref 34 do not have any droplets on their tops, which is why their length is always much shorter. This is probably explained by a rather small Young’s equilibrium contact angle (110
according to our estimates), so some droplets may diffuse to the sidewalls as in the complete wetting case described above. Figures 5a and 6c demonstrate a lateral extension of ∼2000 nm long NWs which should be caused by the precipitation of GaAs onto the wetted parts of sidewalls. Since the droplet in Figure 6c is also elongated, sidewall nucleation 1251

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Figure 7. Experimental and model droplet geometries in the novel VLS mode with the real NW diameter of 101 nm, H = 173 nm and D = 152 nm, yielding the aspect ratio of 1.14.

does not change the droplet configuration, although the droplet inflates as the radius of the NW top increases. Figure 7 demonstrates a good qualitative correlation between the experimental droplet shape after growth and the geometry given by eq 7. When the height H is adjusted, the droplet width D in experimental and model geometries appears to be exactly the same, with less than 10% discrepancy in the NW radius R. The measured contact angle β/ =114
is slightly larger than 110
by our numerical estimates. The aspect ratio H/D = 1.14 is the average of NWs presented in panels a and b of Figure 6. We note that the use of Ga instead of Au to promote the VLS growth of GaAs NWs does not automatically guarantee pure ZB structure. Indeed, while our Ga-catalyzed GaAs NWs and those described in ref 36 are pure ZB, the phase perfection has been obtained in a limited domain of growth conditions. GaAs NWs of ref 37 vary from pure ZB to up to 70% WZ structure as the As flux decreases, and those of ref 40 feature nearly 1 μm long WZ segments. We therefore reiterate that the avoidance of polytypism occurs only in the wetting VLS mode described above, where the droplet shape must be elongated as the NW top penetrates into the liquid. Most of GaAs NWs discussed in refs 37,40 do not seem to have such shape, and thus our considerations are not directly applicable. Many energetic as well as kinetic factors can brake down the set of criteria required to observe the wetting VLS configuration. Among these, we mention the liquid diffusion from the droplet, the influence of vapor environments on the surface energies and various nonstationary growth effects. Also, a fundamental assumption of ref 26 regarding the independence of the liquid-solid surface energy on the crystal phase is absolutely necessary to theoretically explain the ZB phase in the absence of TPL nucleation. As the lack of information on the liquid-solid lateral interfaces of III-V NWs persists, this feature has never been verified experimentally. Nevertheless, the radical improvement of phase purity reported here, together with the observed elongated droplet shape, can by and large support the validity of our model as well as the very occurrence of the wetting VLS growth mode under our MBE conditions. The latter must be carefully optimized to ensure the unusual VLS behavior where the droplet surrounds the NW top, which is the main message of this work. To conclude, we have developed a theoretical model predicting the novel VLS mode with the droplet resting on the corners of top facet and therefore entirely burying the growth front. Such growth occurs when the liquid-vapor surface energy is too low to favor its

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substitution by a more energetically costly solid-vapor interface of NW sidewalls. On the other hand, the liquid-vapor surface should be sufficiently energetic to make a positive Young’s contact angle with the sidewalls. Geometry of elongated droplet has been calculated within the small slope interpolation. It has been shown that the experimentally observed shape of Ga droplets in MBE growth of GaAs NWs is indeed elongated. The novel VLS mode has a major impact on the phase purity of GaAs NWs, because it may suppress the TPL nucleation and the ZB-WZ polytypism caused as a result. Since more studies are required to better understand and control the VLS growth configuration as well as the related crystal structures, we now plan to perform detailed MBE growth experiments and relevant characterization of different III-V NWs catalyzed by low energy group III metals. We also intend to investigate theoretically the droplet shape in a general case and to consider the growth kinetics in the wetting VLS mode.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]ffe.ru.

’ ACKNOWLEDGMENT This work was partially supported by the contracts with the Russian Ministry of Education and Science, scientific programs of the Russian Academy of Sciences, grants from the Russian Foundation for Basic Research, and FP7 projects SOBONA and FUNPROBE. We thank Frank Glas, Jonas Johansson, and Budhikar Mendis for stimulating discussions. ’ REFERENCES (1) Bryllert, T.; Wernersson, L. E.; Lowgren, T.; Samuelson, L. Nanotechnology 2006, 17, S227. (2) Gradecak, S.; Qian, F.; Li, Y.; Park, H. G.; Lieber, C. M. Appl. Phys. Lett. 2005, 87, 173111. (3) Hayden, O.; Zheng, G. F.; Agarwal, P.; Lieber, C. M. Small 2007, 3, 2048. (4) Liang, G. C.; Xiang, J.; Kharche, N.; Klimeck, G.; Lieber, C. M.; Lundstrom, M. Nano Lett. 2007, 7, 642. (5) Pauzauskie, P. J.; Yang, P. Mater. Today 2006, 9 (10), 36. (6) Yang, P.; Yan, R.; Fardy, M. Nano Lett. 2010, 10, 1529. (7) Lu, W.; Lieber, C. M. Nat. Mater. 2007, 6, 841. (8) Wagner, R. S.; Ellis, W. C. Appl. Phys. Lett. 1964, 4, 89. (9) Givargizov, E. I. Highly anisotropic crystals; Springer: Berlin and Heidelberg, 1987. (10) Fr€oberg, L. E.; Seifert, W.; Johansson, J. Phys. Rev. B 2007, 76, No. 153401. (11) Dubrovskii, V. G.; Cirlin, G. E.; Soshnikov, I. P.; Tonkikh, A. A.; Sibirev, N. V.; Samsonenko, Yu. B.; Ustinov, V. M. Phys. Rev. B 2005, 71, No. 205325. (12) Schubert, L.; Werner, P.; Zakharov, N. D.; Gerth, G.; Kolb, F. M.; Long, L.; G€osele, U.; Tan, T. Y. Appl. Phys. Lett. 2004, 84, 4968. (13) Hannon, J. B.; Kodambaka, S.; Ross, F. M.; Tromp, R. M. Nature 2006, 440, 69. (14) Perea, D. E.; Allen, J. E.; May, S. J.; Wessels, B. W.; Seidman, D. N.; Lauhon, L. J. Nano Lett. 2006, 6, 181. (15) Johansson, J.; Karlsson, L. S.; Svensson, C. P. T.; Martensson, T.; Wacaser, B. A.; Deppert, K.; Samuelson, L.; Seifert, W. Nat. Mater. 2006, 5, 574. (16) Moewe, M.; Chuang, L. C.; Dubrovskii, V. G.; Chang-Hasnain, C. J. Appl. Phys 2008, 104, 044313. 1252

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dx.doi.org/10.1021/nl104238d |Nano Lett. 2011, 11, 1247–1253