APPLIED PHYSICS LETTERS 90, 143116 共2007兲
ZnO nanowires and nanobelts: Shape selection and thermodynamic modeling Hong Jin Fana兲 Department of Earth Sciences, University of Cambridge, Cambridge CB2 3EQ, United Kingdom and Max Planck Institute of Microstructure Physics, Weinberg 2, 06120 Halle, Germany
Amanda S. Barnardb兲 Department of Materials, University of Oxford, Oxford OX1 3PH, United Kingdom
Margit Zacharias Department of Physics, University of Paderborn, Warburger Straße 100, 33098 Paderborn, Germany
共Received 17 January 2007; accepted 6 March 2007; published online 6 April 2007兲 The authors show that, during a steady-state vapor phase growth of ZnO nanomaterials, indium ¯ 0兴-axial doping causes the structural change from usual 关0001兴-axial short nanowires to 关112 nanobelts of much larger aspect ratio. They used an analytical thermodynamic model based on geometric summation of the Gibbs free energy to predict the dimension dependence of the nanowires and nanobelts for both pure and In-doped ZnO. The calculation result agrees with the experiment observation that in situ indium doping influences the nucleation and supports the dominating growth of a-axial nanobelts over c-axial nanowires. © 2007 American Institute of Physics. 关DOI: 10.1063/1.2720715兴 Tailoring the crystallographic orientation of semiconductor nanowires 共NWs兲 is one of the key points of the growth control. It has been shown experimentally that the growth direction can be changed by, e.g., applying corresponding lattice-matching substrates for wurtzite NWs,1,2 or using small-sized catalyst for Si NWs,3,4 or changing growth temperature for ZnSe NWs.5 Theoretical calculations have been conducted to describe the thermodynamics and kinetics of semiconductor NWs and predict the size dependent behavior.4–9 Vapor-liquid-solid 共VLS兲 is a widely used mechanism for controlled growth of semiconductor NWs, including ZnO.10,11 There is also great interests in doping ZnO NWs to enhance the electric conductivity or ferromagnetic ordering.12–15 Depending on the doping elements and/or concentration, the ZnO nanostructure can be dramatically different. For example, the In-doped ZnO NWs by Xu et al.16 have an unusual zinc blende crystal structure with periodically twinning, whereas in many other cases the indium doping causes a wurtzite-type belt structure.17 We recently found that, in the carbothermal reduction experiments routinely for ZnO NW growth, introducing an additional indium oxide source causes a transition from usual c-axial NWs to a-axial nanobelts 共NBs兲.18 The growth kinetics that has been proposed for oxide NBs by high-temperature decomposition and crystallization19,20 might not be applicable to explain the variation of shape and crystallographic orientation in this relatively low temperature VLS case. Instead, it can be reasoned that it is correlated to the indium doping. In this letter, we present more experiment evidence that the transition of ZnO nanostructures from c-axial wires to a-axial belts is caused by indium doping. A thermodynamic model is applied to predict the dimension dependence of the structure/orientation selection. The result of the modeling a兲
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supports the hypothesis that indium, even in a trace amount, plays the essential role in the nucleation of NBs and supports its growth. The ZnO nanostructures were synthesized inside a double-tube furnace via VLS mechanism. Details of the fabrication setup can be found elsewhere.18,21For the growth of NBs an indium-contaminated small tube was used 共contaminated after the experiments where an additional In2O3 source was used18兲, while for the growth of NWs, the tube was indium-free. All the rest conditions were identical. During the whole process, the Ar gas flow rate and total pressure were kept constant by using a gas flow controller, an electronically controlled needle valve, and an oil-free pump station, so as to establish a quasiequilibrium environment. The scanning electron microscopy images in Fig. 1 give a comparison of the result. When a clean ZnO source was used, the result is ordered arrays of pure ZnO NWs oriented vertical to the GaN surface. The mean diameter of the ordered NWs is 50 nm. The NWs have 关0001兴 long axis and ¯ 0其 hexagonal cross sections bounded with equivalent 兵112 planes. However, if the growth chamber has indium contamination 共trace amount兲, the substrate surface is dominated with ultralong NBs together with a small amount of irregular-shaped structures. These NBs are randomly oriented and have no alignment relative to the initial gold nan-
FIG. 1. Comparison of the sample surface structure when different source types were used. 共a兲 Pure ZnO + C source and 共b兲 ZnO + C source in a indium-contaminated alumina tube.
0003-6951/2007/90共14兲/143116/3/$23.00 90, 143116-1 © 2007 American Institute of Physics Downloaded 07 Apr 2007 to 131.111.41.167. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
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odot array. They have a typical length of ⬃20 m and widths of 100– 220 nm. Growth of the NBs was also initiated by gold, since no growth was observed at places without Au covering. Transmission electron microscopy analysis shows that the NBs are doped with indium 共atomic ratio of ¯ 0典. In: Zn⬇ 1 : 20兲 and the principle axis is along 具112 In the common growth mode of carbothermal reduction of ZnO,21,22 a nearly constant vapor partial pressure and a quasiequilibrium condition can be assumed so that the growth is nearly determined by thermodynamics. As a result, the NW growth direction is mostly along 关0001兴, in accordance with the crystallographic habits of ZnO. Non-c-axial ZnO NBs are usually observed under high-temperature 共⬎1000 ° C兲 nonsteady growth conditions with or without adding impurities in the source.17,19,20,23 Under this conditions, the growth kinetics can be dramatically different, e.g., the mobility of atoms is high enough to smooth up the highenergy side faces and diffuse to lower-energy front faces. As the ZnO 共0001兲 faces are the highest-energy low-index planes,24,25 a fast growth in 关0001兴 is thermodynamically fa¯ 0典 and 具011 ¯ 0典. vored over in 具112 Our result, together with the result of early growth stages,18 reveals clearly that a trace amount of indium in our experiments is still enough to alter the morphology and growth direction of ZnO nanostructures from an energeti¯ 0兴 direction. The lateral excally favored 关0001兴 to 关112 tended nuclei due to incorporation of In into the Au and Zn alloy are certainly not thermodynamically stable 共nor kinetically preferable兲 if composed of pure ZnO. It is the question whether the postnucleation growth of belt structure is also due to the presence of indium. In order to verify this, we examine the relative stability of the NWs and NBs with dimensions of interest in the absence of indium. The analytical, shape-dependent thermodynamic model used here is based on a geometric summation of the Gibbs free energy.26 The model has proven successful in describing the shape of nanocrystals and NBs.26–28 As the ZnO nanostructures under consideration here are relatively large, a “truncated” version of the model is used, as described in detail in Ref. 26. Since there is no experimental data available for the specific surface energies of ZnO, we used the ab ¯ 0其 = 2.3 J m−2, initio 共all-electron兲 surface energies of ±兵101 ¯ 0其 = 4.1 J m−2, and ±共0001兲 = 5.4 J m−2 calculated by ±兵112 Wander and Harrison with the hybrid B3LYP density functional.29,30 Also, our model results are more related to low-temperature equilibrium conditions, and thus have limited applicability to cases where pure ZnO NBs are grown via nonsteady mass transport.20 The morphology of the most common one-dimensional ZnO structures is geometrically defined in Fig. 2, assuming hexagonal and rectangular cross sections for NW and NB, respectively. Type A1 represents the NW observed herein, type A2 represent an alternative NW structure oriented in the ¯ 0其 facets, types B1 ±关0001兴 direction but enclosed by 兵101 and B2 represent the upper and lower limits of the NBs reported here, and types C1 and C2 represent the upper and lower limits of the NBs observed, e.g., by Jie et al.17 In each case, the model was used to calculate the total free energy as a function of total volume 共in terms of the number of ZnO formula units兲 in Fig. 3共a兲 and aspect ratio in Fig. 3共b兲. In
Appl. Phys. Lett. 90, 143116 共2007兲
FIG. 2. 共Color online兲 Schematic representations of the A1, A2 nanowires, B1, B2 nanobelts, and C1, C2 nanobelts. L refers to length, W to width, T to thickness, and D to diameter.
Fig. 3, all changes are response to extension along the principle axis 共i.e., lengthening兲. We can see from Fig. 3共a兲 that at large volume sizes, pure ±关0001兴 oriented ZnO NWs are clearly thermodynami¯ 0兴 or ±关101 ¯ 0兴 oriented NBs. There cally preferred over ±关112 is a crossover region, but turning to Fig. 3共b兲 we can see that this crossover corresponds to low aspect-ratio nanostructures 共aspect ratio⬍ 1兲 such as nanoplatelets. Over a ratio of ⬃1 共corresponding to a quasi-zero-dimensional nanocrystal兲, pure ZnO NBs are not energetically preferred at any size or aspect ratio. This implies that the stability of NBs over NWs in our In-contamination experiment cannot be thermodynamically accounted for in the absence of In. In addition, Fig. 3 also shows that the A1-type NWs reported here are ¯ 0其 majority predicted to be less stable than A2 type with 兵101 side surfaces. This is likely due to an effect of the surfaceinterface energy of the Au+ In+ Zn ternary liquid alloy catalyst, such as the case of Si 共Ref. 8兲 and ZnSe NWs,5 which was not included in our model. In the calculation above, the comparison between NWs and NBs was made by changing their lengths along 关0001兴 ¯ 0兴 for NBs. Hence, it does not account for NWs and ±关112 for the different crystallographic orientations inherent during lengthening. In the following, we compare the stability of each nanostructure, of both pure and In-doped ZnO, that is extended in the same growth direction. The results of such comparison are shown in Fig. 4. Note that average values of the NB width and thickness are used for defining the aspect ratio, so that the aspect ratio is ⬃30 ¯ 0兴 growth for the NWs and ⬃400 for the NBs. If the 关112 dominates, the morphology predicted for pure ZnO is in agreement with those observed in the In-doped case. The crossover occurs at a NB length of 4 m or a thickness-towidth ratio of ⬃22. Beyond this length, the NBs are ener-
FIG. 3. 共Color online兲 Free energy of the nanowire and nanobelt shapes as a function of 共a兲 the total volume in terms of the number of ZnO formula units and 共b兲 the aspect ratio. The change of aspect ratios is made by lengthening along the corresponding principle axis. Downloaded 07 Apr 2007 to 131.111.41.167. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
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FIG. 4. 共Color online兲 Free energy of the nanowire and nanobelt shapes as a function of the aspect ratio for dominated growth 共a兲 along 具0001典 and 共b兲 ¯ 0典. The estimated values for In-doped nanostructures are also along 具112 ¯ 0其 and 兵101 ¯ 0其 shown, with 5% In incorporated preferentially into the 兵112 nonpolar surfaces.
getically preferred over the NWs and their growth would be thermodynamically encouraged in the absence of In. However, if the 关0001兴 growth dominates, the morphology predicted for pure ZnO nanostructures disagrees with observations in our In-doping experiment. High aspect-ratio pure ZnO NBs are metastable with respect to a morphological transformation to a NW. The crossover occurs at a NB thickness of 31 nm, much larger than those observed in our experiments 共⬇10 nm兲. Therefore, the results of the theoretical modeling indicate that, in order for the large aspect ratio NBs to be thermodynamically preferred over the NWs, indium ¯ 0兴 direction and inhibit has promoted the growth in the 关112 the 关0001兴 growth. As an estimate of the impact that indium incorporation may have on the relative stability of these nanostructures, the above modeling was repeated with substitutional In defects included artificially in the pure ZnO surface energies. The “defect energy” was approximated by comparing known values for the Zn–O and In–O bond enthalpies31 and the free atom enthalpies,32 and by accounting for the fact that Zn or In atoms at the surface will form three bonds with surrounding oxygen atoms and have one dangling bond 共taken as half of a Zn–O or In–O bond兲. Assuming that In atoms incorpo¯ 0其 and 兵101 ¯ 0其 surrate preferentially into the nonpolar 兵112 faces and that the defect density is approximately 5% 共as determined by energy dispersive x-ray spectroscopy兲, we can estimate the free energy of In-doped nanostructures. Results are also shown in Fig. 4 for extensions in both 关0001兴 and ¯ 0兴 directions. We can see that the artificial In defects 关112 have a greater impact on the free energy of the NWs than that of the NBs, and in Fig. 4共a兲 the crossover between the In-doped nanostructres occurs at an aspect ratio of ⬃410, which is consistent with the experimental observations. In general, although this result supports the formation of high aspect ratio NBs over NWs due to indium incorporation, a more definite verification requires explicit, accurate data of surface energies of In-doped ZnO. In conclusion, we show that in situ indium doping 共with a 4 – 6 at. %兲 causes the structural change of the ZnO from
usual c-axial NWs to a-axial NBs. An analytical thermodynamic model was used to predict the dimension dependence of the shape by comparing the total Gibbs surface energies. The modeling result corroborates our hypothesis that In doping influences the nucleation and supports the growth of a-axial NBs over c-axial NWs. Our future work is to model how the atomic arrangement is disordered by indium doping, and how much indium is needed for a crystallographic transition during nucleation. 1
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