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Surface reconstruction and core distortion of silicon and germanium nanowires

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2007 Nanotechnology 18 215703

(http://iopscience.iop.org/0957-4484/18/21/215703)

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Nanotechnology 18 (2007) 215703 (9pp) doi:10.1088/0957-4484/18/21/215703

Surface reconstruction and core distortionof silicon and germanium nanowiresWenliang Liu1, Kaiwang Zhang1,3, Huaping Xiao1, Lijun Meng1,Jun Li1, G Malcolm Stocks2 and Jianxin Zhong1,2,3

1 Department of Physics, Xiangtan University, Xiangtan, Hunan 411105,People’s Republic of China2 Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA

E-mail: kwzhang@xtu.edu.cn and jxzhong@xtu.edu.cn

Received 14 December 2006, in final form 10 April 2007Published 27 April 2007Online at stacks.iop.org/Nano/18/215703

AbstractWe report the results of molecular dynamics simulations for structures ofpristine silicon nanowires and germanium nanowires with bulk cores orientedalong the [110] direction and bounded by the (100) and (110) surfaces in thelateral direction. We found that the (100) surfaces for both silicon andgermanium nanowires undergo 2 × 1 dimerization while their (110) surfacesdo not show reconstruction. The direction of the dimer rows is either parallelor perpendicular to the wire axis depending on the orientation of the surfacedangling bonds. The dimer length for Si is in good agreement with the resultobtained by first-principles calculations. However, the geometry of Si dimersbelongs to the symmetrical 2 × 1 reconstruction rather than the asymmetricalbuckled dimers. We also show that surface reconstruction of a smallnanowire induces significant change in the lattice spacing for the atoms noton the (100) surface, resulting in severe structural distortion of the core of thenanowire.

1. Introduction

Semiconductor nanowires are promising nanomaterials fornovel electronic [1], opto-electronic [2], and sensing [3] appli-cations. A variety of freestanding semiconductor nanowires,including the group IV, III–V, or II–VI semiconductornanowires [1–5], can now be synthesized by a variety ofphysical or chemical methods [5]. Semiconductor nanowireheterostructures with a core–shell structure or a superlatticestructure along the growth axis can also be synthesized us-ing a vapour–liquid–solid mechanism with precise control ofcomposition and growth direction [6]. Experimental resultsshow that a nanowire often grows around a crystalline bulkcore with only a few axial orientations. The diameter of ananowire typically ranges from a few tens of nanometres downto 1 nm, while its length can exceed a few micrometres. Thesurface/volume ratio of a nanowire becomes large as its diame-ter approaches a few nanometres. Therefore, understanding thesurface structure of a small nanowire is an essential element inthe study of semiconductor nanowires.

3 Authors to whom any correspondence should be addressed.

Silicon nanowires (SiNWs) have been widely usedas a model system to uncover the structural features ofsemiconductor nanowires. Recent experiments showed thatSiNWs can grow along the [110] and [112] directions withdiameters in the range of 1.3–7 nm [7]. It has also beenshown that SiNWs of smaller diameters are oriented alongthe [110] direction, while nanowires of larger diameters areoriented along the [112] or [111] direction [8]. Theoreticalstudies of SiNWs have been focused both on the H-terminatedSiNWs [9] and pristine SiNWs [10–14]. The advantage ofusing H-terminated SiNWs is the passivation of dangling bondsof surface atoms, preventing surfaces from reconstruction. Ithas been clearly demonstrated that the band gap of an H-terminated SiNW widens due to quantum confinement [9].Understanding structures of non-passivated pristine SiNWs ismore challenging. Several possible atomic configurations ofthe smallest pristine SiNWs have been suggested by first-principles studies [10] and are very different from the bulkstructure of Si. However, recent experiments have shown thatmost SiNWs grow around bulk Si cores and their propertiesstrongly depend on the surface structure of the wire [7, 8].Thus understanding structures of SiNWs with bulk cores is of

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practical importance. Theoretical studies based on the densityfunctional theory calculations for [100] and [110] SiNWs haveconfirmed the importance of facet edges of nanowires on theirband structures [11, 12]. In particular, it has been shownthat a [100] SiNW of 1.5 nm diameter with a bulk coreis either metallic or semi-metallic depending on its surfacereconstruction [13]. Surface reconstruction of small pristine[110] SiNWs has recently been studied in detail by first-principle calculations [14], in which the [110] SiNW has a bulkcore oriented along the [110] direction with ∼1 nm diameterbounded by two (100) and two (110) planes. It has been shownthat the (100) surfaces are reconstructed with dimerization andthe dimer rows on the two (100) planes are perpendicularto each other. The dimers were found to be asymmetrical(buckled).

The study of [110] SiNWs is of particular interestas experimentally [110] SiNWs have been found to growpreferentially in the small diameter range [8]. It isfundamentally important to understand the surface structureof a semiconductor nanowire as it not only determines theelectronic and mechanical properties of the wire but also laysthe groundwork for studying many other important problemssuch as doping [15, 16] and adsorption of molecules [3].The first-principles calculation [14] found buckled dimerson the (100) surface of SiNWs that are very similar to thedimers on the (100) surface of bulk Si. However, whetherthe dimers on the (100) bulk Si surface are asymmetric(buckled) or symmetric (flat) has been a debated issue. Total-energy calculations based on the semi-empirical tight-bindingpotential [17] and first-principles calculations [18] have shownthat buckled dimers have the lowest energy. However,calculations based on the multi-configuration self-consistentfield theory found that the symmetric 2 × 1 reconstructionis the most stable [19]. Experimentally, scanning tunnellingmicroscopy (STM) measurements showed symmetric 2 ×1 dimers at room temperature [20] but buckled dimers attemperatures around 200 K in one study [21], but another [22]found that dimers are symmetric at low temperature below40 K, suggesting that the 2 × 1 symmetric dimers are the moststable structure at the zero temperature limit. Therefore, itis important to further investigate the phenomena of SiNWdimerization using different approaches. Moreover, it isnot clear whether the conclusions obtained from SiNWs areapplicable to other IV semiconductor nanowires such as Genanowires (GeNWs) [4]. Furthermore, surface reconstructionof a small nanowire may have a severe influence on the latticestructure of its core due to the large surface/volume ratio. Afundamental understanding of how surface reconstruction of ananowire affects its core however has been very limited.

In this paper, we report results of molecular dynamics(MD) simulations for structures of small SiNWs and GeNWs.In our MD simulations, many-body empirical potentials wereused to describe the Si–Si and Ge–Ge interactions. Themajor advantage of using an empirical-potential-based MDsimulation is its computational efficiency and it can thereforemodel a system under large time scales, which is essentialfor identification of the most stable structure of a system oflarge size using global optimization techniques. The standardsimulated annealing global optimization technique was usedin this paper to search for the ground-state structures of the

SiNWs and GeNWs and has not been used in any first-principles studies for semiconductor nanowires due to thetremendous computational cost. Particular attention was paidto examination of the surface reconstruction and its influenceon the structural change of the core of a semiconductornanowire.

2. Simulation method

Our MD simulation was carried out using the materialsexplorer (ultra version), a large scalable professional MDsoftware. The initial structures of our wires have the samegeometry as the NW2 and NW3 SiNWs used in [14] and wereobtained by cutting bulk Si and Ge along the [110] directionto form rectangular shapes bounded by two (100) planes andtwo (110) planes. The only difference between the NW3 wireand the NW2 wire is that the NW3 wire has larger (100)surfaces. We used the NW3 wire to investigate the surface sizeeffects on surface reconstruction. We also used long and shortsimulation super-cells to examine the effects of wire lengthon surface reconstruction. The long super-cell consists of 28atomic layers (308 atoms for the NW2 wire) while the shortone has the same length of 12 layers as that used in [14].The values of the lattice constant (0.543 072 nm for Si and0.565 754 nm for Ge) for the initial structures of Si and Genanowires are from the experimental values of bulk Si and Ge.A periodic boundary condition was used along the nanowireaxis while a free boundary condition was chosen for the othertwo directions. A sufficient vacuum space of 10 atomic layerswas provided in the [001] and [110] directions to model aninfinite one-dimensional system. The well-established many-body Tersoff potentials [23] were used to describe the Si–Siand Ge–Ge interactions and the cut-off distance was chosen tobe 1 nm for all atoms. The temperature was controlled by thevelocity scaling method and the NTV ensemble (ensemble inwhich the number of atoms, the temperature, and the volumeare constant) was used for the simulation environment. EachMD step represents 2 fs. We used the simulated annealingprocess to find the stable structure of a nanowire. In thisprocess, 20 000 MD steps were performed at 300 K forstructural relaxation and then the temperature was increasedto 950 K at a 2.71 K ps−1 rate. The system was equilibrated at950 K for 80 000 steps and then annealed from 950 to 0 K at a3.96 K ps−1 cooling rate. Finally, 20 000 steps were performedat 0 K to fully relax the structure. The simulation results areillustrated in figures 1–5.

We note that the annealing temperature and cooling rateare the two critical parameters in a simulated annealingsimulation. High annealing temperatures are required forcreating a melted state as the initial structure while smallcooling rates are needed for exploring more structuralconfigurations. In reality, cooling rates are limited by thecomputational cost and one needs to find the largest coolingrate for effective simulation. We found that ordered surfacestructures with the lowest energy can be obtained only whenthe cooling rate is not larger than 3.96 K ps−1. A coolingrate larger than 3.96 K ps−1 leads to the same surfacereconstruction but often keeps some parts of the surfacesdisordered with higher energies. Thus, we chose 3.96 K ps−1

as the cooling rate in our simulation. For the annealing

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Figure 1. Structures of NW2 Si nanowires along the [110] direction bounded by (100) surfaces and (110) surfaces. The wire has seven corelayers and its surface dangling bonds on different (100) surfaces are perpendicular to each other. (A) (a)–(c): Initial structure; (d)–(g):reconstructed structure; (h) and (i): space filling plots of (e) and (f). (B): Lattice spacing for core layers parallel to the (100) surface.(C): Lattice spacing for layers perpendicular to the (100) surface. The circles in (B) and (C) represent the atomic layers parallel orperpendicular to the wire axis, respectively.

temperature, one needs to find the temperature regime whereonly the surfaces of a nanowire are melted. We found thattemperatures around 950 K are the best condition for thesurface reconstruction of SiNWs and GeNWs. At temperaturesslightly lower than 950 K (<900 K), surface atoms areoften trapped in high-energy states. However, an annealingtemperature slightly higher than 950 K (>1000 K) leadsto melting of the core of the nanowire, which significantlyincreases the complexity of the configuration space andcomputational burden. Therefore, we used 950 K as theannealing temperature in our simulation to have the [110]orientation of the SiNWs and GeNWs unchanged.

3. Silicon nanowires

We studied the NW2 and NW3 SiNWs to investigate thesurface size effects on surface reconstruction. We also usedsuper-cells of 28 layers and 12 layers long to examine thelength effects on surface reconstruction. Our results show thatthe surface size of a nanowire has a significant influence on the

wire structure. However, wires of different lengths do not showany distinguishable difference in their surface reconstruction,indicating that wires of 12 layers long are sufficient formodelling the structural properties of the nanowire studied. Wefirst describe the results of the NW2 SiNW which has exactlythe same initial structure as that used in [14] for the first-principles study except that our wire is 28 layers long ratherthan 12 layers long. The initial 308 atom structure of ourNW2 consisting of a simulation super-cell with a cross sectionof 0.768 nm × 1.086 nm and a wire length of 5.430 72 nmwithin a simulation super-cell is illustrated in figure 1(A) (a)–(c). The final stable structure of the wire obtained by theMD simulation is given in figure 1(A) (d)–(i) (figure 1(A) (h)and (i) are the same plots as in figure 1(A) (e) and (f) buthave space filling spheres to clearly illustrate the surfacestructure). Figure 1(A) shows that the two (100) surfaces havesevere reconstruction and atoms form dimer rows on the (100)surfaces. No reconstruction is observed on the (110) surfaces.It is clear from figure (A) (h) and (i) that the dimers are the 2×1symmetrical dimers and the dimer rows are perpendicular toeach other on the two (100) surfaces. We found that all dimers

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Figure 2. Structures of NW2 Si nanowires along the [110] direction bounded by (100) surfaces and (110) surfaces. The wire has eight corelayers and its surface dangling bonds on different (100) surfaces are parallel to each other. (A) (a)–(c): Initial structure; (d)–(g): reconstructedstructure; (h) and (i): space filling plots of (e) and (f). (B): Lattice spacing for core layers parallel to the (100) surface. (C): Lattice spacing forlayers perpendicular to the (100) surface. The circles in (B) and (C) represent the atomic layers parallel or perpendicular to the wire axis,respectively.

have a length of 0.236 nm, which is very close to the first-principles result of 0.231 nm. First-principles calculations alsofound perpendicular dimer rows on the (100) surfaces and anabsence of dimer formation on the (110) surfaces. However,in those calculations the dimers were shown to be buckled(asymmetrical) [14].

We found that dimer formation results in a severe changein the lattice spacing of the wire. Lattice spacing as afunction of atomic layers in different directions is illustratedin figures 1(B) and (C). From figure 1(B) one can see thatdimer formation perpendicular to the wire axis results in asignificant reduction in the lattice spacing for the core layersparallel to and close to the (100) surface. The change inlattice spacing is −6.5%, −4.5%, and −4.1%, respectively,for the first, second, and third layers below the (100) surface.On the other hand, dimer formation parallel to the wire axisinduces a small change in lattice spacing. From the continuumtheory of elasticity, one expects that compression on the (100)surface and its neighbouring layers leads to expansion of otherparts of the wire to relieve strain energy. Indeed, figure 1(B)shows that the lattice spacing for the fourth and fifth layers isapproximately 1.9% larger that the bulk value and there is a1% overall expansion of the lattice spacing along the wire axis.

Moreover, figure 1(C) shows that dimer formation results in alarge expansion in lattice spacing for layers perpendicular tothe wire axis. The expansion rates for the (110) surfaces andtheir neighbouring layers are 4.1% and 2.7%, respectively.

We found that the dimer rows on the two (100) surfacesare not necessarily perpendicular to each other. Our MD resultsshow that the orientation of dimers follows the same directionas the Si dangling bonds. Dimer rows are perpendicular orparallel to each other if the dangling bonds of Si atoms onthe two (100) surfaces are perpendicular or parallel to eachother. As an example, we studied a new NW2 SiNW, inwhich one additional layer of Si atoms is added to one of its(100) surfaces. The dangling bands on the two (100) surfacesof this NW2 wire follow the same direction perpendicularto the wire axis. We can see from figure 2(A) that 2 × 1symmetrical dimers form on the two (100) surfaces of theNW2 wire and there is no apparent structural reconstructionon the (110) surfaces. The dimer length was found to be0.236 nm for all dimers. In contrast to the seven-layer structure(figure 1(A)), dimer rows on the two (100) surfaces of theeight-layer structure (figure 2(A)) are parallel to each other.Comparing figure 2 with figure 1, we can see that formationof identical dimer rows on the two (100) surfaces results in

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Figure 3. Structures of NW3 Si nanowires along the [110] direction bounded by (100) surfaces and (110) surfaces. The wire has seven corelayers and its surface dangling bonds on different (100) surfaces are perpendicular to each other. (A) (a)–(c): Initial structure; (d)–(g):reconstructed structure; (h) and (i): space filling plots of (e) and (f). (B): Lattice spacing for core layers parallel to the (100) surface.(C): Lattice spacing for layers perpendicular to the (100) surface. The circles in (B) and (C) represent the atomic layers parallel orperpendicular to the wire axis, respectively.

an even larger change in the lattice spacing of the nanowire.Figure 2(B) shows that the change in lattice spacing for thefirst, second, third, sixth, seventh, and eighth layers close tothe (100) surfaces is −6.6%,−4.3%,−3.6%,−4.3%,−4.4%,and −6.7%, respectively. The lattice spacing for the fourth andfifth layers is approximately 2.6% larger that the bulk valueand there is 2% overall expansion in the lattice spacing alongthe wire axis. Figure 1(C) shows that the expansion rates forthe (110) surfaces and their neighbouring layers are 6.4% and2.4%, respectively.

To understand the surface size effects on surface dimerformation, we studied the same SiNW as used in the first-principles study (NW3). Because we found that the 12-layerwire is sufficiently long for modelling the structural propertiesof the wire, we focused on the NW3 SiNW with the samelength (12 layers) as that used in [14] for comparison ofthe results. The initial 240 atom structure of the NW3 wirewith a cross section of 1.535 nm × 1.086 nm and a wirelength of 2.29 nm is illustrated in figure 3(A). It has the sameorientation and size of (110) surfaces as the NW2 wire but haslarger (100) surfaces. The super-cell for our MD simulationhas 12 layers of Si. Using the same simulated annealingprocess as used for the NW2 wires, we have studied NW3

wires with different types of (100) surfaces and found thesame conclusions except for smaller values of change in thelattice spacing for the core layers. We take the NW3 wirewith perpendicular dangling bonds on its two (100) surfacesto illustrate our results. Figure 3(A) shows that the two (100)surfaces undergo an apparent surface reconstruction forming2 × 1 symmetrical dimers but the (110) surfaces are nearlyidentical to their initial structures. The dimer length has thesame value 0.236 nm as found for NW2 wires. The orientationof dimers follows the same direction of the dangling bondson the (100) surface. There are two rows of dimers parallelto the wire axis on one of the (100) surfaces and three rowsof dimers perpendicular to the wire axis on the other (100)surface. Apparently, dimer rows on the two (100) surfacesare perpendicular to each other. From figure 3(B), we cansee that the maximum change in lattice spacing for the layersclose to the (100) surface is 3.6%, which is much smaller thanthe 6.5% compression observed in the NW2 wire, indicatingthat dimerization on larger (100) surfaces leads to a smallerchange in lattice spacing. For the same size surface, one wouldexpect that more dimers would lead to a larger change in latticespacing. The (110) surface of the NW3 wire has the sameinitial size as the (110) surface of the NW2 wire. Thus, a larger

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Figure 4. Structures of NW2 Ge nanowires along the [110] direction bounded by (100) surfaces and (110) surfaces. The wire has seven corelayers and its surface dangling bonds on different (100) surfaces are perpendicular to each other. (A) (a)–(c): Initial structure; (d)–(g):reconstructed structure; (h) and (i): space filling plots of (e) and (f). (B): Lattice spacing for core layers parallel to the (100) surface.(C): Lattice spacing for layers perpendicular to the (100) surface. The circles in (B) and (C) represent the atomic layers parallel orperpendicular to the wire axis, respectively.

change in lattice spacing for the (110) surfaces is expectedfor the NW3 wire. Indeed, figure 3(C) shows that the (110)surfaces of the NW3 wire have 5.5% expansion, which is largerthan the value of 4.1% for the NW2 wire.

4. Germanium nanowire

We have used the same MD techniques that were used forSiNWs to study the structural features of Ge nanowires(GeNWs). Numerical results show that GeNWs have similarstructures to SiNWs. To demonstrate the qualitative similarityand quantitative difference, we present detailed results forGeNWs with the same initial structures as the NW2 SiNWs.Figure 4 illustrates the initial structure, reconstructed structure,and changes in lattice spacing for the NW2 GeNW boundedby the (100) surfaces with perpendicular dangling bonds.Figure 4(A) clearly shows that atoms on the (100) surfacesform 2 × 1 dimers and the dimer rows on different surfaces

are perpendicular to each other. There is no reconstruction onthe (110) surfaces. The dimer length is 0.249 nm, which islarger than the value for Si dimers. From figures 4(B) and (C),one can see that formation of dimers results in distortion ofthe lattice spacing of the whole wire. The change in latticespacing for the first, second, and third layers parallel to the(100) surface is −7.5%, −3.3%, and −2.5%, respectively. Thelattice spacing for the fourth and fifth layers is approximately1.7% larger than the bulk value and there is a 1% overallexpansion in lattice spacing along the wire axis. Figure 4(C)shows that the expansion of lattice spacing for the (110)surfaces and their nearest-neighbouring layers is 3.4% and1.6%, respectively.

Figure 5 shows the results for a NW2 GeNW with twosymmetrical (100) surfaces, where the dangling bonds on both(100) surfaces are perpendicular to the wire axis. Again, onefinds 2 × 1 dimers on the (100) surfaces and no apparentreconstruction on the (110) surfaces. The dimer rows on thetwo (100) surfaces are parallel to each other and the dimer

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Figure 5. Structures of NW2 Ge nanowires along the [110] direction bounded by (100) surfaces and (110) surfaces. The wire has eight corelayers and its surface dangling bonds on different (100) surfaces are parallel to each other. (A) (a)–(c): Initial structure; (d)–(g): reconstructedstructure; (h) and (i): space filling plots of (e) and (f). (B): Lattice spacing for core layers parallel to the (100) surface. (C): Lattice spacing forlayers perpendicular to the (100) surface. The circles in (B) and (C) represent the atomic layers parallel or perpendicular to the wire axis,respectively.

length has the same value of 0.249 nm. From figures 5(B)and (C), we can see that the wire undergoes a larger distortioncompared to the wire with asymmetrical (100) surfaces asshown in figure 4. The change in lattice spacing for the first,second, third, sixth, seventh, and eighth layers parallel to the(100) surface is −8.0%,−3.0%,−2.1%,−2.1%,−3.0%, and−8.0% respectively. The lattice spacing for the fourth and fifthlayers is approximately 2.5% larger than the bulk value andthere is a 1% overall expansion in the lattice spacing alongthe wire axis. Figure 4(C) shows that expansion in the latticespacing for the (110) surface is 5.5%.

From our simulation results, we can see that GeNWs andSiNWs show the same behaviour of surface reconstruction andthe surface dimerization results in severe distortion of the coresof the nanowires in both cases. Because Ge and Si atoms havedifferent bonding strengths, the dimer length and degree ofwire distortion for a GeNW is quantitatively different from thatfor a SiNW.

5. Conclusions

In summary, using molecular dynamics simulations anda simulated annealing technique, we have studied stablestructures of pristine SiNWs and GeNWs with bulk coresoriented along the [110] direction and bounded by the (100)and (110) planes in the lateral directions. We found thatthe (100) surfaces of a SiNW undergo reconstruction formingsymmetrical 2×1 dimers while the (110) surfaces do not showrecognizable reconstruction. The direction of the dimer rowsis either parallel or perpendicular to the wire axis determinedby the direction of the surface dangling bonds. The dimerlength we obtained is in good agreement with the resultfound by first-principles calculations. However, MD resultsshow symmetrical 2 × 1 Si dimers that are different from theasymmetrical buckled dimers obtained by the first-principlescalculations. Our 2 × 1 dimers are very similar to the 2 × 1dimers for the (100) surface of bulk Si, which have recently

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been observed in experimental studies at low temperatures. Weshould note that the Tersoff potential used in our simulationsdoes not include electronic wavefunctions and thus it maynot be able to reveal the slight energy difference induced bybuckling of dimmers. Thus the discrepancy found between theMD results and the first-principles calculations needs furtherinvestigation. We also show that, different from the surfacereconstruction of bulk Si, the formation of dimers on surfacesof small SiNWs results in a large change in the lattice spacingfor atoms not on the (100) surface, particularly for atomiclayers parallel and close to the (100) surfaces and for the(110) surfaces. Moreover, our numerical results for SiNWsof different sizes indicate that dimerization on smaller (100)surfaces results in larger distortion of the nanowire. The resultsfor GeNWs show that all of the conclusions for SiNWs apply toGeNWs, indicating that the 2×1 reconstruction and the surfacereconstruction-induced core distortion are common features forsmall SiNWs and GeNWs. The simulated annealing globaloptimization technique has not been used in any first-principlesstudies for SiNWs and GeNWs due to the computationalcost. Thus, our study has provided another view of thesurface reconstruction of SiNWs and GeNWs from moleculardynamics and global optimization. We have also developed aframework for describing the large change in lattice spacing ofthe cores of small SiNWs and GeNWs that can be applied tothe study of other semiconductor nanowires. The electronic,thermal, and mechanical properties of a solid are largelydetermined by its lattice spacing. We expect that the largechange in lattice spacing induced by surface reconstruction willsignificantly modify a nanowire’s physical properties, basedupon results using bulk parameters.

Acknowledgments

This work was supported by the Chang Jiang ScholarsProgram, Ministry of Education, China, the Fu Rong ScholarsProgram of Hunan Province, China, the Education Bureau ofHunan Province, China, the Laboratory Directed Research andDevelopment Program of Oak Ridge National Laboratory, andthe Division of Materials Sciences and Engineering, Office ofBasic Energy Sciences, US Department of Energy. Oak RidgeNational Laboratory is managed by UT-Battelle, LLC for theUS Department of Energy under Contract No. DE-AC05-00OR22725.

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