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Surface structure of cubic diamond nanowires A.S. Barnard, S.P. Russo * , I.K. Snook Department of Applied Physics, Royal Melbourne Institute of Technology, GPO Box 2476V, Melbourne, VIC 3001, Australia Received 20 November 2002; accepted for publication 9 May 2003 Abstract Presented are results of our ab initio study of the surface reconstruction and relaxation of (1 0 0) surfaces on dia- mond nanowires. We have used a density function theory within the generalized-gradient approximation using the Vienna ab initio simulation package, to consider dehydrogenated and hydrogenated surfaces. Edges of nanowires offer a new challenge in the determination of surface structure. We have applied the methodology for stepped diamond (1 0 0) surfaces to this problem, and consider it useful in describing diamond nanowire edges to first approximation. We have found that dimer lengths and atomic layer depths of the C(1 0 0)(2 · 1) and C(1 0 0)(2 · 1):H nanowire surfaces differ slightly from those of bulk diamond and nanodiamond surfaces. The aim of this study is provide a better understanding of the effects of nano-scale surfaces on the stability of diamond nanostructures. Ó 2003 Elsevier B.V. All rights reserved. Keywords: Density functional calculations; Surface relaxation and reconstruction; Diamond 1. Introduction The emerging field of molecular nanotechnol- ogy has introduced a wide range potential appli- cations of nanostructured materials, for a variety of purposes. One-dimensional (1-D) nanowires have been proposed as important components, playing an integral part in the design and con- struction of both electronic and optoelectronic nanodevices [1]. Significant work has been com- piled regarding the structure and properties of semiconductor nanowires including silicon [2,3], silicon carbide [4,5] and carbon [6]. The growth of carbon nanowires has been achieved using a number of techniques including laser-induced chemical vapor deposition [7], high pressure treatment of catalyst containing thin films [8], annealing of silicon carbide films [9] and annealing of pressed graphite containing tablets [10]. Aligned diamond nanowhiskers (a term used to describe particular nanowires) have been formed using air plasma etching of polycrystalline diamond films [11]. Dry etching of the diamond films with mo- lybdenum deposits created well-aligned uniformly dispersed nanowhiskers up to 60 nm in diameter with a population density of 50/lm 2 . These dia- mond nanowhiskers showed well-defined charac- teristics of diamond [12]. Diamond (carbon) based materials have been suggested to be the optimal choice for nano- mechanical designs, due to their high elastic modulus and strength-to-weight ratio [13,14]. This has prompted a number of theoretical studies in- vestigating various aspect of diamond at the nano- * Corresponding author. Tel.: +61-3-9925-2601; fax: +61-3- 9925-5290. E-mail address: salvy.russo@rmit.edu.au (S.P. Russo). 0039-6028/03/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0039-6028(03)00733-7 Surface Science 538 (2003) 204–210 www.elsevier.com/locate/susc scale. An important aspect of simulating nanodi- amond structures is to correctly model their surfaces. Clean [15–20] and hydrogen passivated [16–28] C(1 0 0) bulk diamond surfaces have been the topic of many investigations using a variety of experimental and theoretical methods. More re- cently the (1 0 0) surfaces of diamond nanocrystals have been examined [29,30]. To assist in providing a better understanding of the surfaces of diamond nanostructures we are interested in extending these research efforts to include diamond nanowires. Presented here is a density functional theory (DFT) study of the surface structure of selected diamond nanowires using the Vienna ab initio simulation package (VASP) [31,32]. We used ultra soft, gradient corrected Vanderbilt type pseudo- potentials [33] as supplied by Kresse and Hafner [34], and the valence orbitals are expanded on a plane-wave basis up to a kinetic energy cutoff of 290.00 eV. All calculations were performed in the framework of DFT within the generalized-gradi- ent approximation (GGA), with the exchange- correlation functional of Perdew and Wang [35]. This method has been successfully applied to bulk diamond [36] and nanodiamond [37], and has been shown to give results in excellent agreement with experiment and all electron methods [26]. The surface structure has been analysed for two dehydrogenated and two hydrogenated diamond nanowires with cubic morphology. To ensure that the structures are close to equilibrium, both the ions and super-cell volume were structurally re- laxed. Both the symmetry and the lattice parame- ter of the nanowires were free to vary, resulting in expansions or contractions of the entire structures. The relaxations were performed for a minimum of 20 ionic steps (involving changes in the atomic positions), each initially consisting of approxi- mately 50–60 electronic steps (involving changes in the electronic charge density surrounding the at- oms) and converging to a minimum of 3 electronic steps during the final ionic steps. 2. Diamond nanowires Four infinite diamond nanowires were included in this study, consisting of dehydrogenated and monohydrogenated versions of two cubic struc- tures. The structures are periodic along a [1 1 0] direction, with two C(1 0 0)(1 · 1) surfaces and two C(1 1 0)(1 · 1) surfaces along the length of the nanowire. The length of the simulation cell was 1.5 nm, creating (periodic) nanowire segments with two distinct rectangular cross-sections. The smaller segment has an average lateral diameter of 0.6 nm and contains 132 carbon atoms in the simulation length, while the larger segment has an average lateral diameter of 0.85 nm and contains 240 carbon atoms in the simulation length. The hydrogenated segments consisted of C 132 H 72 and C 240 H 96 respectively. While the cross-section con- sidered here represents only a simple case (that may not be currently realistic), it has been chosen as it facilitates the consideration of edges as well as generous surface facets. The finite size of nano- structures, such as nanodiamond and diamond nanowires, lead to Ôfull structureÕ relaxation that effect the surface as well as the bulk-like core of these systems [29]. It is considered important to begin to understand the variations in the structure of diamond nanowires effected by various finite size effects (beginning with a simple case), because at the nanoscale the surface structure plays a sig- nificant role in the electronic properties of the nanowire as a whole. In all cases the initial step of the relaxation in- volved the reconstruction of the C(1 0 0) surfaces to form the (2 · 1) surface structure. As the C(1 1 0) surface does not reconstruct [38], the reconstruc- tion is limited to the C(1 0 0) surfaces under con- sideration. The initial and final (relaxed) structures of the smaller dehydrogenated nanowire are shown in Fig. 1, and final monohydrogenated version in Fig. 2. Figs. 3 and 4 show the dehy- drogenated and monohydrogenated results for the larger nanowire, respectively. Each nanowire is shown from the [1 0 0] direction (left), [1 1 0] di- rection (centre), with the periodic boundaries to the left and right of each image; and along the axis of the nanowire (right). In the case of the larger nanowires, the char- acterization of the C(1 0 0)(2 · 1) surfaces was achieved by considering the difference in the pri- mary d 11 and secondary d 12 dimer lengths, and the first Z 12 and second Z 23 layer depths. A diagram A.S. Barnard et al. / Surface Science 538 (2003) 204–210 205 outlining this nomenclature is given in Fig. 5. Examination of the structures shown in Figs. 1–4 reveals that there are two distinct (1 0 0) surfaces, with dimer rows running parallel and perpendic- Fig. 1. Initial (top) and final relaxed (bottom) dehydrogenated diamond nanowire with simulation cells containing 132 carbon atoms, viewed form the [1 0 0] direction (left), [1 1 0] direction (centre), and along the nanowire axis (right). Fig. 2. Final relaxed monohydrogenated diamond nanowire with simulation cells containing 132 carbon atoms, viewed form the [1 0 0] direction (left), [1 1 0] direction (centre), and along the nanowire axis (right). Fig. 3. Initial (top) and final relaxed (bottom) dehydrogenated diamond nanowire with simulation cells containing 240 carbon atoms, viewed form the [1 0 0] direction (left), [1 1 0] direction (centre), and along the nanowire axis (right). 206 A.S. Barnard et al. / Surface Science 538 (2003) 204–210 ular to the nanowire axis. These have been denoted C(1 0 0)? and C(1 0 0)k respectively, and are shown explicitly in Fig. 6. The surface properties of each of these surface types has been determined for dimers positioned at the nanowire edges, and dimer positions in the centre of the nanowire (1 0 0) facets. Inspection of Table 1 reveals that the dehy- drogenated surface reconstruction and relaxation varies depending upon the region of the nanowire face in both the C(1 0 0)k and C(1 0 0)? cases. The primary d 11 dimer length is reasonably sensitive to region of the surface, and the d 12 dimer length is consistently shorter at the edges than the centre of the facets (although this is more pronounced for the C(1 0 0)? surface). The Z 12 depth is also smaller for dimers situated at the nanowire edges, than those at centre. The Z 23 depth is significantly reduced at the edge of the C(1 0 0)? face being only 0.67 AA, closer to a Z 12 depth than the bulk diamond layer separation of 0.89 AA. Overall the C(1 0 0)k surface with dimer rows parallel to the nanowire axis shows little variation over the sur- face, although a slightly concave surface has re- sulted (indicated by the difference in the Z 12 depth for the edges and surface centre). This concave relaxation is evident when viewing the nanowire along the axis, as in the lower right image of Fig. 3. Saturation of the nanodiamond surfaces with hydrogen produces structures of lower energy that is entirely due to the passivation of surface bonds. However, aside from this, Table 1 shows that monohydrogenation of the nanowire surfaces has an important effect on the surface structure. The addition of the hydrogens removes much of the variation in surface structure over the (1 0 0) faces. The d 11 and d 12 dimer lengths and the Z 12 and Z 23 Fig. 5. Diagram defining the surface structure nomenclature used in this study. The primary d 11 and secondary d 12 dimer lengths, and the first Z 12 and second Z 23 layer depths are shown. Fig. 6. Diagram defining the surface types used in this study. The orientation of the (2 · 1) dimers for the C(1 0 0)? surface (top) and C(1 0 0)k surface (bottom) are shown. The nanowire axis is indicated by dotted line through the centre. Fig. 4. Final relaxed monohydrogenated diamond nanowire with simulation cells containing 240 carbon atoms, viewed form the [1 0 0] direction (left), [1 1 0] direction (centre), and along the nanowire axis (right). A.S. Barnard et al. / Surface Science 538 (2003) 204–210 207 layer depths are similar but not identical for the edges and centres of the C(1 0 0) faces (see Table 1). In addition to the surface reconstruction and relaxation, the nanowires were also found to un- dergo full-crystal relaxations. Both the average lateral diameter and the simulation length was found to contract, although this effect was signif- icantly reduced by surface hydrogenation. These relaxations contribute to the relaxations of the surfaces, and have an impact on the final surface structure. No bucking or twisting of the surface dimers could be discerned due to the Ôedge effectsÕ. 3. Discussion: comparison with bulk and nanodia- mond Ignoring for a moment the variations in surface structure over the (1 0 0) facets, the average pri- mary and secondary dimer lengths and average first and second layer depths (for the dehydroge- nated and monohydrogenated cases) have been compared with bulk diamond and nanodiamond (see Table 2). The results of the dehydrogenated surfaces show that the average d 11 and d 12 dimer lengths and the Z 12 and Z 23 layer depths for diamond nanowires falls between those of nanodia- mond crystals and bulk diamond surfaces. For the monohydrogenated surfaces, the average d 11 and d 12 dimer lengths and the Z 12 and Z 23 layer depths for diamond nanowires are larger than those of both bulk and nanodiamond. This surprising re- sult is most significant in the case of the d 11 dimer length and Z 23 layer depth, both of which are 0.05 AA larger that those of bulk diamond. However, as shown above, edges of the nano- wires cannot be ignored. Using the nomenclature Table 2 Comparison of average nanowire C(1 0 0) surface properties with bulk and nanodiamond Bulk diamond Diamond nanocrystals Diamond nanowires C(1 0 0) d 11 ( AA) 1.385 ± 0.003 1.44 ± 0.06 1.405 ± 0.002 d 12 ( AA) 1.517 ± 0.006 1.49 ± 0.08 1.50 ± 0.02 Z 12 ( AA) 0.68 ± 0.08 0.59 ± 0.07 0.66 ± 0.02 Z 23 ( AA) 0.91 ± 0.08 0.80 ± 0.12 0.90 ± 0.15 C(1 0 0):H d 11 ( AA) 1.632 ± 0.008 1.63 ± 0.02 1.681 ± 0.008 d 12 ( AA) 1.545 ± 0.005 1.54 ± 0.04 1.55 ± 0.01 Z 12 ( AA) 0.81 ± 0.06 0.82 ± 0.04 0.86 ± 0.02 Z 23 ( AA) 0.91 ± 0.09 0.83 ± 0.07 0.92 ± 0.07 The nanowire results are averaged over the ÔedgeÕ and ÔcentreÕ regions. Table 1 Averages of the relaxation and reconstruction properties of the 240 carbon atom cubic nanowire for the (1 0 0) faces, comparing the differences in average reconstruction and relaxation for edges and surfaces C(1 0 0)k centre C(1 0 0)k edge C(1 0 0)? centre C(1 0 0)? edge C(1 0 0) d 11 ( AA) – 1.384 ± 0.002 1.371 ± 0.002 1.460 ± 0.005 d 12 ( AA) 1.51 ± 0.02 1.493 ± 0.004 1.53 ± 0.01 1.455 ± 0.002 Z 12 ( AA) 0.71 ± 0.01 0.62 ± 0.01 0.69 ± 0.02 0.615 ± 0.004 Z 23 ( AA) 1.05 ± 0.02 1.00 ± 0.05 0.90 ± 0.15 0.67 ± 0.04 C(1 0 0):H d 11 ( AA) – 1.701 ± 0.003 1.685 ± 0.008 1.657 ± 0.007 d 12 ( AA) 1.55 ± 0.01 1.548 ± 0.007 1.55 ± 0.01 1.558 ± 0.003 Z 12 ( AA) 0.854 ± 0.002 0.827 ± 0.003 0.88 ± 0.02 0.880 ± 0.002 Z 23 ( AA) 0.94 ± 0.07 0.945 ± 0.003 0.93 ± 0.05 0.85 ± 0.02 208 A.S. Barnard et al. / Surface Science 538 (2003) 204–210 of Chadi [39] single-atom steps on diamond (1 0 0) surfaces are denoted as S A and S B when the direc- tion of the upper terrace (2 · 1) dimers are oriented perpendicular to the step edge and parallel to the step edge respectively. Further, S B type steps may be denoted as S B ðnÞ for the non-bonded type, where there are no re-bonded atoms on the lower terrace; and S B ðbÞ for the bonded type which does have re- bonded atoms on the lower terrace. Therefore, if we consider the edges of the nanowires as exag- gerated steps, then the structure of the edges of the C(1 0 0)k represent S A steps, and the edges of the C(1 0 0)? represent S B ðnÞ steps. Under this as- sumption, the d 11 dimer lengths for these step types (given in Table 1), may be compared with the re- sults for stepped bulk diamond (1 0 0) surfaces. Calculations by Alfonso et al. [40] using DFT LDA molecular dynamics determined that for the dehydrogenated surface the symmetric, unbuckled sp 2 hybridized S A step had a d 11 dimer length of 1.37 AA. Similarly, the symmetric sp 2 hybridized S B step had upper terrace d 11 dimer lengths of 1.48 AA. In the case of the monohydrogenated stepped surface, the S A step had a d 11 dimer length of 1.61 AA. Although the dehydrogenated surfaces com- pared reasonably well with the corresponding stepped diamond surfaces, the monohydrogenated nanowire surfaces did not. The C(1 0 0)k d 11 length for the dehydrogenated diamond nanowire edge was found to be 0.014 AA greater than the S A step on a bulk surface. However, the C(1 0 0)? surface with dimers rows perpendicular to the nanowire axis shows more significant differences between the nanowire edges and facet centres. The d 11 length at the edge was found to be 0.02 AA less than the S B ðnÞ step on a bulk surface. In the monohydrogenated case, the d 11 dimer length of 1.701 AA for the nano- wire C(1 0 0)k edge is 0.091 AA greater than 1.61 AA for the S A bulk diamond step [40]. It is also 0.081 AA greater than S A step results of 1.62 AA determined using the hybrid Density Functional (LDA) Tight- Binding (DF-TB) molecular dynamics study by Skokov et al. [24]. In contrast, the calculated d 11 dimer length of 1.657 AA for the monohydrogenated nanowire C(1 0 0)? edge is only 0.027 AA greater than 1.63 AA for S B type steps [24]. In summary, the dehydrogenated C(1 0 0)k d 11 length is closer to the bulk diamond S A step, whereas the monohydrogenated C(1 0 0)? d 11 length is closer to the bulk diamond S B ðnÞ step. This suggests that to improve surface homogeneity dehydrogenated diamond nanowires should be constructed with C(1 0 0)(2 · 1) dimer rows parallel to the nanowire axis, but monohydrogenated nanowires with dimer rows perpendicular to the nanowire axis. 4. Conclusion The results outlined here show that although a considerably degree of localized variation in sur- face structure exists due to the nanowire edges, hydrogenation of diamond nanowire C(1 0 0) sur- faces reduces these variations. Averaging over the variations, the structure of dehydrogenated cubic surfaces on diamond nanowires are characterized by features in between bulk and nanodiamond cubic surfaces. In contrast however, the feature of monohydrogenated cubic nanowire surfaces do not fall between bulk and nanodiamond. All of the considered features, including dimer lengths and atomic layer depths, exceeding those of bulk and nanodiamond. This highlights that Ôfull structureÕ relaxations are significant, and must be taken into consideration when studying the structure of sur- faces at the nanoscale. Simply scaling the surface properties, or making assumptions regarding sur- face structure that do not include finite size effects is inappropriate. 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