The effect of topological defects and oxygen adsorption on the electronic transport properties of single-walled carbon-nanotubes

Applied Surface Science 211 (2003) 166 183 The effect of topological defects and oxygen adsorption on the electronic transport properties of single-walled carbon-nanotubes M. Grujicic a,*, G. Cao a, R. Singh b a Department of Mechanical Engineering, Clemson University, 241 Engineering Innovation Building, Clemson, SC 29634, USA b Department of Electrical and Computer Engineering, Clemson University, Clemson, SC 29634, USA Received 28 December 2002; received in revised form 8 February 2003; accepted 9 February 2003 Abstract Ab initio density functional theory (DFT) calculations of the interactions between isolated infinitely-long semiconducting zigzag (10, 0) or isolated infinitely-long metallic arm-chair (5, 5) single-walled carbon-nanotubes (SWCNTs) and single oxygenmolecules are carried out in order to determine the character of molecular-oxygen adsorption and its effect on electronic transport properties of these SWCNTs. A Green s function method combined with a nearest-neighbor tight-binding Hamiltonian in a non-orthogonal basis is used to compute the electrical conductance of SWCNTs and its dependence on the presence of topological defects in SWCNTs and of molecular-oxygen adsorbates. The computational results obtained show that in both semiconducting and metallic SWCNTs, oxygen-molecules are physisorbed to the defect-free nanotube walls, but when such walls contain topological defects, oxygen-molecules become strongly chemisorbed. In semiconducting (10, 0) SWCNTs, physisorbed O 2 -molecules are found to significantly increase electrical conductance while the effect of 7-5-5-7 defects is practically annulled by chemisorbed O 2 -molecules. In metallic (5, 5) SWCNTs, both O 2 adsorbates and 7-5-5-7 defects are found to have a relatively small effect on electrical conductance of these nanotubes. # 2003 Elsevier Science B.V. All rights reserved. PACS: 71.20.Tx; 68.45.Da; 72.80.Rj; 73.61.Wp Keywords: Carbon-nanotubes; Adsorption; Density functional theory (DFT) calculations; Electronic transport properties 1. Introduction Since their discovery by Iijima in 1991 [1], carbonnanotubes have been the subject of intensive research interest. This has been fueled by recent experimental breakthroughs in diverse areas ranging from flat panel * Corresponding author. Tel.: þ1-864-656-5639; fax: þ1-864-656-4435. E-mail address: mica.grujicic@ces.clemson.edu (M. Grujicic). displays, to novel microelectronic devices, to hydrogen storage devices, to structural reinforcement, to chemical and electromechanical sensors [2]. Band structure calculations, using different quantum mechanical and semi-empirical methods (e.g. [3 6]), predicted that the electronic transport properties of single-walled carbon-nanotubes (SWCNTs) are highly dependent on their helicity and range from large band-gap semiconducting to metallic. Specifically, arm-chair (N, N) SWCNTs, where N is an 0169-4332/03/$ see front matter # 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/s0169-4332(03)00224-1

M. Grujicic et al. / Applied Surface Science 211 (2003) 166 183 167 integer, are predicted to be always metallic, while semiconducting zig-zag (N, 0) SWCNTs when N is a multiple of 3 are predicted to have a very small bandgap. Due to a strong sp 2 carbon carbon bonding within SWCNTs, the interactions between defect-free SWCNTs walls and gas molecules had been initially expected to be relatively weak and, consequently, the electronic transport properties of SWCNTs had been anticipated to be relatively insensitive to the exposure of SWCNTs to various molecular gases. However, several recent experimental investigations established that electronic transport properties of semiconducting SWCNTs can be quite sensitive to the exposure of SWCNTs to gas molecules [7 9]. In particular, the exposure of some small-gap semiconducting SWCNTs to the molecular-oxygen has been found to make these SWCNTs exhibit metallic behavior [7]. Before one can hope to fully rationalize the aforementioned effect of the exposure of SWCNTs to the molecular-oxygen on the electronic transport properties of SWCNTs, the phenomenon of molecular-oxygen adsorption to the SWCNTs walls needs to be better understood. Specifically, the issue of whether oxygen-molecules are physisorbed or chemisorbed on the SWCNTs walls needs be resolved. Jhi et al. [10] reported that the oxygen-molecules are chemisorbed while Savage et al. [11] found that oxygen-molecules are physisorbed. In addition to resolving this controversy, one should be able to model the effect of molecular-oxygen adsorption on the electrical conductance of SWCNTs and to include potential effects of the contact between SWCNTs and the leads attached to the SWCNTs ends during experimental measurements. It is well established that the effect of such contacts can be significant (e.g. [12]). The objective of the present paper is to carry a comprehensive computational analysis of the effect of molecular-oxygen adsorption on the electronic transport properties of (10, 0) SWCNTs (a representative of relatively-large band-gap semiconducting zig-zag SWCNTs) and (5, 5) SWCNTs (a representative of metallic arm-chair SWCNTs). Since, these nanotube can contain topological defects, adsorption of the molecular-oxygen to both perfect (defect-free) SWCNTs and the ones containing 7-5-5-7 topological defects is considered. The adsorption process is analyzed using a quantum mechanical density functional theory (DFT) approach [13]. The electrical conductance of the nanotubes is computed using a Green s function based approach [14]and a nearest-neighbor tight-binding Hamiltonian in a non-orthogonal basis [15]. The organization of the paper is as follows: a description of the computational cells used in the present work is presented in Section 2.1. In Section 2.2, a brief overview is given of the first-principles DFT method used [13]and of the computational procedure used to analyze the adsorption of molecularoxygen on the SWCNTs walls. The computational procedure used to calculate the electrical conductance of SWCNTs including the effect of SWCNT/lead contacts is presented in Section 2.3. The main results obtained in the present work are presented and discussed in Section 3, while the key conclusions resulted from the present study are summarized in Section 4. 2. Computational procedure 2.1. Computational cell The first-principles DFT analysis of molecular-oxygen adsorption to carbon-nanotubes, carried out in the present work, involves the use of isolated infinitelylong semiconducting zig-zag (10, 0) and isolated infinitely-long metallic arm-chair (5, 5) SWCNTs. In the case of semiconducting zig-zag (10, 0) SWCNTs, a 120-atom supercell is constructed consisting of 3 unit cells of this nanotube stacked in the direction of the nanotube axis. In the case of metallic arm-chair (5, 5) SWCNTs, a 120-atom supercell is constructed consisting of 6 unit cells of this nanotube stacked in the direction of the nanotube axis. The supercells are periodically repeated in the three lattice directions yielding a trigonal array of infinitely-long nanotubes. The axis-to-axis distance between the adjacent nanotubes are set to 14.8 and 12.7 Å for the (10, 0) and (5, 5) SWCNTs, respectively, which results in a distance of about 7.0 Å between the nearest carbon atoms on adjacent nanotubes. This distance is large enough to ensure that the interactions between nearest carbon atoms on the adjacent nanotubes are not very significant and, hence, the nanotubes can be considered as isolated. Also, the lattice parameter of the supercells in the nanotube-axis direction (12.678

168 M. Grujicic et al. / Applie Surface Science 211 (2003) 166 183 and 14.637 Å for the (10, 0) and (5, 5) SWCNTs, respectively) are set large enough to avoid the interactions between defects and/or oxygen-molecule adsorbates in the adjacent supercells. Since the presence of defects in the nanotubes can in principle promote their oxidation, in addition to defect-free semiconducting zig-zag (10, 0) and metallic arm-chair (5, 5) SWCNTs, the same nanotubes containing one 7-5-5-7 defect per supercell are also studied. In the case of this defect, some adjacent hexagons are replaced by pentagons (denoted as 5) and heptagons (denoted as 7). Perspective side views of the fully relaxed (geometrically optimized) atomic structures of defect-free (10, 0) and (5, 5) SWCNTs and the same types of nanotubes containing one 7-5-5-7 defect per one supercell are shown in Fig. 1(a) (d), respectively. To improve clarity, only the sticks (denoting the carbon carbon bonds) but not the Fig. 1. Side views of the fully relaxed structures of: (a) a perfect semiconducting zig-zag (10, 0) SWCNT; (b) the same nanotube containing a single 7-5-5-7 defect; (c) a perfect metallic arm-chair (5, 5) SWCNT; and (d) the same nanotube containing a single 7-5-5-7 defect.

M. Grujicic et al. / Applied Surface Science 211 (2003) 166 183 169 balls (representing the carbon atoms) are shown in Figs. 1(a) (d). The molecular-oxygen adsorption process is modeled as the interactions between a (defect-free or defective) (10, 0) or a (defect-free or defective) (5, 5) SWCNT and a single O 2 -molecule. The DFT method used in the present work [16], which is briefly reviewed in next section, was validated by computing the spin state of an isolated O 2 -molecule. The calculations correctly predict that the (lowest-energy) ground state of an isolated O 2 -molecule is the 3 S g spin-triplet state with the electronic structure: ðs b s Þ2 ðs s Þ2 ðs b z Þ2 ðp b x;y Þ4 ðp x Þ1þ ðp y Þ1þ, where s and p are used to denote sigma and pi molecular orbitals, respectively, superscripts b and to denote the bonding and antibonding orbitals, respectively, subscripts s, x, y, and z to denote molecular orbitals derived from s, p x,p y and p z atomic orbitals, respectively, numerical superscripts to denote the number of electrons in the particular molecular orbital and superscript þ to denote the spin-up state of the electrons. The DFT code is further validated by establishing that the predicted oxygen oxygen bond length (1.209 Å) and the stretching frequency (1539 cm 1 ) are in very good agreement with their experimental counterparts (1.207 Å and 1534 cm 1 ) [17], respectively. 2.2. The density functional theory computational method The computational analysis of molecular-oxygen adsorption to the walls of SWCNTs carried out in the present work is done using the ab initio density functional theory code DMol 3 developed by Accelrys, Inc. [13]. In this code, each electronic wave function is expanded in a localized atom-centered basis set with each basis function defined numerically on a dense radial grid. No pseudo-potential approximation is used for the near-core electrons. Instead, all-electron calculations are performed with a double numerical polarized (DNP) basis set, the most complete basis set available in the DMol 3 code. To improve the computational speed, the localdensity approximation (LDA) [18] for the exchange-correlation potential is often used within the DFT formulation, which assumes that the electron chargeddensity varies slowly on the atomic length scale. However, the LDA method is found not to have the correct asymptotic behavior and generally overestimates the magnitude of the chemical-bond energy. To overcome this overbinding phenomenon, one of the existing density gradient expansion schemes (also referred to as Generalized Gradient Approximations, GGA), which include the effect of charge-density inhomogeneity, needs to be utilized. The Perdew Burke Ernzerhof (PBE) gradient-corrected functional [19] is used in the present work. A standard value of 5.5 Å is assigned to the finite basis-set cut-off radius. The interaction of an O 2 -molecule with a carbonnanotube at various O 2 -molecule/nanotube-surface distances along the minimum-energy reaction path is carried out using the Nudged Elastic Band method [20]. 2.3. Computation of the electrical conductance In this section, a brief overview is given of the procedure used to compute the electrical conductance C of a single finite-length SWCNT connected, at each end, to a semi-infinite lead used in the course of measurement of the conductance, Fig. 2(a). The carbon-nanotube, and the two leads are denoted as NT, L (left lead) and R (right lead), respectively. According to the theory of electronic transport, the conductance of a region containing interacting electrons (e.g. the Fig. 2. (a) A schematic of the model used in the computation of electric conductance involving a finite-length SWCNT contained between two infinite gold pads; (b) 19-atom one (1 1 1)-plane thick gold pads used in the calculations.

170 M. Grujicic et al. / Applie Surface Science 211 (2003) 166 183 NT region in Fig. 2(a)) is controlled by the scattering properties of such region itself and can be expressed using the Landauer formula [21] as CðEÞ ¼ 2e2 TðEÞ (1) h where e is the electron charge (1:6022 10 19 C), h the Planck constant (6:6262 10 34 J/s), and T(E) is the transmission function at an energy level E. The transmission function represents the probability that an electron entering the conductor (SWCNT in the present case) at one end will be transmitted to the other end of the conductor and can be expressed in terms of the Green s functions of the nanotube and the coupling functions between the nanotube and the leads as [14] TðEÞ ¼TrðG L G NT G R G þ NT Þ (2) where Tr denotes the trace matrix-operator, G NT and G þ NT are, respectively, the (retarded) Green s functions and its Hermitian conjugate for the nanotube and the matrices G L and G R describe the effect of coupling of the nanotube to the left and the right leads, respectively. The Green s function appears in many physical concepts including electrostatics, electromagnetics and continuum mechanics. The Green s function can be broadly defined as a differential operator which relates the response at one point in the system to the excitation at another point. In the present case, the Green s function relates the response (the electronic wavefunction) at one point of the SWCNT/lead contact to the electrical excitation at another point of the other SWCNT/lead contact. To compute the Green s function for the nanotube, G NT, the following equation is used [14]: ðe S HÞG ¼ I (3) has to be first solved for the Green s function G of the whole (left lead/nanotube/right lead) system, where e ¼ E þ iz, E the energy-eigenvalues p scalar matrix, Z an arbitrarily small real number, i (¼ ffiffiffiffiffiffiffi 1 ) the imaginary unit. S the (diagonal) system overlap matrix, H the system Hamiltonian matrix and I the identity matrix. As shown by Datta [14], the iz term, which makes a major contribution to the self-energy term of the leads (discussed below), can be omitted for the nanotube. That is, coupling of the nanotube to the leads gives rise to an imaginary term whose magnitude is much larger than the iz term. From Eq. (3), the system Green s function can be determined by inverting the infinite matrix ðe S HÞ of the open system consisting of a SWCNT and two semi-infinite leads and, in turn, partitioned as 2 3 G L G L NT G L NT R 6 7 4 G NT L G NT G NT R 5 G L R NT G R NT G R 2 3 1 e S L H L h L NT 0 6 ¼ h þ 7 4 L NT E S NT H NT h NT R 5 0 h þ NT R e S R H R (4) where the sub-matrices, E S NT H NT, e S L H L and e S R H R pertain to the isolated finite-length nanotube sample and the two isolated semi-infinite leads, respectively, h L NT and h NT R are the nanotube/ lead coupling matrices (non-zero only for the adjacent points of the nanotube and the leads). Superscript þ is used in Eq. (4) and subsequent equations to denote the Hermitian conjugate of a matrix. From Eq. (4), the nanotube Green s (finite-size matrix) function G NT can be defined as G NT ¼ðES NT H NT S L S R Þ 1 (5) where S L ¼ h þ L NT g Lh L NT and S R ¼ h R NT g R h þ R NT are generally referred to as the self-energy terms due to the two semi-infinite leads, and g L ¼ðeS L H L Þ 1 and g R ¼ðeS R H R Þ 1 are the leads Green s functions. A comparison of Eq. (5) with the corresponding equation for an isolated nanotube sample, G NT ¼ðES NT H NT Þ 1, shows that S L and S R act as effective Hamiltonians arising from the interactions of the nanotube sample with the left and the right leads, respectively. Following Tian et al. [22], the leads Green s (infinite matrix) functions, g L and g R, are assumed to be diagonal matrices whose elements take on the values equal to pi times the local electronic density of states (LDOS). Furthermore, for the gold leads used in the present work, it is well-established that the LDOS is dominated by the 6s band and has a nearly constant value of 0.07 ev-atom around the Fermi energy. The tight-binding method based procedures used for calculation of the nanotube Hamiltonian, G NT, the nanotube overlap matrix, S NT,

M. Grujicic et al. / Applied Surface Science 211 (2003) 166 183 171 and the nanotube/lead coupling matrices h L NT and h NT R are discussed in next section. The nanotube/lead coupling matrices appearing in Eq. (2) can next be determined as [14] G I ¼ i ðs I S þ I Þ ði ¼ L; RÞ (6) Once the nanotube Green s function G NT and the coupling matrixes G L and G R are determined via Eqs. (5) and (6), respectively, the transmission function T(E) at the energy level E is obtained using Eq. (2). The total conductance can then be computed using the Landauer Buffiker formula as [14] Z 1 C ¼ 2e2 TðEÞ @f FD h @E 1 de (7) where f FD (E) is the Fermi Dirac distribution function. 2.4. Calculations of Hamiltonian, overlap and coupling matrices via tight-binding The DMol 3 DFT code used in the present work does not provide the Hamiltonian, overlap and coupling matrices needed for computation of the electrical conductance. To overcome this limitation, these matrices are computed using the YAeHMOP tightbinding code [15]. The essential features of the tight-binding method are that the eigenstates (orbital functions) of the Hamiltonian are defined using an atomic-like (orbital) basis set while the exact many-body Hamiltonian operator is replaced with a parameterized Hamiltonian matrix. Since the atomic orbitals associated with different atoms are generally not orthogonal, an overlap matrix is defined to convert a set of non-orthogonal atomic orbitals into an orthogonal one. The name tight-binding is associated with the assumption that the atomic-potential part of the Hamiltonian, which should include the contributions of all atoms in the system, can be replaced with a one which includes only the contributions of the two atoms upon which the orbital function in question is being computed. To compute the Hamiltonian, overlap and coupling matrices, a computational cell consisting of 120 carbon atoms arranged as a (10, 0) or a (5, 5) SWCNT and two 19-atom one-atom thick (1 1 1)-plane nanotube leads attached to each end of the nanotube sample. For carbon the YAeHMOP code includes four atomic orbitals (2s, 2p x,2p y and 2p z ) while for gold nine orbitals (6s, 5d x 2 y 2,5d z 2,5d xy,5d xz,5d yz,6p x,6p y and 6p z ) are considered. However, since the leads Green s functions were defined in the previous section using the 6s LDOS, only the results pertaining to the 6s orbital of gold are used in the calculation of the nanotube/lead coupling matrices h L NT and h NT R. The Hamiltonian and the overlap matrices obtained are of the size n n, where n ¼ 9 19 þ 4 120 þ 9 19 ¼ 822. The system Hamiltonian matrix H and the system overlap metrics S are next partitioned into nine sub-matrices in accordance with Eq. (4). The center 480 480 sub-matrices of H and S are next identified as the nanotube Hamiltonian matrix H NT and the nanotube overlap matrix S NT.The 171 480 sub-matrix located in the first row and the second column and the 480 171 sub-matrix in the second row and the third column of the (3 3) H matrix of sub-matrices are then identified as the nanotube/leads coupling matrices, h L NT and h NT R, respectively. 3. Results and discussion 3.1. Molecular-oxygen adsorption to defect-free SWCNTs In this section, the results of the present first-principles DFT calculations of the interactions between a defect-free semiconducting zig-zag (10, 0) or a defectfree metallic arm-chair (5, 5) SWCNT and a single O 2 -molecule are presented and analyzed. 3.1.1. Semiconducting zig-zag (10, 0) SWCNTs Following Jhi et al. [10], two energetically most favored oxygen-molecule adsorption sites are examined: (a) a carbon carbon bridge site parallel to the nanotube axis; and (b) the center of a carbon-nanotube hexagon. The binding energy calculations (discussed below) showed that boding of an O 2 -molecule adsorbed at a bridge site is significantly stronger than that of an O 2 -molecule adsorbed at the center of a carbon hexagon. This finding suggests that the role of hexagon-center sites in molecular-oxygen adsorption to the walls of (defect-free and defective, semiconducting and metallic) SWCNTs is less significant and, hence, adsorption of the molecular-oxygen at these sites is not considered any further.

172 M. Grujicic et al. / Applie Surface Science 211 (2003) 166 183 Fig. 3. Side views of the fully-relaxed structures of an O 2 -molecule adsorbed to: (a) a perfect semiconducting zig-zag (10, 0) SWCNT; (b) the same nanotube containing a single 7-5-5-7 defect; (c) a perfect metallic arm-chair (5, 5) SWCNT; and (d) the same nanotube containing a single 7-5-5-7 defect. The fully-optimized atomic structure of a perfect semiconducting zig-zag (10, 0) SWCNT containing a single O 2 -molecule adsorbate at a bridge site is shown in Fig. 3(a). To improve clarity, the structure of the nanotube is displayed using a stick (bond) representation while the structure of the O 2 -molecule is displayed using a ball (atom) and a stick (bond) representation. The results displayed in Fig. 3(a) show that in the fully-relaxed structure, the double bond of the O 2 -molecule is aligned with the nanotube axis and that it is located on top of the associated carbon carbon bridge bond. The distance between the midpoint of the oxygen oxygen double bond and the midpoint of the associated carbon carbon bridge bond in this configuration is about d ¼ 2:59 Å. The binding energy E binding (d) between a single oxygen-molecule and the nanotube as a function of the oxygen-molecule/nanotube-surface separation d

M. Grujicic et al. / Applied Surface Science 211 (2003) 166 183 173 can be computed using the following expression: E binding ðdþ ¼E nanotubeþo2 ðdþ E nanotube E O2 (8) where E nanotubeþo2 ðdþ; E nanotube and E O2 are the total energies of the fully-relaxed structures of a nanotube containing a single O 2 adsorbate, an isolated SWCNT and an isolated O 2 -molecule, respectively. To minimize any artificial supercell effects, E nanotubeþo2 ðdþ, E nanotube and E O2 are all calculated in the supercell geometry discussed in Section 2.1. The variation of the binding energy with the O 2 - molecule/nanotube-surface distance is displayed in Fig. 4(a). It is seen that the oxygen adsorption energy (negative of the binding energy at the equilibrium distance) is about 0.08 ev. While the accuracy of lowmagnitude adsorption energies, as is the one in the present case, is often questioned considering DFT s shortcomings in dealing with weak dispersion (van der Waals) forces, the values obtained are generally believed to be accurate to a factor of 2 3. Thus, judging by the magnitude of the adsorption energy (0.08 ev) obtained, oxygen-molecules appear to be physisorbed to a perfect semiconducting zig-zag (10, 0) nanotube. The oxygen-molecule adsorption energy (0.08 ev) obtained in the present work is significantly smaller than the value 0.25 ev reported by Jhi et al. [10] for a semiconducting zig-zag (8, 0) SWCNT. While this difference could be attributed to the effect of nanotube curvature, we computed the oxygen-molecule adsorption energy for the semiconducting zig-zag (8, 0) SWCNT as well and found a value 0.086 ev which is still significantly smaller than the one reported by Jhi et al. [10]. Furthermore, we computed the adsorption energy for a single oxygen-molecule adsorbed to a planar (zero-curvature) graphene sheet and obtained a value 0.077 ev. These findings suggest that the nanotube curvature has only a minor effect on the oxygen-molecule physisorption energy. A possible explanation for the observed discrepancy between our results and the ones reported by Jhi et al. [10] is that Jhi et al. [10] used (less accurate) pseudopotential and local-density approximations in their work, while the present calculations are carried out under the all-electron and generalized gradient conditions. Concerning the results displayed in Fig. 4(a), it should be noted that only the atomic configuration corresponding to the minimum in the binding energy is obtained using unconstrained optimization of the atomic structure. Atomic configurations corresponding to the other energy levels shown in Fig. 4(a), on the other hand, are obtained by constraining the system during optimization to a given reaction path. This reaction path is defined by the fully relaxed nanotube þ O 2 -molecule configuration (Fig. 3(a)), and the one in which the nanotube and the O 2 -molecule are at a large enough distance that their interactions can be neglected. Due to the constrained character of the optimization procedure used, the binding energy corresponding to the saddle point (i.e. the adsorption activation energy, 0.005 ev) are somewhat overestimated. This suggests that there may be no barrier to molecular-oxygen adsorption to perfect carbon-nanotubes. However, one must also recognize that the activation energy for oxygen-molecule desorption (0.08 ev) is also quite small implying a relatively high rate of oxygen-molecule desorption and a low equilibrium surface coverage. To determine the spin state of a single O 2 -molecule interacting with a perfect (10, 0) SWCNT at different O 2 -molecule/nanotube-surface separations, a comprehensive orbital analysis is next carried out. By comparing the charge-density distributions of different orbitals in the nanotube þ O 2 -molecule complex with their counterparts in an isolated O 2 -molecule, the molecular orbitals in the nanotube þ O 2 -molecule complex arising from the O 2 -molecule are identified and their population with electrons determined. The results obtained show that an O 2 -molecule remains in the 3 S g spin-triplet state (the ground state of an isolated O 2 -molecule) as it approaches the nanotube. This finding is consistent with the fact that the adsorption energy obtained (0.08 ev) is too small in comparison to the excitation energies (0.98 and 1.63 ev, respectively) for the singlet states 1 D g : ðs b s Þ2 ðs s Þ2 ðs b z Þ2 ðp b x;y Þ4 ðp x Þ2þ and 1 S þ g : ðsb s Þ2 ðs s Þ2 ðs b z Þ2 ðp b x;y Þ4 ðp x Þ1þ ðp y Þ1 of an isolated O 2 -molecule. Fig. 5(a) shows 0.02 e/å 3 charge-density isosurfaces corresponding to the highest occupied molecular orbital (HOMO) at the G-point (the Brillouin zone origin) arising from an O 2 -molecule at the equilibrium distance from the surface of a perfect (10, 0) SWCNT. It should be noted that in order to improve clarity, the nanotubes shown in Fig. 5(a) (d) are rotated to the right around their axes by 908 relative to their orientation in

174 M. Grujicic et al. / Applie Surface Science 211 (2003) 166 183 Fig. 4. (a) Variation of the binding energy for a single O 2 -molecule adsorbed to a defect-free semiconducting zig-zag (10, 0) and a defect-free metallic arm-chair (5, 5) SWCNT with the adsorbate/nanotube-surface distance. (b) Variation of the binding energy between a single O 2 - molecule adsorbate and a semiconducting zig-zag (10, 0) and a metallic arm-chair (5, 5) SWCNT, each containing a 7-5-5-7 defect with the O 2 -adsorbate/nanotube-defect distance.

M. Grujicic et al. / Applied Surface Science 211 (2003) 166 183 175 Fig. 5. The 0.02 e/å 3 electron-density isosurfaces for the highest energy molecular orbital associated with a single O 2 -molecule adsorbed to: (a) a perfect semiconducting zig-zag (10, 0) SWCNT; (b) the same nanotube containing a single 7-5-5-7 defect; (c) a perfect metallic armchair (5, 5) SWCNT; and (d) the same nanotube containing a single 7-5-5-7 defect. Two different colors are used to denote positive and negative lobes of the orbitals. The orbitals shown in (a) and (c) are also the HOMO orbitals. Fig. 3(a) (d). The HOMO orbital and the molecular orbital just below it (not shown for brevity) are found to contain one electron each in the spin-up state in accordance with the 3 S g spin-triplet state of the O 2 adsorbate. In order words, the two molecular orbitals associated with the highest energies are derived from the O 2 -molecule adsorbed to a defect-free semiconducting zig-zag (10, 0) SWCNT. The two molecular orbitals are associated with a same energy level in an isolated O 2 -molecule, but in an O 2 adsorbate, their energies differ by 0.001 ev. This orbital-energy splitting is caused by interactions between the O 2 -molecule and the SWCNT and its small magnitude implies that these interactions are quite weak. To quantify the charge transfer between a single O 2 adsorbate and the nanotube, a Mulliken population analysis is carried out for the fully-relaxed atomic configuration shown in Fig. 3(a). The results show a very small charge transfer to the O 2 -molecule of approximately 0.01 electrons. This finding further confirms that the interactions between an O 2 adsorbate and a perfect (10, 0) SWCNT are quite weak. 3.1.2. Metallic arm-chair (5, 5) SWCNTs The fully-optimized atomic structure of a defectfree metallic arm-chair (5, 5) SWCNT containing a single O 2 -molecule adsorbate at a bridge site is shown in Fig. 3(c). The results displayed in Fig. 3(c) show

176 M. Grujicic et al. / Applie Surface Science 211 (2003) 166 183 that in the fully-relaxed structure, the double bond of the O 2 -molecule is orthogonal with respect to the nanotube axis and that it is located on top of the associated carbon carbon bridge bond. The distance between the midpoint of the oxygen oxygen double bond and the midpoint of the associated carbon carbon bridge bond in this configuration is about d ¼ 2:56 Å. The variation of the binding energy with the O 2 -molecule/(5, 5)-SWCNT-surface distance is displayed in Fig. 4(a). It is seen that the oxygen adsorption energy is about 0.071 evand thus very close to its (10, 0) SWCNT counterpart (0.08 ev). Judging by the magnitude of the adsorption energy (0.071 ev) obtained, oxygen-molecules appear to be physisorbed to defectfree metallic (5, 5) SWCNTs. The spin state of a single O 2 -molecule physisorbed to a defect-free metallic (5, 5) SWCNT has been found to be the 3 S g spin-triplet state, the ground state of an isolated O 2 -molecule. Fig. 5(c) shows 0.02 e/å 3 charge-density isosurfaces corresponding to the HOMO at the G-point arising from an O 2 -molecule at the equilibrium distance from the surface of a defect-free (5, 5) SWCNT. The HOMO orbital and the molecular orbital just below it (not shown for brevity) are found to contain one electron each in the spin-up state in accordance with the 3 S g spin-triplet state of the O 2adsorbate. In order words, as in the case of a defect-free semiconducting zig-zag (10, 0) SWCNT, the two molecular orbitals associated with the highest energies are derived from the O 2 -molecule adsorbate. The energies of the two molecular orbitals differ by only 0.001 ev confirming weak bonding between an O 2 -molecule and a defect-free (5, 5) SWCNT. The Mulliken population analysis carried out for the fully-relaxed atomic configuration shown in Fig. 3(c) yielded a charge transfer to the O 2 -molecule of approximately 0.01 electrons further confirming that the interactions between an O 2 adsorbate and a defectfree (5, 5) SWCNT are quite weak. In summary, the results presented in this section indicate that the interactions of single O 2 -molecules with defect-free metallic (5, 5) SWCNTs are quite similar with the ones observed in the case of defectfree semiconducting (10, 0) SWCNTs. This finding suggests that the chirality of SWCNTs does not play a major role in the molecular-oxygen adsorption to defect-free SWCNTs. 3.2. Molecular-oxygen adsorption to defective SWCNTs In this section, the results of the present first-principles DFT calculations of the interactions between a semiconducting zig-zag (10, 0) or a metallic arm-chair (5, 5) SWCNT, each containing a 7-5-5-7 defect, and a single O 2 -molecule are presented and analyzed. 3.2.1. Semiconducting zig-zag (10, 0) SWCNT containing a 7-5-5-7 defect The fully-relaxed atomic structure of a semiconducting zig-zag (10, 0) SWCNT containing a 7-5-5-7 defect and a single O 2 adsorbate (per one supercell lattice parameter in the direction of the nanotube axis) is shown in Fig. 3(b). It is seen that the O 2 -molecule is in an orthogonal orientation with respect to the nanotube axis and is on top of the highly strained carbon carbon bond which separates two pentagons in the 7-5-5-7 defect. The separation between the oxygen oxygen and carbon carbon bonds is 1.47 Å. The variation of the binding energy between a single O 2 -molecule and a semiconducting zig-zag (10, 0) SWCNT containing a 7-5-5-7 defect with the O 2 -molecule/nanotube-defect distance is shown in Fig. 4(b). The results displayed in Fig. 4(b) show that the molecular-oxygen adsorption energy is about 0.32 ev and thus considerably larger than that (0.08 ev) obtained in the case of a defect-free (10, 0) SWCNT. Based on the magnitude of the adsorption energy (0.32 ev) obtained, oxygen-molecules appear to be chemisorbed to a semiconducting zigzag (10, 0) SWCNT containing a 7-5-5-7 defect. It should be noted that there is an activation energy (the maximum in the binding energy curve in Fig. 4(b)) of0.67 ev to chemisorption of O 2 -molecules to a 7-5-5-7 defect. The magnitude of this energy controls the rate of molecular-oxygen adsorption to carbon-nanotubes. Examination of the orbital structure of the fullyrelaxed atomic configuration shown in Fig. 3(b) reveals that the nanotube þ O 2 -molecule complex is in a spin-singlet state in which each orbital is populated with two electrons. This means that as an O 2 -molecule approaches the 7-5-5-7 defect of a SWCNT, its spin state changes form the 3 S g spintriplet state (the ground spin-state of an isolated O 2 -molecule) to the 1 D g spin-singlet state.

M. Grujicic et al. / Applied Surface Science 211 (2003) 166 183 177 The 0.02 e/å 3 charge-density isosurface corresponding to the G-point orbital arising from the O 2 -molecule with the highest energy is shown in Fig. 5(b). (The HOMO orbital, which is not shown for brevity, is associated with the 7-5-5-7 defect of the SWCNT.) The orbital shown in Fig. 5(b) is occupied with two electrons in accordance with the 1 D g spinsinglet state of the O 2 adsorbate. The results displayed in Fig. 5(b) also show some projection of the highestenergy molecular orbital arising from the O 2 -molecule to the 7-5-5-7 nanotube defect. This finding is fully consistent with the observed stronger bonding between the O 2 -molecule and the (10, 0) SWCNT containing a 7-5-5-7 defect. The observed stronger O 2 -molecule/nanotube bonding is further justified by comparing the symmetries of the nanotube molecular orbital localized at the O 2 -molecule, Fig. 5(b) with the one localized at the carbon carbon bond which separates two pentagons in the 7-5-5-7 defect (not shown for brevity). It is found that these two orbitals are both of the p antibonding character (relative to the O 2 -molecule), have a symmetry plane which bisects the oxygen oxygen bond, and, hence, are expected to be coupled and promote bonding. The Mulliken population analysis of the fullyrelaxed configuration shown in Fig. 3(b) yielded a charge transfer of approximately 0.44 electrons to the O 2 -molecule. This finding further confirms that the interaction between an O 2 adsorbate and the (10, 0) SWCNT containing a 7-5-5-7 defect is quite strong. 3.2.2. Metallic arm-chair (5, 5) SWCNTs containing a 7-5-5-7 defect The fully-relaxed atomic configuration of a (5, 5) SWCNT containing a 7-5-5-7 defect and an O 2 adsorbate is displayed in Fig. 3(d). It is seen that the O 2 adsorbate is aligned with the nanotube axis and it is located on top of the carbon carbon bond separating two pentagons in the 7-5-5-7 defect. A detailed analysis of the orbital structure of the configuration shown in Fig. 3(d) has been conducted and the main results can be summarized as follows: (a) the adsorption energy of the O 2 -molecule is 0.31 ev, Fig. 4(b); (b) the activation energy for-molecule oxygen adsorption is 0.66 ev; (c) O 2 adsorbate at the equilibrium distance (1.49 Å) is in a spin-singlet state and (d) a charge transfer of 0.46 electrons to the O 2 -molecule takes place. The 0.02 e/å 3 electron-density isosurfaces corresponding to the highest-energy O 2 -molecule derived molecular orbital are shown in Fig. 5(d). It is seen that, as in the case of the semiconducting (10, 0) SWCNT, some projection of this orbital to the 7-5-5-7 defect takes place explaining strong bonding (chemisorption) of the O 2 -molecule to the (5, 5) SWCNT containing a 7-5-5-7 defect. In summary, the findings presented in this section indicate that the interactions of single O 2 -molecules with metallic (5, 5) SWCNTs containing 7-5-5-7 defects are quite similar with the ones observed in the case of semiconducting (10, 0) SWCNTs containing the same type of defects. Furthermore, a comparison of the results presented in Section 3.1 with there counterparts presented in this section suggests that the presence of topological defects but not the SWCNT chirality have a significant effect on the-molecule oxygen adsorption process. 3.3. The effect of defects and oxygen adsorption on the band structure and the density of states of SWCNTs As a first step toward establishing the effect of topological defects and molecular-oxygen adsorbates on the electronic transport properties of SWCNTs, the results of DFT calculations of the electronic band structure and the electronic density of states (DOS) for a semiconducting zig-zag (10, 0) or metallic armchair (5, 5) SWCNT, each containing a 7-5-5-7 defect, and in the absence and in the presence of single O 2 adsorbates are presented and discussed in this section. 3.3.1. Semiconducting zig-zag (10, 0) SWCNTs The electronic band structures in the direction of the nanotube axis for a defect-free semiconducting zig-zag (10, 0) SWCNT, the same defect-free nanotube containing an O 2 adsorbate, the same type of nanotube containing a 7-5-5-7 defect and the same type of nanotube containing a 7-5-5-7 defect and an O 2 adsorbate are shown in Fig. 6(a) (d), respectively. The corresponding DOS plots are displayed in Fig. 7(a) (d). In both Figs. 6(a) (d) and 7(a) (d), the Fermi energy level is set to zero and denoted using a dashed line. The results displayed in Figs. 6(a) and 7(a) show that a defect-free zig-zag (10, 0) SWCNT has an energy gap at the Fermi energy level of 0.7 ev

178 M. Grujicic et al. / Applie Surface Science 211 (2003) 166 183 Fig. 6. Electronic band structure along the nanotube axis for a semiconducting zig-zag (10, 0) SWCNT in the following conditions: (a) defectfree and pure; (b) defect-free þ one O 2 adsorbate; (c) containing one 7-5-5-7 defect and pure; and (d) containing one 7-5-5-7 defect þ one O 2 adsorbate. The Fermi level is located at the zero energy. and, thus, acts as a semiconductor. Physisorption of the O 2 -molecules to the same defect-free SWCNT, Figs. 6(b) and 7(b), is seen to lower this energy gap to 0.5 ev and thus is expected to increase electrical conductance of these SWCNTs. The origin of this effect can be traced to the presence of two additional oxygen-derived orbitals (denoted as O 1 and O 2 )in Fig. 6(b) near the Fermi energy level. The results displayed in Figs. 6(c) and 7(c) show that the presence of a 7-5-5-7 defect in (10, 0) SWCNTs eliminated the energy gap at the Fermi energy level and, thus, makes these nanotubes behave as conductors. On the other hand, the results presented in Figs. 6(d) and 7(d) show that when oxygen is chemisorbed to the zigzag (10, 0) SWCNTs containing 7-5-5-7 defects, an energy gap of 0.6 evat the Fermi level reappears and these nanotubes become semiconducting again. It should be noted that due to a relatively small lattice parameter of the supercell in the nanotube-axis direction (12.678 Å), the concentration of 7-5-5-7 defects is

M. Grujicic et al. / Applied Surface Science 211 (2003) 166 183 179 Fig. 7. Electronic density of states for a semiconducting zig-zag (10, 0) SWCNT in the following conditions: (a) defect-free and pure; (b) defect-free þ one O 2 adsorbate; (c) containing one 7-5-5-7 defect and pure; and (d) containing one 7-5-5-7 defect þ one O 2 adsorbate. The Fermi level is located at the zero energy. unusually high (1 defect per 120 atoms) and, hence, their effect on the band structure and the density of states seen in Figs. 6(a) (d) and 7(a) (d) is exaggerated. Nevertheless, when the concentration of these defects is more realistic (e.g. on the order of 10 5 defects/atom), one may expect that they would reduce the energy gap without eliminating it. Consequently, in accordance with the results displayed in Figs. 6(c) and 7(c) the presence of these defects is expected to generally give rise to some decrease in the energy gap at the Fermi energy level of zig-zag (10, 0) SWCNT. Since the O 2 -molecule chemisorption energy (0.32 ev) to 7-5-5-7 defects is significantly larger than that (0.08 ev) for O 2 -molecules physisorbed to defect-free zig-zag (10, 0) SWCNTs, Fig. 4(a) and (b), O 2 -molecules are expected to be preferentially

180 M. Grujicic et al. / Applie Surface Science 211 (2003) 166 183 adsorbed at these defects. In accordance with the results presented in Figs. 6(d) and 7(d), such adsorption would essentially annul the effect of 7-5-5-7 defects on the energy gap in these SWCNTs. This implies that the main contribution to the adsorptioninduced change in the energy gap at the Fermi energy level and, hence, in electrical conductance, in zig-zag (10, 0) SWCNTs is due to the O 2 -molecules physisorbed to defect-free walls of these nanotubes. 3.3.2. Metallic arm-chair (5, 5) SWCNTs The electronic band structures in the direction of the nanotube axis for a defect-free metallic arm-chair (5, 5) SWCNT, the same defect-free nanotube containing an O 2 adsorbate, the same type of nanotube containing a 7-5-5-7 defect and the same type of nanotube containing a 7-5-5-7 defect and an O 2 adsorbate are shown in Fig. 8(a) (d), respectively. The corresponding DOS plots are displayed in Fig. 8. Electronic band structure along the nanotube axis for a metallic arm-chair (5, 5) SWCNT in the following conditions: (a) defect-free and pure; (b) defect-free þ one O 2 adsorbate; (c) containing one 7-5-5-7 defect and pure; and (d) containing one 7-5-5-7 defect þ one O 2 adsorbate. The Fermi level is located at the zero energy.

M. Grujicic et al. / Applied Surface Science 211 (2003) 166 183 181 Fig. 9. Electronic density of states for a metallic arm-chair (5, 5) SWCNT in the following conditions: (a) defect-free and pure; (b) defect-free þ one O 2 adsorbate; (c) containing one 7-5-5-7 defect and pure; and (d) containing one 7-5-5-7 defect þ one O 2 adsorbate. The Fermi level is located at the zero energy. Fig. 9(a) (d). Again, the Fermi energy level is placed at zero and denoted using a dashed line. The results displayed in Figs. 8(a) (d) and 9(a) (d) show an absence of the energy gap at the Fermi energy level in arm-chair (5, 5) SWCNTs regardless of whether these nanotubes contain topological defects and O 2 adsorbates or not. Consequently, these tubes are metallic regardless of the extent of their crystallattice imperfection and the degree of oxygen adsorption. A close examination of the results presented in Figs. 8(a) (d) and 9(a) (d) reveals the following: (a) O 2 -molecules physisorbed to defect-free (5, 5) SWCNTs increase the DOS at the Fermi energy level, Fig. 9(b); (b) 7-5-5-7 defects also increase the DOS at the Fermi energy level, Fig. 9(c); and (c) O 2-molecule s chemisorbed to 7-5-5-7 defects have a quite small

182 M. Grujicic et al. / Applie Surface Science 211 (2003) 166 183 effect on the DOS at the Fermi energy level, Fig. 9(d). Based on these findings, physisorbed O 2 -molecules and 7-5-5-7 defects are expected to increase electrical conductance of the metallic arm-chair (5, 5) SWCNTs, while the effect of chemisorbed O 2 is expected to be minor. 3.4. The effect of defects and oxygen adsorption on the electrical conductance of SWCNTs In this section, the results of the present Green s function method and the tight-binding method based calculations of the electrical conductance of a semiconducting zig-zag (10, 0) and a metallic arm-chair (5, 5) SWCNT are presented and discussed. The computations are carried out in order to rationalize the effect of topological (7-5-5-7) defects and/or O 2 -adsorbates on the electrical conductance of these SWCNTs. The effect of O 2 -adsorbates and topological defects (7-5-5-7) on electrical conductance of semiconducting zig-zag (10, 0) and metallic arm-chair (5, 5) SWCNTs are displayed in Fig. 10(a) and (b), respectively. It is seen that the results presented in these figures are fully consistent with the corresponding band structure and the DOS results presented in the previous section and can be summarized as following: (a) defect-free (10, 0) SWCNTs are semiconducting and physisorbed O 2 -molecules increase their electrical conductance, 7-5-5-7 defects also increase electrical conductance of these SWCNTs but their effect is essentially annulled by chemisorbed O 2 -molecules; (b) defectfree (5, 5) SWCNTs are metallic and physisorbed O 2 -molecules and 7-5-5-7 defects increase their electrical conductance while the effect of chemisorbed O 2 -molecules appears insignificant; and (c) a relative change in the electrical conductance due to physisorption of O 2 -molecules is significantly larger in semiconducting (10, 0) than in metallic (5, 5) SWCNTs making the former nanotubes a preferred choice in chemical-sensor applications. It should be noted that electrical conductance of the perfect clean metallic arm-chair (5, 5) SWCNTs without inclusion of the effect of contact leads and under the assumption of a ballistic electronic transport has been estimated by Tian and Datta [24] as 4e 2 /h or 15:5 10 5 S. A comparison of this value with the corresponding value (7:98 10 5 S) obtained in the Fig. 10. Effect of O 2 adsorbates and 7-5-5-7 topological defects on electrical conductance of: (a) semiconducting zig-zag (10, 0); and (b) metallic arm-chair (5, 5) SWCNTs. present work (denoted as (5, 5) in Fig. 10(b)) shows that, due to the effect of nanotube/lead contacts, the measured electrical conductance is reduced by 47%. In order words, a considerable (on the order of 5 ko) in-series resistance is introduced due to non-ideal nanotube/lead contacts. The observed contact resistance is typically the result of Schottky barriers and/or contact-surface roughness. Finally, since electrical conductance includes both the material and specimen-geometry contributions, it is interesting to compute the ranges of values for the electrical conductivity (a material property) for the

M. Grujicic et al. / Applied Surface Science 211 (2003) 166 183 183 two types of SWCNTs and compare them with electrical conductivity of leads material gold (4:0 10 7 S/m). Treating the SWCNTs as being one carbonatom thick (the van der Waals diameter of a carbon atom is 0.147 nm [23]), the following ranges for electrical conductivity are obtained: (a) semiconducting zig-zag (10, 0) SWCNTs, ð5:0 7:0Þ10 4 S/m; and (b) metallic arm-chair (5, 5) SWCNTs, ð8:8 9:0Þ10 5 S/m. Despite some uncertainty regarding the computation of the nanotubes thickness, these findings suggest that the electrical conductivity of metallic SWCNTs is about 50 times smaller than that of good metal conductors, like gold. On the other hand, the electrical conductivity of semiconducting SWCNTs is about two orders of magnitude larger than that of a natural semiconductor Ge (8:0 10 2 Siemens/m). 4. Conclusions Based on the results obtained in the present work, the following main conclusions can be drawn: 1. In both zig-zag and arm-chair SWCNTs, O 2 - molecules are physisorbed to defect-free portions of the nanotube walls but chemisorbed to the topological defects such as 7-5-5-7. 2. As already observed by several investigators (e.g. [10]), zig-zag SWCNTs have an energy gap at the Fermi energy level (on the order of 1 ev) which makes them semiconducting while arm-chair SWCNTs do not possess such an energy gap and, hence, behave as conductors. 3. Both topological defects and O 2 adsorbates affect the energy gap at the Fermi energy level in semiconducting SWCNTs and the DOS at the Fermi energy level in metallic SWCNTs and, thus, affect electrical conductance in these nanotubes. However, the effect of topological defects is essentially annulled by chemisorbed O 2 -molecules. 4. The O 2 -adsorption induced relative changes in electrical conductance of semiconducting SWCNTs are considerably larger than the ones in metallic SWCNTs making the former nanotubes more suitable in chemical-sensor applications. Acknowledgements The material presented in this paper is based on work supported by the U.S. Army Grant no. DAAD19-01-1-0661. The authors are indebted to Drs. Bonnie Gersten, Walter Roy, Fred Stanton and William DeRosset of ARL for the support and a continuing interest in the present work. References [1] S. Iijima, Nature (London) 354 (1991) 56. [2] Articles on nanotubes, Phys. World 13 (2002) 29 53. [3] J.W. Mintmire, B.I. Dunlap, C.T. White, Phys. Rev. Lett. 68 (1992) 631. [4] N. Hamada, S. Sawada, A. Oshiyama, Phys. Rev. Lett. 68 (1992) 1579. [5] X. Blasé, L. Benedict, E.L. Shirley, S.G. Louie, Phys. Rev. B 57 (1994) 1878. [6] J.C. Charlier, Ph. Lambin, Phys. Rev. B 57 (1998) R15037. [7] P.G. Collins, K. Bradley, M. Ishigami, A. Zettl, Science 287 (2000) 1801. [8] K. Bradley, S.-H. Jhi, P.G. Collins, J. Hone, M.L. Cohen, S.G. Louie, A. Zettl, Phys. Rev. Lett. 85 (2000) 4361. [9] J. Kong, N.R. Franklin, C. Zhou, M.G. Chapline, S. Peng, K. Cho, H. Dai, Science 287 (2000) 622. [10] S. Jhi, S.G. Louie, M.L. Cohen, Phys. Rev. Lett. 85 (2000) 1710. [11] T. Savage, S. Bhattacharya, B. Sadanadan, J. Gaillard, T.M. Tritt, Y. Sun, Y. Wu, S. Nayak, R. Car, N. Marzari, P.M. Ajayan, A.M. Rao, Phys. Rev. Lett., submitted for publication. [12] N.D. Lang, Ph. Avouris, Phys. Rev. Lett. 81 (1998) 3515. [13] http://www.accelrys.com/mstudio. [14] S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge University Press, Cambridge, 1995. [15] G. Landrum, YAeHMOP (Yet Another Extended Huckel Molecular Orbital Package), Cornell University, Ithaca, NY, 1995 (http://yaehmop.sourceforge.net/). [16] P. Itohenberg, A. Pasquarello, R. Car, C. Lee, D. Vanderilt, Phys. Rev. B 47 (1993) 10142. [17] D.R. Lide (Ed.), Handbook of Chemistry and Physics, 78th ed., CRC Press, New York, 1997/1998. [18] W. Kohn, L.J. Sham, Phys. Rev. 140 (1965) A1133. [19] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [20] H. Jonsson, Ann. Rev. Phys. Chem. 51 (2000) 623. [21] R. Landauer, Phil. Mag. 21 (1970) 863. [22] W. Tian, S. Datta, S. Hong, R. Reifenberger, J.I. Henderson, C.P. Kubiak, J. Chem. Phys. 109 (1998) 2874. [23] M. Grujicic, G. Cao, B. Gersten, Mater. Sci. Eng. B B94 (2002) 247. [24] W. Tian, S. Datta, Phys. Rev. B 49 (1994) 5097.