Electrical conductance of carbon nanotubes with ...

J Nanopart Res (2013) 15:1885 DOI 10.1007/s11051-013-1885-x

RESEARCH PAPER

Electrical conductance of carbon nanotubes with misaligned ends Antonio Pantano • Giuseppe Muratore Nicola Montinaro

•

Received: 22 April 2013 / Accepted: 17 July 2013 Springer Science+Business Media Dordrecht 2013

Abstract During a manufacturing process, when a straight carbon nanotube is placed on a substrate, e.g., production of transistors, its two ends are often misaligned. In this study, we investigate the effects of multiwall carbon nanotubes’ (MWCNTs) outer diameter and chirality on the change in conductance due to misalignment of the two ends. The length of the studied MWCNTs was 120 nm, while the diameters ranged between 4 and 7 nm. A mixed finite elementtight-binding approach was carefully designed to realize reduction in computational time by orders of magnitude in calculating the deformation-induced changes in the electrical transport properties of the nanotubes. Numerical results suggest that armchair MWCNTs of small diameter should work better if used as conductors, while zigzag MWCNTs of large diameter are more suitable for building sensors. Keywords Carbon nanotubes Electromechanical behavior Transport properties Numerical methods

A. Pantano (&) G. Muratore N. Montinaro Dipartimento di Ingegneria Chimica, Gestionale, Informatica e Meccanica, Universita` degli Studi di Palermo, Viale delle Scienze—edificio 8, 90128 Palermo, Italy e-mail: [email protected]

Several novel electronic components and nanoelectromechanical systems (NEMS) based on carbon nanotubes (CNTs) are under development. The ability of accurately predicting the effects of mechanical deformation on electron transport in CNTs is of primary interest in building these devices; moreover, it could help us evaluate defects of the actually synthesized CNTs since the role of imperfections, like missing atoms, could be better understood and used in assessing the type of CNTs that have been produced. Structural features, including diameter, chirality, and distortions can considerably alter conductivity of CNTs (Saito et al. 1998; Bernholc et al. 2002; Tekleab et al. 2001; Dresselhaus et al. 2001) resulting in a behavior ranging from narrow-gap or moderate-gap semiconducting to metallic nature. Undeformed cylindrical defect-free CNTs allow for ballistic transport, though high-resolution images of CNTs often show CNTs that are bent, twisted, or collapsed. These deformations may develop during growth, deposition, and processing, or upon van der Waals interactions with other CNTs, and with surfaces and surface features such as electrodes. For example, Tekleab et al. (2001) have investigated a multiwalled carbon nanotube (MWCNT) held fixed to the substrate in a bent configuration by van der Waals forces from the Au substrate; they have studied the effect of the flexural strain on the local electronic structure of the tube, see Fig. 1a. In case of small strain, no electronic property change was observed, but in areas with high levels of deformation, drastic

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J Nanopart Res (2013) 15:1885

changes in the local electronic structure of the tube were measured experimentally. For the same difficulties caused by the van der Waals interactions with the substrate, the CNT-based transistor operating at microwave frequencies constructed by Li et al. (2004) works with a bent nanotube as seen in Fig. 1b. However, if we could predict how deformation can affect electron transport in CNTs, then it would be possible not only to understand how much distortion they can withstand without losing their pristine properties, but we could also create electronic devices capable of taking advantage of the relationships between conductance and CNT shape, as was done by Postma et al. (2001). By manipulating with an AFM of nanotube, a room-temperature single-electron transistor within an individual metallic CNT between Au electrodes on top of a Si/SiO2 substrate was fabricated, see Fig. 1c. Progress in theoretical understanding as well as experimental study and device realization in this field has been rapid (Kong et al. 2001; Yu et al. 2000; Frank et al. 1998; Paulson et al. 1999; Minot et al. 2003; Liu et al. 2004; Maiti et al. 2002; Lu et al. 2003; Farajian et al. 2003; Buongiorno Nardelli 1999; Rochefort et al. 1999; Yang and Han 2000; Sanvito et al. 2000; Delaney et al. 1999; Kwon and Tomańek 1998; Choi et al. 1999), and already several prototypical devices have been

constructed and demonstrated (Baughman et al. 2002): nanoelectromechanical sensors (Hierold et al. 2007; Lassagne and Bachtold 2010; Mdarhri et al. 2011; Passacantando et al. 2010), nanoswitches (Sani et al. 2012), and electromechanical actuators (Lassagne and Bachtold 2010). Numerical simulations (Liu et al. 2004; Maiti et al. 2002; Lu et al. 2003; Farajian et al. 2003; Buongiorno Nardelli 1999; Rochefort et al. 1999; Yang and Han 2000; Sanvito et al. 2000; Delaney et al. 1999; Kwon and Tomańek 1998; Choi et al. 1999) of the electromechanical behavior of CNTs mostly focus on SWCNTs rather than on the more abundant MWCNTs, and the few studies available in the literature deal with small segments of only two- or three-walled CNTs. This is mainly due to the high computational burden involved in atomistic (i.e., ab initio, tight-binding, molecular dynamics) simulations of MWCNTs of realistic dimensions. Moreover, most discussions on the electronic structure of CNTs assume perfect cylindrical symmetry, but, as stated earlier, this assumption is somewhat based on an oversimplification. In this study, we take advantage of a mixed finite element-tight-binding approach capable of simulating the electromechanical behavior of SWCNTs and MWCNTs of the dimensions used in nanoelectronic devices. To realize the extreme computational savings necessary to work with realistic-sized CNTs, first a

Fig. 1 High-resolution images of CNTs under deformation: a 3D STM image of a bent MWCNT on the clean flat gold substrate, b SEM image of a semiconducting CNT, c Transistor within an individual metallic CNT. Reproduced with permission from Tekleab et al. (2001), 2001, The American Physical

Society. Reproduced with permission from Li et al. (2004), 2004, American Chemical Society. Reproduced with permission from Postma et al. (2001), 2001, The American Association for the Advancement of Science

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continuum-level representation of nanotubes has been developed. Individual tubes are modeled using shell finite elements, where a specific pairing of elastic properties and mechanical thickness of the tube wall enables successful modeling using the elastic shell theory. Using quadrilateral shell elements, it is possible to create an FE mesh of a CNT wall in which the FE nodal coordinates correspond to the atomic positions. Successive 60-degree rotations of shell element pairs bisecting a hexagonal cell in three superimposed FE meshes cancel the artificial mechanical anisotropy caused by any single-orientation quadrilateral meshing of the cell. The effects of nonbonded forces generated from the attractive and repulsive forces, due, respectively, to van der Waals and to Pauli’s exclusion principles, are simulated with special interaction elements that are of critical importance in tube/ tube or tube/substrate interactions, as well as in maintaining the interwall separation in deformed MWCNTs. This new nonlinear structural mechanicsbased approach for modeling CNTs has been verified by comparisons with MD simulations and highresolution micrographs available in the literature; for details on the current mechanical implementation, the reader is referred to our previous studies (Pantano et al. 2003, 2004a, b, c). Within the FE program, which simulates the mechanical deformation of the nanotube structure, the evolving atomic [nodal] coordinates are further processed using a tight-binding (TB) code which calculates deformation-induced changes in electrical transport properties of the nanotube. There the coordinates are used in TB calculations to compute the electronic properties of the system. Our main objective is to predict the effects of deformation on the electrical properties of MWCNTs; hence, adopting a conventional TB code would negate the computational saving obtained using the structural mechanics-based approach to calculate the deformed atomic coordinates. Instead, an innovative TB algorithm was developed, which results in substantial computational savings. Beginning with a recently developed approach, the coherent transport properties of infinitely long or finite conductors spanning the distance between two leads can be computed using two different full sp3, four-orbital, orthogonal TB models (Xu et al. 1992; Charlier et al. 1997) or a nonorthogonal TB model (Porezag et al. 1995). In our case, the full sp3, four-orbital, orthogonal TB model (Porezag et al. 1995)

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has been used. Then, starting from a methodology using a Green’s function and transfer-matrix-based approach for computing the conductance of a system with a large number of atoms (Buongiorno Nardelli 1999; Meunier et al. 2001), a novel approach has been developed (Pantano and Buongiorno Nardelli 2009; Pantano et al. 2013) where each CNT is divided along its length into a given number of shorter CNT segments connected to one another at interfaces. The system is equivalent to the original CNT, but the memory requirements and the computational expenses are reduced by orders of magnitudes. The realized computational efficiency increases with increasing dimensions of the nanotube; for example, in a previous study (Pantano and Buongiorno Nardelli 2009), the analysis of a 60-nmlong (70,70) tube involved a memory requirement of almost five orders of magnitude smaller than a conventional TB algorithm. The portion of the (70,70) tube that can deform was divided along its length into 207 pieces, since the matrices on which the program operates are square with dimensions equal to [(number of atoms)(number of orbitals per atom)]2; thus, the reduction in memory requirement is equal to 2072 = 42849. In the following discussion, the main equations of the adopted computational-efficient methodology are recalled. If a system is assumed to be composed of a conductor C connected to two semi-infinite leads, R and L, then the theory of electronic transport tells us that the conductance through a region of interacting electrons, the C region, is related to the scattering properties of the region itself via the Landauer formula (Landauer 1970): C¼

2e2 ! h

ð1Þ

where ! is the transmission function, and C is the conductance. It states the probability that an electron can transmit from one end of the conductor to the other end. The transmission function can be expressed in terms of the Green’s functions of the conductors and the coupling of the conductor to the leads as follows (Datta 1995; Fisher and Lee 1981; Meir and Wingreen 1992): ! ¼ Tr CL GrC CR GaC

ð2Þ

where GrC and GaC are the retarded and advanced Green’s functions of the conductor, respectively;

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while CL and CR are functions that describe the couplings of the conductor to the leads. To compute the Green’s function of the conductor, we start from the equation for the Green’s function of the whole system: ð2 HÞ G ¼ I

ð3Þ

where e = E ? ig with g being arbitrarily small, and I is the identity matrix. In the hypothesis that the Hamiltonian of the system can be expressed in a discrete real-space matrix representation, the previous equation corresponds to the inversion of an infinite matrix for the open system, consisting of the conductor and the semi-infinite leads. The above Green’s function can be partitioned into submatrices that correspond to the individual subsystems as

0

GL

B @ GCL GLRC

GLC

GLCR

GC

GCR

GRC

GR

ð2 H00 ÞG00 ¼ I þ H01 G10 ; y ð2 H00 ÞG10 ¼ H01 G00 þ H01 G20 . . .. . .. . .. . .

ð7Þ

y ð2 H00 ÞGn0 ¼ H01 Gn1;0 þ H01 Gnþ1;0

1 ð2 HL Þ hLC 0 C y C B ð2 HC Þ hCR C A¼B @ hLC A y 0 hCR ð2 HR Þ 1

0

where the matrix ð2 HC Þ represents the finite isolated conductor, ð2 HR Þ and ð2 HL Þ represent the infinite leads, and hCR and hLC are the coupling matrices that will be nonzero only for adjacent points in the conductor and the leads, respectively. From this equation, it is straightforward to obtain an explicit expression for GC (Datta 1995): GC ¼ ð2 HC RL RR Þ1

ð5Þ

y y where we define RL ¼ hLC gL hLC and RR ¼ hRC gR hRC as the self-energy terms due to the semi-infinite leads, gL ¼ ð2 HL Þ and gR ¼ ð2 HR Þ are the leads’ corresponding Green’s functions. The self-energy terms can be viewed as effective Hamiltonians that arise from the coupling of the conductor with the leads. Once the Green’s functions are known, the coupling functions CL and CR can be easily obtained as follows (Datta 1995): CL ¼ i RrL RaL ; CR ¼ i RrR RaR ð6Þ RaL

RaR

and are where the advanced self-energy terms the Hermitian conjugates of the retarded self-energy RrL and RrR . The core of the problem lies in the

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calculation of the Green’s functions of the semiinfinite leads. It is well known that any solid (or surface) can be viewed as an infinite (semi-infinite in the case of surfaces) stack of principal layers with nearest-neighbor interactions (Lee and Joannopoulos 1981). This corresponds to transforming the original system into a linear chain of principal layers. Within this approach, the matrix elements of Eq. (3) between layer orbitals will yield a set of equations for the Green’s functions:

ð4Þ

where Hnm and Gnm are the matrix elements of the Hamiltonian and the Green’s function between the layer orbitals, respectively, and we assume that in a bulk system H00 = H11 = … and H01 = H12 = …. Following Lopez-Sancho et al. (1984), this chain can be transformed to express the Green’s function of an individual layer in terms of the Green’s function of the preceding (or following) one. This is done via the introduction of the transfer matrices T and T, defined such that G10 ¼ TG00 and G00 ¼ TG10 . The transfer matrix can be easily computed from the Hamiltonian matrix elements via an iterative procedure, as outlined in (Lopez-Sancho et al. 1984). In particular, T and T can be written as T ¼ t0 þ et 0 t1 þ et 0et 1 t2 þ þ et 0et 1et 2 . . .tn ; T ¼ et 0 þ t0et 1 þ t0 t1et 2 þ þ t0 t1 t2 . . .et n . . .. . .. . .. . . ð8Þ where ti and et i are defined via the recursion formulas: 1

2 ti ¼ ðI ti1et i1 et i1 ti1 Þ t11 ; 2 et i ¼ ðI ti1et i1 et i1 ti1 Þ1 et 11

ð9Þ


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and y t0 ¼ ð2 H00 Þ1 H01 ;

et 0 ¼ ð2 H00 Þ1 H01

ð10Þ

The process is repeated until tn and et n \d with d arbitrarily being small. With this proviso, we can write the bulk Green’s function as y 1 GðEÞ ¼ 2 H00 H01 T H01 T

ð11Þ

If we compare the previous expression with Eq. (4) in the hypothesis of leads and conductors being of the same material (bulk conductivity), we can identify the present bulk system, or rather one of its principal layers, with the conductor C, so that H00 HC , H01 y y hCR and H01 hLC . In particular, by comparing with Eq. (5), we obtain the expression of the self-energies of the conductor-leads system: y RL ¼ H01 T;

RR ¼ H01 T

ð12Þ

The coupling functions are then obtained from the sole knowledge of the transfer matrices and the coupling y Hamiltonian matrix elements: CL ¼ Im H01 T and CR ¼ Im H01 T . The present formulation has a very limited computational cost. Moreover, the only quantities that enter into it are the matrix elements of the Hamiltonian operator, with no need for the explicit knowledge of the electron wave functions for the multichannel expansion. In the same way, the conducting portion of the nanotube can be divided into a given number of pieces. This number must be odd, so thus we can divide the tube in 2n ? 1 pieces, where n is any positive integer. For example, we can divide the tube in 5 pieces, the two leads and three conducting segments; in this case, two additional coupling matrices are computed. It is important to underline that with this approach, no reduction in the accuracy of the calculation is introduced by dividing the tube in a given number of pieces, it was expected and was verified that the results from the code for the undivided tube is exactly the same as the results from the code where the tube is divided in 2n ? 1 pieces for whatever value of n positive integer. The electromechanical modeling technique has been successfully validated in a simulation of a laboratory experiments, and results have been presented in a previous study (Pantano and Buongiorno

Nardelli 2009). Kuzumaki and Mitsuda (2004) had measured the change in the electrical conductance under deformation of 60-nm-long MWCNTs in a transmission electron microscope (TEM). A numerical model capable of reproducing the MWCNT used in the experiment was gradually deformed until the same configuration seen in the TEM image was reached, and the TB code predicted the same change in conductance as measured in the experiment. With this validation of the computational approach, we now investigate the effects of outer diameter and chirality of the MWCNT on the change in conductance due to misalignment of the two ends. Four nanotubes were deformed from their initial straight configuration by fixing the atoms of each wall near the two ends, and then by gradually moving these rigid portions in two opposite directions. This type of configuration is frequently used in manufacturing processes where straight CNTs placed on a substrate are needed, for example, while building CNT-based transistors, see Fig. 1. Since actual manufacturing processes of CNTs rarely produce perfectly straight tubes, when they are deposited on a substrate, van der Waals attraction holds them fixed in a bent configuration. Four MWCNTs were deformed to the same level of misalignment between the two ends: two MWCNTs having as outermost wall armchair CNTs, (30,30) and (50,50); and two MWCNTs having as outermost wall zigzag CNTs, (51,0) and (90,0). The outermost walls of the MWCNTs were chosen to be all metallic; the armchair CNTs are always metallic, but the zigzag CNTs are metallic only when their chirality satisfies the equation (n - m) = 3k, where k is an integer; and n and m are the two integers indicating the chirality (n,m) of the CNT. The geometry of the four models of MWCNTs, which are all 120 nm long and each having five walls, is reported in Table 1. The two small MWCNTs, (30,30) and (51,0), and the bigger MWCNTs, (50,50) and (90,0), were chosen to have approximately the same inner and outer diameters. Figure 2 shows the FE model reproducing the (50,50) armchair MWCNT in the undeformed configuration, both in a side view of the entire MWCNT and in diametrical sectional view. A magnification of the outermost wall, shown in the inset of Fig. 2, allows viewing the hexagonal cells. The MWCNTs were all deformed from their initial straight configuration by fixing the atoms of each wall near the two ends, which are 4 nm long, and then by

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Table 1 Geometry of the MWCNTs models Chirality of the outermost CNT

Outer diameter (nm)

Inner diameter (nm)

Length (nm)

Number of walls

(30,30)

4.07

1.35

120

5

(51,0)

3.99

1.27

120

5

(50,50)

6.78

4.06

120

5

(90,0)

7.04

4.32

120

5

Fig. 2 FE model reproducing the (50,50) armchair MWCNT in the undeformed configuration: a side view of the entire MWCNT, and b diametrical sectional view

gradually moving these rigid portions in two opposite directions. Two different deformation levels have been considered, a mild misalignment of 13.2 nm and then major one of 30 nm. For an imposed distance of 13,2 nm between the two ends of the MWCNTs, the deformed configurations of the two armchair MWCNTs are shown in Fig. 3. At the same level of misalignment, the deformed configurations of the two zigzag MWCNTs are shown in Fig. 4. The only MWCNT undergoing buckling at this deformation levels is the (90,0), while the other three can accommodate the strain levels determined by the mild misalignment without experiencing local buckling of their outermost wall. In the

two smaller nanotubes, (30,30) and (51,0), the absence of buckling is due to their smaller diameter, which produces limited strain levels. Buckling deformations are present in the zigzag (90-0) MWCNT and not in the (50,50) MWCNT, since the hexagonal cells are oriented in such a way that they can more easily follow the buckling deformations due to bending. For an imposed distance of 30 nm between the two ends of the MWCNTs, the deformed configurations of the two armchair MWCNTs are shown in Fig. 5. The deformed configurations of the two zigzag MWCNTs are shown in Fig. 6, while Fig. 7 provides a clearer view of the buckling near one of the two ends for (a) (50,50) MWCNT, and (b) (90,0) MWCNT. At this level of misalignment, the two bigger MWCNTs experience high level of buckling near the two ends, while for the smaller tubes, the strain levels are still unable to produce significant buckling deformations. In MWCNTs, the nested van der Waals interactions of the increased number of inner walls radially stiffen the tube, thus limiting the circumferential extent of the kinks. In the areas of the nanotube walls where a kink is present, owing to the distortion caused by the buckling, centers of scattering are created, which reduce the conductivity. At any kink, the local bonding structure is deformed, and the electrons will lose some of the p characters of their corresponding orbitals. As stated elsewhere (Ebbesen and Takada 1995), the curvature in the nanotube walls due to the kink leads to a loss of spatial overlap of the atomic p orbitals that contribute to conjugation and a shift in hybridization of the atoms from the sp2 of graphite to something intermediate between sp2 and sp3. The net result of these orbital effects is an increase in energy locally and an introduction of partial radical character in the p-bonding electrons. The local loss of spatial overlap of the atomic p orbitals in the kinks of the buckling units mainly depends on the local radius of curvature.

Fig. 3 FE simulations of two armchair MWCNTs where the two ends of the tubes have been misaligned by 13.2 nm, deformed configurations of a (30,30) MWCNT, and b (50,50) MWCNT

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Fig. 4 FE simulations of two zigzag MWCNTs where the two ends of the tubes have been misaligned by 13.2 nm, deformed configurations of (a) (51,0) MWCNT, and (b) (90,0) MWCNT

Fig. 5 FE simulations of two armchair MWCNTs where the two ends of the tubes have been misaligned by 30 nm, deformed configurations of a (30,30) MWCNT, and b (50,50) MWCNT

Fig. 6 FE simulations of two zigzag MWCNTs where the two ends of the tubes have been misaligned by 30 nm, deformed configurations of a (51,0) MWCNT, and b (90,0) MWCNT

Fig. 7 FE simulations of two zigzag MWCNTs where the two ends of the tubes have been misaligned by 30 nm, zoom of deformed configurations near one of the two ends for a (50,50) MWCNT, and b (90,0) MWCNT

Figure 8 plots conductance versus energy calculated using the mixed FE-TB approach for the four MWCNTs models of different outer diameter and chirality, both in the undeformed and deformed configurations. The Fermi energy is taken as a reference and shifted to zero. For a bias voltage of

1 V, the computed overall conductance of all four undeformed tubes was the theoretical value, G = 2G0. Once the deformation levels reached those shown in Figs. 5, 6, and 7, the TB code predicted a significant reduction in conductance only for the bigger MWCNTs, (90,0) and (50,50), while for the smaller

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J Nanopart Res (2013) 15:1885 10 MWNT (30,30) Undeformed

9

Conductance G(E) (2e2/h)


10 MWNT (30,30) Deformed

8 7 6 5 4 3 2 1 0 -0.5

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

5 4 3 2 1 0 -0.5

0.5

Energy (eV) -0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

10 MWNT (50,50) Undeformed

9 8



MWNT (51,0) Deformed

6

10


7 6 5 4 3 2 1 0 -0.5

MWNT (51,0) Undeformed

8 7

Energy (eV) -0.4

9

Energy (eV) -0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

9

MWNT (90,0) Undeformed

8


7 6 5 4 3 2 1 0 -0.5

Energy (eV) -0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

Fig. 8 Conductance calculated using the mixed FE–TB approach for 4 MWCNT models of different outer diameters and chiralities, both in the undeformed and deformed configurations where the two ends of the tubes have been misaligned by 30 nm

tubes, (30,30) and (51,0), no change in the conductance was measured. The (90,0) tube is the most distorted tube, the one with the sharpest kinks, as a result of which the change in the conductance was more likely to be stronger in this tube rather than in the (50,50). The significant reduction of the conductance proves that mechanical deformations can significantly affect the electrical properties of CNTs, potentially complicating manufacturing of electrical devices in cases where the CNTs need to be manipulated to be positioned accordingly. The graphs of the conductance for the simulations where the two ends of the MWCNTs have been misaligned by 13.2 nm are not shown since no changes in the conductance were predicted by the TB code for the four MWCNT models. Some remarks of precaution are needed with regard to the possibility of extending these results to MWCNTs of different external diameters and the number of inner walls. In MWCNTs, there are two features that determine the circumferential extent and the sharpness of the kinks formed due to the mechanical deformations: the outermost diameter, and the

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number of inner walls. A larger outermost diameter makes the nanotube to buckle at smaller deformation levels, smaller twisting angles in torsion, and smaller bending angles in bending. For the same outermost diameter, a greater number of interior walls radially stiffen the outermost tube. The strong repulsive interaction among the inner walls requires the interwall distance to remain almost unchanged, and therefore, the kink in the MWCNT will form only if the inner tubes can be deformed. The stiffening effect due to the inner walls does not grow linearly with their number: the more the tubes are present, the smaller must be the diameter the innermost tubes—and the smaller diameter tubes are much stiffer to deform than the larger diameter tubes. Accordingly increasing the number of inner tubes in a MWCNT of given external diameter would radially stiffen the outermost tubes changing the angle of buckling and reducing the circumferential extent and the sharpness of the kinks formed. Thus, conclusions based on our results can be judiciously extended to MWCNTs of different external diameters and the number of inner walls only if the aforesaid remarks are taken into consideration.


During manufacturing processes, when a straight carbon nanotube is placed on a substrate, e.g., production of transistors, its two ends are often misaligned. In this study, we investigated the effects of MWCNTs’ outer diameter and chirality on the change in conductance due to misalignment of the two ends. A mixed finite-element-tight-binding approach which was carefully designed to realize reduction in computational time of orders of magnitude in calculating deformation-induced changes in electrical transport properties of SWCNTs and MWCNTs of the dimensions used in nanoelectronic devices has been developed. According to the numerical results, the conductance of MWCNTs depends strongly on their diameter, since larger MWCNTs reach the buckling much earlier, and their electrical conductivity changes more easily than that of small diameter ones. For the same outer diameter, owing to the different orientations of the hexagonal cells, zigzag MWCNTs are more sensible to deformations induced by misalignment of the ends compared with armchair MWCNTs. Numerical results suggest that small diameter armchair MWCNTs should work better if used as conductors, while larger diameter zigzag MWCNTs are more suitable for building sensors.

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