Theoretical study of crossed and parallel carbon nanotube junctions and three-dimensional grid structures

This work presents a first-principles study of parallel and crossed junctions of single-wall carbon nanotubes (SWNT). The crossed junctions are modeled by two-dimensional grids of zigzag SWNTs. The atomic and electronic structure, stability, and energetics of the junctions are studied for different magnitudes of contact forces pressing the tubes towards each other and hence inducing radial deformations. Under relatively weak contact forces the tubes are linked with intertube bonds which allow a significant conductance through the junction. These interlinking bonds survive even after the contact forces are released and whole structure is fully relaxed. Upon increasing contact force and radial deformation the tube surfaces are flattened but the interlinking bonds are broken to lead to a relatively wider intertube spacing. The intertube conductance through such a junction diminish because of finite potential barrier intervening between the tubes. The linkage of crossing tubes to form stable junctions is enhanced by a vacancy created at the contact. The three-dimensional grid structure formed by SWNTs is also investigated as a possible framework in device integration.

Figure 1

(a) Supercell used to simulate a junction of two crossed tubes. $F_p\left(D\right)$ is the contact force generated due to a fixed distance $D<D_{vdW}$, and $s\left(D\right)$ is optimized spacing between the surfaces of two SWNTs at the contact. (b) Bridge-Hollow (B-H) atomic registry between two parallel zigzag SWNT, where the $\mathrm{C}\mathrm{C}$ bonds of top SWNT along its axis face the hexagon of the bottom SWNT. (c) The same as (b) for the crossbar structure. (d) Hexagon-hexagon (H-H) atomic registry for the crossbar structure. The lattice parameter of the bare (8,0) tube is $c_{\mathit{SWNT}}=4.25\mathrm{\AA }$.

Figure 2

Relaxed atomic structures of two crossed (8,0) SWNTs with different atomic registries (H-H and B-H). B-H junction has been studied for five different spacing values of $s\left(D\right)$ labeled by B-H1, B-H2, B-H3, B-H4 and B-H5.

Figure 3

(a) Variation of relaxed spacing $s$, between two crossed nanotubes and (b) its energy (shown by diamonds) and contact force $F_p$ (shown by triangles) as a function of $D$. The stress per supercell and atomic configuration of the junction are shown by insets. In (a) filled circles, light diamonds and triangles indicate B-H, H-H registries and the B-H registry including a single vacancy, respectively. In (b) diamonds and triangles are joined by lines as a guide to the eye; but the detailed structure of possible local minima are omitted.

Figure 4

Contour plots of total charge density ${\rho }_T$ and SCF electronic potential $V_e$ of B-H2 and B-H3 junctions. In the right panels the potential energy in the white regions is higher than the Fermi energy, i.e. ${\Phi }_B>0$.

Figure 5

Relaxed atomic structure, total charge density ${\rho }_T$ and SCF-electronic potential $V_e$ of the junction of crossed SWNTs. Left panels: B-H5 contact; right panels: B-H5-type contact including a single carbon vacancy. (a) and (b) are charge density contour plots on a lateral plane bisecting the spacing $s$ between tubes. (c) and (d) are the same for the electronic potential energy. While $V_e>E_F$ at the contact and hence ${\Phi }_B>0$ in (c), the potential barrier is collapsed and an orifice is formed between two tubes through the contact in (d).

Figure 6

Relaxed atomic structure of the junctions between two parallel tubes under different contact force or $D$. (a) Large $D$ and hence weak deformation. (b) Small $D$, hence strong deformation. (c) Relaxed junction after the contact force in (b) is released. Parallel tubes have B-H registry.

Figure 7

Relaxed atomic structure of a junction B-H2 after the contact forces $F_p$ are released.

Figure 8

Energy band structure along the $z$-axis shown by an inset, and the relaxed atomic structure of the corresponding 3D grid of the (8,0) zigzag tubes.

Figure 9

An atomistic model which describes the electronic transport through the junction. $\mathbf{L}$ and $\mathbf{R}$ are reservoirs where finite tubes forming the junction are coupled to.

Figure 10

Calculated conductance $G$ versus energy $E$ for various junctions. (a) Distribution ordering of interatomic distances in the B-H2 junction, i.e., $R_{ij}$ versus the number index of sorted distances. The dashed line at $1.75\mathrm{\AA }$ and $2.91\mathrm{\AA }$ correspond to the domains of tight-binding parametrization; (b) the B-B junction of two parallel tubes connected by a carbon atom; (c) the B-H2 junction of crossed tubes. (d) The B-H2 junction relaxed after contact forces are released; (e) B-H3 junction; (f) B-H4 junction; (g) A junction having H-H registry; (h) the B-H6 junction which is B-H5 including a single vacancy. In all plots the coupling parameter is fixed at $\gamma =0.5$. Zero of energy is set at the Fermi level.