Based on the nonequilibrium Green’s function formalism and density-functional theory, we investigate the onset of electrical rectification in a single C59N molecule in conjunction with gold electrodes. Our calculations reveal that rectification is dependent upon the anchoring of the Au atom on C59N; when the Au electrode is singly bonded to a C atom (labeled here as A), the system does not exhibit rectification, whereas when the electrode is connected to the C–C bridge site between two hexagonal rings (labeled here as B), transmission asymmetry is observed, where the rectification ratio reaches up to 2.62 at ±1 V depending on the N doping site relative to the anchoring site. Our analysis of the transmission mechanism shows that N doping of the B configuration causes rectification because more transmission channels are available for transmission in the B configuration than in the A configuration.

Since the introduction of molecular rectifiers based on the donor-σ-acceptor molecular model by Aviram and Ratner in 1974,1 many researchers have explored the mechanisms driving their rectification behavior.2,3 The behavior of a donor–σ–acceptor molecule relies on the geometric structure of the molecule (the donor species is separated from the acceptor species by a σ bridge) and the ionization potential/electron affinity of the components. However, during the past decade, the outstanding development in theoretical methods for simulating nanoelectronic systems, as well as advancement in the fabrication of low-dimensional heterostructures, has enabled many groups to predict significant rectification in many nanostructures that do not have the donor–σ–acceptor character such as graphene nanoribbon heterojunctions,4 N- and B-doped graphene heterostructures,5 H-passivated6 graphene, and boron-nitrogen-carbon heterostructures.7,8 An interesting candidate for molecular rectifiers is substitutionally N-doped C60 (C59N) which was reported by Zhao et al.9 to exhibit strong rectification via the single electron tunneling effect.

The transport behavior of the individual C60 molecule was studied experimentally10 and theoretically.11,12 While an individual C60 molecule does not display appreciable rectification behavior,11,9 the C59N molecule deposited on the alkanethiol self-assembled monolayer (SAM) surfaces displays strong rectification behavior when compared with C60 (cf. Ref. 9). In order to understand the mechanism behind rectification, the authors9 provided a qualitative analysis by modeling the problem as a double barrier tunnel junction, and analysing the asymmetry in the Coulomb blockade by using an orthodox method which agreed well with experiment. However, studying the possible effect of the C59N orientation on transport and understanding the quantum mechanisms involved, require an ab initio investigation in the intrinsic nature of transport across an individual C59N molecule which, to the best of our knowledge, has not been done to date.

In this work, we present results of theoretical investigations into the onset of rectification in the Au–C59N–Au system for two Au-anchoring configurations to C59N/C60 and various substitutional doping locations for the N atom. The basic structure is composed of a left Au electrode, a scattering region, and a right Au electrode, as shown in Fig. 1(a). The scattering region is composed of either the C60 or C59N molecule, in addition to 14 Au atoms from the left electrode and 10 Au atoms from the right electrode. For C59N, we consider two different Au–C59N anchoring configurations, denoted as C59NA (the gold electrode is bonded to a single C atom) and C59NB (the gold electrode is bonded to a C–C bridge site between two hexagons). For C59NA, we consider five different positions of the substitutional N atom located in a hexagonal ring (cf. Fig. 1(b), left). In C59NB, we consider four possible positions for the N atom (cf. Fig. 1(b), right). The latter anchoring configuration is also referred to as η2(6)-coordination in the literature and was found to be more energetically favorable than bonding to the C–C bond between a hexagon and a pentagon (η2(5)-coordination).13 From standard density functional theory (DFT) calculations, we found that the A configuration is slightly more favorable than the B configuration in energy by 0.02 eV. The Au electrodes repeat indefinitely in both directions, thus forming semi-infinite leads. We take the Au–C59 distance to be 2.4 Å obtained from DFT calculations in Ref. 13 (for both A and B configurations).

FIG. 1.

(a) Structure of the Au–C60/C59N–Au system in the A configuration. (b) Illustration of the nine configurations considered, showing the relative position of the N atom with respect to the Au electrode tip atom. The Au atoms are shown as large yellow spheres, C as small yellow spheres, and N as dark blue circles. The shadowed regions indicate the left and right electrodes.

FIG. 1.

(a) Structure of the Au–C60/C59N–Au system in the A configuration. (b) Illustration of the nine configurations considered, showing the relative position of the N atom with respect to the Au electrode tip atom. The Au atoms are shown as large yellow spheres, C as small yellow spheres, and N as dark blue circles. The shadowed regions indicate the left and right electrodes.

Close modal

We perform spin-unrestricted DFT calculations using the generalized gradient approximation for exchange and correlation functional developed by Perdew, Burke, and Ernzerhof14 as implemented in the SIESTA code.15 We use a kinetic energy cutoff of 200 Ry. Our computational procedure involves two steps. First, we perform full relaxation of the atomic structure of the isolated C60/C59N molecule using conjugate gradient optimization and a double-ζ plus polarization (DZP) basis set. Next, we use the relaxed structure to perform transport calculations based on the nonequilibrium Green’s functional (NEGF) method as implemented in the TranSIESTA code.16 In the transport calculation, we use a single-ζ plus polarization (SZP) basis set for the C and N atoms, and a single-ζ (SZ) basis set for the Au atoms. We use a spacing between the structure and its neighboring images of 15 Å in the x and y directions to eliminate interaction between images. We choose the bias voltage range −1 V to 1 V. Regarding the choice of the electrode, we observe that transport across C60 is very dependent upon the electrode used. We utilize a Au(100)-based nanowire electrode structure as shown in Fig. 1(a). The electrodes are created from the bulk gold structure, where the number of atoms in each layer (apart from the two layers of the tip) along the electrode (z) axis is 5,4,5,4, as has been previously done for an Al electrode11 and Ag electrode.17 The left electrode has 32 Au atoms, and the right electrode has 28 Au atoms. The repeating unit cell along the z direction in the electrode has 18 atoms (so, there are 10 Au atoms included in the scattering region from the right electrode and 14 Au atoms from the left electrode).

We present the calculated current-voltage (IV) characteristics in Fig. 2. Transport across C 60 A is almost symmetric, whereas in C 60 B , there is a slight asymmetry (where the right current exceeds the left current at bias 1 V by a factor of 1.4). The reason for this slight asymmetry in C 60 B is that the part of the left electrode within the scattering region has 4 Au atoms more than in the right electrode (there is also a slight asymmetry in C 60 A for the same reason, where the right current exceeds the left current at bias 1 V by a factor of 1.1). This is similar to the slight asymmetry found in Fig. 4 of Ref. 11 upon close inspection. Indeed, we have computed the IV characteristics of C 60 B when it is sandwiched between two Au (111) surfaces, where the electrodes contain an equal number of atoms: each of the left and right electrodes contain 80 Au atoms, 48 of which form the repeating unit in the semi-infinite leads. The resulting IV is perfectly symmetric. However, using this construction for C59N, the calculated rectification is found to be very small (∼1.24).

FIG. 2.

Simulated current-voltage (IV) characteristics of the systems considered: Au–C60–Au in the A and B configurations, the five Au–C59NA–Au configurations, and the four Au–C59NB–Au configurations.

FIG. 2.

Simulated current-voltage (IV) characteristics of the systems considered: Au–C60–Au in the A and B configurations, the five Au–C59NA–Au configurations, and the four Au–C59NB–Au configurations.

Close modal

Transport across C59NA is largely symmetric with an interesting trend in the A configuration that, as the N atom is closer to the electrode anchor site, the conductivity of C59N decreases from ∼15 μA in C59NA1 down to ∼7 μA in C59NA5, where the tip Au atom is directly bonded to the N dopant. In the case of the C59NB structures, rectification is observed for the C59NB1, C59NB2, C59NB3, and C59NB4 structures (maximum rectification ratios (RRs) are 2.62, 2.17, 2.13, and 1.68 respectively ( R R = I + / I , where I± is the current corresponding to positive/negative bias voltage). This shows that rectification drops as the N dopant is further away from the Au-bonded bridge site. These current-voltage characteristics are different from those reported in Ref. 9, because the latter reported the current measured through a different structure, that is, C59N/C60 adsorbed on alkanethiol. This interaction drives the Coulomb Blockade effect which is responsible for the negligible current across the C60/SAM structure and which causes a region of negligible current at low voltages for the case of C59N/SAM.9 

Fundamentally, the variation of the transport properties is a result of the details of the frontier orbitals of C60 and C59N, and their response to applied voltage. In order to understand the calculated rectification behavior, we studied the transmission function T(E, Vbias) as a function of energy E and bias voltage Vbias, as shown in Fig. 3(a) for a structure exhibiting rectification (C59NB1) and one that does not (C59NA3). We also show in Fig. 3(b) the transmission function for Vbias = − 1 V and 1 V as a function of energy for these systems. In these plots, we indicate the energy positions of the wavefunctions of the molecular-projected scattering Hamiltonian (MPSH orbitals).18,19 It can be seen in Fig. 3(b) that the plots of the transmission function in C59NA3 calculated for Vbias = 1 V and −1 V, within the bias window (between the grey vertical dotted-dashed lines), are very similar, with two main peaks at −0.2 eV and 0.2 eV at Vbias = − 1 V and −0.33 eV and 0.1 eV at Vbias = 1 V. The main difference between the two plots is the number of eigenchannel energies, as indicated by vertical blue dashed lines in Fig. 3(b). However, the extra eigenchannels for the case of Vbias = 1 V do not significantly contribute to the transmission (they do not correspond to transmission peaks), and therefore C59NA3 does not exhibit transport asymmetry. The case is different in C59NB1, where the transmission function calculated at Vbias = − 1 V is significantly different from that calculated at Vbias = 1 V. While there are two narrow peaks within the bias window at Vbias = − 1 V, there are three peaks at Vbias = − 1 V with a broad peak at the Fermi energy. In addition, the number of available eignenchannels is much larger at Vbias = 1 V, many of which correspond to transmission peaks. Therefore, transmission at Vbias = 1 V should be higher that at Vbias = − 1 V, consistent with what is observed in the IV plots in Fig 2.

FIG. 3.

(a) The transmission function T(E, Vbias) as a function of energy E and the bias voltage Vbias. (b) The transmission function T(E, Vbias) as a function of energy E at Vbias = − 1, 1 V for the structures C59NB1 (a rectifier) and C59NA3 (not a rectifier), showing the MPSH orbitals of the main transmission channels, as explained in the text. The bias window in (a) is shown as two white dotted lines crossing each other at the center, while in (b) it is shown as two vertical dotted-dashed gray lines. The numbers shown in (b) above the positions of the MPSH orbitals correspond to the labels in Figs. 4(b) and 4(c). Eigenchannel energies are indicated by shorter vertical blue dashed lines.

FIG. 3.

(a) The transmission function T(E, Vbias) as a function of energy E and the bias voltage Vbias. (b) The transmission function T(E, Vbias) as a function of energy E at Vbias = − 1, 1 V for the structures C59NB1 (a rectifier) and C59NA3 (not a rectifier), showing the MPSH orbitals of the main transmission channels, as explained in the text. The bias window in (a) is shown as two white dotted lines crossing each other at the center, while in (b) it is shown as two vertical dotted-dashed gray lines. The numbers shown in (b) above the positions of the MPSH orbitals correspond to the labels in Figs. 4(b) and 4(c). Eigenchannel energies are indicated by shorter vertical blue dashed lines.

Close modal

The spatial distribution of the MPSH orbitals that correspond to the main transmission peaks are shown in Fig. 4 for Vbias = 0, ± 1 V. For the case of C59NA3 in Fig. 4(b), the MPSH orbitals for both Vbias = − 1 V and Vbias = 1 V couple the electrodes to the scattering region, and the transmission functions and MPSH orbital distribution are almost similar, which explains the symmetric transmission. In the case of C59NB1, at Vbias = + 1 V, the LUMO+2, LUMO+1, LUMO, HOMO, HOMO−1, and HOMO−2 orbitals are the main transmission channels, while the HOMO, HOMO−1, and HOMO−2 orbitals are the main transmission channels at Vbias = − 1 V. (Note that, in contrast, only the HOME and LUMO were included in the orthodox analysis of Ref. 9). Inspecting the MPSH orbitals of C59NB1 at Vbias = − 1 V (cf. Fig. 4(c)), it is clear that in the HOMO orbital, the left electrode is almost decoupled from the rest of the structure, which corresponds to weak conductivity. On the other hand, the HOMO−1 and LUMO+2 orbitals in the case of Vbias = 1 V strongly couples the left and right electrodes to the scattering region, and HOMO−2 and LUMO+2 are moderately delocalized across the scattering region. In addition, in the electron hopping picture, the HOMO and LUMO energies of C59NB1 at Vbias = + 1 V are nearly degenerate, therefore an electron coming from the right electrode (corresponding to positive voltage) will hop from HOMO (which is strongly localized at the right electrode) to the LUMO (which is strongly localized at the left electrode). This corresponds to the large peak centered at the Fermi energy. These MPSH orbitals cause the rectification in C59NB1.

FIG. 4.

(a) The HOMO and LUMO MPSH orbitals for C59NA3 and C59NB1 at Vbias = 0 V. (b) The MPSH orbitals for C59NA3 for Vbias = ± 1 V. (c) The MPSH orbitals for C59NB1. The HOMO, HOMO−1, and HOMO−2 orbitals are the main transmission channels at Vbias = − 1 V, whereas at Vbias = + 1 V, the LUMO+2, LUMO+1, LUMO, HOMO, HOMO−1, and HOMO−2 orbitals are the main transmission channels. The arrow shows the direction of an electron hopping from the HOMO to the LUMO, which are near-degenerate states with energies of −0.046 eV and 0.023 eV, respectively. The isosurface value is 0.01 a.u.

FIG. 4.

(a) The HOMO and LUMO MPSH orbitals for C59NA3 and C59NB1 at Vbias = 0 V. (b) The MPSH orbitals for C59NA3 for Vbias = ± 1 V. (c) The MPSH orbitals for C59NB1. The HOMO, HOMO−1, and HOMO−2 orbitals are the main transmission channels at Vbias = − 1 V, whereas at Vbias = + 1 V, the LUMO+2, LUMO+1, LUMO, HOMO, HOMO−1, and HOMO−2 orbitals are the main transmission channels. The arrow shows the direction of an electron hopping from the HOMO to the LUMO, which are near-degenerate states with energies of −0.046 eV and 0.023 eV, respectively. The isosurface value is 0.01 a.u.

Close modal

In conclusion, we have investigated the rectification of a single C59N molecule using the nonequilibrium Green’s function formalism and density functional theory. Our calculations reveal that the rectification effect is dependent upon the orientation of C59N as well as the N doping site relative to the metal electrodes. In particular, when the electrode is bonded to a single C atom, transport is almost symmetric. However, in the case of the η6-coordination where the tip Au atom is bonded to two C atoms, transmission asymmetry is observed, where the rectification ratio reaches ∼2.62 at ±1 V in the C59NB1 configuration. The reason for this is that there is an asymmetry in the transmission function of the B configuration, but a near-symmetry for the A configuration.

This research was undertaken with the assistance of resources from the National Computational Infrastructure (NCI), which is supported by the Australian Government.

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