Communication: Electrical rectification of C₅₉N: The role of anchoring and doping sites

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 C₅₉N^A (the gold electrode is bonded to a single C atom) and C₅₉N^B (the gold electrode is bonded to a C–C bridge site between two hexagons). For C₅₉N^A, we consider five different positions of the substitutional N atom located in a hexagonal ring (cf. Fig. 1(b), left). In C₅₉N^B, 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).

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 (I–V) 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 I–V 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 I–V is perfectly symmetric. However, using this construction for C₅₉N, the calculated rectification is found to be very small (∼1.24).

Transport across C₅₉N^A 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 C₅₉N^A1 down to ∼7 μA in C₅₉N^A5, where the tip Au atom is directly bonded to the N dopant. In the case of the C₅₉N^B structures, rectification is observed for the C₅₉N^B1, C₅₉N^B2, C₅₉N^B3, and C₅₉N^B4 structures (maximum rectification ratios (RRs) are 2.62, 2.17, 2.13, and 1.68 respectively (⁠$RR= I + / I −$⁠, 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, V_bias) as a function of energy E and bias voltage V_bias, as shown in Fig. 3(a) for a structure exhibiting rectification (C₅₉N^B1) and one that does not (C₅₉N^A3). We also show in Fig. 3(b) the transmission function for V_bias = − 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 C₅₉N^A3 calculated for V_bias = 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 V_bias = − 1 V and −0.33 eV and 0.1 eV at V_bias = 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 V_bias = 1 V do not significantly contribute to the transmission (they do not correspond to transmission peaks), and therefore C₅₉N^A3 does not exhibit transport asymmetry. The case is different in C₅₉N^B1, where the transmission function calculated at V_bias = − 1 V is significantly different from that calculated at V_bias = 1 V. While there are two narrow peaks within the bias window at V_bias = − 1 V, there are three peaks at V_bias = − 1 V with a broad peak at the Fermi energy. In addition, the number of available eignenchannels is much larger at V_bias = 1 V, many of which correspond to transmission peaks. Therefore, transmission at V_bias = 1 V should be higher that at V_bias = − 1 V, consistent with what is observed in the I–V plots in Fig 2.

The spatial distribution of the MPSH orbitals that correspond to the main transmission peaks are shown in Fig. 4 for V_bias = 0, ± 1 V. For the case of C₅₉N^A3 in Fig. 4(b), the MPSH orbitals for both V_bias = − 1 V and V_bias = 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 C₅₉N^B1, at V_bias = + 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 V_bias = − 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 C₅₉N^B1 at V_bias = − 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 V_bias = 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 C₅₉N^B1 at V_bias = + 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 C₅₉N^B1.

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 C₅₉N^B1 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.