Current Rectification in Nitrogen- and Boron-Doped Nanographenes

Article pubs.acs.org/JPCC

Current Rectification in Nitrogen- and Boron-Doped Nanographenes and Cyclophanes Aleksandar Staykov,† Xinqian Li,‡ Yuta Tsuji,‡ and Kazunari Yoshizawa*,‡ †

International Institute for Carbon-Neutral Energy Research, and ‡Institute for Material Chemistry and Engineering and International Research Center for Molecular Systems, Kyushu University, Fukuoka 819-0395, Japan S Supporting Information *

ABSTRACT: Electron transport properties of boron- and nitrogen-doped polycyclic aromatic hydrocarbons and cyclophanes are investigated with the nonequilibrium Green’s function method and compared to transport properties of the unsubstituted species. The aim of the study is to derive the effect of the heteroatomic defects on the conductance of nanographenes and to propose new effective ways for current control and design of carbon devices. Of special interest are the electrical current rectifying properties of asymmetrically doped nanographenes and cyclophanes, as well as the rectification mechanism. The mechanisms of donor-π bridgeacceptor and donor-σ bridge-acceptor rectification are used to explain the diode-like properties of asymmetrically doped nanographenes and cyclophanes. The electron-rich nitrogen and electron-poor boron heteroatoms introduce conductance channels within the highest occupied molecular orbital−lowest unoccupied molecular orbital gaps of the hydrocarbons and cyclophanes and significantly enhance the conductance. The combination of nitrogen and boron impurities in one polycyclic aromatic hydrocarbon leads to asymmetrical I/V curves. The rectification is further enhanced in the cyclophanes where the boron impurities are located in one of the layers and the nitrogen impurities in the other. Owing to the efficient separation of the donor and acceptor parts, a higher rectification ratio is estimated. The rectifying properties of the asymmetrically doped carbon materials are derived from the nonequilibrium Green’s function theory. The main reason for the rectification is found to be the interaction of the external electric field induced between the electrodes with the molecular orbitals of the asymmetrically doped hydrocarbons.

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INTRODUCTION With the advance of miniaturization, the elements of the electrical circuits used in modern electronic devices rapidly approach molecular scales. The substitution of micrometer-size devices, e.g., the components of the microelectronics, with nanometer-size devices, e.g., the components of the nanoelectronics, marks the smooth transition between the laws of classical mechanics and the laws of quantum mechanics.1 A whole new series of physical phenomena should be studied and understood before the application of those devices is possible. Among those are the ballistic electron transport, the single molecule resistance, the discrete energy spectrum, the zero-bias current, the interaction of the external electric fields with the discrete molecular orbital levels, etc. In recent decades, a new set of experimental techniques was developed, capable of measuring directly the current through single molecules. Among those, the most important are the scanning tunneling microscopy (STM) technique,2 the self-assembly monolayer technique, the cross-wire technique,3 the mechanically controllable break junction (MCBJ) technique,4 and its statistical approach, developed recently by Taniguchi and coauthors, which allows the simultaneous conductance measurement of thousands of junctions.5 Major research efforts were dedicated © 2012 American Chemical Society

to molecular devices, which could replace the active elements in the widely used electronic circuits such as switches, transistors, diodes, and memories. Significant success was achieved in the design and the fabrication of molecular switches based on the diarylethene molecules by the groups of Irie 6−8 and Feringa.9−13 Photochemical7,10,14 and electrochemical11,12 molecular devices, capable of controlling the flow of the electric current, were designed and fabricated and their properties and limitations were well understood with the help of theoretical methods.15−19 Tour and coauthors fabricated molecular wires that showed remarkable negative differential resistance (NDR) properties.20 They successfully applied those molecules in the design of memory devices. Nanographenes and polycyclic aromatic hydrocarbons (PAHs) were intensively investigated for field effect transistor devices. Those compounds are characterized with relatively large highest occupied molecular orbital−lowest unoccupied molecular orbital (HOMO−LUMO) gaps and high mobility of the delocalized π-electrons, which makes them very Received: April 20, 2012 Revised: July 25, 2012 Published: August 2, 2012 18451

dx.doi.org/10.1021/jp303843k | J. Phys. Chem. C 2012, 116, 18451−18459

The Journal of Physical Chemistry C

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conductance does not follow Ohm’s law dependence from the length of the channel. The ballistic electron transport excludes the possibility of collisions between the electrons and the atoms of the molecule, which means that the resistance for the current is the interface between the conductor and the electrodes. Another consequence from the lack of collisions within the channel is that the electrons do not transfer vibrational energy to the atoms; hence there is no heating of the molecule and the electrons are not losing their phase, for example, coherent regime of electron transport. The steadystate current through a nanoscale system is given with eq 2.27

suitable for electrical current control through gate electrodes. The rectifying and transistor-like properties of hexabenzocoronene linked through an aliphatic bridge to anthraquinone were demonstrated with the STM method by Müllen and Rabe.21 Müllen and coauthors have also introduced a bottom up approach for the synthesis of large polycyclic aromatic hydrocarbons and nanographene sheets.22 That concept allows the design of nanographene materials with impurity defects, which can significantly alter the electronic properties of the material by introducing levels into the band gap. Of special interest are nanographene materials with asymmetrical doping of electron-donor and electron-acceptor impurities because they can lead to diode-like properties. Rectifiers are key elements in the electrical circuits because they control the direction of current flow. The first molecular rectifier was suggested in 1974 by Aviram and Ratner.23 Their conceptual device was the first molecule which could function as an element of the electric circuit. The Aviram−Ratner rectifier was an asymmetrical organic molecule, which consists of two π-electron systems with donor and acceptor properties linked by a σ-bridge. The rectification mechanism was explained with a hoping model where the electron resides in the π-electron systems and tunnels through the σ-bridge. Owing to the difference in the energy levels of the donor and the acceptor parts, the tunneling is possible in the acceptor to donor direction and significantly hindered in the donor to acceptor direction. Aviram−Ratner rectifiers were synthesized and rectifying properties were observed in self-assembled monolayers.24 However, recent investigations have provided evidence that the rectification does not occur due to the donorσ bridge-acceptor mechanism but due to the asymmetrical coupling of the molecules to the electrodes.25,26

I=

2e h

+∞

∫−∞

dET (E)[f (E − μL ) − f (E − μR )]

(2)

In eq 2 e is denoted the electron charge, f is the Fermi function of the electrodes, μL and μR are the chemical potential at the left and the right electrodes, respectively, and T(E) is denoted the transmission probability as a function of electron energy. The transmission probability is given with the following equation: T (E , V ) = trace[ΓLGR ΓR G A ]

(3)

In eq 3 GA and GR are denoted the advanced and the retarded Green’s functions, respectively. ΓL and ΓR are denoted the broadening functions of the electrodes. It is worth noting that the transmission probability is a function of electron energy and applied bias. Thus, the computed zero-bias transmission probability will be different from those for applied biases. The nonequilibrium Green’s function formalism27 (NEGF) is used to describe the ballistic electron transport through a many particle system. For the system shown in Chart 1 HC is

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Chart 1

THEORETICAL BACKGROUND The large amount of the reported experimental data led to the necessity of adequate theoretical models, which can deal with the single molecule electron transport. That model should provide an explanation for the observed results and should suggest reasonable predictions able to lead the experimental research. In the macroscopic world, the conductance (g) is defined by Ohm’s law and is proportional to the area (A) of the conductor, which is perpendicular to the direction of the current, and inverse to its length (L). A g=σ (1) L In eq 1 σ is denoted the conductivity, which is a materialspecific property. The conductivity provides important information for the “free path” of the electrons before they collide with ions from the crystal lattice. Hence, Ohm’s law holds true for conductors with length many times longer than the “free path” of the electrons. Within the molecular device scale, the wave function of an electron, which resides within the source electrode, has a small amplitude on the drain electrode and a finite possibility exists for tunneling between the source and the drain. That possibility will increase when a conductance channel, i.e., an atom or a molecule, is placed in the gap between the electrodes. For such a conductor the electron will not encounter any collisions with the atoms of the molecule, since its “free path” will be longer than the length of the conductor itself. The described electron transport is called ballistic and has several important consequences. For ballistic conductors the conductivity cannot be defined and the

denoted the Hamiltonian matrix of the channel, HL and HR are denoted the Hamiltonian matrices of the left and the right electrodes, and U is the potential due to the external electric field induced between the electrodes. VCL and VLC denote the interaction matrices between the left electrode and the channel. VCR and VRC denote the interaction matrices between the right electrode and the channel. In the setting of the many-particle system in Chart 1 the only physical observable which will change with a change of the direction of current is the potential energy U. Any rectifying properties that can be observed would be a consequence of the sign of U, which depends on the current direction. The potential energy U is added to HC and depending on the current direction the effective Hamiltonian matrix for a nonzero bias system would be HC + U or HC − U. However, rectification will not be observed for symmetrical molecules because the effect of U on HC will be the same magnitude and 18452



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The NEGF method provides an efficient algorithm for the computation of the transmission probability of a many-particle ballistic conductor. The Hamiltonian matrices in eqs 5−8 can be built at different levels of theory. If the main interest is the conductance through the delocalized π-orbitals of an organic wire, then the NEGF method combined with the Hückel molecular orbital theory (NEGH-HMO) would be sufficient to describe the desired properties. Further improvement can be introduced with the extended Hückel method and the Hartree−Fock method. DFT is used in order to include the effect of electron−electron interactions (NEGF-DFT). In this study we use the NEGF-HMO method to demonstrate the important physical phenomena, which govern the molecular rectification. Owing to its computational simplicity, NEGFHMO provides chemical understanding of the investigated system. Quantitative calculations were also conducted with the robust NEGF-DFT method, which provides realistic simulation of the investigated junctions. Investigated Molecular Junctions. From eqs 2−10 we can conclude that current rectification in ballistic conductor can occur through an asymmetrical molecule where levels overlap with the both electrodes. Molecule rectifiers were intensively investigated in the literature.28−35 Different types of asymmetrical wires were suggested. Stokbro and coauthors suggested asymmetrical coupling with the electrodes.25 In their simulation, they have demonstrated rectification through a molecular wire that was strongly coupled to one of the electrodes through a gold−sulfur bond and weakly coupled to the other electrode with gold−hydrogen interaction. Zhao et al. suggested a similar model where the connection to one electrode is achieved through two gold−sulfur bonds and to the second through one gold−sulfur bond.31 Liu et al. demonstrated rectification as a result of hydrogen migration between donor and acceptor groups.29 We have demonstrated rectifying properties of a π−π stacked charge-transfer complex.35 Another type of rectifier is the donor-π bridge-acceptor wire, which is similar to the Aviram−Ratner diode but the σ-bridge is omitted.28 The donor-π bridge-acceptor rectifier is characterized with spatially asymmetrical frontier orbitals where HOMO and LUMO are localized on different parts of the molecule. The external electric field can either further localize the orbitals and reduce the conductance or, when applied in the opposite direction, delocalize them and increase the conductance. In a series of papers Pan and coauthors performed systematic study on the rectifying properties of short organic molecular wires. They investigated the rectification mechanism through a donor-σ bridge-acceptor wire and found rectifying properties in a direction opposite to the one proposed by the Aviram−Rathner rectification mechanism.36 Negative differential resistance was estimated in asymmetrically substituted and asymmetrically coupled to the electrodes Tour wires.37 Novel donor-π bridge-acceptor wires were suggested that show rectifying ratios close to 10.38 Large rectifying ratios were also estimated for molecular wires coupled with different electrode materials.39 In this study we demonstrate the rectification mechanism on an organic wire asymmetrically doped with boron and nitrogen, weakly coupled to the electrodes, shown in Figure 1A. The calculations are performed with the NEGF-HMO method in order to demonstrate clearly the importance of the spatial distribution of the molecular orbitals and the external electric field for the rectifying properties. Further calculations were performed for polycyclic aromatic hydrocarbons with acene-

different signs for both directions of the current. Rectification will be observed for asymmetrical molecules with dipole moments. The potential energy U, for a system without gate electrode, for which we can assume that there is no significant change in the charge, can be given as an interaction between two capacitors with the following equation: U = −eVD

(4)

In eq 4 is assumed that voltage VD is applied to the drain electrode while the chemical potential at the source electrode remains unchanged. The Green’s function of the system shown in Chart 1 is given with the following equation: ⎛ EIL − HL ⎞−1 −VLC 0 ⎜ ⎟ −VCR ⎟ EIC − HC G = ⎜ −VCL ⎜ ⎟ −VRC 0 EIR − HR ⎠ ⎝

(5)

In eq 5 the unity matrices are denoted with I. The major computational problem of eq 5 is the different dimensions of HC, HL, and HR. While HC is a finite square matrix whose dimension depends on the number of atoms and used basis set, HL and HR are infinite, due to the semi-infinite left and right electrodes. A series of linear algebra operations transforms eq 5 to eq 6 where all matrices have finite dimensions. GC(E) = [EIC − HC − Σ L − Σ R ]−1

(6)

In eq 6 ΣL and ΣR are the self-energies of the electrodes, which are given with the following expressions: Σ L = ( −VCL)(EIL − HL)−1(−VLC)

(7)

Σ L = ( −VCR )(EIR − HR )−1( −VRC)

(8)

The matrices VCL, VLC, VCR, and VRC depend on the overlapping of HC with HL and HR, respectively. VCL, VLC, VCR, and VRC represent the escape rates of an electron from a conductance channel, e.g., the probability of an electron to enter or leave the molecule. While HL and HR remain unchanged with the switch of current direction, HC will exhibit a potential energy equal to ± U. Thus, the potential energy caused by the interaction of the external electric field, which is induced from the electrodes, can lead to rectifying properties of a ballistic conductor. To complete the computational model, we have to define the broadening functions ΓL and ΓR. They are derived from the self-energies of the electrodes and are given with the following expressions: ΓL = i[Σ L − Σ†L]

ΓR = i[Σ R −Σ†R ]

(9) (10)

An important consequence of eqs 7−10 is that if one of the matrices VCL, VLC, VCR, and VRC is a zeros matrix, e.g., there is no overlap between the electrode and a conductance channel, then one of the self-energy matrices will be a zeros matrix and one of the broadening functions will be zeros matrix, which will lead to zero transmission probability in eq 3. This result is very important for the understanding of molecular rectifiers. In the Aviram−Ratner model is assumed that the donor (or the acceptor) π orbitals are localized only in one part of the molecule. Such orbitals will overlap only with one of the electrodes and will not contribute to the transmission spectrum. 18453



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the px-orbitals, py-orbitals, and s-orbitals are not considered because they form the σ-skeleton. Doped Nanographene Wafers. The electronic properties of the nanographenes, shown in Figure 1B, are investigated with DFT implemented in the Spartan 10 program.43 Geometry optimization was performed with the B3LYP functional and 6-31G(d) basis set.44 The electron transport calculations were performed for gold junctions with the NEGFDFT method implemented in the ATK 10.8 program.45 That implementation includes full self-consistent treatment of the electrode−molecule−electrode system. The effect of the external electric field in the central region is implemented as a linear potential and polarization of the orbitals. The calculations were performed with the Perdew−Wang (PW) functional with single ζ basis set (SZ) for all Au atoms and double ζ basis set with polarization (DZP) for all other atoms (C, N, B, S, H). The Au electrodes were modeled by 3 × 3 elementary unit cells. Three layers of each electrode with Au (111) surface were included in the central region. The models used for central regions in the electron transport calculations are shown in Figure 2.

Figure 1. Investigated species. (A) Organic wire asymmetrically doped with boron and nitrogen, weakly coupled to single gold atom chain electrodes. (B) PAHs with acene-type edge structure. (C) Cyclophane molecule and boron−nitrogen asymmetrically doped cyclophane molecule.

type edge structure. Polycyclic aromatic hydrocarbons and nanographene sheets are preferred materials in the nanoelectronics, owing to their well-delocalized π-electron system and the high mobility of the valence-band electrons.40,41 The effect of the doping was investigated for boron-doped species, nitrogen-doped species, and boron, nitrogen-doped species, shown in Figure 1B. Further calculations were performed for cyclophane molecules, which are bilayered PAHs linked by σbonds.42 The cyclophane molecules are shown in Figure 1C.

Figure 2. Central regions used in the electron transport calculations of nanographene junctions. CC denotes the unperturbed nanographene junction, BB denotes boron-doped nanographene junction, NN denotes nitrogen-doped nanographene junction, and BN denotes the boron-, nitrogen-doped nanographene junction. Nitrogen is shown with blue color and boron is shown with pink color.

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COMPUTATIONAL METHODS The transmission probabilities for the molecules shown in Figure 1 are calculated using the NEGF formalism described in eqs 6−10.27 Different computational techniques are used for the study of boron-, nitrogen-doped organic wire (Figure 1A), nanographene sheets (Figure 1B), and cyclophanes (Figure 1C). Boron-, Nitrogen-Doped Organic Wire. The boron-, nitrogen-doped organic wire, shown in Figure 1A, is investigated with the NEGF-HMO method. The calculations are performed with our own code. The parameters which were used to construct the Hückel matrix are αN = α + 1.5 β; αB = α − 1.2 β; βC−N = 0.8 β; βC−B = 0.7 β; βAu−Au = 0.6 β; βC−Au = 0.2 β. The nitrogen atom contributes two electrons to the πelectron system and the boron atom contributes zero electrons. The external electric field is added as a linear potential to the diagonal elements of the Hückel matrix. The off-diagonal elements are not affected by the field because it is applied in a perpendicular direction to the pz-orbitals, from which the matrix is constructed.27 The px-orbitals and the s-orbitals will be polarized by the field if we consider that the x axis is the electrode−electrode axis. However, within the Hückel method

Asymmetrically Doped Cyclophanes. The electronic properties of the cyclophanes, shown in Figure 1C, are investigated with the second order Møller−Plesset perturbation theory (MP2) and 6-31(d) basis set implemented in the Spartan 10 program.43,44,46,47 DFT methods underestimate the distortion due to the antibonding interaction between full faceto-face π−π stacked aromatic molecules.48 The geometry optimization was performed with the RI-MP2 approximation, which significantly reduces the computational demands.47 The electron transport calculations were performed for gold junctions with the NEGF-DFT method implemented in the ATK 10.8 program.45 The calculations were performed with the PW functional with SZ basis set for all Au atoms and DZP basis set for all other atoms (C, N, B, S, H). The Au electrodes were modeled by 4 × 4 elementary unit cells. The larger electrode unit cells used for the cyclophanes, compared to those used for the nanaographenes, are required due to cyclophanes’ larger spatial size. Three layers of each electrode with Au (111) surface were included in the central region. The models used for central regions in the electron transport calculations are shown in Figure 3. 18454



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Figure 3. Central regions used in the electron transport calculations of cyclophane junctions. cycloCC denotes the unperturbed cyclophane junction and cycloBN denotes the boron-, nitrogen-doped cyclophane junction. Nitrogen is shown with blue color and boron is shown with pink color.

is 0.6 β. When the external field is applied in the negative direction, the HOMO and LUMO are localized and the energy gap between them is increased to 1.0 β. The small orbital amplitudes at the terminating atoms will determine the small overlap between the energy level and the electrodes. Such a small overlap will be responsible for small escape rates from the molecule and will lead to small transmission probabilities. When the external field is applied in a positive direction HOMO and LUMO are well delocalized with similar amplitudes on the terminating atoms. The energy gap between HOMO and LUMO is reduced to 0.2 β. Figure 4 demonstrates the ability of the applied field to localize/delocalize the frontier orbitals. The different spatial distributions of HOMO and LUMO for fields applied in opposite directions should lead to current rectification. Electron transport calculations were performed with the NEGF-HMO method, and the results for the transmission probabilities are summarized in Figure 5. The calculations show 3 orders of magnitude difference of the transmission probability at the Fermi energy for applied fields in the opposite directions.

Analysis of the molecular projected self-consistent Hamiltonian (MPSH) states was used in the explanation of the obtained results. The MPSH states are the eigenvectors of the Hamiltonian matrix, HC, in eq 8. The matrix does not include the self-energies of the electrodes; however, in the routine of the self-consistent calculation it was affected by the presence of the electrodes. Thus, the MPSH states approximately represent the molecular orbitals of the central region within the junction environment.

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RESULTS AND DISCUSSION Boron-, Nitrogen-Doped Organic Wire. The transmission through the boron-, nitrogen-doped organic wire was investigated with the NEGF-HMO method. Calculations were performed for zero external potential and for applied fields of ±0.6 β. The direction of the external electric field is defined in Chart 2. The values of the potential, which were added to the Chart 2

diagonal elements of the Hückel matrix, are given in β units for the both directions. The results from the electronic calculations with the Hückel theory are summarized in Figure 4. HOMO and LUMO for the zero field case are asymmetrically distributed. HOMO is localized at the electron-acceptor (boron) part of the molecule, while LUMO is localized at the electron-donor (nitrogen) part of the molecule. The energy gap

Figure 5. NEGF-HMO transmission probabilities for external field of −0.6 β, zero external field, and external field of 0.6 β.

Doped Nanographene Wafers. Nanographene sheets and large PAHs are investigated intensively for possible application in nanotechnology.21,22,49−51 They possess well-delocalized πelectron systems characterized with high mobility of the electrons. The band gap of those materials depends on the size, the edge structure, and the defect states.52−55 The pure large PAHs show semiconductor-like properties, while defect states can lead to materials with metallic-like or magnetic properties. The defect types can be vacancies or impurities and the impurities can be peripheral and interstitial.56 In this study we investigate the effect of the boron and nitrogen atoms caused by their electron-acceptor and electron-donor properties, respectively. The boron-, nitrogen-doped graphene

Figure 4. Hückel molecular orbitals of boron-, nitrogen-doped organic wire for A: external field applied in negative direction; B: zero external field; C: external field applied in the positive direction. The phases and the amplitudes of the HOMOs and LUMOs are shown. 18455



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values of the current are calculated as high as 36 μA. The asymmetrical boron-, nitrogen-doped PAH shows rectifying properties as it is expected from the discussion above. However, a low rectifying ratio of 2 was estimated. The reason for the low rectifying properties is the small separation of the donor and acceptor part of the molecule leading to a small dipole moment of 4.82 D. The external field interacts with the dipole and an effective separation of the acceptor and the donor part is required. From the results plotted in Figure 6 we can conclude that the electron transport is achieved through the π-electron system. Thus, in order to enhance the rectifying properties we have to design a π-conjugated system with effective separation of the donor and acceptor parts without the σ-bridge. Those properties are united in the asymmetrically doped cyclophanes. Asymmetrically Doped Cyclophanes. Cyclophanes are a class of organic molecules where two PAHs are linked through aliphatic bonds.42,66 Although that kind of system strongly resembles the π-electron system − σ-bridge − π-electron system model, in many cyclophanes the π-electron systems are connected by additional σ-type overlapping of the 2pz AOs of the carbon atoms at the adjacent PAHs as it is shown in Chart 3. The overlap integral of two homonuclear 2pz AOs is given

materials are intensively investigated for application as p-n junction semiconductor materials.57−60 Boron and nitrogen build bonds in planar sp2 hybridization and can replace carbon in PAHs. When they are interstitial defects, the nitrogen contributes with two electrons to the π-electron system and the boron contributes with zero electrons. However, the pz-orbital of the boron participates in the π-electron delocalization. Electronic and electron transport properties of unsubstituted, as well as of nitrogen-, boron-, and oxygen-doped nanographenes, were investigated previously in the framework of the Pariser− Parr−Pople and Hartree−Fock formalisms.61,62 Those calculations have confirmed the significant heteroatomic effects in the quantum transport. Heteroatoms were shown to localize the electronic density of HOMO and LUMO at certain sites, which led to enhanced electron transport properties.61,62 Our DFT calculations show that carbon-only species are characterized with a large energy gap, while boron defects lower in energy the lowest unoccupied orbitals and nitrogen defects increase the energy of the highest occupied orbitals. The energy gap for the unsubstituted PAH, shown in Figure 1B, is 3 eV, the energy gap for the nitrogen-doped PAH is 1 eV, the energy gap for the boron-doped PAH is 1.2 eV, and the energy gap for the boron-, nitrogen-doped PAH is 2.5 eV. Those results suggest that doped PAHs will be characterized with higher currents for lower applied biases compared to the pure PAHs. The electron transport calculations are performed for dithiolates of the PAHs shown in Figure 2. The molecules are anchored to the electrodes through covalent gold−sulfur bonds. The connecting sites are chosen according to a recently suggested and experimentally verified orbital control rule for electron transport through aromatic hygrocarbons.63−65 The I/ V curves for the pure PAH, boron-doped PAH, nitrogen-doped PAH, and boron-, nitrogen-doped PAH are shown in Figure 6.

Chart 3

with eq 11 and is a function of the distance between the orbitals’ centers, R, and the angle, φ, where φ = 0° corresponds to σ-type overlapping and φ = 90° corresponds to π-type overlapping.67 In cyclophanes, the distance between the two nearest orbital centers in adjacent PAHs is ∼3.0 Å, while the distance between the two nearest orbital centers within the same PAH is ∼1.4 Å. Hence, the π-type overlap integrals between 2pz AOs in the same PAH are larger than the σ-type overlap integrals between 2pz AOs in the adjacent PAHs. For example, the σ-type overlap integral for distance R = 3.0 Å is 0.06, while the π-type overlap integral for distance R = 1.4 Å is 0.43. The σ-type overlap integral between 2pz AOs of the both π-electron systems ensures delocalization of the π-electrons throughout the molecule, while its small value ensures effective separation of the donor and the acceptor parts.

Figure 6. I/V curves for pure PAH (CC), nitrogen-doped PAH (NN), boron-doped PAH (BB), and boron-, nitrogen-doped PAH (BN).

The pure PAH shows lower calculated currents for all applied biases. The doping with either nitrogen or boron significantly increases the values of the computed current. That is especially notable for the boron-doped PAH in the low bias regime under 1 V. In the high bias regime is observed localization of the MPSH state under the Fermi level of the electrodes. This localization leads to the observed negative differential resistance. With the increase of the bias further conducting channels enter in the window between the chemical potentials of the electrodes and the current increases with the applied bias. NDR was not observed for the nitrogen-doped PAH and

S=

∫ pz pz dV = −cos φ ∫ pσ pσ dV + sin φ ∫ pπ pπ dV (11)

In this way, cyclophanes with one acceptor PAH, that is, boron-doped, and one donor PAH, that is, nitrogen-doped, should show significant rectifying properties. In this study we compare the electron transport properties of the boron-, nitrogen-doped cyclophane shown in Figure 1C to the 18456



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the results for one layer PAHs where doped PAHs showed higher values of the computed current compared with the pure PAHs for the same applied bias. The improved electrontransport properties combined with current control properties, that is, rectification, will lead to useful molecular electronic devices. The calculated I/V curves of cycloCC and cycloBN for applied biases in the range from zero to 1.2 V are shown in Figure 9. The calculated current for the cyclophane, cycloCC, is

properties of the unperturbed cyclophane. Geometry optimization was performed with the MP2 method and the optimized geometry is shown in Figure 7. The MP2

Figure 7. Optimized geometry of the investigated cyclophane molecule.

optimization was able to reproduce the important features of the molecular geometry.68 Because of antibonding π−π interaction the face-to-face overlapping of the PAHs is unfavorable. When the aliphatic chains are connected to the same benzene ring the face-to-face overlapping is avoided by small rotational distortion.42 For larger PAHs the slipping distortion is more favorable. Another important feature of the cyclophanes is the bending of the PAHs’ planes. The energy gap of the unperturbed cyclophane is 6.4 eV, and the energy gap of the boron-, nitrogen-doped cyclophane is 3.5 eV. The dipole moment of the boron-, nitrogen-doped cyclophane is 17.97 D. Electron transport calculations are performed for the systems shown in Figure 3 where the unperturbed cyclophane is denoted with cycloCC and the boron-, nitrogen-doped cyclophane with cycloBN. In the zero-bias case, the energy spectra of the central regions and the transmission probabilities as a function of the electron energy are shown in Figure 8. CycloCC is characterized with a large energy gap between the highest occupied and lowest unoccupied MPSH states. The nitrogen and boron impurities supply states within that energy gap, which can provide conductance channels for lower applied biases. The zero-bias transmission spectrum of cycloCC has no peaks close to the Fermi energy, while the transmission spectrum of cycloBN shows many peaks close to the Fermi energy. From the MPSH energy levels and the transmission spectra can be concluded that doped cyclophanes will have better conducting properties. The results are in agreement with

Figure 9. Calculated I/V curves of cyclophane junction, cycloCC, and boron−nitrogen-doped cyclophane junction, cycloBN.

an order of magnitude lower than the current for the unsubstituted PAH. Boron and nitrogen impurities introduce conductance channels within the energy gap of the cyclophane, that is, close to the Fermi energy, and the calculated current is the same order of magnitude as that for the PAHs. However, the boron-, nitrogen-doped cyclophane shows a rectification ratio of 7, which is significantly larger than the rectification ratio of the boron-, nitrogen-doped PAH. We performed analysis of the spatial distribution of the MPSH states of the boron-, nitrogen-doped cyclophane to verify that the rectifying properties are result of asymmetrical orbitals. The results for the MPSH levels close to the Fermi energy are shown in Figure 10. According to eqs 6−10 a conductance channel should possess significant amplitude at

Figure 8. Calculated zero-bias transmission spectra of cyclophane junction, cycloCC, and boron−nitrogen-doped, cyclophane junction, cycloBN. The MPSH levels are denoted with red lines. 18457



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while the delocalized channels result in high transmission probability and high values of the computed current. Within the ballistic electron transport regime the Aviram−Ratner hopping rectification mechanism would not be applicable, due to the limited effect of the external electric field on each of the πelectron systems. However, in the incoherent electron transport regime where electron hopping is essential the Aviram−Ratner model should be dominant. The rectification of asymmetrically doped nanographene wafers was investigated; however, because of the strong delocalization of the π-electron systems and the poor separation of the donor and the acceptor part, the calculated rectification ratio was 2. Higher rectification ratio of 7 was obtained for asymmetrically doped cyclophanes where the donor and the acceptor π-electron systems are connected with weak interlayer π−π staking. The necessary conditions for the design of π-electron molecular rectifiers are asymmetrical molecule, delocalized π-electron system throughout the length of the molecule, and good separation of the donor and acceptor parts. Those conditions are met by the asymmetrically doped cyclophanes, which makes them promising materials in the nanoelectronics.

Figure 10. Spatial distribution of the MPSH states of the boron-, nitrogen-doped cyclophane close to the Fermi energy for zero bias and for biases applied in both opposite directions.

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the connecting sites with the electrodes. For zero-bias only the MPSH state 113 is localized mainly on the boron-doped layer, while MPSH states 114, 115, 116, and 117 are well delocalized throughout the cyclophane structure. When positive bias is applied MPSH states 114, 115, 116, and 117 remain delocalized. If negative bias is applied, MPSH states 116 and 117 are localized on the nitrogen-doped layer of the cyclophane, and MPSH states 114 and 115 are localized on the boron-doped layer. The localization of MPSH states leads to very low transmission probability for electron energies between the chemical potentials of the electrodes and as a result low values for the current were calculated. The mechanism of rectification is very similar to the rectification of the boron-, nitrogen-doped wire shown in Figure 1A and investigated here with the NEGF-HMO theory. The rectification is a result of localization (and delocalization) of molecular orbitals (MPSH states) after interaction with the external electric field induced between the electrodes. However, within the NEGF-HMO theory, because of the computational simplicity of the method the external field was included only a linear potential to the diagonal elements of the Hamiltonian matrix while in the NEGF-DFT method the off-diagonal elements are affected by the field. Nevertheless, the qualitative NEGF-HMO method can provide clear explanation of the rectification in the ballistic regime.

ASSOCIATED CONTENT

S Supporting Information *

Atomic Cartesian coordinates for the optimized geometries of unsubstituted nanographene, boron-doped nanographene, nitrogen-doped nanographene, boron nitrogen-doped nanographene, and cyclophane. This information is available for free via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81-92-8022529. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by World Premier International Research Center Initiative (WPI), Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT), Japan. K.Y. acknowledges Grants-in-Aid (Nos. 18GS0207 and 22245028) for Scientific Research from Japan Society for the Promotion of Science (JSPS) and the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT), the Nanotechnology Support Project of MEXT, the MEXT Project of Integrated Research on Chemical Synthesis, and the Kyushu University Global COE Project for their support of this work, Y.T. acknowledges JSPS for Ph.D. scholarship, XQ.L. acknowledges China Scholarship Council (CSC) for Ph.D. scholarship.

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CONCLUSIONS We have investigated the electrical current rectifying properties of short organic molecules, nanographenes, and cyclophanes for which the predominant electron transport mechanism is ballistic. It was shown that diode-like properties in short molecules can arise as a result of interaction of the external electric field induced between the electrodes with the molecular orbitals. The effect of the field is added as a linear potential within the junction and as polarization perturbation to the molecular orbitals. The external field has a strong effect on the orbital amplitudes of asymmetrical molecules and can lead to localization of conductance channels when applied in one direction and delocalization of the channels when applied in the opposite direction. Localized channels result in low transmission probability, that is, low values of the computed current,

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Current Rectification in Nitrogen- and Boron-Doped Nanographenes

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