⇦Chinese Physics Letters, 2017, Vol. 34, No. 11, Article code 117101 Electronic Transport Properties of Diblock Co-Oligomer Molecule Devices Sandwiched between Nitrogen Doping Armchair Graphene Nanoribbon Electrodes * Meng Ye(叶萌), Cai-Juan Xia(夏蔡娟)**, Ai-Yun Yang(杨爱云), Bo-Qun Zhang(张博群), Yao-Heng Su(苏耀恒), Zhe-Yan Tu(涂喆研), Yue Ma(马越) Affiliations School of Science, Xi'an Polytechnic University, Xi'an 710048 Received 13 July 2017 *Supported by the National Natural Science Foundation of China under Grant Nos 11504283 and 21503153, the Natural Science Foundation of Shaanxi Province under Grant No 2014JM1025, and the Science and Technology Star Project of Shaanxi Province under Grant No 2016KJXX-45.
**Corresponding author. Email: caijuanxia@xpu.edu.cn Citation Text: Ye M, Xia C J, Yang A Y, Zhang B Q and Su Y H et al 2017 Chin. Phys. Lett. 34 117101 Abstract We investigate the electronic transport properties of dipyrimidinyl-diphenyl sandwiched between two armchair graphene nanoribbon electrodes using the nonequilibrium Green function formalism combined with a first-principles method based on density functional theory. Among the three models M1–M3, M1 is not doped with a heteroatom. In the left parts of M2 and M3, nitrogen atoms are doped at two edges of the nanoribbon. In the right parts, nitrogen atoms are doped at one center and at the edges of M2 and M3, respectively. Comparisons of M1, M2 and M3 show obvious rectifying characteristics, and the maximum rectification ratios are up to 42.9 in M2. The results show that the rectifying behavior is strongly dependent on the doping position of electrodes. A higher rectification ratio can be found in the dipyrimidinyl-diphenyl molecular device with asymmetric doping of left and right electrodes, which suggests that this system has a broader application in future logic and memory devices. DOI:10.1088/0256-307X/34/11/117101 PACS:71.15.Mb, 73.23.-b, 85.65.+h © 2017 Chinese Physics Society Article Text In recent years, with the further development of miniaturization of devices, the molecular devices have gradually become a new trend in nanomaterial research. Up to now, many molecular devices have been found with interesting characteristics such as negative differential resistance (NDR),[1-3] spin filtering,[4-6] electronic switching,[7-10] and molecular rectification.[11-13] In particular, various molecular rectifications have been intensively investigated due to their wide range of applications in logic circuits and memory elements.[14,15] However, some of them show poor rectification ratios because of weak contacts to metal electrodes.[16,17] Recently, graphene as a new two-dimensional crystal material shows many peculiar physical and chemical properties.[18,19] A zigzag edge (zGNR) is shown to be metallic, whereas an armchair-edged GNR (aGNR) is semiconducting with the energy gap scaling with the inverse of the ribbon width,[20] which has less weak coupling problems compared with metallic electrode materials like gold. When graphene is used in molecular electronics areas, it shows remarkable properties and wide application prospects.[21,22] In this work, we propose using GNR to fabricate a single dipyrimidinyl-diphenyl molecular device. In some previous works, there are many studies on the dipyrimidinyl-diphenyl molecule attached to gold electrodes, which have displayed rectification and negative differential resistance phenomena.[23] However, Zhang et al. investigated the rectification effect of dipyrimidinyl-diphenyl thiol molecules connected to two gold electrodes, and the maximum rectification ratio value was 3.5.[16] Furthermore, it is well known that the chemical doping in an aGNR plays a pivotal role in determining the conductance behavior.[24-27] Therefore, we investigate the electronic transport properties of dipyrimidinyl-diphenyl anchored with carbon atomic chains sandwiched between two asymmetric N-doped aGNR electrodes. The results show that the rectifying behavior is strongly dependent on the doping position of electrodes. A higher rectification ratio can be found in the dipyrimidinyl-diphenyl molecular device with asymmetric doping of left and right electrodes. The schematic structures of the molecular devices are illustrated in Fig. 1. The dipyrimidinyl-diphenyl anchored with carbon atomic chains sandwiched between two aGNR electrodes, a linear carbon atomic chain derived from graphene as the narrowest GNR is a good conductor when it connects two GNRs.[28-31] For aGNRs the parallel (perpendicular) case corresponds to an even (odd) number of carbon atoms.[30] Thus we take 7-aGNR and select the length of the carbon atomic chains with two carbon atoms,[32] which means that the principal plane of the dipyrimidinyl-diphenyl is almost coplanar with the plane of the aGNR electrodes, and carbon atoms choose a bond way of $\cdots$C–C$\equiv$C–C$\cdots$, which is more stable than $\cdots$C=C=C=C$\cdots$.[30] The molecular devices can be divided into three regions: left electrode, central region, and right electrode. There are three typical models: M1, M2 and M3. For M1 both the left and right electrodes are not doped with heteroatom, whereas two edge carbon atoms are substituted by N atoms in the left electrode in the same way as for M2 and M3. In the right electrode, one center carbon atom and one edge carbon atom are replaced by an N atom for M2 and M3, respectively. All of the edge atoms are saturated with hydrogen atoms to eliminate their dangling bonds.
cpl-34-11-117101-fig1.png
Fig. 1. The models of M1, M2 and M3. For M1 both the left and right electrodes are not doped with heteroatom, and for M2 and M3 two edge carbon atoms are substituted by N atoms in the left electrode in the same way. In the right electrode, one center atom and one edge carbon atom are replaced by nitrogen atoms for M2 and M3, respectively.
In this work, the geometrical and electronic structure optimizations have been carried out by the SIESTA package, and the core electrons are modeled with the Troullier–Martins nonlocal pseudopotential. Using the ATOMISTIX TOOLKIT (ATK) program package we calculate the structural relaxation and the electronic transport properties of the molecular junctions, which are based on a fully self-consistent NEGF formalism combined with first-principles DFT.[33,34] In the electronic transport calculations, the Ceperley-Alder local density approximation (LDA) describes the exchange-correlation potential, and the single-zeta plus single polarization (SZP) basis set can be adopted for all atoms. The current is calculated using the Landauer–Bütiker formula, which is written as $$\begin{align} I(V)=\,&\frac{2e}{h}\int_{\mu_{\rm L}}^{\mu_{\rm R}}[f(E-\mu_{\rm L})\\ &-f(E-\mu_{\rm R})]T(E,V)dE,~~ \tag {1} \end{align} $$ where $f$ is the Fermi function, $\mu_{\rm L/R}$ is the electrochemical potential of the left/right electrode, and the difference in the electrochemical potentials is given by $eV$ with the applied bias voltage $V$, i.e., $\mu_{\rm L}=\mu(0)-eV/2$ and $\mu_{\rm R}=\mu(0)+eV/2$. Furthermore, $\mu_{\rm L/R}(0)=E_{\rm F}$ is the Fermi level. The transmission coefficient of the device is $$\begin{align} T(E,V)=\,&{\rm Tr}[{\it \Gamma}_{\rm L}(E,V)G^{\rm R}(E,V)\\ &\cdot{\it \Gamma}_{\rm R}(E,V)G^{\rm A}(E,V)],~~ \tag {2} \end{align} $$ where $G^{\rm R/A}$ are the retarded and advanced Green functions, and coupling functions ${\it \Gamma}_{\rm L/R}$ are the imaginary parts of the left and right self-energies, respectively.
cpl-34-11-117101-fig2.png
Fig. 2. The current-voltage and rectification ratio curves for molecular junctions M1, M2 and M3. (e) The transmission coefficients for the models with M1 (black curve), M2 (red curve), and M3 (green curve) junction at zero bias, and the energy origin is set to be the Fermi level of the system. (f) The transmission coefficients of M1 and M2 junction under the biases $V_{\rm b}=0.3$, 0.6, 0.9 1.2, 1.4 and 1.5 V. The black dash-dotted lines indicate the position of the bias window [$-V_{\rm b}/2, +V_{\rm b}/2$], and the energy origin is set to be the Fermi level of the system.
The current-voltage ($I$–$V$) characteristic curves of M1, M2 and M3 in the bias range from $-$1.5 to 1.5 V in steps of 0.1 V are given in Fig. 2. It should be pointed out that at each bias, the current is determined self-consistently under the non-equilibrium condition. Obviously, the electronic transport properties of dipyrimidinyl-diphenyl molecules sandwiched between the edge and center N-doped aGNRs are different from each other. The $I$–$V$ curves of M1 and M2 are plotted in Fig. 2(a), and we can see that there are slight current values for M1. However, M2 has large current and striking NDR at large bias voltages. For M2 the current $I$ is nearly zero for small bias voltage $-$0.5–0.5 V, and then increases quickly at positive bias until a maximum value, after that it decreases with the increase of the bias, resulting in the NDR behavior. Eventually, the current value increases gradually and reaches up to 1084 nA. This indicates that the center-doping in the right electrode can give rise to much better NDR performance. Secondly, it is clear that the $I$–$V$ curves of M1 and M2 manifest obvious symmetrical and asymmetrical characteristics respectively to the positive and negative biases. The amplitude of $I$ at large positive bias is significantly greater than that at negative bias with the same magnitude for M2. To clearly show the asymmetry as shown in Fig. 2(b), the bias-dependent rectification ratio (RR) is defined as ${\rm RR}(V)=|I(+V)/I(-V)|$. The maximum values of RR in the calculated bias region for M1 and M2 are 2.19 at 0.6 V and 42.90 at 1.5 V, respectively. These results are larger than the calculation results of Song et al. for the junctions with undoped GNRs,[32] which means that the rectification can be strengthened by doping N atoms at the center of the right electrode. The $I$–$V$ curve and RR of M1 and M3 are shown in Figs. 2(c) and 2(d). From Fig. 2(c), we can see that in the low-bias regions $-$1–1 V, the current is almost zero. Under high voltage, the current value increases with the voltage. Interestingly, the current of M3 is slightly smaller than that of M1 under positive bias voltages. However, under negative bias voltages the current of M3 is slightly larger than that of M1. The current value of M3 is approximately 2 orders of magnitude smaller than that of M2. Moreover, we calculate RR of M3 in Fig. 2(d), and the maximum value is 20 at 1 V, which is smaller than that of M2. To understand the electronic transport mechanism of the substantial differences between the center-doping and edge-doping in the right electrode, we calculate the electronic transmission spectra for M1, M2 and M3 at zero bias, as shown in Fig. 2(e). We can see that the transmission is larger than 1 and lower than 2, which originates from the short length of both carbon atomic chain and dipyrimidinyl-diphenyl molecules. In the limit of long length, both the carbon atomic chain and dipyrimidinyl-diphenyl molecules at most provide one channel. The transmission is the sum of all the migration probabilities. Furthermore, the transmission coefficient of M2 is higher than that of M1, and the transmission peak of M2 is closer to the Fermi level compared with that of M1, which results in the fact that the electrons of M2 can easily transport through the central region. Therefore, the currents for M2 are 2 orders higher than the currents for M1. In contrast, compared with M1 and M2, the transmission peak of M3 is the farthest one, which accounts for the lowest conductivity. To further illustrate the different current-voltage characteristics of M1, M2 and M3, we calculate the molecular projected self-consistent Hamiltonian (MPSH) of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) for M1, M2 and M3 at zero bias in Fig. 3. From the picture, one can see that the spatial distributions of the HOMO for M1 just localize on the dipyrimidinyl-diphenyl molecule. There is no spatial distribution on the left and right aGNRs. The LUMO for M1 delocalizes on the dipyrimidinyl-diphenyl molecule, whereas there is a slight spatial distribution on the aGNR. This significant modification of the HOMO and LUMO weakens the electron delocalization and blocks tunneling across the junction. Thus the corresponding coefficients on both the orbitals are nearly zero. As a result the current value of M1 is very small in all of the bias region. For M2 the spatial distributions just delocalize on the left aGNR and the dipyrimidinyl-diphenyl molecule. There is no spatial distribution on the right aGNR. This means that the transmission coefficients of this orbital are very small. However, the spatial distribution of the LUMO for M2 is delocalized at all devices, which results in large transmission coefficients and current values. The spatial distribution of the HOMO for M3 is similar to M1, which just localizes on the dipyrimidinyl-diphenyl molecule. Therefore, the coefficients of M1 and M3 are almost the same.
cpl-34-11-117101-fig3.png
Fig. 3. The molecular projected self-consistent Hamiltonian (MPSH) of HOMO and LUMO for models M1, M2 and M3 at zero bias.
Figure 2(f) can explain the NDR behavior very well, and the nonequilibrium current is the integration of the transmission coefficient in the bias window [$-V_{\rm b}/2, +V_{\rm b}/2$]. Figure 2(f) shows the transmission spectra of M1 and M2 in the bias region [0.3 V, 1.5 V]. We can see that there is probably no transmission peak in the range 0.3–0.6 V, which means that the current value is nearly zero at the low bias. With the increase of the bias from 0.6 to 1.2 V, the transmission peak of M2 comes into the bias window totally leading to the high currents. When the bias voltage $V_{\rm b}=1.4$ V is applied, the transmission peak in the bias window decreases. However, at $V_{\rm b}=1.5$ V, the transmission peak increases again. By this time, the transmission peak of M1 is still outside the bias window, and only a slight peak can be seen in the transmission window until 1.4–1.5 V. In conclusion, we have investigated the electrical transport properties of the dipyrimidinyl-diphenyl anchored with carbon atomic chains sandwiched between two N-doped aGNR electrodes using the nonequilibrium Green function formalism combined with first-principles density functional theory. The calculated results show that the doping position plays a significant role in the electronic transport properties of dipyrimidinyl-diphenyl molecular junctions. For M2, nitrogen atoms doping at the center of the right electrode can greatly enhance the current value, and can give rise to much better NDR and rectify behaviors. For M3, nitrogen atoms doping at the edge of the right electrode, the current value of M3 is approximately 2 orders of magnitude smaller than that of M2, although to some extent there is a rectification phenomenon. The maximum RR in the calculated bias region for M2 is 42.90 at 1.5 V, which is larger than that of M3, 20 at 1 V. References Large On-Off Ratios and Negative Differential Resistance in a Molecular Electronic DeviceNegative differential resistance and rectifying behaviors in phenalenyl molecular device with different contact geometriesA Dramatic Odd-Even Oscillating Behavior for the Current Rectification and Negative Differential Resistance in Carbon-Chain-Modified Donor-Acceptor Molecular DevicesA spin-filter device based on armchair graphene nanoribbonsSpin filter effects in zigzag-edge graphene nanoribbons with symmetric and asymmetric edge hydrogenationsSpin Caloritronic Transport of 1,3,5-Triphenylverdazyl RadicalCurrent-Induced Hydrogen Tautomerization and Conductance Switching of Naphthalocyanine MoleculesReversible switching in an N-salicylideneaniline molecular device induced by hydrogen transferEffect of Chirality on the Electronic Transport Properties of the Thioxanthene-Based Molecular SwitchNew Dibenzothiophene-Containing Donor−Acceptor Polyimides for High-Performance Memory Device ApplicationsFirst-principles investigation on electronics characteristics of benzene derivatives with different side groupsElectronic transportation through asymmetrically substituted oligo(phenylene ethynylene)s: Studied by first principles nonequilibrium Green’s function formalismRectifying performance of D-π-A molecules based on cyanovinyl aniline derivativesMolecular Rectifying Diodes Based on an Aluminum/4′-Hydroxy-4-biphenyl Carboxylic Acid/p + -Silicon Junction †Length dependence of carbon-doped BN nanowires: A-D Rectification and a route to potential molecular devicesThe effects of contact configurations on the rectification of dipyrimidinyl—diphenyl diblock molecular junctionsObvious variation of rectification behaviors induced by isomeric anchoring groups for dipyrimidinyl–diphenyl molecular junctionsBallistic Transport in Graphene Nanostrips in the Presence of Disorder: Importance of Edge EffectsThe electronic properties of graphenePeculiar Localized State at Zigzag Graphite EdgeHalf-metallic graphene nanoribbonsEdge Hydrogenation-Induced Spin-Filtering and Rectifying Behaviors in the Graphene Nanoribbon HeterojunctionsDiode rectification and negative differential resistance of dipyrimidinyl–diphenyl molecular junctionsGiant Rectification Ratios of Azulene-like Dipole Molecular Junctions Induced by Chemical Doping in Armchair-Edged Graphene Nanoribbon ElectrodesGraphene nanoribbon as a negative differential resistance deviceModulation of rectification and negative differential resistance in graphene nanoribbon by nitrogen dopingN-Doped Zigzag Graphene Nanoribbons on Si(001): a First-Principles CalculationDeriving Carbon Atomic Chains from GrapheneFrom graphene constrictions to single carbon chainsBias Dependence of Rectifying Direction in a Diblock Co-oligomer Molecule with Graphene Nanoribbon ElectrodesElectron Transport Properties of Atomic Carbon Nanowires between Graphene ElectrodesEnergy Gaps in Graphene NanoribbonsDensity-functional method for nonequilibrium electron transportGround State of the Electron Gas by a Stochastic Method
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