⇦Chinese Physics Letters, 2019, Vol. 36, No. 4, Article code 047101 Negative Differential Resistance and Rectifying Effects of Diblock Co-Oligomer Molecule Devices Sandwiched between C$_{2}$N-$h$2D Electrodes * Meng Ye (叶萌), Cai-Juan Xia (夏蔡娟)**, Bo-Qun Zhang (张博群), Yue Ma (马越) Affiliations School of Science, Xi'an Polytechnic University, Xi'an 710048 Received 24 December 2018, online 23 March 2019 *Supported by the National Natural Science Foundation of China under Grant No 11004156, the Science and Technology Star Project of Shaanxi Province under Grant No 2016KJX-45, and the Graduate Innovation Foundation of Xi'an Polytechnic University under Grant No chx201880.
**Corresponding author. Email: caijuanxia@xpu.edu.cn Citation Text: Ye M, Xia C J, Zhang B Q and Ma Y 2019 Chin. Phys. Lett. 36 047101    Abstract Based on nonequilibrium Green's function method in combination with density functional theory, we study the electronic transport properties of dipyrimidinyl-diphenyl molecules embedded in a carbon atomic chain sandwiched between zigzag graphene nanoribbon and different edge geometries C$_{2}$N-$h$2D electrodes. Compared with the graphene electrodes, the C$_{2}$N-$h$2D electrode can cause rectifying and negative differential resistance effects. For C$_{2}$N-$h$2D with zigzag edges, a more remarkable negative differential resistance phenomenon appears, whereas armchair-edged C$_{2}$N-$h$2D can give rise to much better rectifying behavior. These results suggest that this system can be potentially useful for designs of logic and memory devices. DOI:10.1088/0256-307X/36/4/047101 PACS:71.15.Mb, 73.23.-b, 85.65.+h © 2019 Chinese Physics Society Article Text With the miniaturization of electronic devices, designing functional devices using single molecules has become one of the most active research fields in nanoscale science. Various molecular devices have been intensively investigated experimentally and theoretically, although some show poor stability because of weak contacts to metal electrodes.[1,2] In recent years, graphene as a typical two-dimensional (2D) material has attracted numerous attention due to its unique electrical and chemical properties,[3-5] such as high strength, high charge mobility, and excellent transmittance.[6-8] However, the perfect graphene is a zero band gap semiconductor,[9-12] thus many researchers have modified its structures using a variety of methods, including tailoring, doping and introducing vacancy defects.[13,14] Recently, a new 2D crystal material C$_{2}$N-$h$2D with uniform holes and nitrogen atoms is synthesized via a simple wet-chemical reaction.[15,16] Compared with graphene, its band opens a direct gap of 1.7 eV, and the field effect transistor has high on/off ratio of 10$^{7}$.[15] Similar to graphene, cutting a single layer of C$_{2}$N-$h$2D will form two types of C$_{2}$N-$h$2D: zigzag-edged C$_{2}$N-$h$2D and armchair-edged C$_{2}$N-$h$2D. A zigzag-edge C$_{2}$N-$h$2D is shown to be metallic, whereas an armchair-edged C$_{2}$N-$h$2D is semiconducting.[17] The same as graphene, it can be used as an electrode whether it is a metal or a semiconductor.[18] When C$_{2} $N-$h$2D is used in molecular electronics areas, it shows remarkable properties and has a wide range of potential applications.[8] In this work, we propose to fabricate single dipyrimidinyl-diphenyl molecular device using C$_{2}$N-$h$2D. Dipyrimidinyl-diphenyl is an asymmetric single molecule. Many researchers have connected dipyrimidinyl-diphenyl molecules to gold electrodes to construct molecular devices, which has exhibited rectifying and negative differential resistance (NDR) phenomena.[19-21] However, due to the weak coupling problem between the molecule and the metal electrode, the rectification ratio is small.[20-22] Furthermore, the research of dipyrimidinyl-diphenyl molecules connecting with C$_{2}$N-$h$2D electrodes as a molecular device has rarely reported until now. Therefore, we explore the electronic transport properties of a dipyrimidinyl-diphenyl anchored with carbon atomic chains sandwiched between zigzag graphene nanoribbon (zGNRs) and different edge geometries C$_{2}$N-$h$2D electrodes by applying nonequilibrium Green's function (NEGF) formalism combined with first-principles density functional theory (DFT). The results show that compared to the graphene electrode, the C$_{2}$N-$h$2D electrode can cause rectifying and NDR effects. Moreover, the NDR and rectifying behaviors of the molecular junction are observed to be dependent on the edge geometry of the C$_{2}$N-$h$2D electrodes. A more remarkable NDR phenomenon can be found in the dipyrimidinyl-diphenyl molecular device with zigzag C$_{2} $N-$h$2D nanoribbon electrodes, and armchair C$_{2} $N-$h$2D nanoribbon electrodes can give rise to much better rectifying behaviors. The structures are illustrated in Fig. 1. The dipyrimidinyl-diphenyl anchored with carbon atomic chains is sandwiched between two zGNR electrodes or C$_{2}$N-$h$2D nanoribbon electrodes. The entire molecular devices can be divided into three regions: left-hand lead, scattering region, and right-hand lead. There are three typical models, the dipyrimidinyl-diphenyl molecular connected with 8-zGNRs electrodes is named as M1, where 8 is the number of carbon dimer lines across the ribbon width. The dipyrimidinyl-diphenyl molecular attached with two 8-zigzag-edged C$_{2}$N-$h$2D nanoribbon electrodes or 7-armchair-edged C$_{2}$N-$h$2D nanoribbon electrodes are named as M2 and M3, respectively, where 7 and 8 are the numbers of carbon and nitrogen dimer lines across the ribbon width. The lengths of the central scattering regions of M1 and M2 are both 77.4 Å, and the central scattering region of M3 is 80 Å, which are enough to avoid direct coupling between left-hand and right-hand electrodes.[8]
cpl-36-4-047101-fig1.png
Fig. 1. The models of M1, M2 and M3. For M1 the electrodes are zGNRs, for M2 and M3, the electrodes are zigzag-edged C$_{2}$N-$h$2D nanoribbon and armchair-edged C$_{2}$N-$h$2D nanoribbon, respectively.
Based on a fully self-consistent NEGF formalism combined with first-principles DFT, the Atomistix Toolkit (ATK) program package is used to calculate the structural relaxation and the electronic transport properties of the molecular junctions.[23,24] In the electronic transport calculations, the Ceperley–Alder local density approximation (LDA) describes the exchange-correlation potential. A double-zeta plus polarization (DZP) basis set is employed to describe the localized atomic orbitals and a mesh cutoff energy is set to be 150 Ry to save computational time. The current is calculated using the Landauer–Bü tiker formula, which can be written as $$ I(V)=\frac{2e}{h}\int_{\mu_{_{\rm L}}}^{\mu_{_{\rm R}}}[f(E-\mu_{_{\rm L}})-f(E-\mu_{_{\rm R}})]T(E,V)dE,~~ \tag {1} $$ where $f$ is the Fermi function, $\mu_{\rm L/R}$ is the electrochemical potential of the left-hand/right-hand electrode, and the difference in the electrochemical potentials is given by $eV$ with the applied bias voltage $V$. 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's functions, and coupling functions ${\it \Gamma}_{\rm L/R}$ are the imaginary parts of the left-hand and right-hand self-energies, respectively. The current-voltage ($I$–$V$) characteristic curves of the M1, M2 and M3 all in the bias range from $-$1.0 V to 1.0 V in steps of 0.1 V are given in Fig. 2(a). It is obvious that the electronic transport properties of dipyrimidinyl-diphenyl molecules sandwiched between the zGNRs and C$_{2}$N-$h$2D electrodes are different from each other. We can see that the current of M1 almost increases with the voltage over the entire bias range. However, M2 appears an NDR peak at low bias voltages. For M2 the current firstly increases as the bias increases and reaches the maximum when the bias is 0.2 V and then smoothly decreases to zero as the bias increases to 0.5 V. As the bias continues to increase, the current maintains at zero, resulting in the NDR behavior. Clearly, the current value of M3 is higher than M2 and also shows the NDR effect. For M3, the current is nearly zero for small bias voltage $-$0.4 V–0.4 V, and then increases quickly until a maximum value, it then decreases with the increase of bias, leading to the NDR behavior. Eventually, the current value increases gradually and reaches up to $-$921 nA at negative bias. Moreover, from Fig. 2(a), it is clear that the $I$–$V$ curves of M3 manifest obvious asymmetrical characteristics, showing a rectifying behavior. To further explore the rectifying behavior, we calculate the rectifying ratio (RR) varying with the bias voltage as shown in Fig. 2(b). The bias-dependent RR is defined as ${\rm RR}(V)= |I(-V)/I(+V)|$. From Fig. 2(b), we can observe that the RR of M2 is less than 4 all over the bias range, and the maximum RR value of M3 is 15.6 at 0.4 V, which is nearly 4 times larger than M2. However, most reported systems are of small rectifying ratios. For example, Song et al. reported a diblock dipyrimidinyl-diphenyl molecule embedded in a carbon atomic chain that is sandwiched between two aGNR electrodes, and the largest rectifying ratio was no more than 2.[18] It is indicated that we can obtain a large rectifying ratio by selecting armchair edged C$_{2} $N-$h$2D as the electrodes. This will be very useful for designs of molecular rectifying devices.
cpl-36-4-047101-fig2.png
Fig. 2. The current-voltage and rectification ratio curves for molecular junctions M1, M2 and M3.
To understand the interesting electronic transport behaviors, in Fig. 3(a), we calculate the transmission spectra for all systems at different voltages. The nonequilibrium current is the integration of the transmission coefficient in the bias window $[-V_{\rm b}/2, +V_{\rm b}/2]$. The transmission spectrum at 0 V is displayed along in Fig. 3(b) with the molecular projected self-consistent Hamilton (MPSH). From Fig. 3(a), we find that for M3 the transmission peaks in the negative bias window (at $-$0.6 V and $-$1 V) are higher than the position bias window (at 0.6 V and 1 V). As we know, the transmission peaks in the bias window directly contribute to current. Therefore, the negative currents are larger than positive currents and the rectifying behavior occurs. However, the transmission spectra of M1 and M2 at negative bias and positive bias are almost symmetrical, which means that the currents are equivalent. These can give a good explanation for the electronic transport characteristics shown in Fig. 2.
cpl-36-4-047101-fig3.png
Fig. 3. (a) The transmission coefficients for the models with M1 (black curve), M2 (red curve), and M3 (green curve) junction at different biases. The red dash-dotted lines represent the positions of the bias window and the Fermi level is set to zero. (b) The transmission spectra at zero bias. (c) The molecular projected self-consistent Hamiltonian (MPSH) of all models at zero bias.
It is known that the electronic transport spectrum at zero bias is very important to understand the electron transport at low bias. As shown in Fig. 3(b), around the Fermi level there are nonzero transmission coefficients for M1 and M2 but almost zero for M3. It can also be observed that the transmission coefficient of M2 is higher than M1. This observation means that for M1 and M2 the electrons near the Fermi level can easily transport through the scattering region, but difficultly for M3. As a result, the current value of M2 is greater than the current value of M1, and the current value of M3 is almost zero at low bias. To better understand the different $I$–$V$ characteristics of M1, M2 and M3, the spatial distributions of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are also calculated at zero bias using the MPSH, as shown in Fig. 3(c). At zero bias, the transmission peaks of M1 and M2 are mainly derived from the contributions of HOMO and LUMO, while the transmission peaks of M3 are mainly derived from the contributions of HOMO and LUMO-2. From the picture, one can see that the spatial distributions of the HOMO and LUMO for M1 are delocalized at all devices, which leads to low barrier and provides good transport channels for electron transport. This analysis indicates that both the HOMO and LUMO can be motivated to contribute to the current value when the low bias is applied. As a result, M1 shows high conducting behavior. For M2, the spatial distributions are more delocalized than M1, and a fully delocalized orbital ensures that channel opens up for conduction and leads to appearance of a nonzero transmission coefficient near the Fermi level. Therefore, the current value of M2 is higher than M1. In contrast, in M3, the HOMO orbitals are localized on the right-hand armchair edged C$_{2}$N-$h$2D and the LUMO-2 orbitals are localized on the left-hand armchair edged C$_{2}$N-$h$2D. This significant modification of the HOMO and LUMO-2 weakens the electron delocalization and blocks tunneling across the junction. Thus, the corresponding coefficients on both orbitals are nearly zero and, consequently, the current value of M3 is very small in the low bias region. In addition, we also calculate the HOMO-LUMO gap (HLG) of the models. The HLGs of M1, M2 and M3 are 0.016, 0.005 and 0.031 eV, respectively. It is well-known that the smaller the HLG, the more easily it is to rearrange its electron density under the presence of an external electron. This result is in good agreement with the transmission spectrum.
cpl-36-4-047101-fig4.png
Fig. 4. (a) The transmission coefficients of M2 under the biases $V_{\rm b}=0.0$, 0.2, 0.5 and 0.8 V. (b) The transmission coefficients of M3 under the biases $V_{\rm b}=0.4$, 0.6, 0.8 and 1.0 V. The red 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.
To elucidate the NDR mechanism more clearly, Fig. 4 shows the transmission spectra of M2 and M3 under different voltages. Figure 4(a) shows the transmission spectra of M2 under the bias range of 0–0.8 V. We can see that at the zero bias the transmission coefficient is nonzero. As the bias voltage increases from zero to 0.2 V, there is still a transmission peak in the bias window with the applied bias. However, as the bias voltage continues to increase to 0.8 V, no transmission peaks appear in the bias window. Therefore, the current of M2 increases at first and it then decreases until it reaches zero, resulting in an NDR effect. Figure 4(b) is the transmission spectra of M3 at voltages of 0.4 V, 0.6 V, 0.8 V and 1 V, respectively. We can see that there is probably no transmission peak in the range of 0–0.4 V (see Figs. 3 and 4(b)), which means that the current values are nearly zero at low biases. With the increase of the bias from 0.6 to 0.8 V, the transmission peak of M3 appears into the bias window totally leading to the high currents. When the bias voltage is applied $V_{\rm b}=1$ V, the transmission peak in the bias window decreases. Therefore, the $I$–$V$ valley appears, as illustrated in Fig. 2(a). In conclusion, we have performed a first-principles study on electronic and transport properties of the dipyrimidinyl-diphenyl anchored with carbon atomic chains sandwiched between zGNRs and C$_{2}$N-$h$2D electrodes. Our results indicate that compared with the zGNRs electrodes, the C$_{2}$N-$h$2D electrodes can show obvious NDR and rectifying effect. The behaviors are closely related with the edge geometry of the C$_{2}$N-$h$2D electrodes. The molecular junction that has zigzag C$_{2}$N-$h$2D electrodes displays the best NDR property, the rectifying effect of the armchair electrode is more obvious, and the maximum RR is 15.6 at 0.4 V. References Iron-phthalocyanine molecular junction with high spin filter efficiency and negative differential resistanceGraphene and graphene oxide nanogap electrodes fabricated by atomic force microscopy nanolithographyBallistic Transport in Graphene Nanostrips in the Presence of Disorder: Importance of Edge EffectsThe electronic properties of grapheneGrowth of Graphene Nanoribbons and Carbon Onions from PolymerThe rise of grapheneEffects due to backscattering and pseudogap features in graphene nanoribbons with single vacanciesNegative differential resistance and bias-modulated metal-to-insulator transition in zigzag C2N-h2D nanoribbonEffects of stacking order, layer number and external electric field on electronic structures of few-layer C 2 N-h2DGraphene transistorsHigh-speed graphene transistors with a self-aligned nanowire gateTwo-dimensional gas of massless Dirac fermions in grapheneN-Doped Zigzag Graphene Nanoribbons on Si(001): a First-Principles CalculationEffect of Chemical Doping on the Electronic Transport Properties of Tailoring Graphene NanoribbonsNitrogenated holey two-dimensional structuresStructural and phononic characteristics of nitrogenated holey grapheneElectronic, magnetic and transport properties of transition metal-doped holely C 2 N- h 2D nanoribbonsBias Dependence of Rectifying Direction in a Diblock Co-oligomer Molecule with Graphene Nanoribbon ElectrodesThe effects of contact configurations on the rectification of dipyrimidinyl—diphenyl diblock molecular junctionsDiode rectification and negative differential resistance of dipyrimidinyl–diphenyl molecular junctionsElectronic Transport Properties of Diblock Co-Oligomer Molecule Devices Sandwiched between Nitrogen Doping Armchair Graphene Nanoribbon Electrodes *Obvious variation of rectification behaviors induced by isomeric anchoring groups for dipyrimidinyl–diphenyl molecular junctionsDensity-functional method for nonequilibrium electron transportSpecial points for Brillouin-zone integrations
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