First-principles research of the transport properties of phenazine-aluminium complex

DAI Zhenxiang, JIANG Zhongzhu, YANG Qi, ZHENG Ganhong, MA Yongqing

(School of Physics and Materials Science, Anhui University, Hefei 230601, China)



First-principles research of the transport properties of phenazine-aluminium complex

DAI Zhenxiang, JIANG Zhongzhu, YANG Qi, ZHENG Ganhong, MA Yongqing

(School of Physics and Materials Science, Anhui University, Hefei 230601, China)

Via first-principles calculation technique based on the combination of density functional theory with non-equilibrium Green’s function formalism, the transport properties of the phenazine-aluminium complex were probed in the current paper. In our theoretical investigations, the calculation model was composed of the Al-based complex being coupled with two atomic scale Al(100) nanowire electrodes. Our calculations indicated that such an Al-based complex displayed good transmission around the Fermi level in equilibrium. Moreover, it exhibited negative differential resistance effect when voltages were applied. All these results were analyzed via the transmission spectra and projected density of states. Our theoretical calculations suggested that such an Al-based complex would be one potential candidate for the future molecular-scale devices.

electronic transport; first-principles; Al-based complex; negative differential resistance

0　Introduction

Major improvements in the capabilities of electronics have been achieved by the increasing use of silicon-based devices for half a century. However, the current silicon technology is predicted to reach its limits in the near future. Molecular-scale electronic devices have made remarkable progress and attracted much attention in recent years[1-2]. Since the concept of individual molecules as active electronic components was proposed, molecular electronic devices have been accomplished experimentally and theoretically. And consequently, numerous amazing characteristics have been proposed and realized, including rectifiers, negative differential resistance, switches, memory devices and so on[3-5]. It is believed that molecular electronic devices will offer one avenue for extending the silicon technological roadmap.

Besides those better-known molecules, including benzene[6]and OPE[7]etc., experimental and theoretical researches have been struggling to investigate some new molecule systems, and the transport properties and the potential applications in the device applications are also probed for future utilities in the molecular-scale circuit. Recently, Albrecht et al.[8]have synthesized one metal-organic complex by means of inelastic scanning tunneling microscope. Such a complex exhibits one plane geometry. It is composed of two phenazine molecules bridged via one single Au atom. The single metal atom is generally used to bridge the organic molecules to synthesize the metal-organic complexes. For example, one single gold atom has been successfully incorporated in the oligo phenylene ethynylene (OPE) molecule, and one organometallic gold complex has been synthesized and assembled into Langmuir and Langmuir-Blodgett films. The transport properties of these complexes are also experimentally measured, which indicates a beneficial role of metal atom incorporation within the wire-like system[9]. At the same time, the rectangular PTCDA(perylene-3,4,9,10-tetracarboxylic-3,4,9,10-dianhy-dride) molecules and Fe atoms have also been experimentally self-assembled on Au(111) surface[10], and the transport properties of one self-assembled Fe2-PTCDA chain have also been theoretically probed by the first-principles density-functional method[11]. Via some Cu atoms, the organic pyridine-based 2,4,6-tris(4-pyridine)-1,3,5-triazine (T4PT) species are used to fabricate one metal-organic networks experimentally. In these obtained samples, Cu atoms may be twofold coordinated by T4PT molecules[12]. Besides Au, Fe, and Cu atoms mentioned above, aluminum is also used to prepare the metal-organic frameworks since aluminum-organic frameworks may be one kind of very attractive materials for industrial applications[13-14]. Therefore, in the current work one phenazine-aluminium-complex, in which two phenazine molecules are bridged with one aluminum atom, are probed theoretically. In particular, the transport properties are systematically calculated via one molecule-nanowire junction model. Our calculations indicate that such an Al-based complex exhibits good transmission around the Fermi level. Via the nanowire-molecule junction, the complex also displays negative differential resistance(NDR) property. Besides the metal atoms mentioned above, some other elements are also used to construct metal-molecule complex. For example, Barone V et al. recently have theoretically reported binuclear complexes of metals of the VIII group bridged by pyrazine[15].

However, as for these binuclear complexes, their calculations suggest that there exists no NDR phenomenon. Therefore, in the current work, our results indicate the Al-based complex may be one more potential candidate for the future molecular-scale devices.

1　Calculation method and model

In our calculations,the phenazine-aluminium-complex is composed of two phenazine molecules and one single Al atom. All these calculations have been carried out based on nanowire-molecule two-probe model, as shown in Fig.1. In this figure, L,C,and R represent the left electrode, the scattering central region, and the right region, respectively. LS means the left surface region, and RS is the right surface region. In our used model, one phenazine-aluminium-complex molecule is sandwiched between two atomic scale Al(100) nanowire electrodes which extend to reservious at ±∞. Corresponding to the minimum energy, the equilibrium distance between nanowire electrode and the complex is obtained based on total energy calculations, as presented in the following. Four Al atomic layers have been chosen for the electrode cell in thezdirection, and one large enough vacuum layer is included in the electrode cell in thexandydirection so that the device has no interaction with its mirror images. For the electrode cell alongzdirection, one layer contains nine atoms, and the other adjacent layer includes four atoms. In the central scattering region, as indicated by the two vertical lines in Fig.1, the Al-based complex is coupled with five atomic layers to the left electrode, which is referred as left surface (LS) layers, and it is coupled with four atomic layers to the right electrode, which is referred as right surface(RS) layers. The scattering region includes parts of the surface layers which are sufficient to screen the perturbation of the molecule. Before the transport properties calculations, the scattering regions in these models are fully optimized and the force on these atoms is minimized to be smaller than 0.05 eV·Å-1, while keeping all the electrode atoms fixed.

Fig.1　Schematic view of the device model

Via first-principles method based on the combination of density functional theory andnonequilibrium Green’s function[16-17], the electronic transport properties,including equilibrium and non-equilibrium cases, are explored systematically. In the calculations, the solution of poisson equation, with appropriate boundary conditions under a suitable voltage, determines the Hartree potential. The properties of the left and right electrode regions are obtained from the isolated calculations with periodic boundary conditions in all directions. The region between the two electrodes is described with open boundary conditions in the transport direction and periodic boundary conditions in the directions perpendicular to the transport direction. In our calculations, the singleζpolarized basis set (SZP) is used for Al, while doubleζpolarized (DZP) for other atoms. The exchange-correlation potential is described by the local density approximation (LDA). The current under a finite bias is obtained by the Landauer-Büttiker formula[18]

(1)

whereFL(E) andFR(E) are the Fermi-Dirac functions for the left and right electrodes under the bias voltageVb,μLandμRpresents the electrochemical potentials for the left and right electrodes, which is related to the applied voltageVbvia the following formula,μL(Vb)=μL(0)+eVb/2,μR(Vb)=μR(0)-eVb/2. For simplicity,μL(0) andμR(0) are set to zero. The energy region between -eVb/2 andeVb/2, which contributes to the current integral above, is often referred to as the bias window.T(E) is the transmission coefficient.

2　Results and discussions

Firstly, the equilibrium distance between the electrode and the phenazine-aluminium-complex has been calculated. The obtained dependence of total energy on the distance is shown in Fig.2. From this figure, it is easily found that the equilibrium distance between the electrode and the molecule is about 1.90 Angstrom. Based on this distance, the central region is relaxed with the electrode atoms being fixed at the bulk position, and eventually the two-probe model shown in Fig.1 for transport properties is built.

Fig.2　The dependence of total energy on the distance between the molecule and electrode

In Fig.3, the calculated equilibrium transmission spectra are presented. The Fermi level is set to zero. From this figure, it is easily observed that the main transmission energy-region is from -0.5 to 0.15 eV. Therefore, for such aphenazine-aluminium-complex, the main transmission is around the Fermi level. In this region, it is found that the transmission peaks are split. The largest transmission value is up to about 1.6 and the equilibrium conductance is 1.12G0, whereG0is the quantum conductance. Generally speaking, the transmission is closely related to the molecular orbitals, which have been modified by the left and right electrodes. The modified molecular orbitals can be obtained from the molecular projected self-consistent Hamilton(MPSH). Since the MPSH levels are the self-consistent Hamiltonian of the molecule in the presence of the electrodes, so these MPSH levels can reflect the molecule-electrode coupling in the molecular-junction to some extent. Therefore, to understand these interesting characteristics in the transmission spectra, firstly the MPSH levels have been calculated and presented in the Fig.3. It can be observed that there exists well agreement between these MPSH levels and the transmission peaks, which indicates that these transmission peaks originate from the coupling between the molecule and the electrodes.

Fig.3　The equilibrium transmission spectra and the MPSH levels

In order to further illustrate these interesting properties in the equilibrium transmission spectra, especially the transmission around the Fermi level, the projected densities of states (PDOS) on left surface atoms, molecule, and the right surface part are calculated. The results are shown in Fig.4a, including left surface(LS), right region(RS), and molecule region(M). Moreover, the PDOS on the different parts of the whole molecule are also calculated and shown in Fig.4b. The PDOS are calculated by the following formula

(2)

where the ψ(E) is the eigenstate of the whole twoprobe system, φp(E) presents theses states are composed of the atomic orbitals belong to the projected regions. Therefore, based on the PDOS on the molecule, it can be indicated how much the molecule orbitals contribute to these eigenstates of the whole twoprobe system, and eventually the coupling strength between the molecule and the electrodes at one certain energyE. As for Fig.4a, it can be found that the PDOS on the LS and RS are distributed on the whole probed energy region, however, PDOS on the molecule are only distributed two energy ranges. One main region is around the Fermi level, and the other is around 1.1 eV. Therefore, there exists one strong PDOS overlap between LS, RS, and molecule in the vicinity of the Fermi level. This PDOS overlap peak happens in the left vicinity of the Fermi level, which shows the strong correlation with the peak of transmission at almost the same electron energy. This state overlap directly results in the strong transmission in such an energy region, since the electronic states from one electrode can be easily transmitted to the other electrode through the molecule. However, for other energy regions, though there are PDOS overlap between the LS and RS regions, the absence of the molecular state contribution directly leads to zero transmission of the whole molecular-junction. And it is clearly found that the transmission and overlapped PDOS are strongly correlated.

Fig.4　The projected densities of states (PDOS) on the scattering region(a) and the molecule region(b)

In order to further illustrate the effect of the metal atom Al, the PDOS on different parts of the whole molecule are also calculated and presented in Fig.4b. From this figure, it can be seen that around the Fermi level, the PDOS distribution from the metal Al atom is almost equal to those from the left and the right region in the molecule. Therefore, as the linking bridge in the phenazine-aluminium-complex, the central metal Al atom will be one key factor in determining the transport properties of such a molecule.

To systematically investigate the transport properties of such a complex, the non-equilibrium current-voltage(I-V) properties are also calculated. The obtainedI-Vcurve is presented in the Fig.5.

Fig.5　The calculated I-V characteristics of the phenazine-aluminium-complex model junction

From the Fig.5, firstly it can be found that theI-Vcurve is almost symmetrical. This is owing to the symmetrical couple between the Al-based complex and these two nanowire electrodes. Therefore, the following analysis will correspondingly focus on the positive voltage. Secondly, in our calculated voltage range, the current is increased rapidly from the voltage is increased from 0 V to 0.2 V. When the applied voltage is increased further, the current is decreased. Such a behavior, which the current decreases with the increase of the applied bias, is defined as negative differential resistance(NDR). The NDR is one important property widely used in molecular switches and other devices. In such a complex junction, NDR behavior is observed, which means that the phenazine-aluminium-complex may be used as one possible potential candidate for molecular-scale devices. Moreover, the peak-to-valley ratio, which is essential in the device design, is about 3.4 in such a phenazine-aluminium-complex junction. When the applied voltage is increased from 0.4 V to 1.5V, the current is varied very slowly. The current through the molecular-junction is calculated by the Landauer-Buttiker formula. Based on this formal, the current is closely related to the transmission spectra, especially the transmission in the voltage window. And the transmission spectra are the most intuitive representation of the quantum transport behaviors. Therefore, via studying the variation trend of transmission spectra with voltage, it is one direct way to obtain the insight into the particularI-Vcharacteristics. It is well known that, the application of voltage will bring two effects. One is the increase on the voltage window [-Vb/2,Vb/2], and the other is the transmission peaks are shifted correspondingly. In Fig.6, the transmission spectra of voltages varying from 0.1 to 0.5 are given. The dashed lines indicate the bias window. It can be observed that, with the voltage being increased from 0 to 0.2, the transmission peaks are shifted very litter. The increase of the voltage windows directly results in the rapid increase of the current. When the voltage is increased further, the transmission peaks are shifted more and more, and eventually the transmission in the voltage window is decreased. As a result, from 0.2 V to 1.5 V, the current decreases with the increases of the current.

Fig.6　The transmission spectra of the phenazine-aluminium-complex model junction under different voltage

3　Conclusion

In summary, first-principle quantum-transport calculations based on a combined method of DFT and NEGF are performed to investigate the characteristics of the electron transport through the phenazine-aluminium complex. The calculation model is built via the complex being coupled with two atomic scale nanowire electrodes. Our results suggest that, connected with two nanowire electrodes, such a complex exhibits good transmission around the Fermi level in which no voltage being applied, and that the complex also displays negative differential resistance property in case of non-equilibrium. All these obtained results indicate the Al-based complex may have potential applications in the future molecular-scale devices.

References:

[1]JOACHIM C, GIMZEWSKI J K, AVIRAM A. Electronics using hybrid molecular and mono-molecular devices[J]. Nature, 2000, 408: 541-548.

[2]LAMBERT C J. Basic concepts of quantum interference and electron transport in single-molecule electronics [J]. Chem Soc Rev, 2015, 44: 875-888.

[3]ZHAO J, ZENG C G, CHENG X, et al. Single C59N molecule as a molecular rectifier[J]. Phys Rev Lett, 2005, 95: 045502-045505.

[4]KIM W Y, CHOI Y C, MIN S K, et al. Application of quantum chemistry to nanotechnology:electron and spin transport in molecular devices[J]. Chem Soc Rev, 2009, 38: 2319-2333.

[5]ZHAO P, WANG P J, ZHANG Z, et al. Negative differential resistance in a carbon nanotube-based molecular junction[J]. Phys Lett A, 2010, 374: 1167-1171.

[6]NITZAN A, RATNER M A.Electron transport in molecular wire junctions[J]. Science, 2003, 300: 1384-1389.

[7]LIU H M, ZHAO J W, BOEYB F, et al. Asymmetric electron transport realized by decoupling between molecule and electrode[J]. Phys Chem Chem Phys, 2009, 11: 10323-10330.

[8]ALBRECHT F, NEU M, QUEST C,et al. Formation and characterization of a molecule-metal-molecule bridge in real space[J]. J Am Chem Soc, 2013, 135: 9200-9203.

[9]BALLESTEROS L M, MARTIN S, MARQUES-GONZALEZ S, et al. Single gold atom containing oligo(phenylene) ethynylene: assembly into LB films and electrical characterization[J]. J Phys Chem C, 2015, 1: 784-793.

[10]PIERRET A, BOUGEROL C, GAYRAL B, et al. Probing alloy composition gradient and nanometer-scale carrier localization in single AlGaN nanowires by nanocathodoluminescence[J]. Nanotechnology, 2013, 30: 305703-305708.

[11]CHEN Y, HSU S,KAUN C, et al. Spin-polarized negative differential resistance in a self-assembled molecular chain[J]. J Phys Chem C, 2014, 36: 21199-21203.

[12]BERNIEN M, HERMANNS C F, SUN L L, et al. Site-specific bonding of copper adatome to pyridine end groups mediating the formation of two-dimensional coordination networks on metal surfaces[J]. Phys Rev B, 2014, 23: 235409-235419.

[13]GAAB M,TRUKHAN N,MAURER S, et al. The progression of Al-based metal-organic frameworks -from academic research to industrial production and applications[J].Micropor Mesopor Mat, 2012, 157: 131-136.

[14]GANDARA F, FURUKAWA H, LEE S, et al. High methane storage capacity in aluminum metal-organic frameworks[J]. J Am Chem Soc, 2014, 14: 5271-5274.

[15]BARONE V, CACELLI I, FERRETTI A, et al. Transport properties of binuclear metal complexes of the VIII group using a simplified NEGF-DFT approach[J]. Phys Chem Chem Phys, 2013, 27: 11409-11419.

[16]BRANDBYGE M, MOZOS J E L, ORDEJON P, et al. Density-functional method for non-equilibrium electron transport[J]. Phys Rev B, 2002, 65: 165401-165417.

[17]TAYLOR J, GUO H, WANG J. Ab initio modeling of quantum transport properties of molecular electronic devices[J]. Phys Rev B, 2001, 63: 245407-245419.

[18]DATTA S. Electronic transport in mesoscopic systems[M]. New York: Cambridge University Press, 1997: 52-53.

(责任编辑郑小虎)

10.3969/j.issn.1000-2162.2016.05.007

吩嗪-铝复合物体系输运性质的第一性原理研究

戴振翔，蒋中柱，杨启，郑赣鸿，马永青

(安徽大学 物理与材料科学学院，安徽 合肥 230601)

采用密度泛函理论与非平衡格林函数相结合的第一性原理，对由吩嗪分子和单个铝原子构成的复合体系的电荷输运性质进行研究.计算模型是由吩嗪-铝复合物与两个无穷长的Al(100)纳米线电极构成.研究结果表明：在没有施加偏压的平衡状态下该体系在费米能级附近具有良好的电荷透射性能，而在施加偏压的非平衡状态下该体系有负微分电阻效应.结合透射谱及投影态密度，对其输运性质进行了理论解释.从该研究结果可知这类吩嗪-铝复合物在将来的分子尺度器件中具有潜在的应用价值.

电荷输运；第一性原理；铝基复合物；负微分电阻

date:2016-02-16

Supported by the National Natural Science Foundation of China (11204001, 11174004), Anhui Provincial Natural Science Foundation (2013KJS030026, 1208085QA07, 1308085MA04), the Higher Educational Natural Science Foundation of Anhui Province (2013KJT010021，KJ2013A031)，Anhui University Scientific Research Fund (KYXL2012017, KYXL2013009, 201410357005)，“211 Project” of Anhui University (SZJYKC2013020， KYX12013009)

O433.2Document code:AArticle ID:1000-2162(2016)05-0037-08

Author’s brief:DAI Zhenxiang (1975-), male, born in Hunan Province, associate professor of Anhui University,master student supervisor.