The transport properties of the PTCDIs series molecules sandwiched between bulk electrodes

WANG Bing, WANG Wei-wei, DAI Zhen-xiang, ZHENG Gan-hong, MA Yong-qing

(Anhui Key Laboratory of Information Materials and Devices, School of Physics and Materials Science,Anhui University, Hefei 230601, China)



The transport properties of the PTCDIs series molecules sandwiched between bulk electrodes

WANG Bing, WANG Wei-wei, DAI Zhen-xiang*, ZHENG Gan-hong, MA Yong-qing

(Anhui Key Laboratory of Information Materials and Devices, School of Physics and Materials Science,Anhui University, Hefei 230601, China)

The transport properties of the perylene tetracarboxylic diimides (PTCDIs) series molecules PTCDI-Cn(n=0,6) were investigated via first-principles calculations. Our calculation technique was the combination of density functional theory with non-equilibrium Green’s function formalism method. The corresponding molecular-junctions consisted of the PTCDI series molecules sandwiched between three different kinds of bulk electrodes, including Li, Al, and graphene. Based on our calculation results, even sandwiched between two bulk electrodes, the PTCDI-Cn(n=0, 6) molecules also exhibited some interesting properties including negative differential resistance and the rectification effect. These transport properties were systematically analyzed via the calculated transmission spectra and the projected densities states. These calculations suggested these molecules might have great potential utilities in future molecular-scale devices.

electronic transport; first-principles calculation; PTCDI series; rectification

0 Introduction

With the rapid increase of electronic industrial level, integration of chip element becomes very high and the size of chip element becomes increasingly small. But it will encounter many physical laws limit when the device size shrinks to tens of nanometers or smaller. Recently, molecular devices have aroused considerable attention due to their tiny size and diversity of chemical synthesis[1-4]. In other words, these molecular-scale systems exhibit great potential advantage on alternatives to traditional devices. Consequently, many scientists try to make a design of molecular machines from a chemical point of view[5-8]. Some possible molecules used to manufacture devices in nanoscale[9-10]. Many experimental and theoretical works have been proved to demonstrate numerous interesting properties. These properties include negative differential resistance (NDR), rectification[11], the switching behaviors[12], and so on. Among these potential utilities, molecular-scale rectifier is one of the most crucial electronic elements which will be utilized to future logic circuits and high-speed memory elements.

Due to the low cost and commercial availability, perylene tetracarboxylic diimides (PTCDIs) are the most potential molecules for organic electronic applications, and thus the PTCDI molecule and its potential device utilities have been attracted great attention in these decades. Experimentally, Tao et al. have studied the large gate modulation in the current of a room temperature single molecule transistor consisting of the PTCDI molecule[13]. Their investigations have suggested PTCDI may be used as an excellent candidate for resonance tunneling field effect transistors. In particular, it is proved that the millimeter nano-scale band of an asymmetric molecular PTCDI with alkyl side grows by a self-assembly method and the PTCDI’s length has a controllability[14-16]. Recently, Chueh et al. have probed the device performance of n-type PTCDI-C8 organic field-effect transistors with solution-based gelatin dielectric experimentally[17]. Using graphene as source/drain electrodes, one high-performance organic complementary inverter consisting of PTCDI-C13 molecule has been reported[18]. Theoretically Luo et al. have calculated the transport properties of the PTCDI molecular junctions in aqueous solution[19]. Zhu et al. have also probe the spin-filter, spin-valve, and switching effect in the PTCDI molecular junctions contacted with graphene leads[20]. In our previous work, the transport properties of the PTCDIs molecules have been investigated theoretically, in which the PTCDIs molecules are sandwiched between two atomic-scale nanowire electrodes. Some interesting properties including rectification behavior etc. have been discovered. However, the transport properties of molecular-junctions are closely related to the used electrodes. For example, the C59N molecule exhibits the rectifying behavior in carbon nanotube one-dimension electrode junctions, while there is no observable rectification in three-dimension metal-electrode junctions[21]. Accordingly, it is of fundamental and practical importance to investigate the transport properties of these PTCDI series molecules via the bulk electrodes, and especially it is also very necessary to probe whether these molecules still exhibit the rectification behavior when the molecules are sandwiched between two bulk electrodes. So, in the current theoretical calculations, three kinds of electrodes Al, Li, and graphene electrodes are adopted to further explore the transport properties of these molecules. These three kinds of electrodes are often used as the contact electrodes sandwiching the single molecule to fabricate molecular junctions experimentally and theoretically[18,20,22]. For example, Pan et al. paired an Au electrode with, respectively, Li, Pb, Ag electrodes sandwiching the oligo phenylene ethynylene (OPE) molecule to fabricate molecular junctions[22].

In the current work, via the first-principles method, the transport properties of PTCDI-Cn(n=0,6) molecular junctions are probed theoretically. Our calculation methods are based on the combination density functional theory with non-equilibrium Green’s function formalism (NEGF) method, and in the calculations these PTCDI series molecules are sandwiched between two bulk electrodes including Li, Al, and graphene. Our calculation results clearly suggest that, even in case of bulk electrodes, the PTCDI-C6molecule also exhibits rectification behavior. And then, based on our serially theoretical work, the PTCDI-C6molecule can present rectification properties in case of both nanowire and bulk electrodes. Accordingly, our systematic investigations suggest that these molecules present great potential utilities in the future molecular-scale devices.

1 Models and methodology

Fig.1 shows the schematic models of the molecular devices we constructed. The PTCDI-C6molecule is sandwiched between the different bulk electrodes Al, Li, Graphene, which are referred to as models A, B and C respectively. Model M is referred to the PTCDI molecule sandwiched with two Al electrodes. LE, SC, and RE present the left electrode, the scattering region and the right electrode respectively. The molecule PTCDI-Cn(n=0,6) with S atoms ends are sandwiched between two bulk electrodes. Bulk electrode materials include Al, Li and graphene. For convenience, these three different structures are referred as model A, model B and model C. In order to make a comparison, as shown in Fig.1, we have also calculated the molecule-junction consisting of PTCDI and the electrodes Al, which was called as model M. S atoms are placed in the hollow site of the bulk electrode surface. To systematically investigate the possible existence of the rectification behavior of PTCDI series molecule in case of the bulk electrodes, two kinds of crystal orientations are also considered, in which the Al(100) electrode is used in model A and the Li(111) electrode is adopted in model B. In practical calculations, these molecular junctions are divided into three parts from left to right: the left electrode (LE), the scattering region (SE) and the right electrode (RE).

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， while keeping all the electrode atoms fixed. The electronic transport properties are explored by the first-principles non-equilibrium Green function technique (NEGF)[23-24]. 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 and Li atoms, 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[25]

(1)

wherefL(E) andfR(E)aretheFermi-DiracfunctionsfortheleftandrightelectrodesunderthebiasvoltageVb,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.Forsimplicity,μL(0)andμR(0) are set to zero. The energy region between -eVb/2 and -eVb/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 analysis

The calculated current-voltage (I-V) curves in one bias range [-2.4 V, 2.4 V] in steps of 0.2 V for the four models are provided in Fig.2. As for model A shown in Fig.2b, under lower bias, it is found that the current is very small and that to a certain extent there exists one linear variation trend between the applied voltage and the corresponding current.

The current rises rapidly at the higher bias, showing a nonlinear variation behavior. Especially, when the applied bias is up to 1.2 V, the current in the positive voltage is larger than that in the negative voltage, and one evident rectifying behavior appears. Similar rectification behaviors can be observed in the model B and C, as shown in Fig.2c and Fig.2d. In the case of these three bulk electrodes, PTCDI-C6molecule exhibits nonlinear transport properties in the whole calculated voltage region and displays asymmetricalI-Vcurves under the positive and negative voltages. In particular, the rectification properties can be observed in all cases. But for model M in Fig.2a, it can be observed that, for the PTCDI molecule, the current under negative voltage is approximately as large as that under the corresponding positive voltage. TheI-Vcurve is almost symmetric, and there is no obvious rectifying phenomenon. Therefore, for the PTCDI molecule, there are no obvious rectification properties sandwiched between both the atomic Au nanowire electrode and the Al(100) bulk electrodes. However, for the PTCDI-C6molecule, there exists obvious rectification phenomenon in both atomic nanowire electrode[20]and bulk electrodes. More interestingly, regardless of the bulk electrode or the atomic nanowire electrode, the PTCDI-Cn(n=0, 6) both display NDR behavior when the applied bias increases up to one certain value. The NDR effect regardless of the used electrode indicates that these PTCDI series molecules have great potential applications in high-speed switches and memory etc. About the NDR behavior in the molecular junctions, it can be analyzed using our “significant energy regions” models in detail[26].

To systematically explore the transport properties of these junctions, the rectification ratioR(|Vb|) is calculated using the formulaR|Vb|)=I(+|Vb|)/I(-|Vb|).AsshowninFig.3,itcanbeobservedthatthereexistsobviousrectifyingeffectinthecaseofmodelsA-Cinthecalculatedvoltageregions.Moreover,inthecalculatedvoltageregions,thelargestrectificationratioformodelsAis10.9whenthevoltageis1.8V,modelBis36.2incaseof2.2V,and26.7formodelCincaseof1.6V,respectively.Therefore,therectificationratioisfoundtobesensitivetotheelectrodematerialandtheappliedvoltage,originatingfromthedifferentelectricalconductivityoftheseelectrodes,theelectronicsstructureofmolecules,andthecouplingbetweenthem.

In our first-principles theoretical calculations, the current through molecular junctions are obtained from the Landauer-Buttiker formula mentioned above. Therefore, the magnitude of the current in fact depends on the transmission coefficient in the integral regions, i.e., the size of the integral area in the bias windows. As for the rectification behavior, it means that there exists the current through the device and that the corresponding current in the opposite voltage is very small or negligible. Therefore, via calculating and analyzing the transmission spectra as a function of the applied voltage, it will obtain clear and intuitive knowledge on the transport properties of these junctions. Taking model B about the Li(111) electrodes as one example, we thus calculate the energy dependence transmission spectra, as shown in Fig.4. In Fig.4, The dotted line indicates the Fermi energy which is shifted to zero and the region between two black solid lines present the bias window. Since the transmission peaks are intimately associated with the electronic structure of the electrodes, the orbitals of the central molecule, and the coupling between the molecule and electrodes. As for the equilibrium caseVb=0,itisclearlyobservedthattherearefiveobvioustransmissionpeaksintheprobedenergyrange.OneisjustabovetheFermilevel,whichissettozero.Suchapeakiscloselyassociatedwiththelowestunoccupiedmolecularorbital(LUMO),andthetransmissionneartheFermilevelismainlycontributedfromthispeak.Asthevoltageincreasesfrom0to2.4V,thesetransmissionpeakswillbeshifteddowngradually.Asaresult,moreandmoretransmissionpeakswillenterthebiaswindowandcontributethecurrentcorrespondingly.Thereisoneverysmalltransmissionpeakinthebiaswindowatthevoltagewhenthevoltageincreasesuptoabout1.0V.Whenthevoltageis1.6V,asthepeaksareshiftedmore,andthentherearenoticeabletransmissionpeaksenterthebiaswindow.Consequently,thetransmissionspectracontributetothecurrentarecorrespondinglylargerthanthatunderlowbias.However,whenthevoltageischangedfrom0to-2.4V,thetransmissionpeaksareshiftedupcorrespondingly.Andlittletransmissionpeakswillbeshiftedintothebiaswindow.Asaconsequence,thecurrentundernegativevoltagesissuppressedcorrespondingly,andeventuallytherectificationhappens.

In order to further investigate the transport properties these PTCDI series molecules sandwiched with bulk electrodes, taking the case of Li(111) as an example, the projected densities of states (PDOSs) of these junctions onto the central region have also been calculated. The PDOSs are presented in Fig.5, in which Fig.5a corresponding to the equilibrium caseVb=0 V and Fig.5b presents the case of 1.6 V and Fig. 5c for -1.6 V. The PDOSs are projected onto the PTCDI-C6molecule, the left surface atoms, and the right surface atoms respectively. As shown in Fig.5a, it can be observed that there exist three PDOSs overlapping region for the PDOSs of the PTCDI-C6molecule, the left surface atoms, and the right surface atoms. In comparison with the zero-voltage transmission spectra shown in Fig.4, such these state overlapping regions correspond well to the transmission peaks. This illustrates that the strong overlap of states from the electrodes and the molecule in these energy regions, and thus the transmission peaks appear. In other energy regions, though there exist the electronic states from the electrodes, the lack of molecular states directly results in the absence of the transmission peaks. As for the case of 1.6 V, presented in Fig. 5b, there are also some states overlapping regions. In these energy regions, there also exist corresponding transmission peaks originated from these states as shown in Fig.4. However, in the case of -1.6 V indicated in Fig.5c, in our probed energy region it is easily found that the states overlapping regions are nearly negligible in the bias window [-0.8,0.8]. As a consequence, the transmission and the corresponding current in this energy region are both suppressed, which eventually leads to the rectification behavior in these molecular junctions.

3 Conclusion

In summary, based on ab initio non-equilibrium Green’s function method, we have probed the transport properties the PTCDI-Cn(n=0, 6) molecules sandwiched between three different kinds of bulk electrodes. Our calculation results indicate that these molecules exhibit some interesting transport properties including NDR and rectification. Via analyzing the transmission spectra and the projected densities states, these transport properties are systematically analyzed. Our theoretical investigations suggest these molecules may have significant potential utilities in the future molecular-scale devices.

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连接在块体电极之间的PTCDI系列分子体系的输运性质

王 兵,汪伟伟,戴振翔*,郑赣鸿,马永青

(安徽大学 物理与材料科学学院,安徽省信息材料与器件重点实验室,安徽 合肥 230601)

通过采用密度泛函理论与非平衡格林函数的相结合的第一性原理方法,对四甲酰二亚胺系列分子PTCDI-Cn(n=0,6)的电荷输运性质进行了理论计算．在计算中,PTCDI-Cn(n=0,6)分子分别与Al,Li以及石墨烯3种块体电极组成三明治结构分子结．从电流-电压曲线可知PTCDI-C6分子结体系中出现了负微分电阻以及整流等输运性质．结合透射谱以及投影态密度,对其输运性质进行了相应的分析．计算结果表明这类PTCDI系列分子在将来的分子尺度器件中具有较大的应用价值．

电荷输运；第一性原理计算；PTCDI系列分子；整流

10.3969/j.issn.1000-2162.2015.06.008

Foundation item: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)

O433.2 Document code:A Article ID:1000-2162(2015)06-0045-08

Received date:2015-03-31

Author’s brief:WANG Bing (1989-), male, born in Huainan of Anhui Province, master degree candidate of Anhui University;* DAI Zhen-xiang (corresponding author), associate professor of Anhui University, tutor for postgraduate, E-mail:physdai@ahu.edu.cn.