CHENZhi-Peng ZHANG Y-Mei GUO Zhen-Gng LIN Li-Xing YANG E LING Qi-Dn

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The First Principle Study on the Rectification of Molecular Junctions Based on theAlkyl-chain-modified Phenyl Benzothiophene Derivative①

CHENZhi-PengaZHANG Ya-MeiaGUO Zhen-GangcLIN Li-XiangaYANG Ea, b②LING Qi-Dana

a(350007)b(350002)(350108)

Using density functional theory (DFT) combined with nonequilibrium Green’s functioninvestigates the electron-transport properties of several molecular junctions based on the PBTDT-CH=NH molecule, which is modified by one to four alkyl groups forming PBTDT- (CH2)CH=NH. The electronic structures of the isolated molecules (thiol-ended PBTDT- (CH2)CH=N)have been investigated before the electron-transport calculations are performed. The asymmetric current-voltage characteristics have been obtained for the molecular junctions. Rectifying performance of Au/S-PBTDT-CH=N-S/Au molecular junction can be regulated by introducingalkyl chain. TheN3 molecular junctionexhibits the best rectifying effect. Its maximum rectifying ratiois 878, which is 80 times more than that of the molecular junction based on the originalN molecular junction.The current-voltage (I-V) curves of all thesandwich systems in this work are illustrated by transmission spectra and molecular projection density analysis.

thefirst principle, phenyl benzothiophene,alkyl chain, rectification;

1 INTRODUCTION

Molecular electronics has become a promising trend to obtain a variety of functional molecular devices, such as molecular rectifier effect[1-3], nega- tive differential resistance effect (NDR), molecular switch and so on[4]. Molecular rectifier plays an important role in molecular devices. Recently, the electronic transport of single thiophene oligomers has been successfully simulated by the first prin- ciples theory, including the influence of substituent[5, 6], the separation between components, the contact performance of molecular electrode interface,[7]. Many factors can affect molecular rectification[8, 9], so it is necessary to study the effects of different molecular lengths on molecular junctions. The imi- dogen-substituted2-phenylbenzo[d,d?]thieno[3,2-b;4,5-b]dithio-phene molecule (PBTDT-CH=NH) is one of the most promising candidates in organic electronics, because the conjugated molecule PBTDT-CH=NH has good electron transport pro- perties[10-12]. Thus the thiol-ended PBTDT-CH=N molecule modified by one to fouralkyl groups has been studied. The transport properties of Au/S-modifiedPBTDT-CH=N-S/Au have been investi-gated by density functional theory (DFT) combined with nonequilibrium Green’s function.

2 COMPUTATIONAL DETAILS

Fig.1 illustrates the models of molecular junctions N to N4 with metal/molecule/metal structures. In each so-called two probe system, a thiolate-ended molecule based on PBTDT-CH=N is sandwiched between two gold electrodes. The thiol end group is employed widely in the field of molecular devices. Molecules containing thiol end groups can be self-assembled on the Au substrate because the hydrogen atom in the thiol group will be dissociated and strong Au-S covalent bonds will form when the thiol group interacts with Au surface. The two Au(111)-(3×3) surfaces (i.e., each layer consisting of nine gold atoms) with periodic boundary conditions have been used to model the left and right electrodes[13,14].The molecule in the central region of systemN is anoriginal dithiolterminated PBTDT-CH=N. The molecules in the central region of systems N1 to N4 are HS-PBTDT-(CH2)CH=N-SH, HS-PBTDT- (CH2)2CH=N-SH, HS-PBTDT-(CH2)3CH=N-SH, and HS-PBTDT-(CH2)4CH=N-SH, respectively, which are the modified HS-PBTDT-CH=N-SH with one to four alkylgroups.

Fig.1. Schematic view ofthe two-probe Au/S-PBTDT-(CH2)CH=N-S/Au molecular junction (N1); The central molecule HS-PBTDT-(CH2)CH=N-SH replaced by HS-PBTDT-CH=N-SH, HS-PBTDT-(CH2)2CH=N-SH, HS-PBTDT- (CH23CH=N-SH and HS-PBTDT-(CH2)4CH=N-SH is corresponding to N, N2, N3 and N4 molecular junction, respectively. These thiol-ended molecules self-assemble on the Au(111)-(3×3) surface accompanied by the dissociation of hydrogen atoms in the thiol groups, and consist of the two-probe Au/molecule/Au systems with right and left semi-infinite electrode and the scattering region. The black, gray, blue and yellow balls in the central molecule are corresponding to C, H, N and S atoms

The whole computation is composed of two proce-dures. First, the geometry optimization and elec-tronic structures of the isolated molecules in the central region in Fig.1 are performed using the Gaus-sian03 program[15]at the hybrid DFT/B3LYP[16,17]level of theory with the 6-311G(d,p) basis set. The next procedure is the transport computation after the above geometry optimization. The geometries of the isolated molecules are extracted from the optimized extended molecules and then translated into the central region between the two gold electrodes, as illustrated in Fig.1. The two Au(111)-(3×3) surfaces with periodic boundary conditions are used to model the left and right electrodes. The Au/molecule/Au configuration is divided into three parts: left electrode, right electrode, and central scatting region. In the models, there are three gold layers in each left and right electrode unit cell. The scattering region is composed of the isolated molecule together with the respective three gold layers on the left and right sides. The distance between the Au(111) surface and the terminal S atom is 2.28 ?, which falls in the range from 1.90 to 2.39? used by most studies[18]. The electron-transport properties of the metal/mole-cule/metal systems have been investigated usingsoftware package, Atomistix ToolKit(ATK)[19,20], which is based on density functional theory (DFT) combined with the first-principles non-equilibrium Green’s function(NEGF). In this work, a double-polarization (DZP) basis set is used for all atoms of the molecule except H, and a single-with polari-zation (SZP) basis set is used for Au and H atoms. The exchange-correlation potential is described by the Perdew-Burke-Ernzerhof (PBE) version of the generalized gradient approximation (GGA)[21,22]. The convergence criterion is set to 1×10-5Ha for grid integration to obtain accurate results. A-point sampling of 3 × 3 ×100 is used for the metal-electrode models. On a real-space grid, a mesh cutoff energy of the charge density and potentials is set to150 Ha.

In these molecular junctions, the current-voltage (I-V) characteristics is obtained from the Landauer- Bu?ttiker formula[23]:

where 22/=0is the quantum unit of conductance,expresses the elementary charge andshows the Planck’s constant.is the Fermi function, andμand μare respectivelyfor the electrochemical potentials of the right and left electrodes:μ(V)=E+eV/2 andμ(V)=E–eV/2, whereErepresents the Fermi energy of the electrode, and (μ(V),μ(V)) shows the current integralknown as the energy region or the bias window.(, V) is the transmis- sion function for anincident electron with energyat a bias voltageV.

3 RESULTS AND DISCUSSION

3. 1 Electronic structures of theisolated molecules

The molecular electronic structure can affect the conductance of the molecular transport junction. As suggested by Cohen[24], the density distribution of frontier molecular orbital is intrinsic to the molecule rather than to the junction. It is an impor- tant factor determining the conductance of the molecular transport junction. Therefore, the elec- tronic structures of the isolated molecules have been investigated before the electron-transport calcula- tions are performed. Fig. 2 shows the frontier mole- cular orbital diagrams of the highest occupied mole- cular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO). The orbital density distributions of the HOMO and LUMO for all the molecules are not fully delocalized and exhibit some obvious differences. For HS-PBTDT-CH=N-SH, the HOMO density distributions are nearly fully deloca- lized except one-SH group, because there is no orbital density distribution on it.The HOMO density distributions are similar for the -CH2,-(CH2)2, -(CH2)3and-(CH2)4groups modified HS-PBTDT-CH=N-SH molecule (N1 to N4) and mainly delocalized on the PBTDT part.The LUMO of molecule Nareonly localized strongly on the thieno-phene-CH=N-SH part. The LUMO of molecule N1are localized on the PBTDT-CH2CH part. The LUMO of molecule N2 are localized on the PBTDT-CH2CH2CH=N part. The LUMOs of mole- culesN3 and N4 are localized on the PBTDT- CH2CH2part. The delocalized extent of LUMO for molecule N2 is stronger than both of moleculesN3 and N4.

Fig. 2. Frontier molecular orbital shapes of thiol-ended PBTDT-CH=N and its derivatives

3. 2 I-V characteristics and rectification

The current-voltage (I-V) curves of the five two-probe systems N to N4 are plotted in Fig. 3. It is evident that the I-V curves of molecular systems N to N4are obviously asymmetric at zero bias and show obvious p-n junction characteristics. The current of model N increases slowly at positive bias and beforeabout –1.0 V bias voltage, and grows rapidlyafter about –1.2Vbias voltage.The introducing groups of -CH2,-(CH2)2, -(CH2)3and-(CH2)4into the PBTDT-CH=NHmolecule have obvious effects on the current at –2.0 to +2.0 V bias voltage. The current value of system N1 is smaller than that of system N whether at the positive or negative bias. But it grows rapidlyafter about –0.7 V, which indicates that its forward threshold voltage (–0.7 V) is lower than that of system N (–1.2 V). The currents of molecular junctions N2, N3 and N4 are much weaker than that of system N and decrease with increasing the number of alkyl group in the model molecule. Their trends are similar especially for molecular junction N1 and N3. The currents of modelsN2, N3 and N4are very small at +2.0 V toabout –0.8 V, and growafter about –0.8 Vbias voltage.Therefore, their forward threshold voltages (–0.8 V) are lower than that of system N (–1.2 V). And systems N1 to N4 exhibit obvious negative differential resistance behavior (NDR). Overall, the longer the alkyl chain, the smaller the current. This is consistent with the frontier molecular orbitalof the isolated molecule, because the weaker delocalization of the molecular frontier orbitals is corresponding to the longer alkyl chain.

Fig. 3. I?V curvesof systems N～N4 in the bias range from –2.0 to +2.0 V. The positive current means that the current flows from the left electrode to the right electrode and vice versa. The inset shows the rectification ratio (R) as a function of applied voltage forsystemsN to N4

Fig. 4. Transmission spectra (black lines),correspondingPDDOSspectra (redlines)of the N to N4 two-probe systems under zero bias

3. 2 Transmission spectrum and molecular projected density analysis

The transmission coefficients of the N～N4 two-probe systemsand the projected device density of states(PDDOS) of the N to N4 central molecules under zero bias have been analyzed and give insights into the states contributing to the conductivity in Fig. 4. The similarity in the peak structures of PDDOS and the transmission spectra indicates that there are clear correspondences between the energy levels on the central molecules and the transmission spectra. There is a broad transmission peak near the Fermi energy in the N system, maybe originating from strong coupling between the gold electrode and the sulfur atom[24], which is in line with the HOMO of thiol-endedPBTDT-CH=N. Unlike the N system, all the bridge-doped systems have sharp peaks near the Fermi level, in line with the front orbitals of the corresponding isolated molecules. At the zero bias, the electrontransmission mainly depends on the size of the transmission coefficient near the Fermi level. The size of transmission peaks decreases as the alkyl chain grows. This means electrons cannot permeate effectively through the alkyl chain. According to the current depending on their transmission peaks and coefficients, the current values of the N1 to N4systems become smaller than that of system N as the applied bias voltage exceeds the forward threshold voltage, in line with the I-V curves, which indicates that bridge-dopingwith alkyl groups reduces the conductivity of thiol-endedPBTDT-CH=N.On the basis of the resonances in the transmission spectra and the states of PDDOS spectra under zero bias, it can be concluded that the HOMO states mainly contribute to the current of the systems.

In Fig. 3, it is evident that the I-V curves of mole- cular systems Nto N4 are obviously asymmetric at about zero bias.In order to reveal the features of the asymmetry in detail, the rectification ratios of systems Nto N4have been analyzed. The rectifica- tion ratio is defined as

By definition,() = 1 means that there is no rectification.() > 1 means that the current is larger in the negative direction than in the positive direction, and vice versa.

According to asymmetric I-V curves,models N to N4 have obvious rectification effects. Their recti- fication values are up to 9.6, 125, 575, 878 and 529 respectively, as shown in the inset in Fig. 3. It comes out into that the modified alkyl groups have many effects on the thiol-endedPBTDT-CH=N rectifica- tion.

The rectifying for the molecular systems is interpreted by analyzing the transmission spectra. The current through a molecule system is determined by the transmission spectra within the bias window (L(b),R(V)). The region of the bias window is actually (–V/2, +V/2) if the Fermi level is set to zero. Theoretically, the transmission is determined by the molecular electronic structure modified by the applied bias and the coupling between molecule and electrode,. Fig. 5 illustrates the transmission spectra of the two-probe systems N～N4 in the energy range from –2 to +2 eV at their bias voltages of the highest rectification ratios.

Fig. 5. Transmission spectra of two-probe systems N to N4 at special bias of each highestrectification ratio. Red, blue and green dashed lines indicate positive bias voltage,negative bias voltage and bias windows at each bias voltage, respectively

It is noted that transmission spectra of systems N～N4 exhibit a very large difference at positive and negative bias voltages. The transmission resonance peaks within each bias window of systems N～N4at negative biasare much higher than those at the positive bias, except N system. In system N,the transmission peak partly enters the bias window when the negative bias voltage is applied. Applied by the positive bias voltage, there are three peaks within the bias window. From the diagram of N in Fig. 5, the transmission coefficient under –2.0 V is 20 times that at +2.0 V, so the integral area of transmission peak at –2.0 V is about 10 times larger than that at +2.0 V. The negative current is about 10 times that of the forward current at 2.0 V bias because the current is determined by the integral area of the transmission peak of the bias window and the transmission coefficient. In system N1,one broad transmission peak partly goes into the bias window when the positive bias voltage is applied. Applied by the negative bias voltage, there is a narrow peak in the bias window. From the diagram of N1 in Fig. 5, because the transmission coefficient at –0.98 V is 500 times that at +0.98 V, the integral area of transmission peak at –0.98 V is over 100 times larger than that at +0.98 V. Then the negative current is over 100 times that of the forward current, which is in line with the RR of N1 at 0.98 V bias. In system N2, there are one narrow peak and one broad peak in the bias window corresponding to –1.28 and +1.28 V; In systems N3 and N4, there are one complete peak and one half peak in the bias window under the negative bias; There is a little transmission wave within the bias window at +1.47 V in system N3. However, one broad wave completely enters the bias window at +1.6 V in system N4. Without considering transmission coefficient, the integral area is the largest both at –1.6 and +1.6 V in system N4, and the integral area in system N2 is smaller than that in system N3 under negative bias, and the integral area in system N2 is slightly larger than that in system N3 under positive bias. For N2 to N4 systems, their transmission coefficients under negative bias voltage are 1000 times those under positive bias voltage, it can be concluded that the rectifier ratio in N3 system is the largest among the three systems by rough estimates of the integral areas under positive and negative bias.

4 CONCLUSION

The introducing alkyl groups into the thiol-ended PBTDT-CH=N molecule hassignificantly obvious effects on the current at –2.0 to +2.0V bias voltage. The maximum currents of molecular junctions N2, N3 and N4 are much lower than that of system N. Systems N1～N4 exhibit obvious negative dif- ferential resistance behavior (NDR).The electronic structures of the isolated molecules have been investigated before the electron-transport calcula- tions are performed.Rectifying performance of Au/S-PBTDT-CH=N-S/Au molecular junction can be regulated by introducingalkyl chain. According to the transmission coefficient ratio of positive and negative voltages, it can be concluded that the maxi- mum rectifying ratios of systems N2～N4 are stronger than those of systems N and N1. The Nmolecular junction exhibits the weakest rectifying effect, and its maximum rectifying ratiois 9.6. The N3 molecular junctionexhibits the best rectifying effect. Its maximum rectifying ratiois 878, which is 80 times more than that of the molecular junction based on the original thiol-endedPBTDT-CH=N.On the basis of the resonances in the transmission spectra and the states of the PDDOS spectra under zero bias, it can be concluded that the HOMO states mainly contribute to the current of the systems.

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1 February 2018;

8 May 2018

①This work was supported by the National Natural Science Foundation of China (21401023)

. Yang E. E-mail: yangeli66@fjnu.edu.cn

10.14102/j.cnki.0254-5861.2011-1973