J Comput ElectronDOI 10.1007/s10825-013-0482-7

Modeling of Cu-linked rectification devices by varying torsionangles

Sweta Parashar · Pankaj Srivastava ·Manisha Pattanaik

© Springer Science+Business Media New York 2013

Abstract Using the nonequilibrium Green’s function(NEGF) method in combination with the density functionaltheory (DFT), we have analyzed the rectifying performancein Cu-linked molecular devices by varying torsion angles(ϕ = 0◦–90◦). The linking effect of Cu atom has been in-vestigated by calculating current-voltage (I -V ) characteris-tics, rectification performance, transmission functions, pro-jected density of states (PDOS), and molecular projectedself-consistent Hamiltonian (MPSH). Present calculationsrevealed that linking of Cu in combination with conjugateddithiocarboxylate (-CS2) and standard thiol linkers signifi-cantly affects the metal-molecule coupling asymmetry, andthus the rectifying behavior in molecular devices. Further,the subsequent studies show that the left-right combinationof -CS2 linker and Cu atom displays higher rectification ra-tio at various torsion angles in gold–biphenyl–gold junctionsthan thiol and Cu linkers. The calculated results are helpfulnot only in predicting an optimal combination of linkinggroups for realistic applications but also provide the way forbetter control of rectification effects in molecular devices.

Keywords Linking group effects · Torsion angles ·Rectifying performance · First-principles

1 Introduction

Molecular devices have fascinated various communities ofresearchers in recent years as the size of modern microelec-

S. Parashar (�) · P. Srivastava · M. PattanaikNanomaterials Research Group, Computational Nanoscience &Technology Laboratory (CNTL), ABV-Indian Institute ofInformation Technology & Management (ABV-IIITM),Gwalior 474015, Indiae-mail: sweta@iiitm.ac.in

tronic devices is scaling down in a steady pace. Many inter-esting physical properties categorized as field-effect char-acteristics [1], molecular rectification [2–4] negative differ-ential resistance [5, 6], and single-electron characteristics[7, 8], etc. have been studied. The prominent among theseare rectification devices, proposed first by Aviram and Rat-ner [2], play a key role for further development of molecularelectronics as it is the basic functional element for buildingan electronic circuit. Recent experimental [9–12] and theo-retical [13–19] studies on molecular rectifiers, suggest thatmetal-molecule interface coupling greatly affects the trans-port properties. Moreover, the biphenyl-based molecular de-vices are one of the systems most intensely studied as a pro-totype of the rectifying devices. Li and Kosov [13] has beenreported rectification effects when a biphenyl molecule con-nects Au electrodes via dithiocarboxylate (-CS2) and thiol(-SH) linkers. Further, Wang and his co-workers [20] re-cently demonstrated that torsion angle offers the possibilityto modify the rectifying behavior of the biphenyl molecule.However, a lot of issues at various torsion angles such astheir physical mechanism and other related factors (e.g.,electrode materials dependence, metal-molecule couplingstrength asymmetry, etc.) remain to be further addressed.

On the other hand, C2Cu2 molecule was synthesized ex-perimentally and its physical properties were investigatedwidely [21]. Moreover, Cu electrode dependence on trans-port properties of biphenyl-dithiol (BPD) molecule has beenreported [16]. Recently, Wang et al. [22] investigated the ef-fect of linking of Cu atom on transport properties of molec-ular devices. It has been found that linking of Cu atomproduce weak coupling with Au electrodes than that ofthiol linker, and thus leading to weak current. Further, ithas been also reported that dithiocarboxylate linker produceconductance enhancement when compared to thiol linker inbiphenyl based devices [23]. But the physical mechanism

J Comput Electron

Fig. 1 Modeled structure of Cu-linked rectification device. (a) Thebiphenyl molecule connected to two (3 × 3)-(111) Au electrodes viadithiocaboxylate and copper linkers, (b) the dithiocarboxylate is re-placed by a thiol group

of the conductance enhancement is still unclear. Moreover,it has been suggested that this is due to different metal-molecule coupling strengths [23]. It is therefore importantto systematically investigate the metal-molecule interfacethrough (-CS2, -Cu) and (-S, -Cu) linkers. With these mo-tivations, we have performed first-principles calculations toexamine the effect of Cu linking in combination with -CS2

and thiol linkers in the light of rectifying properties at var-ious torsion angles. It turns out that the stronger interfacecoupling induced by -CS2 linker broadens the transmissionpeak near the Fermi energy, which leads to the higher recti-fying performance in molecular devices.

2 Model and computational method

The modeled molecular devices at various torsion angles areillustrated schematically in Fig. 1. For model A, biphenylmolecule connected to Au (1 1 1) electrodes via (-CS2, -Cu)with (3×3) periodicity, illustrated in Fig. 1(a). We replace (-CS2) by sulfur atom and get model B as shown in Fig. 1(b).In all the considered models S and Cu atoms are locatedat the hollow site on the gold triangle. The system is dividedinto three regions: left electrode, right electrode and the cen-tral scattering region. The central region contains parts of theelectrodes to include the screening effect in the calculations.

In the present work, the structures of all the modelshave been optimized. By full optimization, we obtain C–Cu,Au–Cu and Au–S distance as 1.8 Å, 1.85 Å and 2.0 Å re-spectively. All the calculations are carried out by using anab-initio package ATK-VNL [24], which combines densityfunctional theory (DFT) and nonequilibrium Green’s func-tions (NEGF) formalism. ATK is capable of fully and self-consistently modeling and simulating the transport proper-ties of the two-probe systems that can be reasonably re-produced and verified with experimental results [25, 26].In our calculations, we use Perdew-Zunger local density

approximation (LDA) to describe the exchange-correlationfunctional [27]. Only valence electrons are considered, andthe wavefunctions are expanded with localized numerical(pseudo) atom orbitals (PAOs) [28]. In order to save com-putational efforts and improve calculating precision, the va-lence electrons has been expanded in double zeta plus po-larization (DZP) basis set for metal atoms and single zetaplus polarization (SZP) for other atoms. The NEGF/DFTself consistency has been controlled by numerical toleranceof 10−5 eV and the number of energy-points for the integra-tion to calculate the current is set to 100. The geometry op-timizations ended as the residual force on each atom are lessthan 0.05 eV/Å. The Brillouin zone has been sampled with1 × 1 × 150 k-points, and a mesh cutoff energy of 150 Ry isused. Moreover, the current through the device is calculatedusing the Landauer-Buttiker formula [29, 30]

I (V ) = 2e

h

∫ μR

μL

T (E,V )dE (1)

where μL(V ) = μL(0)+eV/2 and μR(V ) = μR(0)−eV/2are the electrochemical potentials of the left and right elec-trodes, respectively. The energy region between −eV/2 and+eV/2, which contributes to the current integral above isreferred as the bias window. T (E,V ) is the transmission co-efficient at energy E and applied bias V can be determinedusing the following formula [31]

T (E,V ) = Tr[ΓL(E,V )GR(E,V )ΓR(E,V )GA(E,V )

](2)

where GR/A are the retarded and advanced Green’s func-tions of the central region, and coupling functions ΓL/R

are the imaginary part of the self-energies of the electrodesΣL/R . Self energy measures the coupling strength betweenthe central region and the electrodes for the Kohn-Sham(K-S) calculation of the extended molecule system. It canbe evaluated by the Green’s function formalism

ΣL/R = C+L/RGL/RCL/R (3)

where CL/R is the coupling matrix of the molecule and theleft/right electrode, and GL/R is the Green’s function of thesemi-infinite electrode [32].

3 Results and discussion

Model A1–A4 and B1–B4 correspond to 0°, 30°, 60° and90° torsion angles in biphenyl molecular devices. Fig-ures 2(a) and 3(a) show the self-consistently current-voltage(I -V ) characteristics for all the models in the bias range of−2.4 to 2.4 V. Several important features in the evolutionof currents are clearly shown: (1) In comparison with mod-els B1–B4, models A1–A4 have highly asymmetric I -V

J Comput Electron

Fig. 2 (a) The current I and (b) the rectification ratio R as a functionof applied bias for models A1–A4, respectively

characteristics which indicate that dithiocarboxylate linkerenhances the rectifying performance as compared to thiollinker. (2) For models B1–B4, however, the currents underthe positive bias are smaller than that of same negative biaswhen the bias voltage is less than 1.0 V. As the bias is fur-ther increased, the effect is opposite. The asymmetries of theI -V curve are illustrated in Figs. 2(b) and 3(b) by rectifica-tion ratio R(V ). The rectification ratio R(V ) is defined asthe ratio of the currents under positive and negative voltagesfor the same voltage magnitude which can be calculatedby R(V ) = I (V )/|I (−V )|. Table 1 displays the maximumR(V ) for all the considered models. Obviously, A mod-els show stronger rectifying performance as compared toB models. For example, the R(V ) reaches 3.65 at an appliedbias of 1.2 V for A1, 7.0 at a bias of 1.4 V for model A4, and3.3 at 1.8 V for B1, 5.13 at a bias of 2.0 V. It has been foundthat the calculated values are much higher than the other

Fig. 3 (a) The current I and (b) the rectification ratio R as a functionof applied bias for models B1–B4, respectively

Table 1 Variation of maximum rectification ratio and HOMO-LUMOgap at torsion angles 0°, 30°, 60°, and 90°

Torsion angles Model A Model B

Rmax (V) HLG Rmax (V) HLG

0° 3.65 at 1.2 V 3.8 3.30 at 1.8 V 3.14

30° 4.55 at 1.2 V 3.94 3.80 at 2.0 V 3.34

60° 5.41 at 1.2 V 4.15 4.39 at 2.0 V 3.38

90° 7.0 at 1.4 V 4.48 5.13 at 2.0 V 4.27

reported results [13, 20]. This enhancement in rectificationis due to the high left-right coupling strength asymmetry inmolecular devices [33]. The observed high rectification ra-tio is crucial parameter for the technological usefulness ofmolecular devices as a rectifier.

Further, the particular mechanism can be interpretedin terms of transmission spectrum [34, 35]. Figures 4(a)

J Comput Electron

Fig. 4 Zero bias transmission spectra for (a) the models A1–A4 and(b) the models B1–B4

and (b) shows the transmission spectra T (E,V ) for allthe models at zero bias. The average Fermi level, whichis an average value of the chemical potentials of the leftand right electrodes, is set to zero. For all the models, itis noting that, first the highest occupied molecular orbital(HOMO) peak is taller and broader than the lowest unoc-cupied molecular orbital (LUMO) at all dihedral angles.Secondly, HOMO is close to the Fermi level which is themain transmission channel for all models. However, for Amodels an additional peak (about 0.8 eV) at the intersec-tion of the tails of HOMO and LUMO is observed. Simi-lar additional peak near the Fermi energy has also been ob-served in 4,4′-biphenyl bis (dithiocarboxylate) (BDCT) and4′-thiolate-biphenyl-4-dithiocarboxylate (TBDT) moleculardevices [13]. To analyze the origin of transmission spec-tra, we have also calculated the projected density of states(PDOS) for models A1 and B1, as shown in Fig. 5. It hasbeen found that the PDOS is similar to the transmission

Fig. 5 Projected density of states for (a) the model A1 (b) themodel B1

spectra for these models. Moreover, an additional peak nearthe Fermi energy for model A1 appears which is due stronginterface coupling induced by dithiocarboxylate linker inmolecular devices.

Generally, the transmission coefficient can be related tothe molecular orbitals which have been modified by theelectrodes. These modified molecular orbitals can be ob-tained from the molecular projected self-consistent Hamil-tonian (MPSH) [36, 37], where the self-consistent of molec-ular junction is projected onto the molecule, and thisMPSH matrix is diagonalized. Using Green’s functionformalism, the mapping of the infinite open two probesystem into a finite system can be evaluated via ma-trix

G =⎛⎜⎝

HL + ΣL VL 0V

†L HC VR

0 V�=R HR + ΣR

⎞⎟⎠ (4)

where HL, HC , and HR denote the Hamiltonian of the leftelectrode, the central scattering region, and the right elec-trode, respectively. VL and VR are the matrix elements in-volving scattering region and the electrodes. ΣL and ΣR arethe self-energies of the electrodes. The eigenstates of MPSHgives the molecular orbitals modified due to molecule-electrode interaction which do not include the self-energyof the electrodes. The real part will give a shift in the trans-mission peaks relative to MPSH states and the complex partof the self-energy broadens the transmission peaks [38]. Fig-ure 6 represents the MPSH orbitals at zero bias and its cor-responding eigen values for all the junction systems. Table 1illustrates the projected HOMO-LUMO gap (HLG) for Aand B models. It is observed that HLG is increased with tor-sion angles i.e. 0°, 30°, 60°, and 90°, and thus the currentsand transmission coefficients are decreased as the barrier of

J Comput Electron

Fig. 6 Spatial distribution and the corresponding eigenvalues (in eV)of HOMO and LUMO for models A1–A4 and B1–B4 at zero bias. Thered and blue colors indicate the positive and negative signs of the wavefunctions, respectively

electron transfer is approximately proportional to the HLG[39]. It is also noticed that the HLG at 90° is relatively largerthan other torsion angles. Further, it is also clearly shown inFig. 6 that HOMO state distributes largely in the right re-gion of the device in A models as compared to B models,namely, more overlap of the orbitals between molecule andthe right electrodes happen. For both A and B models, thelocalization degree of HOMO is enhanced with the increas-ing of the torsion angles. Especially, when the torsion angleis equal to 90° (i.e. the two phenyl rings are perpendicu-lar to each other), the HOMO state almost entirely local-ized at the copper atom and the right phenyl ring. Thus, wecan conclude that the HOMO moves up at an applied pos-itive bias, instead it will move down at an applied negativebias.

In order to further explain the obvious rectification effectin all the models, we plot transmission spectra of models Aand B at bias of ±1.2 V and ±2.0 V, respectively, as shownin Figs. 7(a) and (b). It is clearly shown that the height ofHOMO and LUMO peaks decreases as the dihedral angleincreases. This is analogues to the decrease in current on in-

Fig. 7 The transmission spectra for (a) the models A1–A4 at an ap-plied bias of ±1.2 V and (b) the models B1–B4 at a bias of ±2.0 V,the region between two dashed lines indicates the bias window whichis [−0.6 eV, +0.6 eV] and [−1.0 eV, +1.0 eV], respectively

creasing torsion angle between two phenyl rings. Addition-ally, for A models, the HOMO peak shift toward the higherenergy orientation at an applied positive bias, the right ad-ditional peak shows the opposite behavior. When an appliedbias is less than 1.0 V, the shifting peaks cannot move intothe bias window though the bias window increases, as therate of expansion for the bias windows is smaller than thatof shifting of transmission peaks. When the bias voltage en-hance to 1.2 V, both HOMO and additional broad peak enterthe bias window [−0.6 eV, +0.6 eV] and produce maximumrectifying performance. As the negative bias is applied andincreased further HOMO peak enter the bias window. As aresult current will slightly increase and the rectification ra-tio decreases. While for B models, the HOMO peak shiftsinto the bias window when an increase in positive bias to belarger than 1.6 V, but no additional peak appears in the trans-mission spectra. Thus, we conclude that a strong rectifyingperformance is observed as a result of additional broad peaknear the Fermi energy due to the presence of dithiocarboxy-late linker.

J Comput Electron

4 Conclusion

Using the nonequilibrium Green’s function technique incombination with density functional theory, the rectifyingperformance of biphenyl molecule attached with (-CS2,-Cu) and (-S, -Cu) linkers, at different torsion angles hasbeen investigated. The current-voltage (I -V ) characteristics,rectification performance, transmission functions, projecteddensity of states (PDOS), and molecular projected self-consistent Hamiltonian (MPSH) analysis show that metal-molecule coupling asymmetry plays a crucial role in de-termining the rectifying performances in molecular devices.The transmission spectra analysis reveals that stronger inter-face coupling induced by -CS2 linker broadens the transmis-sion peak near the Fermi energy, and hence significant recti-fying ratio is achieved with (-CS2, -Cu) linkers. The same isalso evident from PDOS calculations. The observed value ismuch higher than other reported results. Hence, (-CS2, -Cu)is an optimal combination of linking groups to enhance therectifying properties in designing ultra-small functional de-vices. The experimental workers are encouraged to verifythese findings.

Acknowledgements Authors are thankful to the ComputationalNanoscience & Technology Laboratory (CNTL), ABV-Indian Insti-tute of Information Technology & Management, Gwalior (India) forproviding computational facilities.

References

1. Lu, J., Yin, S., Peng, L.M., Sun, Z.Z., Wang, X.R.: Proximity andanomalous field-effect characteristics in double-wall carbon nan-otubes. Appl. Phys. Lett. 90, 052109 (2007)

2. Aviram, A., Ratner, M.A.: Molecular rectifiers. Chem. Phys. Lett.29, 277–283 (1974)

3. Metzger, R.M.: Unimolecular electrical rectifiers. Chem. Rev.103, 3803–3834 (2003)

4. Zeng, J., Chen, K.Q., He, J., Zhang, X.J., Sun, C.Q.: Edgehydrogenation-induced spin-filtering and rectifying behaviors ingraphene nanoribbon heterojunctions. J. Phys. Chem. C 115,25072–25076 (2011)

5. Du, Y., Pan, H., Wang, S., Wu, T., Feng, Y.P., Pan, J., Wee, A.T.S.:Symmetrical negative differential resistance behavior of a resistiveswitching device. ACS Nano 6, 2517–2523 (2012)

6. Zheng, X., Lu, W., Abtew, T.A., Meunier, V., Bernholc, J.: Neg-ative differential resistance in C60-based electronic devices. ACSNano 4, 7205–7210 (2010)

7. Chen, J., Reed, M.A., Rawlett, A.M., Tour, J.M.: Large on-off ra-tios and negative differential resistance in molecular electronic de-vice. Science 286, 1550–1552 (1999)

8. Parashar, S., Srivastava, P., Pattanaik, M.: First-principles studyof naphthalene-based single-electron transistor. Appl. Nanosci. 2,385–388 (2012)

9. Kornilovitch, P.E., Bratkovsky, A.M., Stanley Williams, R.: Cur-rent rectification by molecules with asymmetric tunneling barriers.Phys. Rev. B 66, 165436 (2002)

10. Galperin, M., Nitzan, A., Sek, S., Majda, M.: Asymmetric elec-tron transmission across asymmetric alkanethiol bilayer junctions.J. Electroanal. Chem. 550, 337 (2003)

11. Jackel, F., Wang, Z., Watson, M.D., Mullen, K., Rabe, J.P.:Nanoscale array of inversely biased molecular rectifiers. Chem.Phys. Lett. 387, 372 (2004)

12. Yee, S.K., Sun, J., Darancet, P., Tilley, T.D., Majumdar, A.,Neaton, J.B., Segalman, R.A.: Inverse rectification in donor-acceptor molecular heterojunctions. ACS Nano 5, 9256 (2011)

13. Li, Z.Y., Kosov, D.S.: Orbital interaction mechanisms of conduc-tance enhancement and rectification by dithiocaboxylate anchor-ing group. J. Phys. Chem. B 110, 19116 (2006)

14. Hoft, R.C., Armstrong, N., Ford, M.J., Cortie, M.B.: Ab initio andempirical studies on the asymmetry of molecular current-voltagecharacteristics. J. Phys. Condens. Matter 19, 215206 (2007)

15. Liu, H.M., Li, P., Zhao, J.W.: Theoretical investigation on molecu-lar rectification on the basis of asymmetric substitution and protontransfer reaction. J. Chem. Phys. 129, 224704 (2008)

16. Kondo, H., Nara, J., Kino, H., Ohno, T.: Transport properties ofa biphenyl-based molecular junction system—the electrode metaldependence. J. Phys. Condens. Matter 21, 064220 (2009)

17. Jalili, S., Ashrafi, R.: A first principles study on transport prop-erties of benzene-based molecular junctions: the effect of sidegroups and anchoring atoms. Physica E 43, 960 (2011)

18. Guo, C., Zhang, Z.H., Kwong, G., Pan, J.B., Deng, X.Q., Zhang,J.J.: Enormously enhanced rectifying performances by modifica-tion of carbon chains for D-σ -A molecular devices. J. Phys. Chem.C 116, 12900 (2012)

19. Wan, H., Xu, Y., Zhou, G.: Dual conductance, negative differen-tial resistance, and rectifying behavior in a molecular device mod-ulated by side groups. J. Chem. Phys. 136, 18704 (2012)

20. Wang, L.H., Guo, Y., Tian, C.F., Song, X.P., Ding, B.J.: Torsionangle dependence of the rectifying performance in molecular de-vice with asymmetrical anchoring groups. Phys. Lett. A 374, 4876(2010)

21. Sladkov, A.M., Ukhin, L.Y.: Copper and silver acetylides in or-ganic synthesis. Russ. Chem. Rev. 37, 748 (1968)

22. Wang, R.N., Zheng, X.H., Dai, Z.H., Hao, H., Song, L.L., Zeng,Z.: Anchoring group effects in molecular devices: an ab initiostudy on the electronic transport of a carbon-dimmer. Phys. Lett.A 375, 657 (2011)

23. Tivanski, A.V., He, Y., Borguet, E., Liu, H., Walker, G.C.,Waldeck, D.H.: Conjugated thiol linker for enhanced electricalconduction of gold-molecule contacts. J. Phys. Chem. B 109,5398–5402 (2005)

24. AtomistixToolKit version 2011.2.8, QuantumWise A/S. http://quantumwise.com

25. Wang, Y.F., Kroger, J., Berndt, R., Vazquez, H., Brandbyge, M.,Paulsson, M.: Atomic-scale control of electron transport throughsingle molecules. Phys. Rev. Lett. 104, 176802 (2010)

26. Lindsay, S.M., Ratner, M.A.: Molecular transport junctions: clear-ing mists. Adv. Mater. 19, 23–31 (2007)

27. Perdew, J.P., Zunger, A.: Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev.B 23, 5048–5079 (1981)

28. Gonzalez, M.T., Wu, S., Huber, R., Wolen, S.J.V.D., Schonen-berger, C., Calame, M.: Electrical conductance of molecular junc-tions by a robust statistical analysis. Nano Lett. 6, 2238–2242(2006)

29. Landauer, R.: Electrical resistance of disordered one-dimensionallattices. Philos. Mag. 21, 863–867 (1970)

30. Buttiker, M.: Four-terminal phase-coherent conductance. Phys.Rev. Lett. 57, 1761 (1986)

31. Kim, G., Wang, S.C., Lu, W.C., Nardelli, M.B., Bernhole, J.: Ef-fects of end group functionalization and level alignment on elec-tron transport in molecular devices. J. Chem. Phys. 128, 024708(2008)

32. He, H.Y., Pandey, R.: Asymmetric currents in a donor-bridge-acceptor single molecule: revisit of the Aviram-Ratner diode.J. Phys. Chem. C 113, 1575–1579 (2009)

J Comput Electron

33. Taylor, J., Brandbyge, M., Stokbro, K.: Theory of rectification intour wires: the role of electrode coupling. Phys. Rev. Lett. 89,138301 (2002)

34. Long, M.Q., Chen, K.Q., Qing, W., Zou, B.S., Dan, W.H., Shuai,Z.: Negative differential resistance behaviors in porphyrin molec-ular junctions modulated with side groups. Appl. Phys. Lett. 92,243303 (2008)

35. Long, M.Q., Chen, K.Q., Wang, L.L., Zhou, B.S., Shuai, Z.: Neg-ative differential resistance induced by intermolecular interactionin a bimolecular device. Appl. Phys. Lett. 91, 233512 (2007)

36. Zhou, L.P., Yang, S.W., Ng, M.F., Sullivan, M.B., Tan,V.B.C., Shen, L.: One-dimensional iron-cyclopentadienyl sand-wich molecular wire with half metallic, negative differential re-

sistance and high-spin filter efficiency properties. J. Am. Chem.Soc. 130, 4023 (2008)

37. Deng, X.Q., Zhou, J.C., Zhang, Z.H., Tang, G.P., Qiu, M.: Elec-trode metal dependence of the rectifying performance for molec-ular devices: a density functional study. Appl. Phys. Lett. 95,103113 (2009)

38. Staykov, A., Nozaki, D., Yoshizawa, K.: Theoretical study ofdonor-Π -acceptor unimolecular electric rectifier. J. Phys. Chem.C 111, 11699–11705 (2007)

39. Seminario, J.M., Zacarias, A.G., Tour, J.M.: Theoretical study ofa molecular resonant tunneling diode. J. Am. Chem. Soc. 122,3015–3020 (2000)