Transport in a fullerene terminated aromatic molecular device

Journal of Science: Advanced Materials and Devices (2018) 206e212 Contents lists available at ScienceDirect Journal of Science: Advanced Materials and Devices journal homepage: www.elsevier.com/locate/jsamd Original Article Transport in a fullerene terminated aromatic molecular device Rupan Preet Kaur*, Derick Engles Department of Electronics Technology, Guru Nanak Dev University, Amritsar, India a r t i c l e i n f o a b s t r a c t Article history: Received 17 January 2018 Received in revised form 13 February 2018 Accepted 15 February 2018 Available online 23 February 2018 In this work, we propose fullerene molecule C20 as an anchor to fabricate a robust aromatic molecular junction The electron transport properties of this fullerene terminated aromatic molecular device at zero bias and finite bias voltage are investigated by using non-equilibrium Green's function combined with density functional theory Device density of states, transmission spectrum, molecular projected selfconsistent Hamiltonian (MPSH) eigen states, mulliken population, IeV and GeV characteristics conclude the electron transport through inelastic tunneling due to shifting of molecular orbitals (MOs) with bias voltage This transition of MOs leads to variation in the injection gap and HOMOeLUMO gap, which modifies the current and conductance spectrum The studied MPSH states emphasise the role of fullerene anchors in binding anthracene molecule with gold electrodes These simulated results are in good agreement with the experimental results, demonstrating the suitability of C20 fullerenes as anchoring groups © 2018 The Authors Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) Keywords: DFT NEGF HOMO LUMO Mulliken Rectification Introduction Fascinating properties such as electronic switching [1], molecular rectification [2e4], negative differential resistance behaviour [1,5] and single electron characteristics [6] have attracted the scientific community towards the study and modelling of electronic structure of an individual molecule or the group of molecules Various single molecular junctions have been investigated using scanning tunnelling microscope (STM), mechanically controllable break junction (MCBJ), and other techniques [7e9] in the last two decades by many research peers In the simple tunnelling model, the conductance of a single molecular junction depends on the extent of the hybridization and energy difference between the molecular and metal orbitals, the local density of states (LDOS) of the contact metal atoms at the Fermi level, and the degree of pconjugation [10] p-Conjugated molecules are expected to form high conductive wires [11] because molecular orbitals of them are connected through the molecular framework It is obvious that the small energy gap between the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) is favourable for injection and tunnelling of charged carriers These experimental results and numerous contributions on charge * Corresponding author E-mail address: bhullar.rupan@gmail.com (R.P Kaur) Peer review under responsibility of Vietnam National University, Hanoi transport through molecular junctions [12,13] suggest that the transport characteristics are controlled by the intrinsic properties of the molecules, the contacts (“alligator clips”), and the metal leads These include the molecular length, conformation, the gap between HOMO and LUMO, the alignment of this gap to the metal Fermi level, temperature, mechanical stress and the metalmolecule coordination geometry In most of the studies, the AueS bond has been used to connect molecules to metal electrodes, because stable molecular junctions can be easily obtained with this AueS covalent bond However, AueS bond is not always the best metal-molecule bond for the single molecular junction showing high conductivity Through our previously concluded results, we have already proved that selenol group can be an excellent alternative providing enhanced conduction than that of thiol counterpart as AueSe bond is approximately 0.25 eV stronger than the corresponding AueS bond [14] Thus, it is important to develop metal-molecule bonds other than AueS bond to establish highly conductive single molecular junctions [15] Martin et al [16] in 2009 fabricated a molecular junction comprising 1, 4-bis(fulleropyrrolidin-1-yl)benzene with C60 anchor groups and demonstrated more stable conductance than similar thiol-bonded molecules From the theoretical point of view, a serious challenge is to accurately predict quantum transport properties of atomic/molecular scale devices including the IeV curves, without any phenomenological parameters This goal, despite extensive research [17e38], has not yet been achieved satisfactorily https://doi.org/10.1016/j.jsamd.2018.02.003 2468-2179/© 2018 The Authors Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) R.P Kaur, D Engles / Journal of Science: Advanced Materials and Devices (2018) 206e212 In this paper, we present a modelling technique which solves the theoretical challenge within the first principles density functional theory (DFT) [39e41] approach To make our problem hand clear, we consider our model based on using smaller fullerene cage C20 as anchors at either ends of anthracene molecule stringed between two gold electrodes The ultimate aim of this article is to investigate the electron transport through anthracene molecular junction using C20 as an anchoring endgroup The electronic transport properties of so-formed two probe model are adequately explained by considering the evolution of molecular orbitals, HOMOeLUMO gap (HLG), charge transferred and their relation with currentevoltage and conductance-voltage characteristics Model The framework adopted in this work is provided by Landauer model, a validated two probe model for a variety of molecular junctions Its transmission view is a generalization of circuit theory with the gold contacts being treated as a source of carriers, analogous to voltage or current node in the classical circuit theory [42] The circuit plot of a two probe molecular junction is shown in Fig 1, which is implemented in Atomistix tool kit [43], utilizing the nonequilibrium Green's function (NEGF) approach [44] combined with ab-initio density functional theory (DFT) [3,45e47] An active device or extended molecule (EM) region is defined as the central bisfulleroanthracene molecule and finite number of gold atoms on the surface of each involved gold electrode with miller plane (1,1,1) The calculation is performed using the BeckeePerdeweWang parameterization of density-functional theory within the generalized-gradient approximation (GGA) [48] and double-zeta polarized (DZP) basis set [49] for all the atoms to achieve accuracy The proposed molecular junction device can be fabricated experimentally by using mechanically control break junction technique in which a small piece of a gold metallic wire is fixed on a flexible substrate, called a bending beam The cross section of gold wire is reduced between two fixed points by making a notch near the middle of the wire The bending substrate is normally fixed at both ends by counter supports A vertical movement of the push rod can be precisely controlled by a piezoelectric actuator or motor which exerts a force on the bending beam As the beam is bent, the gold metal wire starts to elongate, which results in the reduction of the cross section at the notch and finally results in a complete fracture of gold wire (1,1,1) After breaking the wire, two clean facing nanoelectrodes are generated The distance between the electrodes for both the opened and the closed directions is controlled by the bending or relaxing of the substrate, respectively After integrating bisfulleroanthracene molecule into the gap, they may bridge the two electrodes and the electronic properties of the molecule are further determined as explained below The atomic structure of this model is optimised until its maximum residual force on all atoms is lesser than 0.02 eV/Å The 207 quantum calculations are performed along the transport direction and the Brillouin zone is sampled with   100 points within MonkhorstePack k-point sampling The electrostatic potentials are determined on a read space grid with mesh cut-off energy of 75 Hartrees a.u to achieve balance between computational time and accuracy The DFT-NEGF method employed in this work is explained as following steps [50]: i) The coupling between EM and electrodes is computed by Green's function and its energy integral gives the density matrix for equilibrium as well as non-equilibrium states ii) The transmission function T(E) is calculated from which current and conductance for a series of applied bias voltages are determined by using Equations (1) and (2) respectively e IVị ẳ $ h ZmR TEị ẵf E mL Þef ðE À mR ފ dE (1) mL dI ẳ eẵgmL ; Vị ỵ ịgmR ; Vị ỵ GVị ẳ dV ZmL mR dgE; Vị dV (2) where mL and mR are the electrochemical potentials of left and right metal contacts respectively, gðm; VÞ is the Green's function and ȵ ¼ Vmol/V is the voltage division factor (ȵ ¼ 0.5 for symmetric molecular junction shown in Fig 1) We compute all the electronic transport metrics by varying the electrochemical potential within, V to ỵ2 V The energy region between mL and mR, which contributes to the current integral above, is referred to as the bias window f (ỀmI); (I ¼ L for left lead and R for right lead) are the Fermi-Dirac distribution functions of the left and right electrodes, respectively The above mentioned method is employed to compute electron transport metrics during equilibrium and non-equilibrium conditions, explained in the later section of paper Results and discussion The transport metrics required to foresee the quantum behaviour of C20-Anthracene-C20 molecule bridged between two gold leads are studied for zero bias and variegated bias (À2 V to þ2 V) 3.1 Quantum transport at zero bias The quantum transport calculations at zero bias help us to envision the electronic structure of the device under consideration, by a careful analysis of its density of states (DOS) and transmission spectra Both these parameters presage about the available quantum states in the vicinity of fermi energy (EF) Fig illustrates Lorentzian density of states and transmission spectra at zero bias Fig Schematic illustration of two-probe model comprising C20-anthracene-C20 (bisfulleroanthracene) bridged between two semi-infinite gold wires with miller plane (1,1,1) 208 R.P Kaur, D Engles / Journal of Science: Advanced Materials and Devices (2018) 206e212 Similar results were concluded by T Markussen et al [51] while using C60 fullerene as anchors to bind benzene with gold electrodes Thus, electron tunnelling at zero bias across the molecular bridge occurs via LUMO states of C20 and C60 anchoring groups, pinned close to fermi energy 3.2 Quantum transport at discrete bias Fig DOS and transmission spectra for the two probe model at zero bias where fermi energy EF is at eV Both these spectra portray the available number of quantum states around fermi energy and the probability whether a given energy state is occupied or unoccupied A series of peak with variation in magnitude of width and height detail its coupling strength The resonance of HOMO and LUMO peaks below and above EF foresee their participation in assaying transmissions at zero bias and contributing to finite conductance of 7*10À2 G0 with HOMOeLUMO gap (HLG) of 0.6 eV This low value of HLG, relative to fermi level reflects the formation of strong coupling between C20 and gold electrodes at zero bias The comparison between the DOS and transmission spectra shown in Fig 2a and b depicts a narrow HOMO peak at À0.3 eV and the broader LUMO peak at 0.1e0.3 eV Broad LUMO resonance peak perceives its prominent contribution towards electron transport at zero bias Thus, perfect alignment between C20 fullerene and Au electrodes promotes the flow of electrons across the bridge and portrays the formation of strong coupling between the molecule and electrodes at zero bias as indicated by the molecular projected self-consistent eigen states shown in Fig and Table For the zero bias transmission spectra and DOS, the fermi level EF is located between two peaks of different character with a narrow transmission peak below EF at À0.3 eV with a transmission coefficient T(E) of 0.659 and a broader transmission peak centred around EÀEF at 0.1e0.3 eV with comparatively lower T(E) of 0.589 To analyze the origin of these transmission peaks, we proceed by calculating the eigen states of the device, as suggested by T Markussen et al [51] From the full Hamiltonian H and overlap matrix S of the two probe model, we project onto the subspace spanned by basis functions of the molecule Fig shows the frontier orbitals relevant for the transmission around fermi energy It is inferred that the narrow transmission peak at À0.3 eV is associated with a single HOMO eigen state of 115 at energy À0.227 eV This state results in vanishing orbital weight close to gold electrodes because of which its broadening is weak, resulting in a narrow transmission peak DOS shown in Fig 2a further asserts the origin of narrow transmission peak at À0.3 eV from the HOMO state, which provides a clear correspondence to the transmission function However, broader resonant peak at 0.1 eVe0.3 eV results from six states LUMO, LUMOỵ1, LUMOỵ2, LUMOỵ3, LUMOỵ4 and LUMOỵ5 as shown in Fig On one hand, the highly transmitting HOMO state is only weakly coupled to gold electrodes resulting in narrow transmission peak with small overlap with fermi energy On the other hand, six lowest unoccupied states are strongly coupled to gold electrodes via C20 fullerene molecule leading to broad transmission peaks but with comparatively smaller peak values The contribution of single HOMO and six LUMO states is attributed to the robust binding of anthracene molecule to gold electrodes by using C20 fullerene To enquire the electronic transport characteristics during nonequilibrium conditions, we vary the bias voltage from À2 V to þ2 V to drive the system out of equilibrium The transmission spectrum is studied to investigate about the flow of charge resulting in the flow of current in the device It reveals the strength of electron transport under variegated bias voltages (supplementary material) It is composed of series of peaks whose centres correspond to the conducting state of the junction whereas width and height reflects how strongly the state is coupled to the contacts It shows the coupling between the electrodes and the molecule that leads to overlapping of the hybridized orbitals and a change in HOMOeLUMO gaps The stronger the coupling, more the orbitals are broadened and lesser will be the energy gap to jump for electrons [52] Sharp peaks in the spectrum show maximum transmissions (smaller HOMOeLUMO gap) whereas flatness shows minimum transmissions (greater HOMOeLUMO gap) The resistivity dipoles form due to charge build up in the junction and because of this differing polarization caused by metal contacts, leads to the spread in curves despite the fact that all junctions have same molecule [53,54] The resonant transmission peaks below and above fermi level, HOMO and LUMO respectively, are responsible for the charge transfer and hence participates in conduction Fig presents the computed IeV characteristics of bisfulleroanthracene molecule bonded to gold electrodes As depicted in figure, we consider low bias (±0.4 V) and high bias (±2 V) voltages, two categories of bias voltage are considered to explain the linear characteristics and non-linearity in IeV curves respectively Localization and de-localization of molecular orbitals as shown in Fig results in the flow of current The HLG of molecular junction under consideration ranges from 0.07 eV to 0.68 eV which depicts the metallic nature of the Au-bisfulleroanthracene-Au organic device As the bias voltage is varied from V to ỵ2 V, current increases on account of conduction due to non-resonant tunnelling The currentevoltage characteristics portray coulomb staircase behaviour with little non-linearity at transitory voltage points À1.6 V, À0.8 V, 0.4 V, 1.2 V and 1.6 V This switching of IeV characteristics from linearity to non-linearity is found on account of transitions in charge transfer from one orbital state to other as shown in Table The linear curve shown during 0.4 V to ỵ0.4 V is on account of charge transfer from gold electrodes to central molecule through lowest unoccupied molecular orbital which then switches through highest occupied molecular state as the bias voltage is varied to 0.8 Ve1.2 V which further rolls back through LUMO state at 1.6 V and V The study of IeV characteristics is followed by examining its rectification mechanism which is explained below as shown in Fig 4b To study the amount of asymmetry in IeV characteristics of the two probe device, we determine the rectification ratio (RR) exhibited by device (Fig 4b) which is found to be wiggling from 0.9 to as shown in Table with least value of 0.993 at ±2 V and maximum value of 1.009 at ±0.8 V which indicates the least symmetric and most symmetric coupling points respectively in the slope of IeV characteristics shown in Fig 4a From the values of RR shown in Table 3, it is inferred that the IeV characteristics are almost symmetric about zero bias voltage R.P Kaur, D Engles / Journal of Science: Advanced Materials and Devices (2018) 206e212 209 Fig MPSH eigen states of the device at zero bias Table MPSH orbital energy relative to EF taken as eV HOMO LUMO LUMOỵ1 LUMOỵ2 LUMOỵ3 LUMOỵ4 LUMOỵ5 À0.227 eV 0.0293 0.0521 0.0961 0.0994 0.188 0.2456 As the bias voltage is varied from forward to reverse bias, molecular transmission resonance enters the bias window, and the corresponding increase in current as suggested by K Stokbro et al [55] is expressed as:      eV eV dV ỵT IV ỵ dVị ẳ IVị ỵ G0 T À 2 (3) The molecular orbitals portray shift in energy as the bias voltage is varied which can be observed in Fig where HOMO exhibits major delocalization from À0.53 eV to À0.04 eV whereas LUMO displays delocalized energy states from 0.029 eV to 0.335 eV Linear slope in IeV characteristics from 0.4 V to ỵ0.4 V can be understood by exploring the position of molecular orbitals during ±0.4 V where least injection gap is explicitly observed During this bias range, HOMO and LUMO orbitals pin to fermi energy with least energy gap of À0.0415 eV and 0.03 eV at À0.4 V These orbitals switch to À0.227 eV and 0.0293 eV at zero bias and transit to À0.0415 eV and 0.0297 eV at ỵ0.4 V This is the reason why maximum charge flow from electrodes to the molecule as depicted in Fig 6b is witnessed at À0.4 V, V and ỵ0.4 V At other bias voltage points, fermi level pinning of electrodes to the central molecule is found to be imperfect on account of larger injection gap resulting in lesser charge flow from gold electrodes to bisfulleroanthracene molecule Further, we correlated the results deduced from Table and Fig and they were found to be analogous to each other With variation in bias voltage from À2 V to ỵ2 V, fermi level pining of gold electrodes with either HOMO or LUMO results in charge flow between molecule and electrodes The closer position of MOs (HOMO/LUMO) relative to Ef decides the active MO Maximum conductance at ±2 V is on account of perfect alignment of LUMO orbital with fermi level as LUMO is concluded to be the active MO at these high bias points As the bias voltage is switched from À2 V to À1.2 V, LUMO displaced away from Ef resulting in drop Fig a) IeV curve for the device at discrete bias voltage b) Rectification ratio (RR) for the device at various bias voltages 210 R.P Kaur, D Engles / Journal of Science: Advanced Materials and Devices (2018) 206e212 Fig Delocalization of HOMO and LUMO orbitals as a function of bias voltage Table Evolution of molecular orbitals (MO) at different bias voltages Bias voltage MO Bias voltage MO À2 V À1.6 V À1.2 V À0.8 V À0.4 V 0V LUMO LUMO HOMO HOMO LUMO LUMO 0.4 V 0.8 V 1.2 V 1.6 V 2V e LUMO HOMO HOMO LUMO LUMO e Table RR for applied bias voltages ±V RR ±V RR 0.4 V 0.8 V 1.2 V 1.006 1.009 1.002 1.6 V 2V e 1.007 0.993 e in conductance Similarly, the conductance spectrum shows rising conductance from 1.2 V to V as LUMO shifts closer to Ef Another electrical attribute of the nanoscale device is the differential conductance shown in Fig which is obtained by numerical differentiation of the IeV curve The conductance spectrum shown in Fig demonstrates the variation in conductance ranging from 0.07G0 to 0.35G0, with least equilibrium conductance of 5.45 mS whereas maximum conductance of approximately 27 mS at ±2 V To explore the reason of the same, we compute the mulliken charges on the central molecule and the electron density as the function of bias voltage The charge transfer analysis (Fig 6b) depicts almost a similar curve as obtained in the conductance spectrum Thus, differential conductance, electron density and mulliken charges on the molecule are inter-related to each other The magnitude of charge transferred towards the molecule varies from 0.212 e to 0.247 e but with number of electrons more than 232 as shown in Fig 7b Though the electron density is more than 232, but the electrons near the leading edge of fermi energy participate in the transport phenomenon [56] Maximum charge transfer to molecule due to maximum electron density takes place at ±2 V and minimum diffusion of charge is observed at zero bias with minimum electron density It is inferred that the least accumulation of charge at zero bias poses inability in lifting of Coulomb blockade which results in least zero bias conductance Thus, ±2 V are the bias voltage points where the coupling between molecule and electrodes is strongest whereas zero bias point demonstrates weak coupling regime Moreover, the transition in active molecular orbital with changing bias decides the slope of conductance curve as well [56] As seen in the conductance spectrum, we observe two Fig a) Charge transferred from gold electrodes to central molecule at different bias voltages b) Charge transferred towards the central molecule at different bias voltages R.P Kaur, D Engles / Journal of Science: Advanced Materials and Devices (2018) 206e212 211 Fig a) dI/dV characteristics of the device during non-equilibrium conditions b) Number of electrons as a function of bias voltage Fig Transmission spectra assayed by a) À2 V and b) þ2 V bias points with red line indicating fermi energy level and black lines indicating the bias window major troughs at 0.8 V and ỵ0.8 V At these two bias points, quantum transport conductance switches from HOMO to LUMO and back to HOMO from LUMO as shown in Table In all the transport metrics discussed above, we witness major resemblance in the transport conditions at high bias voltage points ±2 V Thus, to explore this similarity, we study the transmission spectra at V and ỵ2 V shown in Fig The transmission peaks portrayed during the entire energy range at V and ỵ2 V look similar, with almost same broadness and transmission peak values The transmission coefficients at fermi level are obtained as 0.0033 for both À2 V and ỵ2 V We also know that the current and conductance are computed by integrating the transmission area within the bias window and since the spectra are similar, thus their I (V) and G (V) values are calculated to be approximately 14 mA and 27 mS as demonstrated in Figs 4a and 7a Conclusion We investigated the equilibrium and non-equilibrium transport behaviour of a robust C20 fullerene anchored molecular junction by using the DFT-NEGF computational approach The DOS, transmission spectra, molecular orbital analysis, current spectrum, conductance spectrum and mulliken population analysis are computed which show good agreement with each other Our major results include five points: First, zero bias conductance is mainly determined by six unoccupied states LUMO to LUMOỵ5 lying close in energy 0.03e0.25 eV relative to fermi level These states are responsible for the broad transmission peaks shown in zero bias transmission spectra Secondly, the shifting of molecular orbitals by varying bias voltage determines the current spectrum Thirdly, the non-linearity in IeV curve and troughs in GeV curve are attributed to the transitions seen in the active molecular orbitals with variegated bias voltage Fourth, mulliken charges on the central molecule and electron density as a function of bias voltage are closely related to conductance spectrum Lastly, the symmetric conductance spectrum around V with almost equivalent values at forward as well as reverse bias points is on account of their analogous transmission spectra accounting for the quantum flow and transport metrics Appendix A Supplementary data Supplementary data related to this article can be found at https://doi.org/10.1016/j.jsamd.2018.02.003 212 R.P Kaur, D Engles / Journal of Science: Advanced Materials and Devices (2018) 206e212 References [1] L Yu, Z Keane, J Ciszek, L Cheng, J Tour, T Baruah, M Pederson, D Natelson, Kondo resonances and anomalous gate dependence in the electrical conductivity of single-molecule transistors, Phys Rev Lett 95 (2005) 256803 [2] A Aviram, M.A Ratner, Molecular rectifiers, Chem Phys Lett 29 (1974) 277e283 [3] J Taylor, M Brandbyge, K Stokbro, Theory of rectification in tour wires: the role of electrode coupling, Phys Rev Lett 89 (2002) (1338301-1e138301-4) [4] K Konstadinidis, P Zhang, R.L Opila, D.L Allara, An in-situ X-ray photoelectron study of the 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N.J Tao, Electron transport in molecular junctions, Nat Nanotechnol (2006) 173 [10] T Tada, D Nozaki, M Kondo, S Hamayama, K Yoshizawa, Oscillations of conductance in molecular junctions of carbon... account of their analogous transmission spectra accounting for the quantum flow and transport metrics Appendix A Supplementary data Supplementary data related to this article can be found at https://doi.org/10.1016/j.jsamd.2018.02.003