Transport in a fullerene terminated aromatic molecular device

conductance spectrum and mulliken population analysis are computed which show good agreement with each other. Our major results include ﬁ ve points: First, zero bias conductance is mainl[r]

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Original Article

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 Article history:

Received 17 January 2018 Received in revised form 13 February 2018 Accepted 15 February 2018 Available online 23 February 2018

Keywords:

DFT NEGF HOMO LUMO Mulliken Rectiﬁcation

a b s t r a c t

In this work, we propose fullerene molecule C20as an anchor to fabricate a robust aromatic molecular junction The electron transport properties of this fullerene terminated aromatic molecular device at zero bias andﬁnite bias voltage are investigated by using non-equilibrium Green's function combined with density functional theory Device density of states, transmission spectrum, molecular projected self-consistent 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/)

1 Introduction

Fascinating properties such as electronic switching[1], molec-ular rectiﬁcation[2e4], negative differential resistance behaviour [1,5]and single electron characteristics[6]have attracted the sci-entiﬁc 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 ofp -conjugation [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

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 metal-molecule 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 con-duction than that of thiol counterpart as AueSe bond is approxi-mately 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 junc-tions[15] Martin et al.[16]in 2009 fabricated a molecular junction comprising 1, 4-bis(fulleropyrrolidin-1-yl)benzene with C60anchor 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

*Corresponding author

E-mail address:bhullar.rupan@gmail.com(R.P Kaur)

Peer review under responsibility of Vietnam National University, Hanoi

Contents lists available atScienceDirect

Journal of Science: Advanced Materials and Devices

j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / j s a m d

https://doi.org/10.1016/j.jsamd.2018.02.003

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In this paper, we present a modelling technique which solves the theoretical challenge within theﬁrst principles density func-tional theory (DFT)[39e41]approach To make our problem hand clear, we consider our model based on using smaller fullerene cage C20as anchors at either ends of anthracene molecule stringed be-tween 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

2 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, anal-ogous to voltage or current node in the classical circuit theory[42] The circuit plot of a two probe molecular junction is shown inFig 1, which is implemented in Atomistix tool kit[43], utilizing the non-equilibrium Green's function (NEGF) approach[44]combined with ab-initio density functional theory (DFT)[3,45e47] An active de-vice or extended molecule (EM) region is defined as the central bisfulleroanthracene molecule andfinite 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 accu-racy 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 isfixed on a flexible substrate, called a bending beam The cross section of gold wire is reduced between twofixed points by making a notch near the middle of the wire The bending substrate is normallyfixed 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 andfinally 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

quantum calculations are performed along the transport direction and the Brillouin zone is sampled with 11100 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 deter-mined by using Equations(1) and (2)respectively

IVị ẳ2e h$

ZmR mL

TEị ẵfEmLịefEmRịdE (1)

GVị ẳ dI

dVẳeẵgmL;Vị ỵ 1ịgmR;Vị ỵ

ZmL

mR

dgE;Vị dV (2)

wheremLandmRare the electrochemical potentials of left and right metal contacts respectively, gðm;VÞ is the Green's function and ȵ¼Vmol/V is the voltage division factor (ȵ¼0.5 for symmetric molecular junction shown inFig 1) We compute all the electronic transport metrics by varying the electrochemical potential within,2 V toỵ2 V The energy region betweenmLandmR, which contributes to the current integral above, is referred to as the bias window f (EmI); (I¼L 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 condi-tions, explained in the later section of paper

3 Results and discussion

The transport metrics required to foresee the quantum behav-iour of C20-Anthracene-C20 molecule bridged between two gold leads are studied for zero bias and variegated bias (2 V toỵ2 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 quan-tum states in the vicinity of fermi energy (EF) Fig illustrates Lorentzian density of states and transmission spectra at zero bias

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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*102 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 inFig 2a and b depicts a narrow HOMO peak at0.3 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 inFig 3andTable

For the zero bias transmission spectra and DOS, the fermi level EFis located between two peaks of different character with a nar-row transmission peak below EFat0.3 eV with a transmission coefﬁcient T(E) of 0.659 and a broader transmission peak centred around EEFat 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 Mar-kussen 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 3shows the frontier orbitals relevant for the transmission around fermi energy It is inferred that the narrow transmission peak at0.3 eV is associated with a single HOMO eigen state of 115 at energy 0.227 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 at0.3 eV from the HOMO state, which provides a clear corre-spondence to the transmission function However, broader reso-nant peak at 0.1 eVe0.3 eV results from six states LUMO, LUMOỵ1, LUMOỵ2, LUMOỵ3, LUMOỵ4 and LUMOỵ5 as shown inFig 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

Similar results were concluded by T Markussen et al.[51] while using C60fullerene as anchors to bind benzene with gold elec-trodes Thus, electron tunnelling at zero bias across the molecular bridge occurs via LUMO states of C20and C60anchoring groups, pinned close to fermi energy

3.2 Quantum transport at discrete bias

To enquire the electronic transport characteristics during non-equilibrium conditions, we vary the bias voltage from2 V toỵ2 V to drive the system out of equilibrium The transmission spectrum is studied to investigate about theflow of charge resulting in the flow of current in the device It reveals the strength of electron transport under variegated bias voltages (supplementary mate-rial) 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 4presents the computed IeV characteristics of bisfuller-oanthracene 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 Local-ization and de-localLocal-ization of molecular orbitals as shown inFig results in theflow 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 from2 V toỵ2 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 points1.6 V,0.8 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 inTable The linear curve shown during0.4 V toỵ0.4 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 inFig 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 inTable with least value of 0.993 at±2 V and maximum value of 1.009 at±0.8 V which indicates the least sym-metric and most symsym-metric coupling points respectively in the slope of IeV characteristics shown inFig 4a From the values of RR shown inTable 3, it is inferred that the IeV characteristics are almost symmetric about zero bias voltage

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As the bias voltage is varied from forward to reverse bias, mo-lecular transmission resonance enters the bias window, and the corresponding increase in current as suggested by K Stokbro et al [55]is expressed as:

IVỵdVị ẳIVị þG0

T

eV

ỵT

eV

dV

2 (3)

The molecular orbitals portray shift in energy as the bias voltage is varied which can be observed inFig 5where HOMO exhibits major delocalization from0.53 eV to 0.04 eV whereas LUMO displays delocalized energy states from 0.029 eV to 0.335 eV Linear slope in IeV characteristics from0.4 V toỵ0.4 V can be under-stood 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 0.0415 eV and 0.03 eV at 0.4 V These orbitals switch to 0.227 eV and 0.0293 eV at zero bias and transit to 0.0415 eV and 0.0297 eV at ỵ0.4 V This is the reason why maximum chargeflow from electrodes to the molecule as depicted in Fig 6b is witnessed at0.4 V, V andỵ0.4 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 bisfuller-oanthracene molecule Further, we correlated the results deduced fromTable 2andFig 5and they were found to be analogous to each other With variation in bias voltage from2 V toỵ2 V, fermi level pining of gold electrodes with either HOMO or LUMO results in chargeflow 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 from2 V to1.2 V, LUMO displaced away from Efresulting in drop Fig 3.MPSH eigen states of the device at zero bias

Table

MPSH orbital energy relative to EFtaken as eV

HOMO LUMO LUMOỵ1 LUMOỵ2 LUMOỵ3 LUMOỵ4 LUMOỵ5

0.227 eV 0.0293 0.0521 0.0961 0.0994 0.188 0.2456

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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 dif-ferential conductance shown in Fig 7which is obtained by nu-merical differentiation of the IeV curve The conductance spectrum

shown inFig 7demonstrates the variation in conductance ranging from 0.07G0 to 0.35G0, with least equilibrium conductance of 5.45mS whereas maximum conductance of approximately 27mS 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) de-picts almost a similar curve as obtained in the conductance spec-trum 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 inFig 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 accu-mulation 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 5.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

2 V LUMO 0.4 V LUMO

1.6 V LUMO 0.8 V HOMO

1.2 V HOMO 1.2 V HOMO

0.8 V HOMO 1.6 V LUMO

0.4 V LUMO V LUMO

0 V LUMO e e

Table

RR for applied bias voltages

±V RR ±V RR

0.4 V 1.006 1.6 V 1.007

0.8 V 1.009 V 0.993

1.2 V 1.002 e e

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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 inTable

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 at2 V andỵ2 V shown inFig The transmission peaks portrayed during the entire energy range at2 V andỵ2 V look similar, with almost same broadness and transmission peak values The transmission coefﬁcients at fermi level are obtained as 0.0033 for both 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 14mA and 27mS as demonstrated inFigs 4a and 7a

4 Conclusion

We investigated the equilibrium and non-equilibrium transport behaviour of a robust C20fullerene anchored molecular junction by using the DFT-NEGF computational approach The DOS, trans-mission spectra, molecular orbital analysis, current spectrum,

conductance spectrum and mulliken population analysis are computed which show good agreement with each other Our major results includeﬁve 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 quantumﬂow 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

Fig 7.a) dI/dV characteristics of the device during non-equilibrium conditions b) Number of electrons as a function of bias voltage

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