Transport in a fullerene terminated aromatic molecular device

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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

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 ( />

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 of

p

-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:(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

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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 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 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 ẵfE

m

LịefE

m

RịdE (1)

GVị ẳ dI

dVẳeẵg

m

L;Vị ỵ 1ịg

m

R;Vị þ

ZmL

mR

dgðE;VÞ
dV (2)

where

mL

and

mR

are the electrochemical potentials of left and right
metal contacts respectively, g

m

;Vị is the Green's function and
ẳVmol/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 between

mL

and

mR

, which
contributes to the current integral above, is referred to as the bias
window. f (E

mI

); (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. 2 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 1.

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 eV_e0.3 eV results from six states LUMO, LUMO_ỵ1,
LUMOỵ2, LUMOỵ3, LUMOỵ4 and LUMOỵ5 as shown inFig. 3. 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. 5
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 2. 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 2 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 1 as shown inTable 3 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 ỵG0

T

eV
2

ỵT

eV
2

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, 0 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 1

MPSH orbital energy relative to EFtaken as 0 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 2 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
5.45

m

S whereas maximum conductance of approximately 27

m

S 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 2

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 2 V LUMO

0 V LUMO e e

Table 3

RR for applied bias voltages.

±V RR ±V RR

0.4 V 1.006 1.6 V 1.007

0.8 V 1.009 2 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 2.

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 and_ỵ2 V shown inFig. 8. 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 2 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

m

A and
27

m

S 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 0 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
/>

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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