Electronic structure and transport properties of decagonal Al-Cu-Co alloys

Electronic structure and transport properties of sulfur-passivated graphenenanoribbonsBikash Mandal, Sunandan Sarkar, Anup Pramanik, and Pranab Sarkar Citation: J. Appl. Phys. 112, 113710 (2012); doi: 10.1063/1.4768524 View online: http://dx.doi.org/10.1063/1.4768524 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v112/i11 Published by the American Institute of Physics. Related ArticlesElectron-state engineering of bilayer graphene by ionic molecules Appl. Phys. Lett. 101, 233106 (2012) Response to “Comment on ‘Chiral tunneling in trilayer graphene’” [ Appl. Phys. Lett. 101, 226101 (2012)] Appl. Phys. Lett. 101, 226102 (2012) Communication: Oscillated band gaps of B/N-codoped α-graphyne J. Chem. Phys. 137, 201101 (2012) Oscillating magnetocaloric effect on graphenes Appl. Phys. Lett. 101, 222405 (2012) A graphene composed of pentagons and octagons AIP Advances 2, 042147 (2012) Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors

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Electronic structure and transport properties of sulfur-passivatedgraphene nanoribbons

Bikash Mandal, Sunandan Sarkar, Anup Pramanik, and Pranab Sarkara)

Department of Chemistry, Visva-Bharati University, Santiniketan 731235, India

(Received 5 October 2012; accepted 6 November 2012; published online 7 December 2012)

Electronic structure of newly synthesized sulfur-terminated graphene nanoribbons (S-GNRs) has been

presented from the calculations based on ab initio density functional theory and non-equilibrium

Green’s function (NEGF) method. The calculations reveal that zigzag-edged S-GNRs (Z-S-GNRs)

are thermodynamically more stable than armchair edged S-GNRs (A-S-GNRs). It has been observed

that the band gap of S-GNRs depends both on ribbon width and edge symmetry. The calculated band

gap, in case of A-S-GNRs, is also supported by the presence of threshold bias in the I-V

characteristics obtained from NEGF formalism. It is shown that all A-S-GNRs having width up to

1.50 nm are semiconducting but the Z-S-GNRs of similar widths are metallic. For A-S-GNRs, the

width dependent band-gap hierarchy follows three different trends which seem to be different from

that of H-passivated GNRs. The band-gaps for A-S-GNRs arise from both quantum confinement as

well as crucial effect of edge, where the passivating S atoms play an important role. Band-gap may be

further tuned by introducing other passivating atoms like Se and Te. The semiconducting ribbons,

when attached to doped metallic ribbons, show negative differential resistance phenomena as

indicated by the observed I-V characteristics. VC 2012 American Institute of Physics.

[http://dx.doi.org/10.1063/1.4768524]

I. INTRODUCTION

In spite of unique electronic and physical properties of

graphene,1 its application in electronic devices is limited due

to lack of band-gap. However, the problem is resolved by

forming one dimensional nano-strips of fixed width, naming

graphene nanoribbons (GNRs),2–14 thereby introducing

band-gap in it. Furthermore, the discovery, that the band-gap

is tunable by altering the edge structure and width,2–4,7–14

opens the new age of modern semiconducting materials. The

electronic band structure of GNRs has been subject of great

interest for a long time so as to determine the optical and

transport properties of it. Graphene nanoribons show distinct

electronic properties depending upon the edge symmetry of

it.4,5 Armchair GNRs (A-GNRs) are found to be more stable

than zigzag-edged GNRs (Z-GNRs).15

Z-GNRs exhibit metallic character in ferromagnetic

state and semiconducting in antiferromagnetic ground state,

the energy difference between those two states, however, in

the order of few meV per edge atom.10 The ground-state spin

polarization may be attributed to the localization of the con-

duction bands at the edges which can also be modulated with

a transverse electric field, applied perpendicular to the rib-

bon’s axis, resulting half metalicity of the ribbons. On the

other hand, high level density functional theory (DFT) calcu-

lations predict that all armchair graphene nanoribbons

(A-GNRs) are semiconductors11–13,16,17 with different

energy gaps depending upon the width of the ribbons,

although, tight binding (TB) calculations demonstrate 3-fold

periodic pattern in band-gap variation with every third

ribbon width showing a metallic character.18 It has been

shown that the origin of energy gaps for A-GNRs arises from

both quantum confinement and crucial effect of the edges.

The band-gap of A-GNR is inversely proportional to its

width. Based on first principle calculations, Son et al.11 show

that the band-gap (D) as a function of ribbon width (Na) fol-

lows three different series with a gap size hierarchy,

D3nþ1 > D3n > D3nþ2, where Na measures the number of

dimer lines across the ribbon width and n is a positive

integer.

The possibility of edge passivation of graphene nanorib-

bon by sulfur atoms has recently been proved in laboratory.19

The selective affinity of the nanoribbons to sulfur atoms was

also confirmed by energy dispersive X-ray spectroscopy.

Chamberlain et al.,20 both by experimental and theoretical cal-

culation, show that the thermodynamic stability of nanoribbons

is dependent on the S-GNR edge structure, and to a lesser

extent, the width of the ribbon. According to them,

for nanoribbons of similar widths, the polythiaperipolycene-

type edges of zigzag S-GNRs are more stable than the

polythiophene-type edges of armchair S-GNRs. Both the edge

structure and the width define the electronic properties of

S-GNRs which can vary widely from metallic to semiconduc-

tor to insulator. Their DFT calculations show that the elec-

tronic band structures for the different S-GNRs vary

dramatically from semiconductor in the case of Z-S-GNRs to

metallic to insulator for the A-S-GNRs, depending on the

nanoribbon width. On the basis of their generalized gradient

approximation (GGA)-Perdew-Burke-Ernzerhof (PBE) results,

the authors20 have demonstrated that 4-A-S-GNR is metallic

which creates an open debate whether hopping integrals

between edge atoms11 are capable of opening the band-gap for

A-S-GNRs or not. Very recently,21 dispersion-corrected

a)Author to whom correspondence should be addressed. E-mail: pranab.

[email protected].

0021-8979/2012/112(11)/113710/6/$30.00 VC 2012 American Institute of Physics112, 113710-1

JOURNAL OF APPLIED PHYSICS 112, 113710 (2012)

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density functional theory has been applied to investigate the

structure and electronic properties of S-GNRs encapsulated in

carbon nanotube. Their hybrid DFT calculations demonstrate

that unlike H- and O-GNRs, the S-GNR with zigzag edge is

metallic even when deformed inside carbon nanotubes.

In this paper we present the geometry and detailed elec-

tronic structure of recently synthesized sulfur-terminated

A-GNRs with different widths on the basis of systematic abinitio density functional theory within GG approximation

using PBE exchange functional. The variation of band-gap

with increasing ribbon width is also explored. The calcula-

tions reveal that the trend of band-gap variation for

S-terminated ribbon appears to be different from that of

H-terminated one. The tunable electronic properties shown

by S-GNRs may make them highly versatile 1D materials

with promising potential applications in electronic and opti-

cal devices. As for example, the semiconducting ribbons are

when attached to metallic leads, they show negative differen-

tial resistance (NDR) behavior in certain bias windows.22–24

Much efforts have been devoted for modeling new NDR

devices by means of structural modulation or by introducing

foreign elements25–27 into GNRs which may have potential

application in logic circuit, switching, amplification as well

as in memory storage. So, we wish to extend our research for

studying quantum conductance behavior of the A-S-GNRs

sandwiched in between metallic leads.

The paper is arranged as follows. A brief computational

description is made in Sec. II. Section III starts with the

results of relative thermodynamic stability. In the later part

we describe the band structure and general trends of band-

gap variation. Following this section, we present the trans-

port properties showing I-V characteristics with different

leads. Finally, conclusive remarks are drawn in Sec. IV.

II. METHOD OF COMPUTATION

Geometry relaxations and electronic structure calcula-

tions were performed using a double-f plus polarization

function (DZP) basis set and norm-conservative Troullier-

Martins pseudo-potentials (PP)28 for representing the valence

and inner electrons as implemented in SIESTA package.29 A

real space mesh cutoff of 300 Ry has been used throughout

the entire calculation. The exchange-correlation functional

of the GGA is represented by the PBE approximation.30 The

convergence criteria for the density matrix are taken as 10�4.

The conjugate gradient method is used to relax all the atoms

until the maximum absolute force was less than 0.001 eV/A.

The k-point sampling was done with 1� 1� 15 Monkhorst-

Pack k-points.

A set of transport properties were calculated using

TranSIESTA module within the SIESTA package, which is

based on the combination of density functional theory and

non-equilibrium Green’s function (NEGF) method.31,32 The

generalized gradient approximation in the PBE form is

employed for the exchange correlation functional. We used

similar basis and convergence criteria as was implemented

during geometry optimization. In the NEGF self-consistent

loop, the charge density was integrated over 400 energy

points along the semicircle in the complex plane. We used

undoped or doped ribbons as left and right electrodes thereby

sandwiching the central scattering region (SR) and current

was calculated from the Landauer-Buttiker formula, accord-

ing to which the current I(Vb) is given by

IðVbÞ ¼2e

h

ð1�1

TðE;VbÞ½fLðE� lLÞ � fRðE� lRÞ�dE; (1)

where T(E;Vb) being transmission function, fLðRÞ is the

Fermi-Dirac distribution function for left (right) lead, and

lLðRÞ is the electrochemical potential of the left (right) lead

such that eVb ¼ lL � lR.

III. RESULTS AND DISCUSSION

First, we optimize the lattice constants of 2D graphene

sheet and those of the sulfur terminated Z-GNRs and

A-GNRs of different width. Here, it should be pointed out

that, following the previous convention10,11 we also classify

Na-A-GNR and Nz-Z-GNR of different width, where Na is

the number of dimer lines (or equivalent to number of C

atoms in a zigzag chain) across the A-GNR width and Nz is

the number of zigzag chains across the Z-GNR width. Table I

displays the optimized lattice constants and relative stability

of various ribbons with different edge structures, where the

free energy of formation of a species (DGf ) is defined by

DGf ¼ ls �P

le, s and e denoting the particular species

and constituting elements, respectively. We wish to mention

here that, for representing elemental C, H, and S we consid-

ered two-dimensional graphene sheet, free H2 molecule, and

S8 molecule, respectively. It is significant to note that unlike

hydrogen-terminated ribbons, sulfur-terminated Z-GNRs are

energetically more stable than A-GNRs of similar width,

however, in any case these are more stable than the bare rib-

bon as indicated by the table. The extra stability gained by

the S-terminated ribbons in comparison to the bare ribbons

may easily be understood on the basis of saturation of valen-

cies. On the other hand, the favored perpendicular orienta-

tion of unhybridised p orbitals of S atom is reflected by the

greater stability of the S-terminated zigzag ribbons. In case

of A-GNRs the S atoms suffer from angle strain where the p

orbitals are inclined with an C-S-C angle of �968. As shown

in Table I, the optimized lattice constant of A-GNRs gradu-

ally increases with increasing the ribbon width, of course,

TABLE I. Optimized lattice constant and free energy of formation of some

nanoribbons of different edge symmetry and passivation.

Ribbon L.C. (A) DGf (eV/atom)

Zigzag C8S4 4.95 0.0878

S12S4 4.95 0.0657

C16S4 4.95 0.0529

C12H4 4.95 0.0367

C12 4.94 1.0231

Armchair C8S2 4.05 0.2255

C12S2 4.12 0.1740

C16S2 4.16 0.1473

C12H4 4.33 �0.0029

C12 4.39 0.8016

113710-2 Mandal et al. J. Appl. Phys. 112, 113710 (2012)

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with a nonlinear trend. Table I also indicates that sulfur pas-

sivated ribbons are relatively less stable than hydrogen passi-

vated one, but the energy of destabilization is only 0.02 eV/

atom for the width of 0.65 nm. So, from the thermodynamic

point of view S-terminated ribbons are comparable with H-

terminated one. Fig. 1 displays optimized geometry of arm-

chair and zigzag edged S-terminated ribbons. Although our

results qualitatively resemble the previous calculation of

Chamberlian et al.,20 the values of DGf are much lower than

previously reported values. However, no experimental result

is available for comparison.

Next, to have an insight into the electronic structure of

the S-passivated ribbons, we have performed band structure

calculations of them in the same level of theory. The calcula-

tions reveal that the narrowest A-GNR (3-A-GNR) in our

calculation has the highest band-gap of 1.88 eV effectively

making it a semiconductor. With increasing ribbon width the

overall variation of band gap appears zigzag, but a closer ob-

servation indicates a regular decreasing trend of three sepa-

rate series namely, Na¼ 3n, 3nþ 1, and 3nþ 2, where n is

having positive integral values. We wish to mention here

that, while defining ribbon width, we consider C-C perpen-

dicular distance across the periodic direction as in the case

of A-H-GNRs. As shown in Fig. 2, for a particular value of

n, the 3n series has the highest band gap and the 3nþ 1 series

has the lowest one with a general trend of band gap variation

as D3n > D3nþ2 > D3nþ1. It is interesting to note that the cur-

rent trend does not resemble the same for the H-terminated

ribbons as reported from TB or DFT calculations.11 In the

previous case the 3nþ 1 series showed the highest band gap

trend. To see the effect of width we extended our calculation

for the ribbon as wide as 1.50 nm (13-A-S-GNR, of 3nþ 1

series) but still failed to obtain zero band gap which is in

severe contrast to the recently reported result,20 where the

authors report 4-A-S-GNR as a metallic system. Fig. 3 dis-

plays the band-structures of 4-6-A-S-GNR, those are

obtained from our DFT calculations, clearly indicating a

band gap of 0.67 eV for 4-A-S-GNR. In general, GGA under-

estimates the band gaps for 2D carbon-base materials. In

addition, band gap is very sensitive to the size of the basis

function, threshold energy, and maximum force tolerance on

each atom. Thus, further experimental verification is

required for the present conflict.

It has been demonstrated that11 quantum confinement is

the determining factor in the semiconducting behavior of

Na-A-GNRs. Additionally, the edge effects also play a cru-

cial role in showing band gap of the ribbons. As can be seen

in Fig. 1, the edge carbon atoms are passivated by sulfur

atoms of the A-GNRs and their p orbitals take part in the

extended delocalization of the p orbitals of C atoms of GNR

which is reflected from the electron distribution plots for the

frontier molecular orbitals of the ribbons as shown in Fig. 4.

Thus, the actual effective width of S-GNRs is the perpendic-

ular S-S distance across the periodic direction and conse-

quently Na-H-GNR would become (Naþ 2)-S-GNR. More

precisely, 3n, 3nþ 1, and 3nþ 2 series of H-GNRs would

appear 3nþ 2, 3n, and 3nþ 1 series for S-GNRs, respec-

tively. So, considering the effective width for A-S-GNRs, 3n

series would show the highest band-gap, while 3nþ 1 having

the lowest one for any integral value of n. Thus, the results

resemble the previous trend obtained from first-principle

calculation for A-H-GNRs reported by Son et al.11 A

detailed study was also made for similar ribbons, passivated

FIG. 1. Optimized geometry of 4-A-S-GNR (a) and 3-Z-S-GNR (b), gray

and yellow coloured balls are C and S atoms, respectively.

2 4 6 8 10 12 14 16Width (n)

0

0.5

1

1.5

2

Ban

d G

ap (e

V)

3n3n+13n+2

FIG. 2. Band gap variation of A-S-GNRs of different widths.

Γ Z-4

-2

0

2

4

Ener

gy (e

V)

Γ Z-4

-2

0

2

4

Ener

gy (e

V)

Γ Z-4

-2

0

2

4

Ener

gy (e

V)

(a) (b) (c)

FIG. 3. Band structure of Na-A-S-GNRs of different widths: (a) for Na ¼ 4,

(b) for Na ¼ 5, (c) for Na ¼ 6. Fermi energy is set to zero.

113710-3 Mandal et al. J. Appl. Phys. 112, 113710 (2012)

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by Se and Te, for which the band-gap hierarchy becomes

D3n > D3nþ1 > D3nþ2 as can be found in Fig. 5.

We have performed non-equilibrium Green’s function

analysis32 to have the current-voltage (I-V) characteristics of

4-A-S-GNR using same ribbon as both leads and the

observed I-V curve (shown in Fig. 6(a)) indicates a require-

ment of positive or negative threshold voltage to have a finite

current which is exactly equal to the band gap of the system.

The zero bias transmission function (Fig. 6(b)) curve is again

in support of the nonzero band gap of the system. We wish

to mention here that similar band gap was also noted for

A-H-GNR from transmission function measurement.33 The

two transmission peaks near Fermi level correspond to the

HOMO and LUMO of the scattering region. Thus the trans-

mission spectra apparently mimic the band structure of the

scattering region. A similar analysis of the I-V curve

obtained from 13-A-S-GNR also resembles the semiconduct-

ing nature of it, where the threshold voltage is lowered and

FIG. 4. Electron density distribution of LUMO

(blue) and HOMO (red) states of Na-A-S-GNRs

of different width, (a) and (b) for Na ¼ 4, (c)

and (d) for Na ¼ 5, (e) and (f) for Na ¼ 6, and

6-A-H-GNR ((g) and (h)). The isosurface value

was used as 0.05 e�3.

2 4 6 8 10 12 14 16Width (n)

0

0.5

1

1.5

2

Ban

d G

ap (e

V)

3n3n+13n+2

FIG. 5. Band gap variation of A-Se-GNRs of different widths.

-100

-50

0

50

100

-3 -2 -1 0 1 2 3Applied bias (V)

-250

-125

0

125Cur

rent

(μΑ

)

-3 -2 -1 0 1 2 3E-Ef (eV)

Tran

smis

sion

(T(E

,Vb))

(a)

(c)

(b)

(d)FIG. 6. I-V characteristics and zero bias trans-

mission function as a function of relative Fermi

energy for 4-A-S-GNR ((a) and (b)) and 13-A-

S-GNR ((c) and (d)).

113710-4 Mandal et al. J. Appl. Phys. 112, 113710 (2012)

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again equal to the band gap of 0.23 eV. So, both DFT and

NEGF method clearly indicate semiconducting behavior of

the armchair ribbons.

On contrary, we report all S-terminated Z-GNRs studied

here are not semiconducting as suggested by Chamberlain

et al.,20 but nonmagnetic metals. Our results strongly support

the recent results of hybrid DFT calculations made by Lebe-

deva et al.21 It is worth noting that H-terminated Z-GNRs

are semiconducting with non-zero magnetic moment. So,

replacement of H by S converts the ribbons from magnetic

semiconductors to nonmagnetic metals. The band structures

of some Nz-Z-S-GNR are presented in Fig. 7 indicating band

crossing at the zone boundary.

The width dependent band-gap variation of A-GNRs has

been well exploited in semiconductor-based nanoelectronics

devices because these materials show NDR in different range

of applied bias when attached to metallic leads.22–25 Proper

doping of hetero-atoms like B, N converts the semiconduct-

ing ribbons into metallic one25,34 and thus when we use

2B-doped A-S-GNR as metallic leads, pronounced NDR phe-

nomena are observed as shown in Fig. 8, for 5-A-S-GNR as a

model system. Doped metallic leads serve the function of left

and right hand electrodes (LHE, RHE), and the undoped rib-

bon is treated as SR which also contains part of electrodes for

screening the interaction between SR and electrodes.35,36

Fig. 8 reveals that within the bias ranging from 0.6 to 1.8 V

there is a gradual drop in current from 59 to 23 lA with a

PVR of 2.5, where peak to valley ratio (PVR) is defined as

the ratio of current at peak (Imax) to that at valley (Imin). A

similar phenomenon is also observed in the negative bias

window from �0.6 to �1.0, however, the PVR is much lower

1.4 only. The observer NDR phenomena can be well under-

stood from the nature of the transmission function T(E;Vb)

within the bias window which in turn depends on the relative

position of the energy bands. As can be seen from Fig. 9,

transmission functions corresponding to different resonant

tunneling increases from 0 to 0.6 V thereby increasing the

integrated current as obtained from Landauer-Buttiker for-

mula. Further increase in positive bias reduces T(E;Vb) val-

ues because of mismatching of frontier energy bands of the

scattering region and the leads which ultimately reduces the

total current within the bias window (�Vb=2;þVb=2).

Γ Z-4

-2

0

2

4

Ener

gy (e

V)

Γ Z-4

-2

0

2

4

Ener

gy (e

V)

(a) (b)

FIG. 7. Band structure of Nz-Z-S-GNR of different widths: (a) for Nz ¼ 2,

(b) for Nz ¼ 3. Fermi energy is set to zero.

FIG. 8. I-V characteristics 5-A-S-GNR using 2B-doped 5-A-S-GNR as me-

tallic leads. The inset figure represents the three different regions for trans-

port calculation along z axis; gray, brown, and yellow balls represent C, B,

and S atoms, respectively.

-3 -2 -1 0 1 2 3E-Ef (eV)

Tran

smis

sion

(T(E

,Vb))

(a)

(b)

(c)

FIG. 9. Transmission function as a function of relative Fermi energy at zero

bias (a), 0.6 V (b), and 1.8 V (c). Vertical dotted red lines indicate bias

window.

113710-5 Mandal et al. J. Appl. Phys. 112, 113710 (2012)

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IV. CONCLUSIONS

In conclusion, newly synthesized S-GNRs are realizable

from the thermodynamic stand point as compared to

H-GNRs. All S-GNRs are thermodynamically more stable

than the bare ribbons and their stability depends on the edge

structure as well as ribbon width. Unlike hydrogen-

terminated graphene ribbons sulfur-terminated zigzag rib-

bons are more stable than armchair ribbons of similar width.

This is mainly because of the favored orientation of unhybri-

dised p orbitals of the terminal S atoms and greater S-S inter-

action in Z-S-GNRs. Band structure analysis of the ribbons

reveals that A-S-GNRs are semiconducting and their band

gap decreases with increasing ribbon width following the

sequence D3n > D3nþ2 > D3nþ1 which seems to be different

from that of A-H-GNRs. However, a deep insight reveals

that p-orbitals of terminal sulfur atoms take part into

extended delocalization of the ribbons thereby taking into

account the S atoms as part of ribbon width. Thus, the cor-

rected band-gap sequence, D3nþ1 > D3n > D3nþ2, resembles

the same for A-H-GNRs. So, the participation of S atoms in

the frontier orbitals is the crucial point for determining band

gap hierarchy. Similar things happen for Se and Te passi-

vated A-GNRs also, where D3nþ2 goes below D3nþ1 due to

more pronounced edge effect. The I-V characteristics

obtained from the NEGF analysis using semiconducting

leads demand a threshold voltage to have a finite current

which is again in support of the semiconducting nature of the

A-S-GNRs. On the other hand, while using doped metallic

ribbons as leads, there appears NDR in different bias regions.

Although GGA-PBE underestimates the band opening to

some extent, we do hope that our findings will motivate the

experimentalists for measuring the band-gap for A-S-GNR

so as to implement it in the future generation graphene-based

nanoelectronics and optical devices.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial sup-

port from DST, New Delhi [SR/NM/NS-49/2007], through

research grants. The first three authors are thankful to CSIR,

Govt. of India for providing them research associateship/

fellowship.

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