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Physica E 42 (2009) 46–50

Contents lists available at ScienceDirect

Physica E

1386-94

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/physe

Structural stability and electronic properties of GaSb nanowires

Satyendra Singh a, Pankaj Srivastava b,�, Abhay Mishra c

a Department of Physics, Hindustan College of Science & Technology, Farah, Mathura 281122,. Indiab Applied Physics Group, ABV-Indian Institute of Information Technology & Management (ABV-IIITM), Gwalior 474010, Indiac Department of Applied Physics, Madhav Institute of Technology & Science, Gwalior 474005, India

a r t i c l e i n f o

Article history:

Received 20 July 2009

Received in revised form

17 August 2009

Accepted 18 August 2009Available online 22 August 2009

PACS:

73.21.Hb

61.46.Df

Keywords:

GaSb nanowires

Electronic band structure

Density of states

Total energy

77/$ - see front matter & 2009 Elsevier B.V. A

016/j.physe.2009.08.017

esponding author. Tel.: +917512449825; fax

ail address: pankajs@iiitm.ac.in (P. Srivastava)

a b s t r a c t

The structural stability and electronic properties of four different shapes of GaSb nanowire have been

studied by ab-initio method using the generalized gradient approximations. The different structures

were two atom linear wire, two atom zigzag wire, four atom square wire and six atom hexagonal wire.

The geometry optimization and the stability of all nanowires were investigated. We explore the

minimum energy atomic configuration for all the considered shapes. We find that four atom square wire

configuration has greater stability in comparison to other shapes. The analysis of density of states and

band structures of optimized nanowires predicts that semiconducting nanowires may be metallic or

semiconducting. The behavior entirely depends upon the geometrical structure.

& 2009 Elsevier B.V. All rights reserved.

1. Introduction

Semiconductor nanowires exhibit novel electronic and opticalproperties owing to their unique structural one-dimensionalityand possible quantum confinement effect in two dimensions.GaSb-based semiconducting nanowires have attracted muchinterest over the last 10 years with potential applications innanoscale lasers, detectors, sensors and other informationtechnology components [1–4]. GaSb semiconducting nanowirescan be used as semiconductor subwavelength-wire lasers infuture photonic integrated circuits for communications applica-tions [5]. GaSb-based semiconducting nanowires are of greatinterest for both high speed electronic and optoelectronicapplications in the mid infrared region. This is due to very highhole mobility of GaSb and the wide range of band gaps availablefor GaSb-based alloys (0.8–4.4mm).

Experimentally various methods have been developed tosynthesize high quality GaSb nanowires. Structural characteristicsof GaSb nanowire hetrostructures grown by metalorganic chemi-cal vapor deposition were determined by Gao et al. [6]. Vaddirajuet al. [7] reported the synthesis of Group-III Antimonide (GaSb)nanowires. Kuczkowski et al. [8] synthesized GaSb nanowires

ll rights reserved.

: +91751 2460313.

.

using single source precursor. GaSb nanowires were successfullydemonstrated lasing from a single GaSb submicrometer-sizedwire in the IR wavelength regime by Chin et al. [9]. Controlledpolytypic and twin-plane superlattices III–V nanowires werereported by Caroff et al. [10]. Burk et al. [11] studied the effectof MOCVD growth conditions on the catalyst composition andstructural properties of GaSb nanowires. Jeppsson et al. [12]reported Au-assisted growth of GaAs/GaSb nanowire hetrostruc-tures grown by MOVPE. Again Jeppsson et al. [13] reported thegrowth and characterization of GaSb nanowires grown by MOVPE.Xu et al. [14] studied the electrical characterization of single GaSbnanowire field effect transistors. Electrical and optical character-ization of individual GaSb nanowires were determined by Xu et al.[15]. Catalyst composition and structural properties of GaSbnanowires grown by Au-assisted metalorganic chemical vapordeposition was reported by Weng et al. [16].

Thus, on experimental side a lot of work has not been done onits synthesis and growth aspect but neither experimentally northeoretically any group investigated the stability factor andelectronic properties on its different shapes and structures. It iswell-known fact that at nanoscale, geometrical shape andstructure play an important role for their electronic and opticalproperties. During literature survey we did not come across any ofthe theoretical work on this particular GaSb nanowire, thismotivates us to consider four different shapes of GaSb nanowireand then investigate the stability and electronic properties of very

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Table 1The variation of inter atomic distance x (nm) with energy (eV/atom).

x (nm), x ¼ Ga–Sb distance Total energy (eV/atom)2_atom linear wire 2_atom zigzag wire 4_atom square wire 6_atom hexagonal wire

0.06 �543.20 �767.38 �456.97 �463.75

0.10 �950.15 �951.73 �943.87 �865.55

0.16 �978.86 �975.60 �977.83 �952.50

0.22 �983.10 �981.81 �984.22 �971.34

0.26 �982.28 �983.25 �984.25 �979.46

0.32 �982.68 �982.72 �983.53 �982.80

0.38 �982.37 �983.29 �982.90 �983.20

0.42 �981.48 �982.52 �982.86 �982.86

0.48 �981.00 �982.74 �980.73 �983.340.52 �980.01 �982.55 �982.73 �981.70

0.58 �979.28 �982.21 �982.60 �974.37

0.64 �974.10 �982.20 �983.02 �982.94

0.68 �982.56 �980.84 �983.60 �980.15

0.74 �982.60 �982.01 �984.20 �982.63

0.80 �983.07 �982.40 �984.43 �980.13

The most stable structure are bold-faced ones.

Table 2The interatomic distances and the total energy of optimized structures.

Structure Ga–Sb distance (nm) Ga–Ga distance (nm) Total energy (eV/atom)

2_atom linear 0.22 0.44 �983.10

2_atom zigzag 0.38 0.76 �983.29

4_atom square 0.80 1.38 �984.43

6_atom hexagonal 0.48 0.83 �983.34

Fig. 1. Geometrical structures of GaSb nanowires (a) two atom linear wire, (b) two atom zigzag wire, (c) four atom square wire, (d) six atom hexagonal wire.

S. Singh et al. / Physica E 42 (2009) 46–50 47

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0.0

-1000

-900

-800

-700

-600

-500

-400

Ene

rgy

(eV

/ato

m)

X (nm)

2_atom linear wire 2_atom zigzag wire 4_atom square wire 6_atom hexagonal wire

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Fig. 2. The variation of interatomic distance x (nm) with energy (eV) for different

nanowires.

-25

-50

0

50

100

150

200

250

300

350

400

450

DO

S (e

lect

ron/

Ha/

cell)

energy (eV)

2_linear E f = - 4.40 eV 2_zigzag E f= - 3.78 eV 4_square E f = - 3.83 eV 6_hexagonal E f= -4.33 eV

-20 -15 -10 -5 0

Fig. 3. The variation of energy (eV) with density of states (DOS) for all nanowires

0.0-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

Ene

rgy

(eV

)

2_atom GaSb linear wire

Ef

kz0.1 0.2 0.3 0.4 0.5

Fig. 4. Band structure for two atom linear wire.

0.0

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2E

nerg

y (e

V)

2_atom GaSb zigzag wire

Ef

kz

0.1 0.2 0.3 0.4 0.5

Fig. 5. Band structure for two atom zigzag wire.

S. Singh et al. / Physica E 42 (2009) 46–5048

thin nanowires up to six atoms. We have extensively investigatedthe variation of interatomic distance with energy as well asdensity of states and band structure of nanostructures.

2. Computational details

We have employed ab-initio DFT calculations [17,18] within theplane-wave pseudopotential method to investigate the structuresof GaSb nanowires. The pseudopotential method has been verysuccessful in exploring the structural and electronic properties ofvarious materials [19]. We have used ABINIT code [20]. In thiscalculation the generalized gradient approximation and theexchange-correlation functional of Perdew, Burke, and Ernzerhofwere applied [21]. For the atomic cores we have used theexchange-correlation potential of Troullier and Martins [22], thesepseudopotentials were taken from ABINIT web page [20]. Thevarious potentials were tested by doing calculations on bulk GaSbmaterial and the results of LDA FHI TM were found to beconsistent with the experimental ones.

All the calculations have been performed in a self-consistentmanner. The studied structures have been optimized for Hell-mann–Feynman forces as small as 10�3 eV/A on each atom. Thecalculations were performed with a kinetic energy cut-off of30 hartee. The wires were positioned in a super cell of side 20 a.u.along the x and y directions. The axis of the wire was taken alongthe z-direction and the periodic boundary conditions wereapplied. The Monkhorst-pack method [23] with 15k-pointssampling along the z-direction was used in the integration ofthe Brillouin zone. All atoms were allowed to relax without anyimposed constraint. In order to check the self-consistent calcula-tions we have determined the self-consistent optimized value forthe lattice parameter of bulk GaSb. Our calculated value of 5.92 Ais close to the experimental value of 6.09 A. However, thecalculated bulk lattice constant is low by nearly 3% as comparedto experimental value. This low value is normal while usingABINIT, as we have tested for many bulk materials. All thestructures have been optimized to achieve minimum energy byrelaxing the atomic positions in the unit cell. The magnitude of

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0.0-40

-35

-30

-25

-20

-15

-10

-5

0

5

Ene

rgy

(eV

)

Ef

4_atom GaSb square wire

kz

0.1 0.2 0.3 0.4 0.5

Fig. 6. Band structure for four atom square wire.

0.0

-50

-40

-30

-20

-10

0

10

Ene

rgy

(eV

)

Ef

6_atom GaSb hexagonal wire

kz0.1 0.2 0.3 0.4 0.5

Fig. 7. Band structure for six atom hexagonal wire.

S. Singh et al. / Physica E 42 (2009) 46–50 49

atomic relaxation depends on the plane cut-off energy and oneshould obtain convergence with respect to cut-off energy too.

3. Results and discussion

We have investigated four different structures of galliumantimonide nanowires naming two atom linear wire, two atomzigzag wire, four atom square wire and six atom hexagonal wire.Here it should be noted that in the present paper we have nottaken into account the surface atoms or passivation of any otheratom except pure GaSb material. As we have considered simplyvarious geometrical structures and the wires are positioned in asuper cell of large side along the x and y directions and extend theunit cell of the wire along the z-direction separated by the latticeparameter. In Table 1, we have shown the variation of interatomicdistance with energy for various structures. The interatomicdistance at which we get minimum energy configuration has beendepicted in bold letters. The optimized distances and the energies

of all stabilized nanowires are presented in Table 2. The geometryof all considered nanowire structures are shown in Fig. 1. Allstructural parameters were optimized independently for eachstructure to explore the minimum energy configuration.

First, we have calculated the total energy as a function of x ¼ ‘a’for an infinite linear wire, where ‘a’ is the Ga–Sb distance of theorder of 0.04 nm and then investigate the effect of total energy. Thetwo atom linear wire shows minimum energy at an interatomicdistance of 0.22 nm. No dimerization was found for the linear wire.The wire becomes stable at �983.10 eV. In two atom zigzagstructure the minimum energy comes out at 0.38 nm distance, i.e.�983.29 eV. The zigzag wire has slightly lower energy in compar-ison to a linear wire. For four atom square wire, the energy isminimum at 0.80 nm as that of linear wire, its energy is�984.43 eV.The minimum energy configuration for six atom hexagonal wire isfound at the interatomic distance of 0.48 nm and its energy is�983.34 eV. The detailed investigation of all the structures revealsthat four atom square cross sectional wire has the minimum energyconfiguration in comparison to others and therefore treated to bethe most stable structure. The variation of interatomic distance withenergy are clearly depicted in Fig. 2, for all structures.

We have analyzed the nature of density of states (DOS) thatcorresponds to optimized interatomic distance for all structures.The variation of energy with DOS has been shown in Fig. 3. Onecan observe that DOS is high for two atom linear and zigzagstructures near the Fermi level, whereas the DOS is lower for fouratom square wire structure and we have already predicted this tobe the most stable structure in our calculation. In fact the DOS isnegligible/lower in case of nanowires near the Fermi level becauseof confinement of states. The four atom square wire has almostthe same character as expected experimentally. The DOS of sixatom hexagonal structure is somewhat similar to that of a linearwire. The Fermi level of DOS lies between �3.78 eV and �4.40 eV.

It is universally accepted that the band structure of a nanowireis different from that of the bulk material. The bulk material of III–Vsemiconductors has a Td point group symmetry. When a nanowireis formed the symmetry of the structure will be lowered, due toconfinement of states. The 3-fold degenerate states in the bulk tendto split into other symmetric states in the nanowire. The splitting ofstates has interesting effect on the electronic band structure of thenanowires. The band structures of all GaSb nanowires are shown inFigs. 4–7. Here we observe some interesting features. The bandstructure of two atom linear wire in Fig. 4, clearly shows themetallic behavior of the wire, as many bands crosses the Fermilevel. The Fermi energy is located at �3.60 eV. At the G-point thedifference of energy value between the valence band andconduction band is small in comparison to X-point. The bandstructure of zigzag wire (Fig. 5) also exhibit metallic character as isevident from figure. Here the Fermi energy is at �2.80 eV. In fouratom square wire the states are far below the Fermi level as shownin Fig. 6 (Ef ¼ �1.70 eV). In six atom hexagonal wire the bands areagain, below the Fermi level as shown in Fig. 7, (Ef ¼ 0.71 eV),showing different nature from the other two structures.

Thus, we conclude that geometrical structure plays an importantrole in nanowires when we investigate the ground state properties.Initially taken semiconducting nanowires may be metallic orsemiconducting or insulating it entirely depends upon the size andshape of the structure. The electronic properties exhibit remarkablechange just by changing the number of atoms and geometricalstructure. This signifies the effect of shape and size at the nanoscale.

4. Conclusions

The present ab-initio investigation reveals that size and shapeplays an important role in nanowires. The electronic band

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S. Singh et al. / Physica E 42 (2009) 46–5050

structures get changed which is evident from our findings. Ourcalculation predicts that four atom square nanowire have greaterstability and energetically more favorable, in comparison toothers. The DOS in case of four atom square wire are found tobe lower near the Fermi level as expected. The band structureinvestigation reveals remarkable features at nano dimensions.Two atom linear wire and two atom zigzag wire are found to bemetallic, whereas four atom square wire configuration and sixatom hexagonal wire configuration are showing different beha-vior. Thus, we come to the conclusion that size and shape of thestructure are the main driving forces in deciding nanowires asinterconnect for optoelectronic and photonic applications. Ourpredictions may help to fabricate semiconducting materials asinterconnects for nanodevice applications as per their require-ment.

Acknowledgments

The authors are thankful to Computational Nanoscience andTechnology Laboratory (CNTL) of ABV-Indian Institute of Informa-tion Technology and Management (ABV-IIITM), Gwalior forproviding the infrastructural facilities for computational work.

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