P

Aa

b

c

a

ARRA

P66776

KPHEA

1

tpobrtcdfspddistt

IL

0d

Materials Chemistry and Physics 125 (2011) 66–71

Contents lists available at ScienceDirect

Materials Chemistry and Physics

journa l homepage: www.e lsev ier .com/ locate /matchemphys

ressure induced phase transformation and electronic properties of AlAs

nurag Srivastavaa,∗, Neha Tyagia, U.S. Sharmab, R.K. Singhc

Advance Materials Research Lab, Indian Institute of Information Technology & Management, Gwalior, M.P. 474010, IndiaDepartment of Physics, RJIT, BSF Academy, Tekanpur, Gwalior 475005, IndiaSchool of Basic Sciences, ITM University, Gurgaon, HRY. 122017, India

r t i c l e i n f o

rticle history:eceived 8 June 2010eceived in revised form 26 July 2010ccepted 18 August 2010

ACS:2.50.±p8.35.Rh1.20.Nr

a b s t r a c t

We have performed the first-principle study to analyze the structural and electronic properties of alu-minum arsenide under the application of pressure. The computations have been carried out using theground state total energy calculation approach of the system. The first-principle approach has been usedto compute the stability of various phases of AlAs, like original zinc blende (B3), intermediate NiAs (B8),NaCl (B1) and CsCl (B2) type as a function of pressure. The study observes a B3–B8, B3–B1 and B3–B2transitions at 6.99 GPa, 8.18 GPa and 73.43 GPa. The computed phase transition pressures, lattice parame-ters, bulk modulus, and energy gaps are in good agreement with their experimental as well as theoreticalcounterparts. Band structure and density of states analysis have also been performed and results have

1.15.Mb4.70.Kb

eywords:hase transition

been discussed in detail.© 2010 Elsevier B.V. All rights reserved.

igh pressurelectronic propertieslAs

. Introduction

The operating characteristics of the electronic and optoelec-ronic devices not only talks about the materials engineering at aractical level but they are also required for better understandingf the properties of materials and associated fundamental scienceehind them. Theoretical investigations as well as experimentalesearches are therefore of vital interest to all those working inhis area of research. The electronic and structural properties of theomplex systems have attracted considerable interest in both fun-amental and applied physics. A large amount of work has beenocused on theoretical understanding of a variety of compoundemiconductors and their related properties. These compoundslay an important role in microelectronics, for example, in theevelopment of light emitting diodes and high frequency low noiseevices for mobile telephones and advanced materials for spintron-

cs [1–13]. The most remarkable aspect of tetrahedrally coordinatedtructures is their low density. The openness of these semiconduc-ors is highlighted by the fact that for the homopolar members,he ratio of the volume of touching atom spheres to that of the

∗ Corresponding author at: Advance Materials Research Lab, Indian Institute ofnformation Technology & Management, E-110, First Floor, IIITM Campus Morenaink Road, Gwalior, M.P. 474010, India. Tel.: +91 751 2449826.

E-mail addresses: profanurag@gmail.com, anurags@iiitm.ac.in (A. Srivastava).

254-0584/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.matchemphys.2010.08.072

unit cell is 0.34 which is less than half for the close-packed ele-ment structure (0.74). It is not surprising, because under pressuretetrahedrally coordinated semiconductors can be transformed tothe structure with higher density [14]. Froyen and Cohen [15] andMartin [16] reported first on the phase transition in AlAs which wasbased on ab initio pseudopotential calculation and suggested thatthe high pressure structure could be either rocksalt (B1) or NiAs(B8). Weinstein et al. [17] reported the pressure induced structuraltransition by microscopic examination at 12.3 GPa on loading butthe structure was unknown. Greene et al. [18] have performed anEDXD study on AlAs up to 46 GPa and found that AlAs transformsto NiAs structure. This was the first experimental observation ofIII–V compound transforming into the NiAs structure. The equilib-rium transformation pressure was found to be 7 ± 5 GPa, averagingthe large hysteresis. Onodera et al. [19] have reported B3–B8 phasetransition in AlAs at 14.2 GPa by high pressure X-ray diffraction andelectrical resistivity measurements.

Many methods of calculations have been used to confirm theseresults. One of them is to relate the high pressure behavior ofthese semiconductors to the type of chemical bonding betweenthe nearest atoms by examining the electronic charge density

evolution, which has been correlated to the empirical qualitativeconcept as ionicity [20,21]. The first-principles electronic struc-ture calculations have allowed detailed studies of the energeticsof the group IVA elements and the groups IIIA–VA and IIB–VIAcompounds under high pressures [22]. Theoretically, III-arsenide

emistry and Physics 125 (2011) 66–71 67

cfcsmgRtih(((

paecs

ttstr7oioaPsbsoe

2

etTmEdptiadaoectficAgsl(ea

A. Srivastava et al. / Materials Ch

ompounds have been studied by employing different approaches;rom phenomenological methods such as k.p. theory or empiri-al pseudo-potentials methods [23] to atomistic ab initio methods,uch as the full-potential linear augmented plane wave (FP-LAPW)ethod within local density approximation (LDA) or generalized

radient approximation (GGA) and pseudopotential methods [24].ecently, Wang et al. [25] have reported the first-principle study ofhe phase transition of AlAs in three crystallographic structures,.e., B3 (zinc blende), B8 (nickel arsenide) and B1 (rock salt) atigh pressures using the full-potential linearized muffin-tin orbitalFP-LMTO) scheme within the generalized gradient approximationGGA) correction in the framework of the density functional theoryDFT) and based on the condition of equal enthalpies.

Singh et al. [26–28] have successfully applied three-body-otential approach to describe the high pressure phase transitionnd other properties of Al based compound semiconductors. Theffect of pressure on the structural stability of some III–V and IV–VIompound semiconductor based alloys has also been investigateduccessfully with three-body-potential (TBP) approach [29,30].

Cai and Chen [31] have reported a possible mechanism for B3–B8ransition, characterized by the space group of C2221, and observedhat there are relatively small values of activation enthalpy andtrain anisotropy for B3–B8 transition of AlAs in comparison tohe B3–B1 case. The calculated transition pressure from B3 to B8anges from 6.1 GPa [32] to 9.15 GPa [31], and B3 to B1 phase, from.4 GPa [32] to 11.88 GPa [31]. Not much information is availablen B3–B2 transition in this compound. Looking to the technologicalmportance of this material and success of first-principle meth-ds, we thought it pertinent to analyze the transitions due to thepplication of pressure and thereby its material characteristics.articularly three transitions B3–B8, B3–B1 and B3–B2 have beentudied. Further the present work also computes lattice constant,ulk modulus and its pressure derivative, band structure and den-ity of state in different phases of AlAs. These calculations provide ane stop shop for fundamental understanding of the structural andlectronic properties of the aluminum arsenide.

. Computational details

The present computations of the structural and electronic prop-rties of aluminum arsenide have been performed using ATKool [33]. Atomistix ToolKit (ATK) is a further development ofranSIESTA-C [34,35] which, in turn, is based on the technology,odels and algorithms developed in the academic code TranSI-

STA and, in part, McDCal [36], employing localized basis sets aseveloped in SIESTA [37]. The density functional theory (DFT) is, inrinciple a very good theory to predict ground state properties (e.g.otal energy, atomic structure, Bulk modulus, etc.). However, DFTs not a theory to address efficiently the excited state propertiesnd hence DFT typically underestimates the band gap of semicon-uctors and insulators by 20–30%. The ATK has been proved to bevery efficient tool in predicting the transport properties [38–40]f variety of bulk as well as nanostructured materials, where thelectronic properties have also been discussed in detail. The norm-onserving pseudopotential is used in density function theory forotal energy calculation of polyatomic systems. The electronic con-guration of AlAs is Al: Ne 3s23p1, and As: Ar 3d104s24p3. In thealculation of pseudopotential, the inner-cell configurations forl (1s22s22p6), and As (1s22s22p63s23p63d10) have been distin-uished from the valence electrons of Al (3s23p1) and As (4s24p3)

hells, respectively. The Perdew Zunger (PZ) type parameterizedocal density approximation (LDA) exchange correlation functionalLDA-PZ) [41], Perdew, Burke and Ernzerhof (PBE) [42] type param-terized generalized gradient approximation (GGA-PBE) and Zhangnd Yang revised PBE (rev PBE) [43,44] type GGA have been used

Fig. 1. Energy vs volume curve for B3, B8, B1 and B2 type phases of AlAs.

for the present computations. In self-consistent manner, the calcu-lation is performed using steepest descent geometric optimizationtechnique with Pulay algorithm [45] for iteration mixing. The meshcut-off is taken as 150Ryd with a k-mesh of 5 × 5 × 5. LDA-PZ typepotential computes total energy much lower than that of GGA-revPBE and GGA-PBE approaches. The total energy for original B3type AlAs using LDA-PZ potential is −469.39 eV and with GGA revPBE potential −324.49 eV, which indicates that LDA-PZ potential, isquite good for the calculation of energies of AlAs in different struc-tural phases like B3, B1, B2 and B8. To get better understanding offundamental physics associated with different phases of AlAs, theFermi energies, binding energies and band energies have also beencomputed using LDA-PZ potential and given in Table 3.

Classical understanding on the phase stability of solids sug-gests that as the pressure is applied, a particular phase of the solidbecomes unstable and causes a change in the density and the vol-ume, which in turn leads to the overlapping of the electron shells(charge transfer mechanism) and thus the phase transition takesplace. Under the application of pressure, the B3 type III–V semi-conductors are expected to transform into the NaCl (B1) structureand there is possibility of some intermediate NiAs (B8) type phaseand further increase in pressure may cause stability of CsCl (B2)type structure. The stability of the phase of the solid can be definedin terms of its Gibbs free energy (G = U + PV − TS). This free energyat T = 0 K corresponds to the cohesive energy due to the mutualinteraction of the ions. S is the vibrational entropy at absolute tem-perature T and V is the volume of the unit cell at pressure P.

3. Results and discussions

3.1. Energy vs volume (E–V) curve, lattice parameter and bulkmodulus

To test the stability of various phases of AlAs, like B3, B8, B1and B2 under the ambient condition as well as under compres-sion, the calculated total energies have been plotted as a functionof volume in Fig. 1. In ambient condition B3 structure has beenfound to be with minimum energy and same under compressionfirst stabilizes in B8 type, then B1 and finally to the CsCl (B2) typewith the lowest energy. The positive lattice energy difference of thetwo competitive structures at zero pressure very well explains the

relative stability criterion given by Sangster et al. [46]. The latticeparameter corresponding to minima of the E–V curves correspondsto zero pressure, termed as the equilibrium or theoretical latticeconstant.

68 A. Srivastava et al. / Materials Chemistry and Physics 125 (2011) 66–71

Table 1The lattice constants (a), bulk modulus B0 and its pressure derivative B′

0 calculated using LDA scheme for AlAs.

Material Lattice constant a (in Å) B0 (GPa) B′0

PWa Exp. Others PWa Exp. Others PWa Exp. Others

AlAs-B3 5.64 (LDA)5.72 (GGA-PBE)5.77 (GGArevPBE)

5.66 [18,48] 5.61 [4]5.63 [7]5.65 [49]

76.41 82.0 [50] 74.40 [4]77.09 [49]64.5 [25]

4.16 5.0 ± 1 [18]10.7 ± 1.4 [19]

4.18 [4]4.53 [49]3.88 [25]

AlAs-B8 3.72(LDA) 3.79 [18] 3.77 [28]3.72 [32]

56.0 73.0 ± 7 [18]101 ± 26 [19]

84.9 [25]93.3 [32]

4.86 4.6 ± 0.7 [18]4.0 [19]

4.29 [25]4.58 [32]

AlAs-B1 5.24 (LDA) – 5.31 [28]5.22 [32]5.19 [15]

96.60 – 79.8 [25]91.5 [32]

5.51 – 4.68 [25]4.3 [32]

–

barTmtBtAtrce

pntbcHtv

3

wpeuwatcbsttA

TP

AlAs-B2 3.22(LDA) – 4.97 [52]3.56 [51]

78.53

a PW: present work.

In our observations, the equilibrium lattice constant 5.64 A haseen computed using LDA-PZ scheme and is found to be lowers compared to those revealed from GGA-PBE (5.72 A) and GGA-evPBE (5.77 A) approaches for the original B3 type phase of AlAs.he calculated lattice parameter for B3 type phase is in close agree-ent with the reported experimental value 5.66 A [18,48] and other

heoretical values [4,7,49]. Similarly the lattice parameters for B1,8 and B2 type phases have also been in close match with the otherheoretical as well as experimental values. The stability analysis oflAs in B8 type phase, corresponds to the c/a ratio of 1.59 A, where

he equilibrium lattice parameters a and c are 3.72 A and 5.91 A,espectively. The c/a ratio, and individual lattice parameters a andare in close agreement with their theoretical [25,32] as well asxperimental [18] counterparts as shown in Table 1.

The bulk modulus and its pressure derivative in all the testedhases B3, B8, B1 and B2 type have been computed using Mur-aghan equation of state [47] and their values are compared withheir experimental and theoretical counterparts. The computedulk modulus B0 for B3, B8, B1 and B2 type phases has also beenalculated and are in good agreement with the reported values.owever in the case of B8 type phase B0 is comparatively less and

he pressure derivative B′0 is slightly higher than the other reported

alues in Table 1.

.2. High pressure phase transition

In order to study the high pressure phase transition in AlAs,e have obtained converged values in B3, B1, B2 and B8 typehases. These values have been utilized to determine the totalnergy at different lattice parameters and plots of energy vs vol-me for all the tested phases (B3, B8, B1 and B2) as shown in Fig. 1,here, total energies correspond to each phase have been plotted

s a function of volume and by drawing tangent of E–V curves ofwo competitive structure, the transition pressure has been cal-ulated. Another method of calculation of transition pressure is

y observing the crossover of free energies of two competitivetructures as a function of pressure. It is clear from the E–V curvehat under the ambient condition, AlAs crystallizes in B3 struc-ure. Under the application of pressure original B3 type phase oflAs first transforms to NiAs (B8) type phase at around 6.61 GPa

able 2hase transition pressure in AlAs.

Phase transition pressure (GPa)

Transition type PW Exp

B3 → B8 6.99 7 ± 5 [18], 14B3 → B1 8.18 –B3 → B2 73.43 –

– 6.03 – –

and further compression leads to the B1 phase stable at around8.18 GPa and finally the most stable hypothetical CsCl (B2) typephase at around 73.43 GPa. The computed values of transition pres-sure are in good agreement with their experimental [18,19] aswell as theoretical [25,28,31,32,51,52] counterpart and comparedin Table 2.

3.3. Band structure and density of state (DOS)

In order to have more insight towards understanding the changein behavior of the material from one particular type of phase toanother under the influence of pressure, the electronic propertieshave been studied. In the electronic properties, the band structureand density of state for AlAs have been analyzed at the theoreticalequilibrium lattice constants in all the stable phases obtained inthe present study. For the B3 type phase, band structure has beencomputed with GGA-revPBE, GGA-PBE and LDA-PZ exchange corre-lation functional approaches. In Fig. 2(a), it is seen that the variousbands have prominent maxima at the central point � and min-ima at the point X of the Brillouin zone. AlAs is an indirect band gapsemiconductor because the top of the valence band and the bottomof the conduction band are not at the same center point (� ) in theBrillouin zone. Using LDA-PZ, GGA-PBE and GGA-revPBE exchangecorrelation functional, the study computes the indirect band gap(Eg) of AlAs as 1.33 eV, 1.53 eV and 1.65 eV respectively. The bandbelow the � 7,8 point constitutes the valence band and those abovethe point X6 form the conduction band. The band structure alsoshows a direct gap of around 2.28 eV at point � 7,8 in valence bandto � 6 in conduction band, hence, X6 is the lowest energy point ofthe conduction band and � 7,8 is the highest point of the valenceband. At room temperature, the gap is sufficiently small so that fewelectrons are thermally excited from the valence band to the con-duction band and few excited electrons gather in the region of theconduction band immediately above its minimum at X6, a regionthat is termed as “Valley”. In Fig. 2(b), the valence band is crossing

the Fermi level at the point � 6,7,8 and conduction band is com-ing below the Fermi level at the point X6 that clearly indicates B1type phase of AlAs is metallic in nature. In Fig. 2(c), the valenceband is crossing the Fermi level between the points � and X, whilethe conduction band is coming below the Fermi level at the point

Others

.2 [19] 5.34 [25], 6.1 [32], 7.12 [31], 9.15 [31]6.24 [25], 7.4 [32], 8.25 [31], 11.88 [31], 7.5 [28]77.9 [51], 76.8 [52]

A. Srivastava et al. / Materials Chemistry and Physics 125 (2011) 66–71 69

F r B1 ts

�IpTattoTth

TB

ig. 2. (a) Band structure plot for B3 type phase of AlAs, (b) band structure plot fotructure plot for B8 type phase of AlAs.

6 that shows again the metallic nature in case of B2 type phase.n Fig. 2(d), the valence bands are crossing the Fermi level at theoint � 8 and the conduction band is also touching the Fermi level.his shows that alike B1 and B2 phases, B8 type phase of AlAs islso metallic. Due to compression, the change of material charac-eristics from semiconductor to metallic can be seen very well fromheir band structure, DOS plots and through the numerical values

f band gap, Fermi energy and band energy as reported in Table 3.he computed values of indirect band gaps of AlAs are compara-ively less than the experimental value and other reported values;owever, it is close to some reported values.

able 3and gap (Eg), Fermi energy and band energy for AlAs.

Material Bandgap Eg(eV)

PWa Exp. Othe

AlAs-B3 1.33(I)[LDA]1.53(I) [GGA]1.65(I)[GGArev]1.88[GGArev]1.72[GGA]2.28[LDA]

2.16 [48] 2.051.842.18

AlAs-B8 – – –AlAs-B1 – – –AlAs-B2 – – –

a PW: present work.

ype phase of AlAs, (c) band structure plot for B2 type phase of AlAs, and (d) band

The densities of states for all the four tested phases (B3, B1, B2and B8) have been shown in Fig. 3(a)–(d). For B3 type phase of AlAs,the nature of peaks is shown in Fig. 3(a), where one can notice thatthere is a band gap at the Fermi level. In this phase, the highestmagnitude peak appears in the conduction band region at around2.44 eV. The DOS for B1 type phase of AlAs is shown in Fig. 3(b),there appears one prominent peak near −1.72 eV and two peaks

in the conduction band region among which the highest peak isaround 4.92 eV. The DOS for B2 type phase of AlAs is depicted inFig. 3(c), where there is no prominent peak in the valence bandregion but there are two peaks in the conduction band region out

Fermi energy (eV) Band energy (eV)

rs

[4], 2.36 [49],[9], 1.29 [5],[5], 1.56 [10]

3.92 (LDA) −76.37 (LDA)

−3.94 (LDA) −80.42 (LDA)−4.35 (LDA) −77.15 (LDA)−3.77 (LDA) −76.62 (LDA)

70 A. Srivastava et al. / Materials Chemistry and Physics 125 (2011) 66–71

F r B1 tyo

oBtwo4

4

pecanolottct

ig. 3. (a) Density of state plot for B3 type phase of AlAs, (b) density of state plot fof state plot for B8 type phase of AlAs.

f which one is at 2.8 eV and the second one is near 4.24 eV. For8 type phase of AlAs, we have shown DOS in Fig. 3(d). There arehree prominent peaks appearing in the valence band region out ofhich the highest peak appears around −4.72 eV and also there is

ne peak in the conduction band region which is occurring around.48 eV.

. Conclusion

The present first-principle study computes the pressure inducedhase transitions, band structure, density of states, lattice param-ter and bulk modulus of AlAs, using the LDA-PZ exchangeorrelation scheme. It is clearly noted from the band structure plotss well as the density of states that the original semiconductingature of AlAs in B3 type phase has been transformed to a metallicne in B1, B8 and B2 type phases due to compression. The calcu-ated bulk modulus for all the tested phases of AlAs compared with

ther reported values shows a close match, except in case of B8ype phase, where bulk modulus is less and its pressure deriva-ive is slightly higher to their experimental as well as theoreticalounterparts. As not much information is available about the B3–B2ransition, bulk modulus and pressure derivative in B2 type phase,

[[[[

pe phase of AlAs, (c) density of state plot for B2 type phase of AlAs, and (d) density

the present result will certainly serve as a guide to the investigatorsin future.

Acknowledgments

The authors are thankful to ABV-Indian Institute of Informa-tion Technology and Management, Gwalior for the financial supportprovided to the work as the Faculty initiation grant.

References

[1] O. Berolo, J.C. Woolley, J.A. Van Vechten, Phys. Rev. B 8 (1973) 3794.[2] S. Kalvoda, B. Paulus, P. Fulde, H. Stoll, Phys. Rev. B 55 (1997) 4027.[3] G. Klimeck, R.C. Bowen, T.B. Boykin, T.A. Cwik, Superlatt. Microstruct. 27 (2000)

519.[4] S.Q. Wang, H.Q. Ye, Phys. Rev. B 66 (2002) 235111.[5] K.A. Johnson, N.W. Ashcroft, Phys. Rev. B 58 (1998) 15548.[6] M.D. Ventra, P. Fernández, Phys. Rev. B 56 (1997) R12698.[7] S.Zh. Karazhanov, L.C.L.Y. Voon, Fiz. Tekh. Poluprovodn. 39 (2) (2005) 177.

[8] C.B. Geller, W. Wolf, S. Picozzi, et al., Appl. Phys. Lett. 79 (2001) 368.[9] S.H. Wei, A. Zunger, Phys. Rev. B 39 (1989) 3279.10] R.W. Jansen, O.F. Sankey, Phys. Rev. B 36 (1987) 6520.11] W.Y. Ching, M.-Z. Huang, Phys. Rev. B 47 (1993) 9479.12] J.-Q. Wang, Z.-Q. Gu, M.-F. Li, W.-Y. Lai, Phys. Rev. B 46 (1992) 12358.13] M.-Z. Huang, W.Y. Ching, Phys. Rev. B 47 (1993) 9449.

emistr

[

[[

[[[

[[[[[[[[[[[

[[[[

[

[[

[[[

[[[[[[[[

[[50] Londolt-Bornshtein, Numerical Data and Functional Relationships in Science

and Technology. New Series. Group III: Crystal and Solid State Physics. Semicon-

A. Srivastava et al. / Materials Ch

14] J.C. Phillips, Bonds and Bands in Semiconductors, Academic Press, San Diego,1973.

15] S. Froyen, M.L. Cohen, Phys. Rev. B 28 (1983) 3258.16] R.M. Martin, in: O. Engstrom (Ed.), Eighteenth International Conference on the

Physics of Semiconductors, Stockholm, Sweden, 1986, World Scientific, Singa-pore, 1987, p. 639.

17] B.A. Weinstein, S.K. Hark, R.D. Burnham, et al., Phys. Rev. Lett. 58 (1987) 781.18] R.G. Greene, H. Luov, T. Li, A.L. Ruoff, Phys. Rev. Lett. 72 (1994) 2045.19] A. Onodera, M. Mimasaka, I. Sakamoto, et al., J. Phys. Chem. Solids 60 (1999)

167.20] M.T. Yin, M.L. Cohen, Phys. Rev. B 24 (1981) 6121.21] M.L. Cohen, S.G. Louie, Annu. Rev. Phys. Chem. 35 (1984) 537.22] A. Mujica, A. Rubio, A. Munoz, R.J. Needs, Rev. Mod. Phys. 75 (2003) 863.23] K. Kim, P.R.C. Kent, A. Zunger, C.B. Geller, Phys. Rev. B 66 (2002) 045208.24] W.E. Pickett, Comput. Phys. Rep. 9 (1989) 117.25] H.-Y. Wang, X.-S. Li, C.-Y. Li, K.-F. Wang, Mater. Chem. Phys. 117 (2009) 373.26] R.K. Singh, Phys. Rep. (Netherlands) 85 (1982) 259.27] R.K. Singh, S. Singh, Phys. Rev. B 45 (1992) 1019.28] D. Varshney, G. Joshi, N. Kaurav, R.K. Singh, J. Phys. Chem. Solids 70 (2009) 451.29] A. Srivastava, R.K. Singh, Phase Transit. 77 (2004) 397.30] A. Srivastava, R.K. Singh, R. Ahuja, B. Johansson, Phys. Stat. Sol. (b) 237 (2003)

448.31] J. Cai, N. Chen, Phys. Rev. B 75 (2007) 174116.32] G.C. Liu, Z.W. Lu, B.M. Klein, Phys. Rev. B 51 (1995) 5678.33] Atomistix ToolKit version x.x, QuantumWise A/S (www.quantumwise.com).34] M. Brandbyge, J.-L. Mozos, P. Ordejon, J. Taylor, K. Stokbro, Phys. Rev. B 65 (2002)

165401.

[[

y and Physics 125 (2011) 66–71 71

35] K. Stokbro, J. Taylor, M. Brandbyge, P. Ordejon, Ann. N.Y. Acad. Sci. 1006 (2003)212.

36] J. Taylor, H. Guo, J. Wang, Phys. Rev. B 63 (2001) 245407.37] J.M. Soler, E. Artacho, J.D. Gale, A. Garcia, J. Junquera, P. Ordejon, D. Sanchez-

Portal, J. Phys.: Condens. Matter 14 (2002) 2745.38] Z. Hou, M. Yee, 7th IEEE Conference on Nanotechnology, 2007, p. 554.39] F.-P. OuYang, H. Xu, M.-J. Li, J. Xiao, Acta Phys. Chim. Sin. 24 (2008) 328.40] M.-F. Ng, L. Zhou, S.-W. Yang, L.Y. Sim, V.B.C. Tan, P. Wu, Phys. Rev. B 76 (2007)

155435.41] J.P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048.42] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865.43] Y. Zhang, W. Yang, Phys. Rev. Lett. 80 (1998) 890.44] B. Hammer, L.B. Hansen, J.K. Norskov, Phys. Rev. B 59 (1999) 7413.45] P. Pulay, Chem. Phys. Lett. 73 (1980) 393.46] M.J.L. Sangster, U. Schroder, R.M. Atwood, J. Phys. C11 (1978) 1523.47] F.D. Murnaghan, Proc. Natl. Acad. Sci. U.S.A. 30 (1944) 244.48] S.M. Sze, Physics of Semiconductor Device, Wiley Interscience Publication, New

York, 1981, pp. 848–849.49] D.V. Khanin, S.E. Kul’kova, Russ. Phys. J. 48 (2005) 70.

ductors. Physics of Group IV Elements and III–V Compounds, vol. 22, SpringerVerlag, Berlin, 1987.

51] A. Mujica, R.J. Needs, A. Munoz, Phys. Rev. B 52 (1995) 8881.52] D.C. Gupta, S. Kulshrestha, Phase Transit. 82 (2009) 850.