Density Functional Approach to study structural and electronic properties of III-Sb semiconductors by modified Becke-Johnson Potential

The First National Conference on Electronics and New Technologies (NCENT’2015)

May 19-20, M'Sila, Algeria

1

Density Functional Approach to study structural and electronic properties of III-Sb semiconductors by

modified Becke-Johnson Potential

Moufdi Hadjab^a,*, Hmza Bennacer ^b, Smail Berrah^c, Hamza Abid ^d and Issam Mohamed Ziane ^d

a Welding and NDT Research Centre (CSC). BP 64, CHERAGA-ALGIERS (Thin films and Applications Unit {UDCMA}, Setif)

b Department of Electronic, faculty of technology, University of Msila, BP 166, 28000 MSILA

c Department of Electronic, faculty of technology, University of A/Rahmen Mira, BEJAIA

d Applied Materials Laboratory, Research Center, University Djillali Liabes, 22000 SIDI BEL ABBES

* [email protected]

Abstract—In this paper, we present the structure and electronic properties of the semiconductors III-Sb binaries, using a first- principles calculations have been performed, using the Full Potential Linearized Augmented Plane Wave (FP-LAPW) calculations based on Density Functional Theory (DFT) [1-2].

The local density approximation (LDA) [3] and the revised Perdew-Burke-Ernzerhof generalized gradient approximation (GGA-PBEsol) [4] were used only in calculating structural properties, the modified Becke–Johnson (mBJ-GGA) approach [5] were used to calculate the electronic properties. Our calculations are in good agreement with the theoretical works and experimental data, deducing the possibility of these materials to be used in the optoelectronics devices.

Keywords-component; FP-LAPW, DFT, mBJ-GGA, wien2k, structural and electronic properties

I. INTRODUCTION

III- Antimonides are semiconductors of great physical interests because of their useful optoelectronic properties. InSb, is particularly interesting for both band structure theory and infrared optoelectronic device applications. GaSb has been mostly studied for its fundamental properties than for technological applications; AlSb is an indirect edge semiconductor, which is particularly interesting for GaAlSb based optoelectronic devices in the 1.3–1.6 mm wavelength range and for the solar energy conversion [6].

In this work we report the results of a study of structural properties, such as lattice parameters a, the bulk modulus B and its first derivate B’, and the electronic properties as the electronic band structure, total and partials densities of states (DOS) of AlSb, GaSb and InSb crystals in zinc-blende at ambient conditions, by the use of full potential linear augmented plane wave (FP-LAPW) within the density functional theory (DFT) as accomplished in the wien2k computer package [7].

II. COMPUTATIONAL DETAILS

To obtain energy eigenvalues convergence, the plane wave expansion with an RMT×KMAX was equal to 9, where RMT is the smallest radii of the muffin-tin spheres and KMAX is the cut- off for the wave function basis. The RMT values were taken to be 2.2 atomic unit (a.u) for Al, Ga, In, and 2.5 for Sb, for AlSb, GaSb and InSb binary compounds. The spherical harmonics inside non-overlapping muffin tin (MT) spheres surrounding the atoms are expanded up to lmax=10, The Fourier-expanded charge density was truncated at Gmax=12 (a.u)^-1. The irreducible wedge of the Brillouin zone was described by a mesh of 47 special k-points, for all binary compounds, Self-consistent calculations are considered to have converged when the total energy of the system is stable within less than 10^-5 Ryd.

Figure 1. Crystal structure of III-Sb (primitive cell).

III. RESULTS AND DISCUSSIONS

A. Structural parameters

The optimum equilibrium structural parameters of III-Sb binaries zinc-blende were obtained by fitting the total energy versus volume to the Murnaghan’s equation of states [8]:

The First National Conference on Electronics and New Technologies (NCENT’2015)

May 19-20, M'Sila, Algeria

2 1 1

1 ) /

( _'

0 0 0 '

0 0 ' 0 0

0 − −







 +

+ −

= B

V B B

V V B

V E B V

E (1)

Where E0 is the equilibrium energy, B0 the bulk modulus, B0’ is the first derivate of B0. We calculated the total energy versus unit cell volume of AlSb, GaSb and InSb binary compounds as exposed in Fig. 1.

The equilibrium volume, the optimum structural constants (a), (B) and (B’), were calculated within de LDA and PBEsol- GGA approximations and compared with the experimental values and other theatrical calculation results, are obtained and listed in Table.1. The analysis of our results shows a very good agreement between our results and other previous theoretical works. We observe from our results that the computed lattice parameter within the LDA is lower than the experimental value by about 0.315 % for AlSb, 0.557% for GaSb and 0.31% for InSb, while the computed values with PBEsol-GGA are 0.484

% larger for AlSb, 0.46 % for GaSb and 0.719 % for InSb, which is owing to the general tendency of these approximations, PBEsol-GGA overestim- ate the lattice constant while the LDA underestimate it. Also, we calculated the bulk modulus (B) and its first derivative (B’), it’s obvious from these that the computed bulk lattice constant obtained from LDA and PBEsol-GGA approximations, are also in good agreement with the available experimental data and other theoretical results.

300 320 340 360 380 400 420 440 460 480

-13446,38 -13446,37 -13446,36 -13446,35 -13446,34 -13440,225 -13440,220 -13440,215 -13440,210 -13440,205 -13440,200 -13440,195

AlSb LDA AlSb PBEsol-GGA

Energy (Ryd)

Volume (a.u)³

300 320 340 360 380 400 420 440 460 480

-16847,01 -16847,00 -16846,99 -16846,98 -16846,97 -16846,96 -16839,045 -16839,040 -16839,035 -16839,030 -16839,025 -16839,020

-16839,015 GaSb LDA

GaSb PBEsol-GGA

Energy (Ryd)

Volume (a.u)³

380 400 420 440 460 480 500 520

-24722,970 -24722,965 -24722,960 -24722,955 -24722,950 -24722,945 -24722,940 -24712,6515 -24712,6478 -24712,6441 -24712,6404 -24712,6367

-24712,6330 InSb LDA

InSb PBEsol-GGA

Energy (Ryd)

Volume (a.u)³

Figure 1. Total energy versus volume using LDA and PBEsol-GGA approximations for AlSb, GaSb and InSb binary compounds.

TABLE I. THE LATTICE CONSTANT , THE BULK MODULUS AND ITS FIRST DERIVATIVE OF III-SB COMPOUNDS COMPARED TO EXPERIMENTAL AND

THEORETICAL DATA.

Compounds Method a(Å) B(GPa) B’

AlSb

Present work FP-LDA 6.1159 56.8368 4.5724

AlSb FP-GGA

(PBEsol)

6.1656 53.1319 4.3408

Experiment 6.1355 [9, 10] 58 [9]

Other Calculations

6.0788 [11]

6.22 [12] 61.0 [12]

6.0863 [13] 58.1 [13] 3.93 [13]

6.0909 [14]

6.09 [15] 56.1 [15]

6.153 [16] 54.3 [16] 4.01 [16]

GaSb

Present work FP-LDA 6.0619 55.5187 4.8878

FP-GGA (PBEsol)

6.1231 51.3727 4.7719

Experiment 6.0959[9, 10] 56 [9]

Other Calculations

5.938 [11]

6.23 [12] 59.0 [12]

6.0327 [14]

5.981 [15] 56.70 [15] 4.662 [15]

6.032 [16] 55.70 [16] 3.830 [16]

5.939 [17] 79.94 [17]

InSb

Present work FP-LDA 6.4586 46.5040 4.8255

FP-GGA (PBEsol)

6.5256 43.1302 4.5738

Experiment 6.479 [9, 10] 46 [9]

Other Calculations

6.2863 [11]

6.56 [12] 50 [12]

6.346 [15] 64.72 [15] 4.688 [15]

6.359 [16] 47 [16] 5.21 [16]

6.346 [17] 47.74 [17]

6.464 [18] 48 [18] 4.5 [18]

The First National Conference on Electronics and New Technologies (NCENT’2015)

May 19-20, M'Sila, Algeria

3 B. Electronic properties

Fig. 2 shows the calculated band structure of III-Sb binary compounds with mBJ-GGA along the high symmetry direction in the Brillouin zone, it is obvious from the figures that GaSb and InSb are direct band-gap, because the top valence and the bottom conduction are situated at Γ-point, for AlSb is indirect band-gap compound.

From Table 2, the results by using LDA, PBEsol-GGA, EV-GGA and mBJ-LDA/GGA approximations, indicate values of the energy band-gap for AlSb, GaSb and InSb. It’s clear that the use of modified Becke-Johnson potential [5] has significantly improved the band-gaps values computed, which are in good agreement with the experimental data) with ordinary PBEsol-GGA approach, for more detail about this approach it’s better to check the ref. 5. In Fig. 3, we plot the total and partial densities of states (TDOS and PDOS) of our III-Sb compounds. Because of the similarity between LDA, PBEsol-GGA, EV-GGA and mBJ-GGA/LDA approximations to investigate the density of states (DOS), we have presented only the DOS obtained with the mBJ-GGA presented in fig. 3, the Fermi level is set to be zero, also, the appearance of three different regions separated from each other by gaps, which are;

low, intermediate and higher band.

To get a profound understanding of the electronic properties of III-Sb compounds, we analyzed the involvement of each atomic character by decomposing the TDOS into the partial contributions of s, p and d orbitals.

TABLE II. THE ENERGY BAND GAP (EG) FOR ALSB,GASB AND INSB

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

AlSb EF

∆ Z

Λ Γ ^{X W K}

L W

Energy (eV)

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

GaSb EF

∆ Z

Λ Γ ^{X W K}

L W

Energy (eV)

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

InSb EF

∆ Z

Λ Γ ^{X W K}

L W

Energy (eV)

Figure 2. Calculated band structure for III-Sb using mBJ-GGA.

Compounds Method Eg(eV) ∆Eg (%) Type of band-gap

AlSb

Present work mBJ-LDA 1.738 7.616 Indirect (Г − ∆_min) mBJ-GGA 1.735 7.43 Indirect (Г − ∆min) LDA 1. 137 -30.15 Indirect (Г − ∆_min) PBEsol-GGA 1.156 9.536 Indirect (Г − ∆_min) EV-GGA 1.755 8.669 Indirect (Г − ∆_min)

Experiment 1.615 [10] Indirect (Г − ∆_min)

Other Calculations 1.67 [15]

1.86 [22]

GaSb

Present work mBJ-LDA 1.036 27,995 Direct (Г− Г) mBJ-GGA 0.844 4,277 Direct (Г− Г) LDA 0 -98,733 Direct (Г− Г) PBEsol-GGA 0 -100 Direct (Г− Г) EV-GGA 0.35 -56,79 Direct (Г− Г)

Experiment 0.81[19] Direct (Г− Г)

Other Calculations 0.547 [15]

0.78 [20]

0.73 [21]

InSb

Present work mBJ-LDA 0.512 113.33 Direct (Г− Г) mBJ-GGA 0.331 29.58 Direct (Г− Г)

LDA 0 -100 Direct (Г− Г)

PBEsol-GGA 0 -100 Direct (Г− Г) EV-GGA 0.04 -83.33 Direct (Г− Г)

Experiment 0.24 [19] Direct (Г− Г)

Other Calculations 0.213 [15]

0.23 [20]

0.26 [21]

The First National Conference on Electronics and New Technologies (NCENT’2015)

May 19-20, M'Sila, Algeria

4

-14 -12-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

0,00 0,34 0,68 1,02 0,00 0,28 0,56 0,84 0 1 2 3 4

EF Sb s

Sb p Sb d

Energy (eV) E_F

Total and Partials Densities of States (electron/eV)

Al s Al p AlSb

E_F AlSb Tot

Al Tot Sb Tot

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

0,00 0,25 0,50 0,75 0,0 0,2 0,4 0,6 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5

EF

Energy (eV)

Sb s Sb p Sb d

EF Ga s

Ga p Ga d

Total and Partials Densities of States (electron/eV)

GaSb ^{GaSb Tot}

Ga Tot Sb Tot EF

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

0,00 0,33 0,66 0,99 0,00 0,16 0,32 0,48 0,00 0,85 1,70 2,55 3,40

EF Sb s

Sb p Sb d

EF In s

In p In d EF InSb

InSb Tot In Tot Sb Tot

Total and Partials Densities of States (electron/eV)

Energy (eV)

Figure 3. Total and partial densities of states for AlSb, GaSb and InSb calculated within mBJ-GGA.

IV. CONCUSION

The purpose of this work is to study the Structural and electronic properties of the cubic Zinc-blende AlSb, GaSb and InSb, using the numerical simulation method based on First Principale calculations. The present calculations gives a new results concerning structural and electronic properties of the binaries compounds.These materials presents a particular interest in the optoelectronic devices area and solar cell.

REFERENCES

[1] P. Hohenberg and W. Kohn, Phys. Rev. B, 136, (1964) 864.

[2] W. Kohn and L. J. Sham, ibid., 140, (1965) A1133.

[3] J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992).

[4] J. P. Perdew, S. Burke and M. Ernzerhof, Phys. Rev. Lett., 77, (1996) 3865.

[5] F. Tran, P. Blaha, Phys. Rev. Lett. 102 (2009) 226401.

[6] A. B. Djurišić, E. H. Li, A. D. Rakić, and M. L. Majewski, Appl. Phys.

A 70, (2000) 29-32.

[7] P. Blaha, K. Schwarz, G. H. Madsen, D. Kvasnicka, J. Luitz, FP- L/APW+lo Program for Calculating Crystal Properties, Techn.

WIEN2K, Austria, 2001.

[8] F. D. Murnaghan, Proc. Nat. Acad. Sci. USA 30, 244 (1944).

[9] K. H. Hellwege and O. Madelung, Landolt-Börnstein New Serie, Group III, Vol. 17a (Springer, Berlin, 1982).

[10] Sadao Adachi, Properties of Group-IV, III–V and II–VI Semiconductors, John Wiley & Sons, England, 2005.

[11] S. Zh. Karazhanov and L. C. Lew Yan Voon, Fizika i Tekhnika Poluprovodnikov, Vol. 39, No. 2, 2005, pp. 177–188.

[12] M. Causà, R. Dovesi and C. Roetti, “Pseudopotential Hartree-Fock Study of Seventeen III-V and IV-IV Semi-conductors,” Physical Review B, Vol. 43, No. 14, 1991, pp. 11937-11943.

[13] P. Rodríguez- Hernández et al.: High Presure Phases of AlSb, phys. Stat.

sol. (b) 198, 455 (1996), pp. 455-459

[14] Paolo Giannozzi and S. de Gironcoli, Ab initio calculation of phonon dispersions in semiconductors, Phys. Rev. B, vol. 43, No. 9, 1990 , pp.

7231-7242

[15] S. Q. Wang and H. Q. Ye, J. Phys. Condens. Matter 14 (2002) 9579–

9587

[16] S. B. Zhang and Marvin L. Cohen, Phys. Rev. B 35, 7604 (1987) [17] S. Kalvoda, B. Paulus, and P. Fulde, Phys. Rev. B 55, 4027 (1997) [18] S. Massidda, A. Continenza, and A. J. Freeman Phys. Rev. B41 12 079

(1990)

[19] C. Kittel, Physique de l’état solide, 7th Ed., New York:John Wiley, 1998, p. 183.

[20] A. Belabbes et al., Electronic bands of III-V semiconductor polytypes and their alignment, Phys. Rev. B 86, 075208 (2012)

[21] Yoon-Suk Kim et al., Towards efficient band structure and effective mass calculations for III-V direct band-gap semiconductors, Phys. Rev.

B 82, 205212 (2010)

[22] I. Topol, Band structure of A1Sb, Czech. J. Phys. B 24 (1974)