Pseudopotential calculations of AlSb under pressure

Accepted Manuscript Pseudopotential calculations of AlSb under pressure

H. Algarni, O.A. Al-Hagan, N. Bouarissa, M.A. Khan, T.F. Alhuwaymel PII: DOI: Reference:

S1386-1425(17)30748-5 doi: 10.1016/j.saa.2017.09.029 SAA 15463

To appear in:

Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy

Received date: Revised date: Accepted date:

7 July 2017 19 August 2017 12 September 2017

Please cite this article as: H. Algarni, O.A. Al-Hagan, N. Bouarissa, M.A. Khan, T.F. Alhuwaymel , Pseudopotential calculations of AlSb under pressure, Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy (2017), doi: 10.1016/j.saa.2017.09.029

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ACCEPTED MANUSCRIPT Pseudopotential calculations of AlSb under pressure H. Algarni1,2, O. A. Al-Hagan1, N. Bouarissa3,*, M. A. Khan1, T. F. Alhuwaymel4 1

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Research Center for Advanced Materials Science (RCAMS), King Khalid University, P. O. Box 9004, Abha 61413, Saudi Arabia

Laboratory of Materials Physics and Its Applications, University of M'sila, 28000 M'sila, Algeria National Centre for Nanotechnology, King Abdulaziz City for Science and Technology (KACST), P. O. Box 6086, Riyadh 11442, Saudi Arabia

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Department of Physics, Faculty of Science, King Khalid University, P. O. Box 9004, Abha 61413, Saudi Arabia

Abstract

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The dependence on hydrostatic pressure of the electronic and optical properties of zinc-blende AlSb semiconducting material in the pressure range of 0-20 kbar has been

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reported using a pseudopotential approach. At zero pressure, our findings showed that the electron and heavy hole effective masses are 0.11 and 0.38 m0, respectively. Moreover, our

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results yielded values of 3.3289 and 11.08 for refractive index and high frequency

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dielectric constant, respectively. These results are found to be in good accord with experiment. Upon compression, all physical parameters of interest showed a monotonic

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behavior. The pressure-induced energy shifts for the optical transition related to band-gaps indicated that AlSb remains an indirect (Г-X) band-gap semiconductor at pressures from 0

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to 20 kbar. The trend in all features of interest versus pressure has been presented and discussed. It is found that the lattice parameter is reduced from 0.61355 to 0.60705 nm when pressure is raised from 0 to 20 kbar. The present investigation may be useful for midinfrared lasers applications, detectors and communication devices.

Keywords: Pressure; Electronic structure; Optical properties; AlSb; Pseudopotentials.

* Corresponding author. [email protected]

ACCEPTED MANUSCRIPT 1. Introduction Aluminum antimonide (AlSb) is an indirect band-gap semiconductor of the group III-V family that is formed from aluminum and antimony. It is an environment-friendly material [1,2]. The reserves of both aluminum and antimony are very rich in the earth [3]. The material of interest has found applications in many technological area. It is a good

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candidate for high-speed and low-power electronic devices [4]. It has also been considered

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as one of the most promising materials for photovoltaic applications [3,5] where it can be

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used to emit and convert light energy efficiently and as optical filters, lenses, mirrors, etc [6]. Besides, AlSb crystal finds applications in light emitting diodes, detectors, lasers, and

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communication devices [6].

At ambient pressure AlSb crystallizes in the zinc-blende structure [7,8]. Applied

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pressure leads to the decrease of the volume of the material under load, and hence to the transformation of its structure to what was assumed the ß-tin structure. The latter coexists

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with the zinc-blende structure between about 7 and 10 GPa [9]. As a matter of fact,

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pressure is an attractive thermodynamic variable that gives the possibility of studying the change in the fundamental properties of materials as inter-atomic distances are varied in a

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systematic way [10-16].

In this regard, previous efforts have been made by Bouarissa [10,13,14] in order to

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study the hydrostatic pressure effect on direct-band gap compound semiconductors. However, these efforts did not include the indirect band gap compound AlSb. This has inspired us to carry out such a calculation on AlSb. On the experimental side, although very recent studies on the structural, electrical, electronic and optical properties of AlSb thin films have been reported using different techniques [17-19], the investigation of highpressure on AlSb semiconducting material seems to be limited. This is probably due to its hygroscopicity and the consequent sample-handling problems. In this respect, the present

ACCEPTED MANUSCRIPT contribution deals with the pressure effect on some fundamental properties of zinc-blende AlSb. The aim of the present work is to show to what extent the hydrostatic pressure effect can influence the electronic structure and optical properties of AlSb and to offer opportunities to gain a deeper understanding of the relevant physical parameters of AlSb occurring under compression. Thus, electronic and optical band parameters have been

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computed and their pressure dependence has been examined and discussed using a

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pseudopotential approach. The results are compared where possible with experiment and

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showed generally reasonably good accord. The knowledge of these basic properties can be

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exploited in device applications.

2. Computational details

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All the calculations performed in the present contribution are mainly based on the empirical pseudopotential method (EPM). More details about the EPM can be found in the

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book by Martin [20]. The method was developed so as to solve Schrödinger equation for

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crystals without the exact knowledge of the potential experienced by an electron in the lattice. This is a many body problem in the calculation of the electronic band structure. In

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the EPM, the potential is a Fourier expanded in plane waves and hence an eigenvalue equation can be established in order to determine a relationship between the electron

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energy E and its wave vector k. The Fourier coefficients for the potentials are determined empirically by fitting the calculated inter-band optical transition energies at certain selected points in the Brillouin zone to known measurements. In the present paper, the experimental band-gap energies at the high-symmetry points Г, X and L in the Brillouin zone fixed in the fits for AlSb at zero pressure are given in Table 1. The empirical pseudopotential parameters are optimized using a non-linear least-squares method as reported in Refs. [22,23]. To achieve convergence, 136 plane waves are considered.

ACCEPTED MANUSCRIPT For pressures greater than zero, the first-order pressure coefficients of Г, X and L band-gap energies are fitted to those quoted in Ref. [24] in order to determine the pseudopotential form factors. The lattice parameter at pressures other than zero has been calculated using the Murnaghan equation of state. The equilibrium bulk modulus (B0) and its first pressure derivative (B0' ) are taken to be 5.82  1011 dyn/cm2 and 4.55 [25]. Table 2

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lists the final adjusted pseudopotential form factors of AlSb at various pressures in the

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range 0-20 kbar.

3. Results and discussion

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The variation in the lattice parameter as a function of pressure for AlSb is displayed in Fig.1. Note that for the zinc-blende phase, the lattice parameter of AlSb is reduced from

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0.61355 to 0.60705 nm when the hydrostatic pressure is increased from 0 to 20 kbar. The increase of pressure leads to more cloud overlap of electrons and hence to an increase of

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the charge transfer from Al to Sb reducing thus the bond length and decreasing the lattice

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parameter.

Fig.2 shows the pressure dependence of the optical transitions related to the direct

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(Г-Г) and indirect (Г-X) and (Г-L) band-gap energies for AlSb in the zinc-blende structure. We observe that the direct energy band-gap (Г-Г) and the indirect (Г-L) one increase with

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increasing pressure up to 20 kbar. This behavior is commonly reported for tetrahedral binary semiconductors [26,27]. However, this is not the case for the indirect (Г-X) bandgap which decreases with raising pressure. This can be attributed to the fact that under compression there is an electron transfer from the minimum of the conduction band at Г high-symmetry point in the Brillouin zone to the minimum of the conduction band at X point. One may also note the absence of crossing between the indirect band-gap (Г-X) curve and the curves representing the direct (Г-Г) and indirect (Г-L) band-gap energies.

ACCEPTED MANUSCRIPT This indicates that the material of interest remains an indirect (Г-X) band-gap semiconductor within a whole range of the pressure being considered in this work. The effective mass of charge carriers is an important parameter for the description of the carrier transport properties in semiconducting materials [28]. For that purpose, the electron and heavy-hole effective masses in AlSb have been calculated using the same

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procedure as that used by Bouarissa [29]. Based on the results of the band structure

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calculation of AlSb, the electron effective mass (me*) is determined at the Г high-symmetry point in the Brillouin zone for the lowest conduction band, whereas the heavy-hole

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effective mass (mhh*) is obtained at the Г for the highest valence band. Our findings at zero

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pressure showed that the values of me*and mhh* in zinc-blende AlSb are 0.11 and 0.38 (in units of the electron free-particle mass m0). These results agree reasonably well with the

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experimental ones of me*(AlSb) = 0.121 and mhh*(AlSb) = 0.5 reported in Ref. [30]. The variation in the electron and heavy-hole effective masses as a function of

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hydrostatic pressure for AlSb is plotted in Figs. 3 and 4, respectively. Note that when the

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zinc-blende AlSb is compressed at pressures ranging from 0 to 20 kbar, the me* and mhh* increase from 0.11 to 0.123 and from 0.38 to 0.43 (in units of m0), respectively. The

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behavior is monotonic for both band parameters of interest. In fact, as pressure is applied, the volume decreases, and hence the inter-atomic spacing of the atoms in the fourfold-

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coordinated structure will be reduced (more closely packed atoms), leading thus to a stronger interaction between the charge carrier and the lattice as compared to that at zero pressure. This of course increases the charge carrier effective masses. Qualitatively, the same trend has been reported for me* in rocksalt YN when pressure is applied [31]. The increase of me* and mhh* with increasing pressure contribute in the decrease of the mobility of the electrons and heavy-holes in the material of interest when the latter is compressed.

ACCEPTED MANUSCRIPT The hydrostatic pressure dependence of the valence band width (VBW) for zincblende AlSb is shown in Fig.5. It can be noticed from Fig.5 that the VBW increases continuously with increasing pressure from 0 to 20 kbar. The same qualitative behavior has been generally reported for tetrahedral binary semiconductors under hydrostatic pressure [32,33]. According to Benmakhlouf et al. [32], this can be traced back to the increase of

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the overlaps with neighboring orbitals. As a matter of fact, applied pressure affects both the

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valence and conduction bands of the material of interest which is a semiconductor at zero

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pressure. This will affect the strong sp3 covalent bonds that exist at zero pressure resulting in less semiconductor-like material which has tendency to a metallic character as pressure

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is further increased.

Another interesting fundamental property of semiconducting materials is the

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refractive index ( n ). The latter describes the propagation of light through the material medium. In the present paper, n has been calculated at zero pressure using the Reddy and

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Ahammed model [34],

Eg

(1)

is taken to be the fundamental band-gap energy. The model has been preferred

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where

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 4 154  n  E  0.365  g  

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to other models existing in the literature because it has already proved to give the best accord with experiment for AlSb at zero pressure compared to other models [35]. At zero pressure, our results yielded a value of n = 3.3289. The discrepancy between this value and the experimental one of 3.2327 reported in [36] is within 3%. Very recently, Elkenany [8] has calculated n of AlSb at different temperatures using the Moss model. His results provided a value for n of 2.8660 at a temperature of 300 K. This value seems to be underestimated with respect to that of 3.3289 determined in the present calculations (the

ACCEPTED MANUSCRIPT deviation between the two values is within 17%). This discrepancy is essentially due to the difference in the two models used for the calculation of n . Upon compression, the variation of n versus pressure is assumed to be linear with

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1 dn 6 10 / bar n dp = - 0.33 [24]. Thus, n has been determined at various pressures ranging

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from 0 to 20 kbar. The variation in n as a function of pressure for AlSb is displayed in Fig.6. Note that n decreases continuously with increasing pressure on going from 0 to 20

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kbar. The behaviour of n versus hydrostatic pressure is attributed to the reduction of the

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electronic polarizability of the material of interest under pressure.

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The dielectric constant is another important physical parameter that may serve in the measurement of the ability of a substance to insulate charges from each other. In this

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work, the high-frequency dielectric constant (   ) is calculated using the relation,

   n2

(2)

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The value of   at zero pressure as determined by the present work is 11.08. This value agrees to within 12% with the experimental one of 9.88 reported in Ref. [25]. Nevertheless, a comparison between our obtained value and that of 8.2140 calculated by Elkenany [8] for

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AlSb at a temperature of 300 K shows a large discrepancy (about 35%). Once again this

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deviation is attributed to the fact that the model employed by Elkenany for calculating n and hence   is different from that used in the present work. The dependence on hydrostatic pressure of the   of zinc-blende AlSb is shown in Fig.7. We observe that   decreases monotonically with increasing pressure. This is a common behaviour of   versus pressure in most tetrahedral semiconductors [37]. The effect of pressure on   seems to be useful in this case. It decreases   . As a matter of fact, a high value of the dielectric constant is not necessarily desirable. Generally, when

ACCEPTED MANUSCRIPT subjected to intense electric fields, materials with large dielectric constants break down more easily than those with low dielectric constants.

4. Conclusion In summary, a pseudopotential approach was used to perform calculations on

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dependence on hydrostatic pressure of the lattice parameter, energy band-gaps, electron

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and heavy-hole effective masses, valence band width, refractive index and dielectric

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constant of zinc-blende AlSb. At zero pressure, our results regarding the electron and heavy hole effective masses were found to be 0.11 and 0.38 m0, respectively. These values

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agree well with the experimental results reported in the literature. In addition, the refractive index and the high-frequency dielectric constant yielded values of 3.3289 and 11.08,

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respectively. These findings agree with experiment to within 3% and 12%, respectively. All fundamental physical parameters of interest showed a monotonic behavior with

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increasing pressure up to 20 kbar. The lattice parameter was found to decrease from

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0.61355 to 0.60705 nm when applied pressure is increased from 0 to 20 kbar. The optical transition related to the direct and indirect band gaps under pressure effect indicated that

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the material under study remains an indirect (Г-X) band-gap semiconductor at pressures in the whole range 0-20 kbar. In this pressure range, the electron and heavy-hole effective

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masses were found to increase from 0.11 to 0.123 m0 and from 0.38 to 0.43 m0, respectively. The trend in these physical quantities as a function of pressure suggested that the mobility of the charge carriers in AlSb decreases under pressure. The decrease of the refractive index and high-frequency dielectric constant with increasing pressure in the material in question was discussed.

ACCEPTED MANUSCRIPT Acknowledgements The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through research groups program under grant

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number R.G.P. 2/4/38.

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ACCEPTED MANUSCRIPT [32] F. Benmakhlouf, A. Bechiri, N. Bouarissa, Zinc-blende ZnS under pressure: predicted electronic properties, Solid-State Electron. 47 (2003) 1335-1338 [33] M. Boucenna, N. Bouarissa, Predicted electronic properties of GaAs under hydrostatic pressure, Mater. Chem. Phys. 84 (2004) 375-379 [34] R. R. Reddy, Y. N. Ahammed, A study on the Moss relation, Infrared Phys. Technol.

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[35] M. S. Al-Assiri, N. Bouarissa, Electronic band structure and derived properties of

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[37] A. R. Goñi, K. Syassen, 1998, Optical properties of semiconductors under pressure (review), Semiconductors and Semimetals, vol.54, ed. T. Suskiy and W. Paul (New York:

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Academic) pp.247-425

ACCEPTED MANUSCRIPT Figure captions Fig. 1. Lattice parameter in AlSb versus pressure. Fig. 2. Direct (Г-Г) and indirect (Г-X) and (Г-L) band-gap energies in AlSb versus pressure.

Fig. 4. Heavy-hole effective mass in AlSb versus pressure.

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Fig. 5. Valence band width in AlSb versus pressure.

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Fig. 3. Electron effective mass at Г point in AlSb versus pressure.

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Fig.6. Refractive index in AlSb versus pressure.

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Fig.7. High-frequency dielectric constant in AlSb versus pressure.

ACCEPTED MANUSCRIPT Table 1. Experimental band-gap energies [21] for AlSb fixed in the fits at zero pressure. EГ-X (eV)

EГ-L (eV)

2.30

1.615

2.211

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EГ-Г (eV)

ACCEPTED MANUSCRIPT Table 2. Pseudopotential parameters for zinc-blende AlSb at pressures (p) in the range 0-

P=0 kbar

P=5 kbar

P=10 kbar

P=15 kbar

P=20 kbar

VS(3)

-0.225597

-0.223732

-0.221471

-0.219438

-0.217605

VS(8)

0.028086

0.025325

0.021853

0.018512

0.015273

VS(11)

0.062230

0.065721

0.069888

0.073990

0.078050

VA(3)

0.007109

0.007109

0.007109

0.007109

0.007109

VA(4)

0.058960

0.058960

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20 kbar. Pseudopotential

0.058960

0.058960

0.058960

VA(11)

0.004544

0.004544

0.004544

0.004544

0.004544

form factors

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(Ry)

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AlSb

0.612

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0.610

0.608

0.606 0

5

10

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Lattice parameter (nm)

0.614

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Pressure (kbar)

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Figure 1.

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2.6

2.2

 X -L

1.8

1.4 0

5

10

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1.6

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Pressure (kbar)

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Figure 2.

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AlSb

2.0

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Band gap energy (eV)

2.4

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0.120

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0.116

AlSb

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0.112

0.108 0

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Electron effective mass (m0 units)

0.124

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Pressure (kbar)

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Figure 3.

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0.43

AlSb 0.42

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0.41

0.40

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0.39

0.38

0.37 0

5

10

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Heavy hole effective mass (m0 units)

0.44

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Pressure (kbar)

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Figure 4.

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9.90

AlSb

9.86

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9.84

9.82

9.80

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Valence band width (eV)

9.88

9.76 0

5

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9.78

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Pressure (kbar)

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Figure 5.

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3.330

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3.320

3.315

AlSb

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3.310

3.305 0

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Refractive index

3.325

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Pressure (kbar)

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Figure 6.

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11.08

AlSb

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11.04

11.00

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10.96

10.92 0

5

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High-frequency dielectric constant

11.12

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Pressure (kbar)

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Figure 7.

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ACCEPTED MANUSCRIPT Graphical abstract

2.6

2.2

AlSb

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 X -L

1.8

1.4 0

5

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1.6

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Pressure (kbar)

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Band gap energy (eV)

2.4

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ACCEPTED MANUSCRIPT Highlights

►Pressure dependence of electronic band structure of AlSb.

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► Refractive index and high-frequency dielectric constant of AlSb under pressure effect.

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► The present investigation may be useful for mid-infrared lasers applications, detectors and communication devices.