Theoretical prediction of the fundamental properties of ternary bismuth tellurohalides

Materials Science in Semiconductor Processing 27 (2014) 605–610

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Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp

Theoretical prediction of the fundamental properties of ternary bismuth tellurohalides Shiyi Zhou a,n, Jianping Long a, Wen Huang b a b

College of Materials and Chemistry & Chemical Engineering, Chengdu University of Technology, Chengdu 610059, P.R. China College of Electronic Engineering, Chongqing University of Post and Telecommunications, Chongqing, 400065, P.R. China

a r t i c l e i n f o

Keywords: Electronic properties Elastic properties Thermodynamic properties Minimum thermal conductivity

abstract The fundamental physics properties of the ternary bismuth tellurohalides (BiTeX (X ¼ Br, I and Cl)) were investigated by using the ultra-soft pseudo-potential plane-wave (UPPW) within the general gradient approximation (GGA) in the frame of density functional theory (DFT). The calculated lattice constants are found in good agreement with the available experimental data. The calculated energy gaps are overestimated compared to the measured ones because the spin-orbit interaction (SOI) is not taken into account in this work. The elastic constants, shear modulus, Young's modulus, Poisson's ratioσ and the ratio B/G of BiTeX were calculated. According to the obtained results, the BiTeX are mechanically stable and the BiTeBr and BiTeI can be classified as brittle material, while the BiTeCl can be classified as ductile material. The shear anisotropic factors and the elastic anisotropy are also discussed. Finally, the Debye temperature and minimum thermal conductivity are obtained using theoretical elastic constants for the first time. & 2014 Elsevier Ltd. All rights reserved.

1. Introduction In recent years, the AVBV1CVII compounds have been studied intensively due to their particular physical properties [1]. The BiTeX (X¼Br, I and Cl) crystals, which belong to layered compounds of type AVBV1CVII (A¼Bi, B¼Te and C¼Br, I or Cl), have been investigated by a number of scientists [2–7]. Horak reported [8] that the BiTeBr is a natural n-type semiconductor with the energy gap 0.59 eV at room temperature. Shevelkov et al. [9] refined the crystal structures of BiTeX base on X-ray powder diffraction data using a full-profile Rietveld method. Sobolev et al. [10] calculated the dielectric permittivity and volume electron energy loss spectra of the ferroelectric semiconductor BiTeI. Sakano et al. [11] investigated the two-dimensional highly spin-polarized electron accumulation layers commonly appearing near the surface of n-type polar semiconductors

n

Corresponding author. Tel.: þ 86 13882258638; fax: þ 86 28 84079074. E-mail address: [email protected] (S. Zhou).

http://dx.doi.org/10.1016/j.mssp.2014.07.043 1369-8001/& 2014 Elsevier Ltd. All rights reserved.

BiTeX by angular-resolved photoemission spectroscopy. Crepaldi et al. [12] reported a detailed photon-energydependent study of the CD-ARPES spectra in BiTeX. Landolt et al. [13] observed a giant Rashba-type spin splitting in the electronic bulk conduction and valence bands of the semiconductor BiTeCl by angle-resolved photoemission spectroscopy (ARPES). Apart from those properties, the production methods, electrical conductivity, thermoelectric properties, Hall coefficient and magnetic properties of BiTeX were reported [14–19]. However, to the best of our knowledge, up to now, the elastic properties, Debye temperature and thermal conductivity of the ternary BiTeX have not been studied at all. The objective of the present work is, therefore, to calculate these physical properties of BiTeX. 2. Calculation methods Our calculations were performed using the CASTEP code [20], which is based on the state-of-the-art of the density functional theory (DFT). The Perdew-Burke-Ernzerhof for

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solid (PBEsol) [21] was used for the exchange-correlation potential and the ultra-soft pseudo-potential plane-wave (UPPW) was employed to calculate the interaction of valence electrons with the ions. Using the UPPW, 6 s26p3 of Bi, 5 s25p4 of Te, 4 s24p5 of Br, 5 s25p5 of I and 3 s23p5 of Cl were treated explicitly as valence electrons. In this study, the cutoff energy of plane-wave is 600 eV, which was large enough to obtain good convergence. In the Brillouin zone integrations, 10  10  12 Monkhorst-Pack k-points mesh were used. The structural parameters of BiTeX were calculated by using the Brodyden-Fletcher-Goldfarb-Shanno (BFGS) [22–25] method.

3. Results and discussions 3.1. Structure properties BiTeCl has a hexagonal crystal structure (space group P63mc, No.186) of alternating layers of Cl, Bi and Te atoms as illustrated in Fig. 1(a). The crystal has no inversion symmetry due to the continuous stacking order of the three atomic layers. The c parameter appeared to be nearly twice as large as that of BiTeBr and BiTeI. BiTeBr, with space group P3-m1 (NO. 164), crystallizes in a CdI2 type with the Te and Br atoms statistically distributed within a two-layered packing. The Bi atoms occupy all octahedral interstices in each second layer (Fig. 1(b)). The crystal structure of BiTeI, the trigonal space group of P3m1 (NO. 156), has a non-centrosymmetric layered structure along its crystallographic c axis with three atoms in one unit cell. Within each unit, a Bi atom is sandwiched between one Te and I, forming a triple layer (Fig. 1(c)). The calculated lattice parameters and atomic positions of BiTeX are summarized in Table 1, together with the available experimental data for comparison. The lattice constants

a ¼4.21292 Å, c¼12.5313 Å of BiTeCl, a ¼4.25027 Å, c¼ 6.59554 Å of BiTeBr and a ¼4.32834 Å, c¼6.90572 Å of BiTeI, respectively. They are in good agreement with the experimental data, and the deviations from the experimental data are less than 1.66%. These results show and confirm that the method used in this study is reliable, thereby the optimized lattice constants can be used for future calculations of other parameters.

3.2. Electronic properties The total density of states (TDOS) and partial density of states (PDOS) of BiTeX are presented in Fig. 2. There is no overlapping between valence and conduction bands, the gap is not weaker and the DOS at the Fermi level (EF) has a smaller value, therefore, these features indicate that the BiTeX are semiconductors. The calculated energy gap is 0.8 eV for BiTeI, 1.1 eV for BiTeBr and 1.2 eV for BiTeCl, respectively. It is worthy to note here that our calculated energy gap values for BiTeX are almost twice higher than that of the experimental values and the results of the full potential linear augmented plane wave (FP-LAPW) approach (0.48 0.7 eV) [7,8,10,17,19,26]. The reason for this difference is that the spin-orbit interaction (SOI) is not taken into account in our work. Recently, electronic structure calculations using DFT method on BiTeX were reported [3,4,12,17]. From their results, we can see that the number of bands is markedly increased once the SOI are included in the calculations. Bands are found to be clearly doubled at certain momentum points, indicating that the energy states are no longer degenerated with respect to the spin direction when the SOI are taken into account for BiTeX. In Fig. 2, the TDOS of BiTeI and BiTeBr shows similar appearance as that of BiTeCl. For the BiTeX, both the valence band (VB) and conduction band (CB) are mainly composed of the 6p states of Bi and hybridized with small

Fig. 1. The crystal structure of BiTeX: (a) BiTeCl, (b) BiTeBr, (c) BiTeI.

S. Zhou et al. / Materials Science in Semiconductor Processing 27 (2014) 605–610

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Table 1 Lattice parameters and atomic positions of BiTeX compared to available experimental data. Compound BiTeCl

Wyckoff Positions

Lattice Parameters(Å) BiTeBr

Wyckoff Positions Lattice Parameters(Å)

BiTeI

Wyckoff Positions

Lattice Parameters(Å)

amount of s states, whereas the Te-5p and X-5p most strongly contribute to the VB down to –5 eV below EF.

3.3. Elastic properties The elastic constants of solids are among the most fundamental properties, and give important information, such as interatomic bonding, equations of state (EOS) and phonon spectra. Also, they give important information concerning the elastic response of a crystal to an external pressure. To calculate the elastic constants, we have applied the non-volume-conserving method in CASTEP code which has been applied with successful results in some previous works. For the trigonal crystal, we get the following stability criteria [27]: C 11  jC 12 j 40 ðC 11 þ C 12 ÞC 33 2C 213 40 ðC 11  C 12 ÞC 44 2C 214 40

ð1Þ

For the hexagonal crystals, its five independent elastic constants should satisfy the well-known Born stability criteria [27] C 11 4 0; C 33 4 0; C 44 4 0; C 11  C 12 4 0; ðC 11 þ C 12 ÞC 33  2C 213 4 0

ð2Þ The computed elastic constants of BiTeX are shown in Table 2. According to the above criteria, it is clear that the BiTeX are mechanically stable at ambient pressure. For the trigonal and hexagonal system, the Voigt bounds onGV andBV , the Reuss bounds on GR andBR are [28] GV ¼

1 1 ð2C 11 þC 33  C 12 2C 13 Þ þ ð2C 44 þC 66 Þ 15 5

2 1 BV ¼ ðC 11 þ C 12 þ2C 13 þ C 33 Þ 9 2 BR ¼

ðC 11 þC 12 ÞC 33  2C 213 C 11 þ C 12 þ2C 33 4C 13

ð3Þ

ð4Þ

ð5Þ

Cal.

Exp.[9, 26]

Bi(2b)(2/3,1/3,0.6340) Te(2b)(2/3,1/3,0.2797) Cl(2a)(0,0,0.5085) a ¼4.21292 c ¼12.5313 Bi(1a)(0,0,0) Te/Br(2d)(1/3,2/3,0.2591) a ¼4.2503 c ¼6.596 Bi(1a)(0,0,-0.0349) Te(1c)(2/3,1/3,0.7160) I(1b)(1/3,2/3,0.2627) a ¼4.3283 c ¼6.906

Bi(2b)(2/3,1/3,0.6405) Te(2b)(2/3,1/3,0.2797) Cl(2a)(0,0,0.5060) a ¼ 4.2412 b ¼12.4026 Bi(1a)(0,0,0) Te/Br(2d)(1/3,2/3,0.2784) a ¼ 4.2662 c ¼ 6.487 Bi(1a)(0,0,0) Te(1c)(2/3,1/3,0.6928) I(1b)(1/3,2/3,0.2510) a ¼ 4.3392 c ¼ 6.854

GR ¼

5C 2 C 44 C 66 2½3BV C 44 C 66 þ C 2 ðC 44 þC 66 Þ

; C 2 ¼ ðC 11 þ C 22 ÞC 33  2C 213 ð6Þ

The bulk modulus B and shear modulus G can be estimated by Voigt-Reuss-Hill approximation [29]. The Young's modulus E and Poisson's ratioσ can be computed by the following equations [30], respectively: E¼

9BG 3B þ G

ð7Þ

σ¼

3B  2G 2ð3B þGÞ

ð8Þ

The calculated values of bulk, shear and Young's modulus, as well as Poisson's ratio of the BiTeX are given in Table 3. The bulk modulus measures the resistance that material offers to changes in its volume. From Table 3, we can see that the bulk modulus of BiTeCl is larger than the BiTeBr and BiTeI, indicating the BiTeCl is less compressible than the others. The Young's modulus is a good indicator about the stiffness of the material. The higher the Young's modulus, the stiffer the material. From Table 3, we can observe that the Young's modulus increases when the Cl and Br substituted by I, indicating BiTeCl is stiffer than BiTeBr and BiTeCl. To the best of our knowledge, up to now, although no experimental data are available about the elastic constants of BiTeX compounds to compare with these calculated results, the obtained data would be helpful for further investigation. The ratio of bulk modulus to shear modulus of crystalline phases can predict the brittle and ductile behavior of materials. If B/G41.75 the material will behave in a ductile manner or else the material demonstrates brittleness [31]. The values of B, G, E, σ and the ratio B/G are given in Table 3. The obtained B/G ratio is 6.10 for BiTeCl, 1.54 for BiTeBr and 1.60 for BiTeI, according to those values BiTeI and BiTeBr behave in brittle manner, while the BiTeCl behave in a ductile manner. The Poisson's ratioσ is a good indicative of bonding and stiffness in materials. It can formally take values between 0.0 and 0.5 [32]. The values of the Poisson ratioσ is small for covalent materials (σ ¼0.1), for ionic materialsσ is usually to 0.25, for metallic materialsσ lies between 0.25

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Fig. 2. The total density of states of BiTeX: (a) BiTeCl, (b) BiTeBr, (c) BiTeI. Table 2 The calculated elastic constants C ij (in GPa) of BiTeX. Compounds

C 11

C 33

C 44

C 12

C 13

C 14

BiTeCl BiTeBr BiTeI

56.6 59.3 60.4

96.6 28.6 42.0

1.7 14.9 24.3

20.8 14.6 14.1

47.6 13.1 20.2

/  8.5  12.5

and 0.45. In our work, the value of σ is about 0.42 for BiTeCl, 0.23 for BiTeBr and 0.24 for BiTeI, which indicates that metallic contributions in intra-atomic bonding should be assumed for BiTeCl, and ionic contributions for BiTeBr and BiTeI.

Elastic anisotropy of crystals reflects a different character of bonding in different directions and has an important implication since it correlates with the possibility to induce microcracks in materials. We have estimated the elastic anisotropy in terms of compressibility and shear for polycrystalline material as [33]: 8 9 BR < AB ¼ BBV   100% = V þ BR ð9Þ GR : AG ¼ GGV   100% ; V þ GR For isotropic crystals AB and AG are zero, and departures from zero imply bulk anisotropy in the crystal. As shown in Table 3, both of BiTeX exhibit large anisotropy in shear. Moreover, the results of AB show that BiTeI has better isotropy than BiTeBr and BiTeCl in compression.

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Table 3 Calculated bulk modulus B(all in GPa), shear modulus G(all in GPa), Young's modulus E (all in GPa), the ratio B/G, Poisson's ratio σ and anisotropic factor of BiTeX. Compounds

BV

BR

BH

GV

GR

GH

B G

E

σ

AB

AG

AU

BiTeCl BiTeBr BiTeI

49.1 25.4 30.2

36.8 22.5 29.8

42.9 24.0 30.0

10.5 17.5 21.6

3.6 13.5 16.0

7.0 15.5 18.8

6.10 1.54 1.60

20.0 38.3 46.6

0.42 0.23 0.24

14.37 6.10 0.72

49.40 13.05 14.75

10.10 1.63 1.74

To further investigate the anisotropy, Ranganathan et al. [34] introduced a concept of universal anisotropy index: AU ¼ 5

GV B V þ 6 GR BR

ð10Þ

AU ¼ 0 represents locally isotropic crystals and A 4 0denotes the extent of crystal anisotropy. The calculated value of AU is 10.10 for BiTeCl, 1.63 for BiTeBr and 1.74 for BiTeI, suggesting again these compounds have stronger anisotropy. U

Table 4 Calculated density (ρin g/cm3), transverse, longitudinal, average sound velocity (vt ,vl ,vm in m/s), the Debye temperatures (θD in K) and the minimum thermal conductivity (K min in Wm-1 K-1) of BiTeX. Compounds

ρ

vt

vl

vm

θD

K min

BiTeCl BiTeBr BiTeI

6.41457 6.56503 6.86913

1047.4 1537.3 1653.7

2856.0 2607.6 2831.2

1189.2 1703.4 1834.0

111.4 154.9 163.3

0.273 0.295 0.306

conductivity can be calculated by kB 2 n3 ð2vt þ vl Þ 2:48

3.4. Thermodynamic properties

kmin ¼

The Debye temperature (θD ) is not a strictly determined parameter, various estimates may be obtained through well established empirical or semiempirical formulas. One of the semiempirical formulas can be used to estimate the Debye temperature through elastic constants, averaged sound velocity (vm ), longitudinal sound velocity (vl ) and transverse sound velocity (vt ) [35–38].

where n is the number of atoms per unit volume. The calculated minimum thermal conductivity of BiTeX is given in Table 4. It is observed that the calculated minimum thermal conductivity of BiTeI is larger than BiTeBr and BiTeCl.

θD ¼

 1 h 3n N A ρ 3 Þ vm ð k 4π M "

vm ¼

1 2 1 ð þ Þ 3 v3t v3l

ð11Þ

#  13 ð12Þ

B þ 43G 1 Þ2 vl ¼ ð

ð13Þ

G1 vt ¼ ð Þ2

ð14Þ

ρ

ρ

where h is Planck constant, k is Boltzmann constant; NA is Avogadro number; ρis the density; Mis the molecular weight; and n is the number of atoms in the unit cell. The calculated values ofvm ,vl ,vt and θD of BiTeX at 0 K are given in Table 4. It is observed that the calculated Debye temperature of BiTeI is larger than BiTeBr and BiTeCl. Therefore, BiTeI is harder with a large wave velocity and has higher thermal conductivity than BiTeCl. Thermal conductivity K is the property of a material that indicates its ability to conduct heat. However, in order to know if the material is a potential application for thermal barrier coating, its thermal conductivity needs to be investigated. A number of similar expressions have been derived for thermal conductivity. For instance, Cahill and Pohl [39] suggested that the minimum thermal

ð15Þ

4. Conclusions In present work, the electronic, elastic and thermodynamic properties of BiTeX (X ¼Cl, Br and I) have been studied by means of DFT within the GGA. The calculated lattice parameters of BiTeX are in good agreement with the experimental data, and deviated from measured data are less than 1.67%. The elastic properties such as shear modulus and Young's modulus are calculated. From our results, we observe that BiTeX in mechanically stable. The values of B/G are smaller than 1.75 for BiTeBr and BiTeI, while it is bigger than 1.75 for BiTeCl. Therefore, BiTeBr and BiTeI can be classified as brittle material, while BiTeCl can be classified as ductile material. The calculated Debye temperature of BiTeI was found to be higher compared to that of BiTeBr and BiTeCl, which reveals that BiTeI is harder and has higher thermal conductivity than BiTeBr and BiTeCl. To the best of our knowledge, there are no experimental data available about the elastic constants and thermodynamic properties of BiTeX. The results obtained in this work could provide a useful reference for future studies. References [1] S. Adachi, Properties of Semiconductor Alloys: Group-IV, III–V and II–VI Semiconductors, John Wiley & Sons Ltd., UK, 2009. [2] E. Dönges, Z. anorg, Allgem. Chem. 265 (1951) 56. [3] S.V. Eremeev, I.P. Rusinov, I.A. Nechaev, E.V. Chulkov, New J. Phy. 15 (2013) 075015. [4] M. Kanou, T. Sasagawa, J. Phys.: Condens. Matter. 25 (2013) 135801.

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