First-principle calculations of the electronic, optical and elastic properties of ZnSiP2 semiconductor

Journal of Alloys and Compounds 582 (2014) 101–107

Contents lists available at ScienceDirect

Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom

First-principle calculations of the electronic, optical and elastic properties of ZnSiP2 semiconductor V. Kumar ⇑, S.K. Tripathy Department of Electronics Engineering, Indian School of Mines, Dhanbad 826 004, India

a r t i c l e

i n f o

Article history: Received 25 May 2013 Received in revised form 1 August 2013 Accepted 3 August 2013 Available online 14 August 2013 Keywords: ZnSiP2 semiconductor DFT calculation Electronic structure Optical properties Elastic constants

a b s t r a c t The plane wave pseudo-potential method within density functional theory (DFT) has been used to investigate the structural, electronic, optical and elastic properties of ZnSiP2 chalcopyrite semiconductor. The lattice constants are calculated from the optimized unit cells and compare with the experimental value. The band structure, total density of states (TDOS) and partial density of states (PDOS) have been discussed. The energy gap has been calculated along the U direction found to be 1.383 eV, which shows that ZnSiP2 is pseudo-direct in nature. We have also analyzed the frequency dependent dielectric constant e(x) and calculated the birefringence (Dn). The optical properties under three different hydrostatic pressures of 0 GPa, 10 GPa and 20 GPa have been described for the first time in the energy range 0–20 eV. The values of bulk modulus (B), pressure derivative of bulk modulus (B⁄), elastic constants (Cij), Young’s modulus (Y), anisotropic factor (A) and Poisson’s ratio (m) have been calculated. The calculated values of all above parameters are compared with the available experimental values and the values reported by different workers. A fairly good agreement has been found between them. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Recently, an increasing attention has been given towards the study of ZnSiP2 ternary chalcopyrite semiconductor because of its interesting structural, electronic, optical and elastic properties [1]. The chalcopyrite semiconductors crystallize in the tetragonal  structure at ambient condition with space group (I 4 2d) and has four formula units per unit cell, which is a ternary analog of well known zincblende III–V binary semiconductors. ZnSiP2 is an important material of II–IV–V2 group and possesses a high nonlinear susceptibility with adequate bifringence, which makes it very useful for an efficient second harmonic generation and phase matching. Its application has been realized for high power optical frequency conversion in the near and mid-infrared regions. It has great promise for various applications in the fields of quantum electronics, spintronics and optoelectronics [2]. There have been various experimental and theoretical approaches to explain the different properties of ZnSiP2 semiconductor [1–6]. The phonon lines in this semiconductor have been observed by infrared reflectivity and Raman measurements [2], and later on analyzed by different workers using Group Theory for mode prediction [3,4]. Shirakata et al. [5] have discussed the hydrostatic-pressure dependence of the first-order Raman spectra of ZnSiP2 crystal and the Gruneisen parameter of each Raman

⇑ Corresponding author. Tel.: +91 9431122030. E-mail address: [email protected] (V. Kumar). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.08.025

mode. The crystal structure and phonon structure analysis have been carried out using X-ray diffraction and Raman Spectroscopy by Pena-Pedraza et al. [6]. The full potential linear augmented plane wave plus local orbit (FP-LAPW+lo) method has been used to find out the reflectivity spectra of ZnXP2 (X = Si, Ge, Sn) semiconductors [7], electronic properties of ASiAs2 (A = Zn, Cd) compounds [8], and the effect of cations on band structure of ZnGeAs2 pnictides [9]. First principle calculations have been carried out to describe the magnetic properties of Mn-doped II–IV–V2 semiconductors [10] and electronic properties of II–IV–V2 (II = Be, Mg, Zn, Cd; IV = Si, Ge, Sn; V = P, As) semiconductors [11,12]. Density functional theory (DFT) has been used by several researchers to explain the structural, electronic and optical properties of I– III–VI2 and II–IV–V2 groups of semiconductors [13–15]. The electroreflectance studies of ZnSiP2 have been discussed by Shay et al. [16]. Kumar et al. [17–20] have explained the various electronic [17], elastic [18], thermal [19] and nonlinear [20] properties of ternary chalcopyrites using plasma oscillations theory of solids. Other workers [21,22] have proposed various empirical relations to calculate the elastic constants, energy gaps and electronic polarizability of different binary and ternary semiconductors. Arab et al. [23] have investigated the structural, elastic and electronic properties of ZnSiP2 semiconductor under high pressure and found that the structure of ZnSiP2 is stable up to 35 GPa. So far, no study on optical properties has been carried out under different pressure. Therefore, it has been thought of interest to study the various optical properties of ZnSiP2 under different hydrostatic pressures in

102

V. Kumar, S.K. Tripathy / Journal of Alloys and Compounds 582 (2014) 101–107

addition to electronic properties. In this paper, the first-principle calculations within density functional theory (DFT) have been used to calculate the lattice constants, energy gap, bulk modulus (B), derivative of bulk modulus (B⁄). The optical properties such as dielectric constant, refractive index, reflectivity, absorption coefficient, extinction coefficient and electron energy loss spectrum at 0 GPa, 10 GPa and 20 GPa pressures have been calculated in the energy range 0–20 eV. We have also calculated the elastic constants (Cij), Poisson’s ratio (m), Young modulus (Y) and anisotropic factor (A) of ZnSiP2 semiconductor. The calculated values of all parameters are compared with the available experimental values and the values reported by different workers. A fairly good agreement has been obtained between them. 2. Computational details We have performed the first-principle calculation using Cambridge Sequential Total Energy Package (CASTEP) simulation software [24]. The calculations are based on the local density approximation (LDA) with exchange–correlation Ceperley–Alders potential [25] parameterized by Perdew–Zunger scheme [26]. Norm-conserving pseudo-potentials [27] have been used with plane wave basis set cut-off at 400 eV. The crystal reciprocal-lattice and integration over the Brillouin zone have been performed using 5  5  2 Monkhorst–pack [28]. During the optimization of geometry, the total energy difference of 5  107 eV/atom, Hellmann– Feynman ionic force of 0.01 eV/Å, maximum stress of 0.02 GPa and maximum displacement of 5  104 Å have been used. Optimized structure has been obtained by applying Broyden, Fletcher, Goldfarb and Shanno (BFGS) scheme [29]. 3. Results and discussion 3.1. The structural properties of ZnSiP2 The chalcopyrite crystal belongs to the body centered tetrag onal (bct) with space group (I 4 2d) and closely related to sphalerite and diamond structures. Each unit of chalcopyrite structure contains eight atoms per unit cell. The atomic positions of ZnSiP2 crystal are Zn (0, 0, 0), Si (0, 0, 0, .5) and P (u, 0.25, 0.125), where u is the distortion parameter. We have optimized the equilibrium structure using local density approximation (LDA) method. The total energy versus volume diagram of ZnSiP2 is shown in

ZnSiP2

-256.9

Total Energy (Hartree)

-257.0

-257.1

-257.2

-257.3

-257.4

-257.5 1400

1600

1800

2000

2200

2400

2600

Volume (Bohr3) Fig. 1. Total energy versus volume curve of ZnSiP2.

2800

Fig. 1. The optimized lattice parameters are given in Table 1 along with the theoretical and experimental values. Reasonably good agreement has been obtained between them. The calculated values of lattice parameters are underestimated approximately by 0.05% from the experimental values [30]. We have also calculated the value of the internal parameter (u) of ZnSiP2 and listed in Table 1 along with the experimental value and the values reported by different researchers [12,23,32]. Table 1 shows that the calculated value of u is in good agreement with the experimental and reported values. Further, we have fitted the total energy versus volume data in Birch–Murnaghan equation of states (EOS) [31] to obtain the value of bulk modulus (B) and the derivative of bulk modulus (B⁄). We have also calculated the value of B using the empirical relation proposed by Kumar et al. [18]. The calculated values B and B⁄ listed in Table 1, which are in good agreement with the experimental and reported values. Our calculated value of B is more close to the experimental value in comparison to the value reported by earlier workers [23].

3.2. The electronic properties of ZnSiP2 The band structure of the ZnSiP2 is plotted along the high symmetry axes of the Brillouin zone and shown in Fig. 2, which depicts that the calculated value of the energy gap, along the C direction at G point, is 1.383 eV. The value of energy gap obtained using LDA scheme is 31% smaller than the experimental value of 2.01 eV [16]. Our calculated value of energy gap is closer to the experimental value than the value reported by earlier workers [14,23,33]. It is important to mention that the LDA method underestimates the value of energy gap and this error is due to the discontinuity of exchange–correlation energy. The calculated value of energy gap (Eg) is listed in Table 1 along with the experimental and reported values [14,16,23,33]. The density of states plays an important role in analyzing the physical properties of a semiconductor. We have depicted the total densities of states (TDOS) and partial densities of states (PDOS) of ZnSiP2 semiconductor. The PDOS signify the angular momentum character, the orbital character and the states of hybridization of the semiconductor. The TDOS and PDOS for Zn- s/p/d, Si- s/p and P- s/p states are plotted from 14 eV to 10 eV and shown in Fig. 3. The Fermi energy level is set to zero. Here we have taken Zn 4s, Zn 3d, Si 3s, Si 3p, P 3s and P 3p as the valence electron states. The energy bands located between 6.76 eV and 6.58 eV are mainly due to Zn-3d state. The Zn-3d state is an important for band gap variation, which is due to the p-d hybridization. Further, the valence band region is divided into three parts. The first part varies from 12.82 eV to 9.39 eV and is dominated by P-p and Si- p/s states with minor contributions from Zn-s state. The second part varies from 8.32 eV to 4.84 eV is mainly derived from major contributions from Zn-3d and small contributions of P-p and Si-s states. The last part varies from 4.54 eV to Fermi energy level (EF = 0.0 eV) and is dominated by P-p and Si-p states, however, small contributions of Zn-s state can be observed in this energy region. The conduction band, from 1.383 eV to 7.56 eV, comes primarily from Si-s, p states and Zn- s, p states with some contributions from P- s, p states. Fig. 3 shows that there exist a strong interaction between P-p and Si-p states at around 3.74 eV. Furthermore, we have calculated the crystal field splitting at U point in the absence of the spin–orbit coupling as shown in the magnified diagram inserted in Fig. 2. In Fig. 2, the doubly degenerated top of the valence band at U point yield crystal field splitting energy Dcf which is equal to 0.114 eV in comparison to the experimental value of 0.130 eV [35]. The value of crystal field splitting is also in good agreement with the experimental value.

103

V. Kumar, S.K. Tripathy / Journal of Alloys and Compounds 582 (2014) 101–107

Table 1 The lattice constants (a and c), internal parameter (u), energy gap (Eg), bulk modulus (B), pressure derivative of bulk modulus (B⁄) and plasmon energy (⁄xp) of ZnSiP2 semiconductor. Lattice parameter (Å)

a b

Eg (eV)

B (GPa) a

This work

a = 5.398, c = 10.435

0.267

1.383

79.30 88.42b 80.04c

Expt. values

a = 5.407 [6], c = 10.453 [6] a = 5.400 [30], c = 10.438[30] a = 5.399 [32], c = 10.436 [32]

0.2691 [30] 0.272 [32]

2.01 [16]

79.00 [34]

Theoretical values

a = 5.400 [23], c = 10.500 [23]

0.269 [12] 0.268 [23]

1.22 [14] 1.34 [23] 2.96 [33]

84.35 [23] 93.13 [18] 88.00 [22]

B⁄

(⁄xp) (eV)

4.770a

15.95

4.160[23]

17.02 [19]

Calculated from EOS. Calculated from volume compression. Calculated using relations given in Ref. [18].

Energy (eV)

c

u

14 12 10 8 6 4 2 0 -2 -4 -6 -8 -10 -12 -14 -16

0.0 -0.2 -0.4 -0.6 -0.8 -1.0

Z

G

X

P

N

G

Fig. 2. Band structure of ZnSiP2. In the inserted figure shows the magnified view of uppermost valence band.

shown in Fig. 4b. The static dielectric constants are found to be zz 10.42 and 11.77, respectively, for exx 1 ð0Þ and e1 ð0Þ. The uniaxial tot anisotropy deb¼ ðek0  e? Þ= e c is equal to 0.114, which indicates 0 0 that there exists strong anisotropy in ZnSiP2 semiconductor [37]. The reflectivity curves Rxx(x) and Rzz(x) for x and z axes are shown in Fig. 4c. Figs. 4a–4c show that ZnSiP2 is an anisotropic material and having wide applications in the field of second harmonic generation (SHG), optical parametric oscillators (OPO) and phase matching conditions. Fig. 5 shows that birefringence of ZnSiP2 semiconductor and the static value of the birefringence Dn(0) is found to be 0.203. Unfortunately, no experimental data are available for the comparison of Dn(0). However, in Fig. 5 we have compared the values of birefringence plotting the curve between Dn(0) and energy with that of Chiker et al. [38]. The dispersion of the birefringence Dn(x) is interesting in the absorbing region, which is below the energy gap. Furthermore, we have found a strong peak at 1.96 eV and the curve of birefringence bending in the high energy region rapidly, and the phase matching condition no longer be satisfied.

3.3. Dielectric and birefringence

3.4. The pressure dependence of optical properties

The optical properties of ZnSiP2 material can be measured from the complex dielectric function e(x). In the presence of electric ! field E , the frequency dependent dielectric function is divided into two parts: the intraband and the interband transitions. The information related to the intraband transition is useful for the metals and the interband for the semiconductors. The interband transition is further divided into two: the direct band and the indirect band transitions. With the help of momentum matrix elements between occupied and unoccupied wave functions, it is possible to calculate the direct interband contribution to the imaginary part of the dielectric function e2(x). Fig. 4a shows the absorptive part of the electronic dielectric zz function e2(x) along x-axis exx 2 ðxÞ, and along z-axis e2 ðxÞ from which one can observe that there exist an anisotropy between x and z directions. Our analysis of e2(x) curve shows that the first critical point occurs at 1.27 eV, which gives the threshold for direct optical transition between highest valence and lowest conduction bands. After this point the curve increases rapidly. This is because of the increasing number of k-points contributing towards e2(x). zz The main peaks of exx 2 ðxÞ and e2 ðxÞ are located at 3.7 eV and 3.8 eV, respectively, which are due to the transition between upper valence band and the second conduction band. zz The real part of dielectric functions exx 1 ðxÞ and e1 ðxÞ can be calculated from the imaginary part of dielectric functions using Krazz mer–Kronig relations [36]. The plots of exx 1 ðxÞ and e1 ðxÞ are

From the dielectric function, all other optical properties such as refractive index n(x), reflectivity R(x), extinction coefficient k(x), absorption coefficient a(x) and energy loss function L(x) have been calculated using the relations given in the literature [13]. The imaginary and real parts of dielectric constant are shown in Figs. 6a and 6b, respectively, which shows that e1(0) = 11.77 for ZnSiP2 against the reported value of 11.24 by [7]. The calculated value of e1(0) is slightly higher than the reported value. It is well known that the dielectric constant of any semiconductor is the absolute sum of electronic and lattice dielectric constants [39,40]. The lattice term cannot be neglected due to the ionic character present in ZnSiP2, which makes calculated value of dielectric constant slightly higher than reported values by Chiker et al. [7]. Chiker et al. have not considered the contribution of lattice term in their calculation due to which their reported value is less than our calculated value. The simulated imaginary part of the dielectric constant e2(x) at three different pressures is shown in Fig. 6a. The absorption starts from 1.09 eV, 1.37 eV and 1.42 eV, respectively, at 0 GPa, 10 GPa and 20 GPa pressures and peaks are obtained at 3.78 eV, 4.01 eV and 4.18 eV, respectively. These peaks are marked by ‘+’ sign on the curves of Fig. 6a and the curves of the following figures. This shows that the absorption edge shifts towards the high energy region as the pressure increases, which has also been observed by other workers [13].

104

V. Kumar, S.K. Tripathy / Journal of Alloys and Compounds 582 (2014) 101–107

5

PDOS

4

P-s P-p

3 2

TDOS

PDOS

PDOS

PDOS

1 0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 1.8 0.0 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 30 25 20 15 10 5 0 35 30 25 20 15 10 5 0

Si-s Si-p

Zn-s Zn-p

Zn-d

Total

-14

-12

-10

-12.82

-8

-6

-4

-2

0

Energy (eV)

-9.39

2

4

6

8

10

7.56

1.383

Fig. 3. Total density of states (TDOS) and partial density of states (PDOS) of ZnSiP2.

20

20

ε2xx (ω) ε2zz (ω)

18

ε1xx (ω) ε1zz (ω)

15

16 10

ε1 (ω)

14

ε2 (ω)

12

5

10 0

8 6

-5

4 -10 2

0

2

4

6

8

10

Energy (eV)

0 0

2

4

6

8

10

Energy (eV) zz Fig. 4a. The calculated imaginary part exx 2 ðxÞ and e2 ðxÞ of the dielectric function of ZnSiP2.

The real part of dielectric constant e1(x) is shown in Fig. 6b, which shows that the absorption edge shifts towards the higher energy region as the pressure increases. At 0 GPa, the peak is observed at 2.34 eV, which is due to Si-3p ? Zn-4s transition. Afterwards a sharp decrease in e1(0) is observed, which reaches a minimum value at 6.60 eV in the energy range 0–20 eV. Similarly the peaks at 2.74 eV and 2.97 eV are observed, at 10 GPa and 20 GPa pressures, respectively. The values of dielectric constant e1(0) decreases as pressure increases and found to be 11.77, 11.37 and 11.31, respectively, at 0 GPa, 10 GPa and 20 GPa pressures. The values of e1(0) are listed in Table 2 along with the values reported by different researchers.

Fig. 4b. The calculated real part ZnSiP2.

zz exx 1 ðxÞ and e1 ðxÞ of the dielectric function of

Refractive index n(0) of ZnSiP2 semiconductor is presented in Fig. 7a, which shows that the values of n(0) are 3.43, 3.37 and 3.36, respectively, at 0 GPa, 10 GPa and 20 GPa pressures in the energy range 0–20 eV. These values are listed in Table 2 along with the available reported values at 0 GPa pressure. From these data, we observe that the refractive index decreases with the increase of pressure. Fig. 7a also suggests that n(0) lies in the far-infrared region, which increases to a maximum value in the visible region and finally decreases with the further increase in energy. The extinction coefficient curve displays in Fig. 7b. The global maxima of extinction coefficient occur at about 4.38 eV, which corresponds to the zero value of dispersive part of dielectric constant shown in Fig. 6b at 0 GPa pressure.

105

V. Kumar, S.K. Tripathy / Journal of Alloys and Compounds 582 (2014) 101–107

1.0

0 GPa 10 GPa 20 GPa

20 0.8

15

10

R (ω)

ε1 (ω)

0.6

5

0.4 0 0.2

-5

Rxx (ω) Rzz (ω)

-10

0.0 0

5

10

15

0

20

2

4

6

8

10

12

14

16

18

20

E (eV)

Energy (eV)

Fig. 6b. The calculated real part of dielectric constant of ZnSiP2 compound.

Fig. 4c. The calculated reflectivity Rxx(x) and Rzz(x) of ZnSiP2.

Table 2 The dielectric constant e1(0) and refractive index n(0) at 0 GPa, 10 GPa and 20 GPa pressures of ZnSiP2 semiconductor. Pressure

----- Our values X Ref [38]

0.4

Birefringence

0.2

0.0

a b c

-0.2

-0.4

-0.6 0

5

10

15

20

Energy (eV) Fig. 5. The calculated birefringence Dn(x) spectrum.

25 0 GPa 10 GPa 20 GPa

20

ε2 (ω)

15

10

5

0 0

2

4

6

8

10

12

14

16

18

20

E (eV) Fig. 6a. The calculated imaginary part of dielectric constant of ZnSiP2 compound.

e1(0)

n(0)

This work

Theoretical values

This work

Theoretical values

0 GPa

11.77

11.24a

3.43

3.4b, (3.1, 2.85, 2.59, 2.78)c

10 GPa 20 GPa

11.37 11.31

3.37 3.36

Ref. [7]. Ref. [22]. Ref. [41].

The reflectivity R(x) curve of ZnSiP2 semiconductor is shown in Fig. 8a. The peaks of R(x) are obtained at 14.05 eV, 14.81 eV and 15.34 eV, respectively, at 0 GPa, 10 GPa and 20 GPa pressures, which tells us that the R(x) increases with the increase of energy in the UV region. The peaks of reflectivity shift towards the higher energy region as the pressure increases from 0 to 10 GPa and 10 to 20 GPa. From Fig. 8a, we can observe that the values of reflectivity are 0.3, 0.294 and 0.293 at 0 GPa, 10 GPa and 20 GPa pressures, respectively. The absorption coefficient a(x) of ZnSiP2 is shown in Fig. 8b in which we have considered that the incident radiation is linearly polarized along the [1 0 0] direction with the smearing potential of 0.5 eV. From Fig. 8b, we can see that the fundamental absorption edges start from 1.27 eV, 1.77 eV and 1.86 eV, respectively, at 0 GPa, 10 GPa and 20 GPa pressures and the corresponding peaks lie at 6.84 eV, 7.12 eV and 7.31 eV. The change in absorption edge with respect to pressure is due to increase in the band gap. At the same time lattice constant decreases, this results in increasing the covalent bonding and antibonding energy difference. The energy-loss spectrum of ZnSiP2 is shown in Fig. 8c, which tells about the energy-loss of a fast electron traversing in the semiconductor [42]. The point at which, highest loss-function occurs, i.e. 15.95 eV, corresponds to the plasmon energy (⁄xp) of the ZnSiP2 semiconductor. This is in close agreement with the reported values of ⁄xp = 17.02 eV [19]. At this point, the real and imaginary part of the dielectric function is almost zero and corresponds to the trailing edge of R(x) [43]. The calculated and reported values of plasmon energies are listed in Table 1. The peaks of plasmon energy lie at 15.95 eV, 16.89 eV and 17.61 eV, respectively, at 0, 10 and 20 GPa pressures, which show that the plasmon energy curve shifts towards the higher energy region with the increase of pressure.

106

V. Kumar, S.K. Tripathy / Journal of Alloys and Compounds 582 (2014) 101–107

350000

5 0 GPa 10 GPa 20 GPa

4

0 GPa 10 GPa 20 GPa

300000 250000

α (ω)

n (ω)

3

2

200000 150000 100000

1

50000 0 0 0

2

4

6

8

10

12

14

16

18

0

20

2

4

6

8

10

12

14

16

18

20

E (eV)

E (eV)

Fig. 8b. The calculated absorption coefficient of ZnSiP2.

Fig. 7a. The refractive index of ZnSiP2.

45 3.5 40

0 GPa 10 GPa 20 GPa

3.0

30

L (ω)

2.5

k (ω)

0 GPa 10 GPa 20 GPa

35

2.0 1.5

25 20 15

1.0

10 5

0.5

0 0

0.0 0

2

4

6

8

10

12

14

16

18

2

4

6

8

10

12

14

16

18

20

E (eV)

20

E (eV) Fig. 8c. The electron energy loss spectra of ZnSiP2. Fig. 7b. Extinction coefficient spectra of ZnSiP2.

3.5. Elastic properties We have further calculated the values of elastic stiffness constants Cij, i.e.,C11, C12, C13, C33, C44, C66 using the volume conserving technique at 0 GPa pressure. For the chalcopyrite semiconductor, the elastic constant must satisfy the following Born–Huang stability criteria [44]:

1.0

0 GPa 10 GPa 20 GPa

R (ω)

0.8

0.6

0.4

0.2 0

2

4

6

8

10

12

14

E (eV) Fig. 8a. Reflectivity curve of ZnSiP2.

16

18

20

C 11 > 0; C 33 > 0; C 44 > 0; C 66 > 0

ð1Þ

ðC 11  C 12 Þ > 0; ðC 11 þ C 33  2C 13 Þ > 0

ð2Þ

½2ðC 11 þ C 12 Þ þ C 33 þ 4C 13  > 0

ð3Þ

The calculated values of all six elastic constants are listed in Table 3, which are in fair agreement with the values reported by earlier researchers [21,23,45]. The ratio of elastic constants C11/ C33 = 1.12, C12/C13 = 1.04 and C44/C66 = 1.12 suggest that ZnSiP2 has pseudo-cubic nature. Many years ago, Voigt and Reuss have developed relationship between the elastic constants (Cij), Voigt’s bulk modulus (BV), Voigt’s shear modulus (GV) and the Reuss’s shear modulus (GR) [46], which are further correlated with the

107

V. Kumar, S.K. Tripathy / Journal of Alloys and Compounds 582 (2014) 101–107 Table 3 The elastic constants (Cij) in GPa, Poisson ratio (m), Zener anisotropic factor (A), Young modulus (Y) in GPa of ZnSiP2 semiconductor.

This work Theoretical values

a b c

C11

C12

C13

C33

C44

C66

m

A

Y

118.93 90.9a 136.68b 96c

39.96 56.8a 54.79b 57c

38.17 54a 60.79b 54c

105.42 85.2a 133.11b 84c

54.75 31.2a 71.91b 32c

48.77 28.4a 69.63b 32c

0.208 0.23b

1.38

111.71 136.4b

Ref. [21]. Ref. [23] using ‘DFT’. Ref. [45] using ‘rigid ion model’.

anisotropic shear modulus G = (GV + GR)/2. The other elastic properties such as Poisson ratio (m), Zener anisotropy factor (A) and Young modulus (Y) can be calculated using the relations [47]:

  1 B  2=3G 2 B þ 1=3G

ð4Þ

A ¼ 2C 44 =ðC 11  C 12 Þ

ð5Þ

m¼

Y¼

9GB G þ 3B

ð6Þ

The calculated values of m, A and Y using Eqs. (4)–(6), are 0.237, 1.73 and 102.560, respectively, for ZnSiP2 semiconductor and listed in Table 3 along with the values reported by other workers. 4. Conclusions We have successfully performed the first-principle calculation to study the various electronic, optical and elastic properties of ZnSiP2 semiconductor using CASTEP software. The calculated values of lattice constants (a, c), energy gap (Eg), bulk modulus (B), pressure derivative of bulk modulus (B⁄), plasmon energy (⁄xp) are listed in Table 1 along with the experimental values and the values reported by different workers. The crystal splitting (Dcf) value has been calculated and compared with the experimental value. Due to anisoptropy nature of ZnSiP2 semiconductor, the birefringence (Dn) has been calculated and depicted in Fig. 5. We have also calculated the values of e1(0) and n(0) at 0 GPa, 10 GPa and 20 GPa pressures and the calculated values of these parameters are listed in Table 2 along with the available reported values at 0 GPa pressure. The values of these parameters at 10 GPa and 20 GPa are reported for the first time in this paper. The data listed in Table 2 show that when pressure increases from 0 to 10 GPa and 10 to 20 GPa, the values of e1(0) and n(0) decreases. It is also observed that the changes are more prominent when the pressure changes from 0 to 10 GPa than 10 to 20 GPa. Further, we have calculated the values of elastic constants C11, C12, C13, C33, C44, C66, m, A and Y of ZnSiP2. The calculated values of these parameters are listed in Table 3 along with the reported values. The ratio of elastic constants C11/C33 = 1.12, C12/C13 = 1.04 and C44/C66 = 1.12 suggest that ZnSiP2 has pseudo-cubic nature. In almost all the cases, our calculated values are in better agreement with the experimental values than the values reported by earlier workers, which demonstrates the soundness of the present calculations. Acknowledgements The authors are thankful to Prof. D.C. Panigrahi, Director, Indian School of Mines, Dhanbad, for his continuous encouragement and inspiration in conducting this work. References [1] J.L. Shay, J.H. Wernick, Ternary Chalcopyrite Semiconductors: Growth, Electronic Properties and Applications, Pergamon Press, New York, 1975.

[2] G.D. Holah, J. Phys. C5 (1972) 1893. [3] S.A. Lopez-Rivera, H. Galindo, B. Fontal, M. Briceno, Phys. Rev. B 30 (1984) 7097–7104. [4] S. Gorban, V.A. Gorynya, V.I. Lugovoi, N.P. Krasnolob, G.I. Salivon, I.I. Tychina, Phys. Status Solidi B 93 (2) (1979) 531–538. [5] S. Shirakata, T. Shirakawa, J. Nakai, II nuovo Cimento della Societa italiana de Fisica 2 (6) (1983) 2058–2063. [6] H. Pena-Pedraza, S.A. Lopez-Rivera, J.M. Martin, J.M. Delgado, Ch. Power, Mater. Sci. Eng. B 177 (2012) 1465–1469. [7] F. Chiker, B. Abbar, S. Bresson, B. Khelifa, C. Mathieu, A. Tadjer, J. Solid State Chem. 177 (2004) 3859–3867. [8] F. Boukabrine, F. Chiker, H. Khachai, A. Haddou, N. Baki, R. Khenata, B. Abbar, A. Khalfi, Physica B 406 (2011) 169–176. [9] H.S. Saini, M. Singh, Ali H. Reshak, M.K. Kashyap, J. Alloys Comp. 518 (2012) 74–79. [10] S.C. Erwin, I. Zutic, Nat. Mater. 3 (2004) 410–414. [11] J.E. Jaffe, Alex Zunger, Phys. Rev. B 29 (1984) 1882–1906. [12] V.L. Shaposhnikov, A.V. Krivosheeva, V.E. Borisenko, Phys. Rev. B 85 (2012) 205201. 1–9. [13] S. Sahin, Y.O. Ciftci, K. Colakoglu, N. Korozlu, J. Alloys Comp. 529 (2012) 1–7. [14] S.N. Rashkeev, S. Limpijumnong, W.L. Lambrecht, Phys. Rev. B 59 (1999) 2737– 2748. [15] W.R.L. Lambrecht, S.N. Rashkeev, J. Phys. Chem. Solids 64 (2003) 1615–1619. [16] J.L. Shay, B. Tell, E. Buehler, J.H. Wernick, Phys. Rev. Lett. 30 (1973) 983–986. [17] V. Kumar Srivastava, Phys. Rev. B 36 (1987) 5044–5046. [18] V. Kumar, A.K. Shrivastava, Vijeta Jha, J. Phys. Chem. Solids 71 (2010) 1513– 1520. [19] V. Kumar, A.K. Shrivastava, Rajib Banerji, D. Dhirhe, Solid State Commun. 149 (2009) 1008–1011. [20] V. Kumar, S.K. Tripathy, Vijeta Jha, Appl. Phys. Lett. 101 (2012) 192105. 1–5. [21] A.S. Verma, S. Sharma, R. Bhandari, B.K. Sarkar, V.K. Jindal, Mater. Chem. Phys. 132 (2012) 416–420. [22] R.R. Reddy, K.R. Gopal, K. Narasimhulu, L.S.S. Reddy, K.R. Kumar, G. Balakrishnaiah, M. Ravi Kumar, J. Alloys Comp. 473 (2009) 28–35. [23] F. Arab, F.A. Sahraoui, K. Haddadi, L. Louail, Comput. Mater. Sci. 65 (2012) 520– 527. [24] M.D. Segall, J.D. Philip, M.J. Lindan, C.J. Probert, P.J. Pickard, S. Hasnip, J. Clark, M.C. Payne de, J. Phys. Condens. Matter 14 (2002) 2717–2743. [25] D.M. Ceperley, M. Alder, Phys. Rev. Lett. 45 (1980) 566–569. [26] P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048–5079. [27] D.R. Hamann, M. Schluter, C. Chiang, Phys. Rev. Lett. 43 (1979) 1494–1497. [28] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188–5192. [29] T.H. Fischer, J. Almlof, J. Phys. Chem. 96 (1992) 9768–9774. [30] O. Madelung, U. Rossler, M. Schulz (Eds.), Londolt-Bornstein, in Condensed Matter, Ternary Compounds, Organic Semiconductor, New Series, Group III, vol. 41E, Springer-Verlag, Berlin, 2000. [31] F. Birch, J. Geophys. Res. 83 (1978) 1257–1268. [32] A.A. Vaipolin, Fiz. Trerd. Tela 15 (1973) 1430–1435 (Sov. Phys. Solid State 15 (1973) 965). [33] C. Rincon, Phys. Status Solidi A 134 (1992) 383–389. [34] B.N. Oshcherin, Phys. Status Solidi A 51 (1979) k175–k179. [35] R.G. Humphreys, B.R. Pamplin, J. De Physique C-3 (1975) 159–162. [36] H. Tributsch, Z Naturforsch A 32A (1977) 972–985. [37] Ali Hussain Reshak, Ph.D. thesis, Indian Institute of Technology-Rookee, India, 2005. [38] F. Chiker, Z. Kebbab, R. Miloua, N. Benramdane, Solid State Commun. 151 (2011) 1568–1573. [39] H. Momida, T. Hamada, Y. Takagi, T. Yamamoto, T. Uda, T. Ohno, Phys. Rev. B 73 (2006) 054108. 1–10. [40] T. Yamamoto, H. Momida, T. Hamada, T. Uda, T. Ohno, Thin Solid Films 486 (2005) 136–140. [41] R.R. Reddy, Y. Nazeer Ahammed, K. Rama Gopal, D.V. Raghuram, Opt. Mater. 10 (1998) 95–100. [42] A. Bouhemadou, R. Khenata, Comput. Mater. Sci. 39 (2007) 803–807. [43] R. Saniz, L.H. Ye, T. Shishidou, A.J. Freeman, Phys. Rev. B 74 (2006) 014209. 1–7. [44] J. Sun, H.T. Wang, N.B. Ming, J. He, Y. Tian, Appl. Phys. Lett. 84 (2004) 4544– 4546. [45] A.S. Poplavnoi, Izv. Vyssh. Uchebn. Zaved. Fiz. 29 (1986) 5. [46] H. Fu, D. Li, F. Peng, T. Gao, X. Cheng, Comput. Mater. Sci. 44 (2008) 774–778. [47] B. Mayer, H. Anton, E. Bott, M. Methfessel, J. Sticht, P.C. Schmidt, Intermetallics 11 (2003) 23–32.