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Structure, stability, electronic and thermoelectric properties of strontium chalcogenides
Journal Pre-proof Structure, Stability, Electronic and Thermoelectric Properties of Strontium Chalcogenides
Kaptan Rajput, Debesh R. Roy PII:
S1386-9477(19)31511-5
DOI:
https://doi.org/10.1016/j.physe.2020.113965
Reference:
PHYSE 113965
To appear in:
Physica E: Low-dimensional Systems and Nanostructures
Received Date:
02 October 2019
Accepted Date:
10 January 2020
Please cite this article as: Kaptan Rajput, Debesh R. Roy, Structure, Stability, Electronic and Thermoelectric Properties of Strontium Chalcogenides, Physica E: Low-dimensional Systems and Nanostructures (2020), https://doi.org/10.1016/j.physe.2020.113965
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GRAPHICAL ABSTRACT
Structure, Stability, Electronic and Thermoelectric Properties of Strontium Chalcogenides Kaptan Rajput and Debesh R. Roy* Materials and Biophysics Group, Department of Applied Physics, S. V. National Institute of Technology, Surat 395007, INDIA
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Structure, Stability, Electronic and Thermoelectric Properties of Strontium Chalcogenides Kaptan Rajput and Debesh R. Roy*
Materials and Biophysics Group, Department of Applied Physics, S. V. National Institute of Technology, Surat 395007, INDIA
Abstract The present investigation reports a critical insight on the temperature dependent transport properties of strontium chalcogenides (SrX; X=O, S, Se and Te) in their rock salt (rs-SrX) and hexagonal monolayer (h-SrX) phases, for the first time. For an initial check on the stability of these phases (rs-SrX and h-SrX), we have carried out phonon dispersion analysis under PAWGGA level of calculations. Although, some of these structures are reported to be unstable under lower level (PAW-LDA) of calculations in past, our PAW-GGA computations reveals all the rsSrX and h-SrX phases to be dynamically stable. The stability of all these structures along with wide band (indirect) gap certainly motivates us to look for their thermoelectric properties, for the first time. The electronic band structures and projected density of states (PDOS) of these materials are computed to understand their electronic properties. Finally, in order to obtain temperature dependent transport properties for the considered series, we have utilized the semiclassical Boltzmann transport equations (BTE). The Seebeck coefficient (S), electrical conductivity (σ), thermal conductivity (κ) and figure of merit (ZT) are calculated using BTE. Couple of monolayers (h-SrS and h-SrTe) and bulk (rock salt) phases (rs-SrO and rs-SrS) are come up with excellent thermoelectric properties through the present investigation.
Keywords: Strontium chalcogenides, Density functional theory, Band structure, Density of states, Thermoelectrics *Email: [email protected] ; Tel: +91 (261) 2204184; Fax: +91 (261) 2227334 ORCID ID: 0000-0001-9155-388X (DRR)
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Introduction A rapid evolution in personal transportations in comparison to the public transportations, industrialization, home appliances etc. in the twenty-first century causes severe depletion of gasoline and electricity in the environment. According to the recent surveys, transportation utilizes about 30% consumption of the primary energy resources, and exhaust CO2 gases which pollutes the environment and enhances the global warming. The increasing energy requirement of today’s technologically advanced society demands efficient, novel and eco-friendly resources. Due to the depletion of the fossil fuel it becomes essential to search for alternative renewable energy resources to generate electricity. In this regard, the thermoelectric module attracts great attention which can be utilized to convert the waste heat into electricity. An extensive effort has been tendered by the researches on the development suitable thermoelectric materials. The group II (alkaline-earth) chalcogenides materials, viz. GII-X (X=O, S, Se and Te) gained huge attention due to their closed shell ionic configuration and provides interesting results in the area of optoelectronic devices [1–3]. Among various GII chalcogenides, strontium chalcogenides (SrX, X=O, S, Se and Te) have gained major interest for their diverse applications in microelectronics, catalysis and optoelectronic devices [4–6]. There are several experimental as well as theoretical reports on SrX materials among which the pressure dependent structural properties (especially phase change from NaCl to CsCl) is widely studied [7, 8]. Also, investigations on various physicochemical properties such as electronic band structure and its dependence on pressure, optical and vibrational properties, elastic properties and metallification process of SrX have been attempted successfully by the researchers [9–17]. The electronic and vibrational properties of monolayer hexagonal SrX are investigated by Zheng et al. [18] in past. They have reported the monolayer hexagonal phases the SrO and SrTe to be unstable under local density approximation of density functional theory (DFT) [19, 20] with electronic band gap range from 1.63 to 2.77 eV [18]. Although a number of studies on various physicochemical properties of SrX series is performed by the researchers, no work on the thermoelectric properties is attempted so far for both the bulk (rock-salt) and hexagonal monolayer phases of SrX (X=O, S, Se and Te) materials. The present work is a sincere attempt along this direction. Various thermoelectric properties, e.g. Seebeck coefficient (S), electrical (σ) and thermal (κ) conductivities, figure of merit (ZT) etc. are calculated and compared for both the rock-salt and monolayer phases. It is noticed from our past study [21] on calcium chalcogenides that reduction of dimension (bulk to monolayer) results in
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decrease of thermal conductivity (κ), whereas their Seebeck coefficient (S) and electrical conductivity (σ) enhances. It was revealed from the work that the monolayer CaS may achieve significant ZT for a wide range of temperature. The purpose of the present investigation is to look for the stability and thermoelectric efficiency for strontium chalcogenides series, viz. SrX (X=O, S, Se and Te) in both of their bulk (rs-SrX) and hexagonal monolayer (h-SrX) phases. A systematic step by step investigation on the geometry, vibrational, electronic and thermoelectric properties of SrX series is performed. The entire work is carried out by utilizing the density functional theory (DFT) [19, 20] methods and semi-classical Boltzmann transport equations (BTE) [22].
Computational Methods All the computations in the present work are performed under the density functional theory (DFT) [19, 20] investigation by utilizing Vienna ab initio simulation package (VASP) [23]. The projector augmented wave (PAW) method was employed to specify the effect of the ionic cores and generalized gradient approximation (GGA) as Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional to consider the electron-electron interactions [24, 25]. The kinetic energy cutoff is considered as 500 eV for both the rock-salt and hexagonal monolayer phases. The k-point mesh with Monkhorst-Pack (MP) scheme is considered as 20×20×20 and 20×20×1 for rock-salt and monolayer phases, respectively. On adopting the small displacement method, we have obtained the phonon dispersion spectrum for both the phases. To obtain the frequencies and high symmetrical k-path relations, we have utilized the PHON software [26]. Also, for the computation of projected density of states (PDOS) we have considered higher kpoint mesh as 27×27×27 for rock-salt and 27×27×1 for monolayer phases to avoid any inconsistency between band structures and their respective PDOS. Finally, for obtaining the thermoelectric properties of the considered phases, we have adopted 40×40×40 and 40×40×1 dense k-point meshes with the Monkhorst-Pack (MP) scheme. The electron transport properties are calculated based on the semi-classical Boltzmann transport equations (BTE), where the constant time approximation and rigid band approximations (RBA) are considered by utilizing the BoltzTraP code [22].
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Results and Discussion In the present work, we have tendered a sincere effort on investigating two different phases of strontium chalcogenides (SrX; X=O, S, Se and Te), viz. rock-salt (rs-SrX) and hexagonal monolayer (h-SrX). The energy minimized structures for the most stable form of rsSrX and h-SrX are obtained under GGA-PBE level of calculations and presented in Fig. 1. The rock salt phase consists of two atoms as Sr and X, where Sr is sits at origin and the X atom is placed at center of the unit cell with face centered cubic (fcc) lattice architecture. On the other hand, in hexagonal monolayer phase, Sr and X atoms lies in hexagonal symmetry in the unit cell.
Fig. 1 Energy minimized geometries of the strontium chalcogenides (SrX; X=O, S, Se and Te) in (a) rock-salt and (b) hexagonal monolayer phases. The hexagonal monolayer phase is presented in both the top and side views. The obtained lattice parameters (a) for different SrX phases are provided in Table 1.
Table 1 presents the obtained lattice parameters and cohesive energies of both the rock salt and monolayer phases of strontium chalcogenides (SrX; X=O, S, Se and Te). The computed lattice constants are found to be in good agreement with the available experimental results and other theoretical results. It may be noted that when an atom get arranged in crystalline state from gaseous state, the formation energy is stored in the form of cohesive energy (Ecoh). This cohesive energy provides the information on the stability of materials in terms of mechanical strength of the materials. It is also known that cohesive energy of semiconductors and insulators are larger in comparison to metals [27]. The obtained range of cohesive energy for SrX phases are quite large
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between 6.872 eV and 11.895 eV, which essentially identifies our considered strontium chalcogenides (SrX) as the member of semiconductor or insulator families. Table 1 The obtained lattice constants (a) along with the available experimental and others computed data, and cohesive energy (Ec) of rock salt and monolayer phases of strontium chalcogenides (SrX; X=O, S, Se and Te). Compounds SrO SrS SrSe SrTe
Phases
a (Ǻ)
Others calc. a (Ǻ)
Expt. a (Ǻ)
Ecoh (eV)
rock-salt hexagonal rock-salt hexagonal rock-salt hexagonal rock-salt hexagonal
5.184 4.041 6.055 4.841 6.300 5.050 6.718 5.434
5.180 [28], 5.198[29] 3.980 [18] 6.050 [31], 6.076 [32] 4.760 [18] 6.290 [31], 6.320 [32] 4.950 [18] 6.71 [31], 6.760[32] 5.320 [18]
5.160[30]
11.895 10.877 9.001 8.617 9.128 7.855 8.113 6.872
6.024[33] 6.230[7] 6.660[8]
Vibrational and electronic properties of SrX The vibrational properties are having the major importance in materials study which essentially can provide the information on the materials dynamical stability. In order to investigate vibrational properties of the considered phases of SrX, we have obtained frequency relations along the high symmetrical k-path, viz. phonon dispersion relation. In the following section, we have also reported various electronic properties which includes electronic band structure and projected density of state for all the considered SrX (X=O, S, Se and Te) compounds in both of their rock-salt and monolayer phases. 1. Strontium Oxide (SrO) The calculated frequency relation along the high symmetrical k-path (phonon spectra) at zero pressure and zero Kelvin for both the phases of strontium oxide (SrO) are represented in Fig. 2(a) and (b), respectively. Fig. 2(a) and (b) indicates that for both the considered phases, acoustical branches lie within the positive frequency region. It is noticed from a previously published literature by Zheng at el. [18] that the hexagonal monolayer SrO is non-stable under a lower level (local density approximations) of calculation. In the present work at a higher level (GGA-PBE) of calculations, we have found that the hexagonal monolayer of SrO (h-SrO) is
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dynamically stable phase. In both the phases of SrO, there exists six phononic modes in which 3 belongs to acoustical branches and remaining are optical branches. These branches are generally having dependency on the number of atoms in unit-cell. All the positive acoustical branches for both the rock salt and monolayer phases indicate their dynamical stability.
Fig. 2 The phonon dispersion curves of SrO for (a) rock-salt and (b) hexagonal monolayer phases.
After obtaining the dynamical stability for both the rs-SrO and h-SrO, we have further explored their electronic band structure with the respective optimized lattice parameters, and are represented in Fig. 3(a) and (b). The position of the valence band maximum (VBM) and the conduction band minimum (CBM) for both the phases may be noted from the figures, which shows that VBM lies at Γ point for rock-salt phases and at K point for hexagonal monolayer phase. On the other hand, the CBM lies at X for rock-salt and at Γ for hexagonal monolayer phases. Overall, it is found that both the rock-salt and monolayer phases are having indirect energy band gaps of 3.28 eV and 1.76 eV, respectively.
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Fig. 3 The electronic band structures of SrO for (a) rock-salt and (b) hexagonal monolayer phases.
The electronic properties of materials may be understood more significantly through the investigation on their orbital contributions in their respective existing phases. In order to obtain the electronic characteristics of materials, we have computed the projected density of state (PDOS) and are represented in the Fig. 4(a) and (b) for rock-salt and hexagonal monolayer phases, respectively. It may be noticed from Fig. 4 that the orbital contributions in both the phases are quite similar, e.g. in both the phases near the Fermi level in valence band, the porbital of oxygen atom shows larger and p-orbital of strontium atom shows the minimum contributions. On the other hand, in conduction band region, the s-orbital of strontium atom and p-orbital oxygen atom shows minimum contribution in case of rock-salt phase, whereas in hexagonal monolayer case only s-orbital of strontium atom shows contribution. It may be understood that indirect energy band gap for both the phases arises due to the major contribution of p-orbital of oxygen and s-orbital of strontium atoms.
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Fig. 4 The projected density of state (PDOS) of SrO for (a) rock-salt and (b) hexagonal monolayer phases.
2. Strontium Sulfide (SrS) The obtained frequency relation along the high symmetrical k-path at ambient conditions for rock-salt and hexagonal monolayer phases of strontium sulfide (SrS) are depicted in Fig. 5(a) and (b), respectively. Similar to the SrO (Fig. 2), it is noticed that the acoustical branches of strontium sulfide are also lies in the positive frequency region. Also, there are six phononic modes available for both the phases having three modes each for acoustical and optical branches. The positive frequency domain of the acoustical branches indicates the dynamical stability for both the rock-salt and hexagonal monolayer phases of SrS.
Fig. 5 The phonon dispersion curves of SrS for (a) rock-salt and (b) hexagonal monolayer phases.
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We have further investigated the electronic properties of strontium sulfide (SrS) with its optimized lattice parameters for both the rock-salt and hexagonal phases as shown in Fig. 6(a) and (b), respectively. The locations of the valence band maximum (VBM) and the conduction band minimum (CBM) for the rock-salt phase are found similar to that of rs-SrO. The VBM is found to be at Γ point for rock-salt phase and at M point for hexagonal monolayer phase, and the CBM’s are located at X point for rock-salt phase and at Γ point for hexagonal monolayer phase. In a nutshell, it is found that both the rock-salt and monolayer phases of SrS are having indirect energy band gaps of 2.49 eV and 2.88 eV, respectively.
Fig. 6 The electronic band structures of SrS for (a) rock-salt and (b) hexagonal monolayer phases. The projected density of states (PDOS) of SrS phases are reported in Fig. 7(a) and (b) for rock-salt and monolayer phases, respectively. It may be noted from Fig. 7 that the orbital contributions in both the phases are quite similar, and also having similar behavior with PDOS of SrO phases. Near the Fermi level in valence band, the p-orbital of sulfur atoms shows major contribution, whereas the p-orbital of strontium atom shows lesser contribution for both the phases. On the other hand, in conduction band region, the s and p-orbital of surfer atoms and porbital of strontium atoms shows contributions in case of rock-salt phase, but has lower contribution in compare to the same as in VBM. In case of hexagonal monolayer, s and p-orbitals of sulfur atom and s-orbital of strontium shows major contributions. Overall, it appears from the PDOS analysis of SrS that the indirect energy band gap in both the considered phases arises due to the major contributions of p-orbital of sulfur and s- and p-orbital of strontium atoms.
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Fig. 7 The projected density of state (PDOS) of SrS for (a) rock-salt and (b) hexagonal monolayer phases.
3. Strontium Selenide (SrSe) The computed phonon dispersion spectra along the high symmetrical k-path for both the rock-salt and hexagonal monolayer phases of strontium selenide (SrSe) are depicted in Fig. 8(a) and (b), respectively. It may be noted that similar to SrO and SrS (Figs. 2 and 5), strontium selenide also shows positive acoustical branches in its allowed frequency domain. Also, in both the phases, available phononic modes are found to be six as also noticed in case of SrO and SrS. All the positive frequency domain of the acoustical branches confirms the dynamical stability for both the rock-salt and hexagonal monolayer phases of SrSe.
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Fig. 8 The phonon dispersion curves of SrSe for (a) rock-salt and (b) hexagonal monolayer phases.
The electronic properties of both the dynamically stable rock-salt and hexagonal monolayer phases at ambient conditions are further explored with their optimized lattice parameters, and presented in Fig. 9(a) and (b), respectively. The locations of valence band maximum (VBM) and the conduction band minimum (CBM) are found to be similar as that of SrO and SrS. The VBM lies at Γ point for rock-salt phase and at M point for hexagonal monolayer phase. The CBM lies at X for rock-salt phase and at Γ for hexagonal monolayer one. The band structures of both the rock-salt and monolayer phases of SrSe indicates their indirect nature of energy band gaps as 2.23 eV and 2.75 eV, respectively.
Fig. 9 The electronic band structures of SrSe for (a) rock-salt and (b) hexagonal monolayer phases.
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The projected density of state (PDOS) analysis of SrSe is reported in Fig. 10(a) and (b) for its rock-salt and hexagonal monolayer phases, respectively. It may be noted from the Fig. 10 that the orbital contributions in both the phases are quite similar to that of the SrO and SrS (Fig. 4 and Fig. 7). It is found that near the Fermi level in valence band of SrSe, the p-orbital of selenium atom shows major and p-orbital of strontium atom shows lower contributions in both the phases. In conduction band region, the s and p-orbitals of selenium atom and p-orbital of strontium atom shows major contributions for rock-salt phase. In case of hexagonal monolayer phase, the p-orbital of selenium atom and s-orbital of strontium shows major contributions. It may be concluded that the indirect energy band gap of SrSe arises due to the major contribution of p-orbitals of sulfur and strontium atoms for both the rock-salt and hexagonal monolayer phases.
Fig. 10 The projected density of states (PDOS) of SrSe for (a) rock-salt and (b) hexagonal monolayer phases. 4. Strontium Telluride (SrTe) The calculated phonon dispersion analysis along the high symmetrical k-path (at zero pressure and zero Kelvin) for both the rock-salt and hexagonal monolayer phases of strontium telluride (SrTe) are represented in Fig. 11(a) and (b), respectively. It may be noted that for both the phases of SrTe, all the acoustical modes are belongs to the positive frequency domain. However, in a previous work by Zheng at el. [18], the hexagonal monolayer phase of SrTe was reported to be unstable at a lower (LDA-pseudopotential based) level of calculations. In the present work, our considered higher level of calculation with ultra-soft pseudopotentials at the
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GGA-PBE level essentially reveal the hexagonal monolayer phase of SrTe as dynamically stable, with all of its acoustical modes as positive. Out of six phononic modes in both phases of SrTe, three of each belongs to acoustical and optical branches similar to the all other SrX (X=O, S and Se).
Fig. 11 The phonon dispersion curves of SrTe for (a) rock salt and (b) hexagonal monolayer phases. The electronic properties at ambient conditions with optimized lattice parameters for both rock-salt and hexagonal monolayer phases of SrTe are reported in Fig. 12(a) and (b), respectively. The VBM of SrTe is found to exist at Γ point for rock-salt phases, and at K point for hexagonal monolayer phase. Also, the CBM is found to exist at X point for rock-salt and at Γ point for hexagonal monolayer phases. Both the phases of SrTe are found to be indirect energy band gap semiconductors with energy gaps as 1.76 eV and 2.63 eV for the rock-salt and hexagonal monolayer structures, respectively.
Fig. 12 The electronic band structures of SrTe for (a) rock-salt and (b) hexagonal monolayer phases.
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The projected density of states (PDOS) of SrTe is reported in Fig. 13(a) and (b) for rocksalt and hexagonal monolayer phases, respectively. The orbital contributions in both the phases are found to be quite similar for VBM, and also having similar nature to the other SrX (X=O, S and Se). The p-orbital of Te atom shows major and p-orbital of Sr atom shows lower contributions near the Fermi level in VBM, for both the phases. In CBM region, s-orbital of Sr and Te atoms shows distinct contributions for rock-salt phase whereas for h-SrTe, the s and porbital of tellurium atom shows negligible contribution.
Fig. 13 The projected density of states (PDOS) of SrTe for (a) rock salt and (b) hexagonal monolayer phases.
In the present work, we have found all the considered strontium chalcogenides (SrX; X=O, S, Se and Te) as dynamically stable in both the rock-salt and hexagonal monolayer phases, and are indirect band gap semiconductors. The computed energy band gaps for all the considered phases along with the available values in literature by other researchers are presented in Table 2. It may be noted that our computed electronic band structures and energy gaps for all compounds are quite similar to that as reported by Khenata et al. [32] and Zheng et al. [18]. Also, a decreasing trend in energy band gap is noticed on increasing the size of chalcogenides atoms (Eg: SrO > SrS > SrSe > SrTe).
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Table 2 The calculated electronic band gaps of rock-salt and hexagonal monolayer phases of strontium chalcogenides (SrX; X=O, S, Se and Te) along with the same from other’s calculated values. Band Gap (Eg, eV)
Compounds
Phases
Direct
Indirect
SrO
rock-salt hexagonal rock-salt hexagonal rock-salt hexagonal rock-salt hexagonal
3.812 2.404 3.573 2.941 2.862 2.759 2.740 2.681
3.278 1.765 2.494 2.876 2.232 2.755 1.760 2.631
SrS SrSe SrTe
Other calc. (eV) Direct
Indirect
4.10 [34] 3.200 1.630 3.74 [32] 2.450 2.770 3.22 [32] 2.190 2.690 3.20 [32] 1.73 2.650
[34] [18] [32] [18] [32] [18] [32] [18]
Thermoelectric properties of SrX It may be noted that all the SrX phases are found to be wide and indirect band gap semiconductors (except for h-SrO and rs-SrTe), which motivate us to explore their possibilities in thermoelectrical applications especially generation of maximum thermoelectric power [35]. In a past work by Wickramaratne et al. [36] on thermoelectric investigation for layer based gallium and indium chalcogenides, it was noticed that single layer systems with wide energy gaps shows better thermoelectric properties compared to their multi-layers (of lower energy gaps) [36]. The present section provides a systematic study on the temperature dependent transport properties, viz. thermal conductivity (κ), electrical conductivity (σ), Seebeck coefficient (S) and figure of merit (ZT) for both the rock-salt and hexagonal monolayer phases of SrX, and represented in Fig. 14. The figure of merit (ZT) at a temperature T K of a material is defined as follows: ZT
S 2 T
(1)
Fig. 14(a) presents the response of thermal conductivity (κ) as a function of absolute temperature (T) for all the considered rock salt and monolayer phases of SrX compounds. The response of heat transport is recorded for a vast temperature range of 100-1200 K. The heat response behavior is mainly depends on the materials chemical compositions, structural
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symmetry, phase transition, grain size, temperature and pressure. In our present work, we have optimized the behavior of heat transport with respect to temperature and phases. It may be noted from the figure that the heat response in thermal conductivity is found to be larger in case of rock-salt phases in general compared to their hexagonal monolayer counterparts. The SrO in rock-salt phase shows larger thermal conductivity in the series, whereas the hexagonal monolayers of SrS and SrTe shows the minimum (also compared to their respective bulk counterparts). The electron transport response characteristics of materials in terms of electrical conductivity (σ) for both the rock-salt and hexagonal monolayer phases of SrX are presented in Fig. 14(b), for the temperature range of 100-1200 K. The electrical conductivity is primarily depends on the type of materials dimension, chemical composition and the stress states. The electrical conductivity for both the phases is noticed with slightly decreasing in nature with respect to the temperature rise. It may be noted that all the considered materials are having large electrical conductivities in which monolayer SrSe shows the maximum, and monolayers of SrS and SrTe shows the lowest in the series. Since electrical conductivity in a material depends on availability of charge carriers in wide band gap semiconductors, the presence of low amounts of charge carriers in the considered materials essentially leads a decreasing nature in σ with increase of temperature.
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Fig. 14 The calculated (a) thermal conductivity (κ), (b) electrical conductivity (σ), (c) Seebeck coefficient (S) and (d) figure of merit (ZT) for both the rock salt and hexagonal monolayer phases of SrX (X=O, S, Se and Te). The calculated Seebeck coefficient (thermoelectric power) with respect to temperature (range of 100-1200 K) for all the considered strontium chalcogenides (SrX) is reported in Fig. 14(c). It is understood that the temperature difference inside a material leads to the flows of charge carriers from hotter to colder side, resulting a potential difference known as thermoelectric voltage from which the Seebeck coefficients of SrX compounds are calculated. The sign of Seebeck coefficient does essentially decides the type of majority charge carriers in the system. Fig. 14(c) shows that both the types of carriers do exist in our considered materials, viz. (i) materials belongs in positive Seebeck coefficient region having the holes as majority charge carriers and (ii) materials lies in the negative Seebeck coefficient region has electrons as
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the majority charge carriers. It may be observed that monolayer SrS and SrSe as well as rock-salt SrO lies in the positive Seebeck region and the remaining appears in negative Seebeck region. Wickramaratne et al. [36] reported that the ring diameter of a monolayer plays significant role in thermoelectric properties of the materials. They have observed that the increase in ring diameter increases the Fermi energy resulting the modification in Seebeck coefficient. It may be noted from the present work that the maximum Seebeck coefficient in hexagonal monolayer of SrTe arises due to its maximum ring diameter compared to the other compounds in the SrX series. Finally, in order to check the efficiency of the considered thermoelectric materials we have computed the figure of merit (ZT) for both the rock-salt and hexagonal monolayer phases of SrX using Eqn. 1, and presented in Fig. 14(d). It may be noted from the Eqn. 1 that the figure of merit which essentially classifies the performance of a thermoelectric material depends on κ, σ and S at a given temperature. A good thermoelectric material should possess high Seebeck coefficient (S) and electrical conductivity (σ), and low thermal conductivity (κ). Fig. 14(d) shows that all the considered materials in both the rock-salt and monolayer phases has an increasing nature of ZT with respect to increasing temperature ranging between 100-1200 K. These results are quite similar to our previous study on calcium chacogenides in rock-salt and hexagonal monolayer phases [21]. It is heartening to note that all the considered materials possess good thermoelectric behaviors except for monolayers of SrO and SrSe. Overall, a couple of monolayer (h-SrTe and h-SrS) and rock salt phases (rs-SrO and rs-SrS) are found to be excellent thermoelectric materials with ZT > 0.8 for the temperature beyond 600 K, in which monolayers shows little better efficiency. This ZT value of these compounds are found to be comparable with the same to our previously reported CaS monolayer [21]. The strontium sulfide in both of its monolayer and rock salt phases reveal to be the best thermoelectric material in the considered SrX chalcogenides series.
Concluding Remarks In summary, detail investigation on the temperature dependent transport properties of rock-salt and hexagonal monolayer phases of strontium chalcogenides (SrX; X=O, S, Se and Te) is reported for the first time. It is heartening to note that under density functional GGA-PBE level of calculations, all of our considered strontium chalcogenides (SrX) in both of their rock-
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salt and monolayer phases are found to be dynamically stable, and therefore experimentally viable. Such observation overrules for few of these materials as reported to be unstable in past at a lower (DFT-LDA) level of calculation. The band characteristics are found to be similar for both the phases and all the SrX are found to be wide band (indirect) gap semiconductors, except for h-SrO and rs-SrTe. The calculated energy band gap for rock salt phase and monolayer phases are found to be in good agreement with available work by other researchers. PDOS analysis indicates that in both the rock-salt and monolayer phases, the p-orbitals of chalcogens atom near the Fermi level shows the major contribution in VBM region, whereas in CBM region the sorbital of strontium atom shows dominant contribution in general. The indirect energy band gap of all the considered SrX (in rock-salt and monolayer phases) may be understood due to the major contribution of p-orbital of chalcogens and p-orbital of strontium atoms. It is notable that couple of monolayer (h-SrS and h-SrTe) and rock salt phases (rs-SrO and rs-SrS) are reveal to be excellent thermoelectric materials with ZT > 0.8 (with a maximum of 1.44 for SrTe) for the temperature beyond 600 K. The strontium sulfide (in both of its monolayer and rock salt phases) reveals to be the best thermoelectric material in the considered series. The outcome of the present work will certainly help the experimentalist for their synthesis and relevant thermo power applications in future.
CRediT author statement: Kaptan Rajput: Methodology, Software, Investigation, Writing-Original Draft. Debesh R. Roy: Conceptualization, Supervision, Investigation, Funding Acquisition, Resources, WritingReviewing and Editing, Validation. Acknowledgements DRR is thankful to the SERB, New Delhi, Govt. of India for financial support (Grant No. EMR/2016/005830). KR is thankful to the SVNIT, Surat for his institute research fellowship (FIR-D17PH002). DRR and KR are also thankful for the High-Performance Computing facility at CDAC, Pune and IUAC, New Delhi. Conflict of Interest The authors declare that they have no conflict of interest.
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References [1] Pandey R, Sivaraman S (1991) Spectroscopic properties of defects in alkaline-earth sulfides. Journal of Physics and Chemistry of Solids 52:211–225 [2] Nakanishi Y, Ito T, Hatanaka Y, Shimaoka G (1993) Preparation and luminescent properties of SrSe: Ce thin films. Applied surface science 65:515–519 [3] Rao RP (1986) The preparation and thermoluminescence of alkaline earth sulphide phosphors. Journal of materials science 21:3357–3386 [4] Kaneko Y, Koda T (1988) New developments in IIa–VIb (alkaline-earth chalcogenide) binary semiconductors. Journal of Crystal Growth 86:72–78 [5] Asano S, Yamashita N, Nakao Y (1978) Luminescence of the Pb2+-Ion Dimer Center in CaS and CaSe Phosphors. Physica Status Solidi (b) 89:663–673 [6] Yamashita N, Ohira T, Mizuochi H, Asano S (1984) Luminescence of Pb2+ centers in SrS and SrSe phosphors. Journal of the Physical Society of Japan 53:419–426 [7] Luo H, Greene RG, Ruoff AL (1994) High-pressure phase transformation and the equation of state of SrSe. Physical Review B 49:15341 [8] Zimmer HG, Winzen H, Syassen K (1985) High-pressure phase transitions in CaTe and SrTe. Physical Review B 32:4066 [9] Labidi S, Meradji H, Labidi M, Ghemid S, Drablia S, Hassan FEH (2009) First principles calculations of structural, electronic and thermodynamic properties of SrS, SrSe, SrTe compounds and SrS1− xSex alloy. Physics Procedia 2:1205–1212 [10] Syassen K, Christensen NE, Winzen H, Fischer K, Evers J (1987) Optical response and band-structure calculations of alkaline-earth tellurides under pressure. Physical Review B 35:4052 [11] Dadsetani M, Pourghazi A (2006) Optical properties of strontium monochalcogenides from first principles. Physical Review B 73:195102 [12] Marinelli F, Dupin H, Lichanot A (2000) Comparison of elastic constants and electronic structures in the series of the alkaline-earth selenides: a quantum chemical approach. Journal of Physics and Chemistry of Solids 61:1707–1715 [13] Pandey R, Lepak P, Jaffe JE (1992) Electronic structure of alkaline-earth selenides. Physical Review B 46:4976 [14] Bhardwaj P, Singh S, Gaur NK (2009) Phase transition, mechanical properties and stability of strontium chalcogenides under high pressure. Journal of Molecular Structure: THEOCHEM 897:95–99 [15] Varshney D, Kaurav N, Kinge R, Singh RK (2008) High pressure structural (B1–B2) phase transition and elastic properties of II–VI semiconducting Srchalcogens. Computational Materials Science 41:529–537 [16] Xiao-Cui Y, Ai-Min H, Jie Y, Yong-Hao H, Gang P, Chun-Xiao G, Guang-Tian Z (2008) Theoretical prediction for structural stabilities and optical properties of SrS, SrSe and SrTe under high pressure. Chinese Physics Letters 25:1807 [17] Banu IS, Rajagopalan M, Palanivel B, Kalpana G, Shenbagaraman P (1998) Structural and electronic properties of SrS, SrSe, and SrTe under pressure. Journal of low temperature physics 112:211–226
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[18] Zheng H, Li X-B, Chen N-K, Xie S-Y, Tian WQ, Chen Y, Xia H, Zhang SB, Sun H-B (2015) Monolayer II-VI semiconductors: A first-principles prediction. Physical Review B 92:115307 [19] Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136:B864 [20] Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140:A1133 [21] Rajput K, Roy DR (2019) h-CaS and h-CaSenanosheets in CaX (X= O, S, Se and Te) series: promising thermoelectric materials under DFT investigation. Applied Nanoscience 1–12 [22] Madsen GK, Singh DJ (2006) BoltzTraP. A code for calculating band-structure dependent quantities. Computer Physics Communications 175:67–71 [23] Kresse G, Furthmüller J (1996) Software VASP, vienna (1999). Phys Rev B 54:169 [24] Kresse G, Joubert D (1999) Fromultrasoft pseudopotentials to the projector augmentedwave method. Physical Review B 59:1758 [25] Blöchl PE (1994) Projector augmented-wave method. Physical review B 50:17953 [26] Alfe D (2009) PHON: A program to calculate phonons using the small displacement method. Computer Physics Communications 180:2622–2633 [27] Philipsen PHT, Baerends EJ (1996) Cohesive energy of 3d transition metals: density functional theory atomic and bulk calculations. Physical Review B 54:5326 [28] Cortona P, Monteleone AV (1996) Ab initio calculations of cohesive and structural properties of the alkali-earth oxides. Journal of Physics: Condensed Matter 8:8983 [29] Ghebouli MA, Ghebouli B, Bouhemadou A, Fatmi M, Bouamama K (2011) Structural, electronic, optical and thermodynamic properties of SrxCa1− xO, BaxSr1− xO and BaxCa1− xO alloys. Journal of Alloys and Compounds 509:1440–1447 [30] Liu L, Bassett WA (1973) Changes of the crystal structure and the lattice parameter of SrO at high pressure. Journal of Geophysical Research 78:8470–8473 [31] Souadkia M, Bennecer B, Kalarasse F, Mellouki A (2011) Ab initio calculation of vibrational and thermodynamic properties of SrX (S, Se, Te) in the B1 (NaCl) and B2 (CsCl) structures. Computational Materials Science 50:1701–1710 [32] Khenata R, Baltache H, Rérat M, Driz M, Sahnoun M, Bouhafs B, Abbar B (2003) Firstprinciple study of structural, electronic and elastic properties of SrS, SrSe and SrTe under pressure. Physica B: Condensed Matter 339:208–215 [33] Syassen K (1985) Pressure‐Induced Structural Transition in SrS. physica status solidi (a) 91:11–15 [34] Kalpana G, Palanivel B, Rajagopalan M (1995) Electronic and structural properties of alkaline-earth oxides under high pressure. Physical Review B 52:4 [35] Khachai H, Khenata R, Haddou A, Bouhemadou A, Boukortt A, Soudini B, Boukabrine F, Abid H (2009) First-principles study of structural, electronic and elastic properties under pressure of calcium chalcogenides. Phys Proc 2:921–925 [36] Wickramaratne D, Zahid F, Lake RK (2015) Electronic and thermoelectric properties of van der Waals materials with ring-shaped valence bands. Journal of Applied Physics 118:075101
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Conflicts of interest The authors declare that they have no conflict of interest.
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CRediT author statement: Kaptan Rajput: Methodology, Software, Investigation, Writing-Original Draft. Debesh R. Roy: Conceptualization, Supervision, Investigation, Funding Acquisition, Resources, Writing-Reviewing and Editing, Validation.
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Highlights
Presents first report on the thermoelectric properties of strontium chalcogenides (SrX)
SrX (X=O, S, Se, Te) in rock salt and monolayer phases are found to be stable
All the SrX are found mostly to be indirect wide band gap semiconductors
SrS in both phases reveals as the best thermoelectric material (ZT~1) in the series
Kaptan Rajput, Debesh R. Roy PII:
S1386-9477(19)31511-5
DOI:
https://doi.org/10.1016/j.physe.2020.113965
Reference:
PHYSE 113965
To appear in:
Physica E: Low-dimensional Systems and Nanostructures
Received Date:
02 October 2019
Accepted Date:
10 January 2020
Please cite this article as: Kaptan Rajput, Debesh R. Roy, Structure, Stability, Electronic and Thermoelectric Properties of Strontium Chalcogenides, Physica E: Low-dimensional Systems and Nanostructures (2020), https://doi.org/10.1016/j.physe.2020.113965
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GRAPHICAL ABSTRACT
Structure, Stability, Electronic and Thermoelectric Properties of Strontium Chalcogenides Kaptan Rajput and Debesh R. Roy* Materials and Biophysics Group, Department of Applied Physics, S. V. National Institute of Technology, Surat 395007, INDIA
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Structure, Stability, Electronic and Thermoelectric Properties of Strontium Chalcogenides Kaptan Rajput and Debesh R. Roy*
Materials and Biophysics Group, Department of Applied Physics, S. V. National Institute of Technology, Surat 395007, INDIA
Abstract The present investigation reports a critical insight on the temperature dependent transport properties of strontium chalcogenides (SrX; X=O, S, Se and Te) in their rock salt (rs-SrX) and hexagonal monolayer (h-SrX) phases, for the first time. For an initial check on the stability of these phases (rs-SrX and h-SrX), we have carried out phonon dispersion analysis under PAWGGA level of calculations. Although, some of these structures are reported to be unstable under lower level (PAW-LDA) of calculations in past, our PAW-GGA computations reveals all the rsSrX and h-SrX phases to be dynamically stable. The stability of all these structures along with wide band (indirect) gap certainly motivates us to look for their thermoelectric properties, for the first time. The electronic band structures and projected density of states (PDOS) of these materials are computed to understand their electronic properties. Finally, in order to obtain temperature dependent transport properties for the considered series, we have utilized the semiclassical Boltzmann transport equations (BTE). The Seebeck coefficient (S), electrical conductivity (σ), thermal conductivity (κ) and figure of merit (ZT) are calculated using BTE. Couple of monolayers (h-SrS and h-SrTe) and bulk (rock salt) phases (rs-SrO and rs-SrS) are come up with excellent thermoelectric properties through the present investigation.
Keywords: Strontium chalcogenides, Density functional theory, Band structure, Density of states, Thermoelectrics *Email: [email protected] ; Tel: +91 (261) 2204184; Fax: +91 (261) 2227334 ORCID ID: 0000-0001-9155-388X (DRR)
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Introduction A rapid evolution in personal transportations in comparison to the public transportations, industrialization, home appliances etc. in the twenty-first century causes severe depletion of gasoline and electricity in the environment. According to the recent surveys, transportation utilizes about 30% consumption of the primary energy resources, and exhaust CO2 gases which pollutes the environment and enhances the global warming. The increasing energy requirement of today’s technologically advanced society demands efficient, novel and eco-friendly resources. Due to the depletion of the fossil fuel it becomes essential to search for alternative renewable energy resources to generate electricity. In this regard, the thermoelectric module attracts great attention which can be utilized to convert the waste heat into electricity. An extensive effort has been tendered by the researches on the development suitable thermoelectric materials. The group II (alkaline-earth) chalcogenides materials, viz. GII-X (X=O, S, Se and Te) gained huge attention due to their closed shell ionic configuration and provides interesting results in the area of optoelectronic devices [1–3]. Among various GII chalcogenides, strontium chalcogenides (SrX, X=O, S, Se and Te) have gained major interest for their diverse applications in microelectronics, catalysis and optoelectronic devices [4–6]. There are several experimental as well as theoretical reports on SrX materials among which the pressure dependent structural properties (especially phase change from NaCl to CsCl) is widely studied [7, 8]. Also, investigations on various physicochemical properties such as electronic band structure and its dependence on pressure, optical and vibrational properties, elastic properties and metallification process of SrX have been attempted successfully by the researchers [9–17]. The electronic and vibrational properties of monolayer hexagonal SrX are investigated by Zheng et al. [18] in past. They have reported the monolayer hexagonal phases the SrO and SrTe to be unstable under local density approximation of density functional theory (DFT) [19, 20] with electronic band gap range from 1.63 to 2.77 eV [18]. Although a number of studies on various physicochemical properties of SrX series is performed by the researchers, no work on the thermoelectric properties is attempted so far for both the bulk (rock-salt) and hexagonal monolayer phases of SrX (X=O, S, Se and Te) materials. The present work is a sincere attempt along this direction. Various thermoelectric properties, e.g. Seebeck coefficient (S), electrical (σ) and thermal (κ) conductivities, figure of merit (ZT) etc. are calculated and compared for both the rock-salt and monolayer phases. It is noticed from our past study [21] on calcium chalcogenides that reduction of dimension (bulk to monolayer) results in
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decrease of thermal conductivity (κ), whereas their Seebeck coefficient (S) and electrical conductivity (σ) enhances. It was revealed from the work that the monolayer CaS may achieve significant ZT for a wide range of temperature. The purpose of the present investigation is to look for the stability and thermoelectric efficiency for strontium chalcogenides series, viz. SrX (X=O, S, Se and Te) in both of their bulk (rs-SrX) and hexagonal monolayer (h-SrX) phases. A systematic step by step investigation on the geometry, vibrational, electronic and thermoelectric properties of SrX series is performed. The entire work is carried out by utilizing the density functional theory (DFT) [19, 20] methods and semi-classical Boltzmann transport equations (BTE) [22].
Computational Methods All the computations in the present work are performed under the density functional theory (DFT) [19, 20] investigation by utilizing Vienna ab initio simulation package (VASP) [23]. The projector augmented wave (PAW) method was employed to specify the effect of the ionic cores and generalized gradient approximation (GGA) as Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional to consider the electron-electron interactions [24, 25]. The kinetic energy cutoff is considered as 500 eV for both the rock-salt and hexagonal monolayer phases. The k-point mesh with Monkhorst-Pack (MP) scheme is considered as 20×20×20 and 20×20×1 for rock-salt and monolayer phases, respectively. On adopting the small displacement method, we have obtained the phonon dispersion spectrum for both the phases. To obtain the frequencies and high symmetrical k-path relations, we have utilized the PHON software [26]. Also, for the computation of projected density of states (PDOS) we have considered higher kpoint mesh as 27×27×27 for rock-salt and 27×27×1 for monolayer phases to avoid any inconsistency between band structures and their respective PDOS. Finally, for obtaining the thermoelectric properties of the considered phases, we have adopted 40×40×40 and 40×40×1 dense k-point meshes with the Monkhorst-Pack (MP) scheme. The electron transport properties are calculated based on the semi-classical Boltzmann transport equations (BTE), where the constant time approximation and rigid band approximations (RBA) are considered by utilizing the BoltzTraP code [22].
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Results and Discussion In the present work, we have tendered a sincere effort on investigating two different phases of strontium chalcogenides (SrX; X=O, S, Se and Te), viz. rock-salt (rs-SrX) and hexagonal monolayer (h-SrX). The energy minimized structures for the most stable form of rsSrX and h-SrX are obtained under GGA-PBE level of calculations and presented in Fig. 1. The rock salt phase consists of two atoms as Sr and X, where Sr is sits at origin and the X atom is placed at center of the unit cell with face centered cubic (fcc) lattice architecture. On the other hand, in hexagonal monolayer phase, Sr and X atoms lies in hexagonal symmetry in the unit cell.
Fig. 1 Energy minimized geometries of the strontium chalcogenides (SrX; X=O, S, Se and Te) in (a) rock-salt and (b) hexagonal monolayer phases. The hexagonal monolayer phase is presented in both the top and side views. The obtained lattice parameters (a) for different SrX phases are provided in Table 1.
Table 1 presents the obtained lattice parameters and cohesive energies of both the rock salt and monolayer phases of strontium chalcogenides (SrX; X=O, S, Se and Te). The computed lattice constants are found to be in good agreement with the available experimental results and other theoretical results. It may be noted that when an atom get arranged in crystalline state from gaseous state, the formation energy is stored in the form of cohesive energy (Ecoh). This cohesive energy provides the information on the stability of materials in terms of mechanical strength of the materials. It is also known that cohesive energy of semiconductors and insulators are larger in comparison to metals [27]. The obtained range of cohesive energy for SrX phases are quite large
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between 6.872 eV and 11.895 eV, which essentially identifies our considered strontium chalcogenides (SrX) as the member of semiconductor or insulator families. Table 1 The obtained lattice constants (a) along with the available experimental and others computed data, and cohesive energy (Ec) of rock salt and monolayer phases of strontium chalcogenides (SrX; X=O, S, Se and Te). Compounds SrO SrS SrSe SrTe
Phases
a (Ǻ)
Others calc. a (Ǻ)
Expt. a (Ǻ)
Ecoh (eV)
rock-salt hexagonal rock-salt hexagonal rock-salt hexagonal rock-salt hexagonal
5.184 4.041 6.055 4.841 6.300 5.050 6.718 5.434
5.180 [28], 5.198[29] 3.980 [18] 6.050 [31], 6.076 [32] 4.760 [18] 6.290 [31], 6.320 [32] 4.950 [18] 6.71 [31], 6.760[32] 5.320 [18]
5.160[30]
11.895 10.877 9.001 8.617 9.128 7.855 8.113 6.872
6.024[33] 6.230[7] 6.660[8]
Vibrational and electronic properties of SrX The vibrational properties are having the major importance in materials study which essentially can provide the information on the materials dynamical stability. In order to investigate vibrational properties of the considered phases of SrX, we have obtained frequency relations along the high symmetrical k-path, viz. phonon dispersion relation. In the following section, we have also reported various electronic properties which includes electronic band structure and projected density of state for all the considered SrX (X=O, S, Se and Te) compounds in both of their rock-salt and monolayer phases. 1. Strontium Oxide (SrO) The calculated frequency relation along the high symmetrical k-path (phonon spectra) at zero pressure and zero Kelvin for both the phases of strontium oxide (SrO) are represented in Fig. 2(a) and (b), respectively. Fig. 2(a) and (b) indicates that for both the considered phases, acoustical branches lie within the positive frequency region. It is noticed from a previously published literature by Zheng at el. [18] that the hexagonal monolayer SrO is non-stable under a lower level (local density approximations) of calculation. In the present work at a higher level (GGA-PBE) of calculations, we have found that the hexagonal monolayer of SrO (h-SrO) is
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dynamically stable phase. In both the phases of SrO, there exists six phononic modes in which 3 belongs to acoustical branches and remaining are optical branches. These branches are generally having dependency on the number of atoms in unit-cell. All the positive acoustical branches for both the rock salt and monolayer phases indicate their dynamical stability.
Fig. 2 The phonon dispersion curves of SrO for (a) rock-salt and (b) hexagonal monolayer phases.
After obtaining the dynamical stability for both the rs-SrO and h-SrO, we have further explored their electronic band structure with the respective optimized lattice parameters, and are represented in Fig. 3(a) and (b). The position of the valence band maximum (VBM) and the conduction band minimum (CBM) for both the phases may be noted from the figures, which shows that VBM lies at Γ point for rock-salt phases and at K point for hexagonal monolayer phase. On the other hand, the CBM lies at X for rock-salt and at Γ for hexagonal monolayer phases. Overall, it is found that both the rock-salt and monolayer phases are having indirect energy band gaps of 3.28 eV and 1.76 eV, respectively.
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Fig. 3 The electronic band structures of SrO for (a) rock-salt and (b) hexagonal monolayer phases.
The electronic properties of materials may be understood more significantly through the investigation on their orbital contributions in their respective existing phases. In order to obtain the electronic characteristics of materials, we have computed the projected density of state (PDOS) and are represented in the Fig. 4(a) and (b) for rock-salt and hexagonal monolayer phases, respectively. It may be noticed from Fig. 4 that the orbital contributions in both the phases are quite similar, e.g. in both the phases near the Fermi level in valence band, the porbital of oxygen atom shows larger and p-orbital of strontium atom shows the minimum contributions. On the other hand, in conduction band region, the s-orbital of strontium atom and p-orbital oxygen atom shows minimum contribution in case of rock-salt phase, whereas in hexagonal monolayer case only s-orbital of strontium atom shows contribution. It may be understood that indirect energy band gap for both the phases arises due to the major contribution of p-orbital of oxygen and s-orbital of strontium atoms.
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Fig. 4 The projected density of state (PDOS) of SrO for (a) rock-salt and (b) hexagonal monolayer phases.
2. Strontium Sulfide (SrS) The obtained frequency relation along the high symmetrical k-path at ambient conditions for rock-salt and hexagonal monolayer phases of strontium sulfide (SrS) are depicted in Fig. 5(a) and (b), respectively. Similar to the SrO (Fig. 2), it is noticed that the acoustical branches of strontium sulfide are also lies in the positive frequency region. Also, there are six phononic modes available for both the phases having three modes each for acoustical and optical branches. The positive frequency domain of the acoustical branches indicates the dynamical stability for both the rock-salt and hexagonal monolayer phases of SrS.
Fig. 5 The phonon dispersion curves of SrS for (a) rock-salt and (b) hexagonal monolayer phases.
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We have further investigated the electronic properties of strontium sulfide (SrS) with its optimized lattice parameters for both the rock-salt and hexagonal phases as shown in Fig. 6(a) and (b), respectively. The locations of the valence band maximum (VBM) and the conduction band minimum (CBM) for the rock-salt phase are found similar to that of rs-SrO. The VBM is found to be at Γ point for rock-salt phase and at M point for hexagonal monolayer phase, and the CBM’s are located at X point for rock-salt phase and at Γ point for hexagonal monolayer phase. In a nutshell, it is found that both the rock-salt and monolayer phases of SrS are having indirect energy band gaps of 2.49 eV and 2.88 eV, respectively.
Fig. 6 The electronic band structures of SrS for (a) rock-salt and (b) hexagonal monolayer phases. The projected density of states (PDOS) of SrS phases are reported in Fig. 7(a) and (b) for rock-salt and monolayer phases, respectively. It may be noted from Fig. 7 that the orbital contributions in both the phases are quite similar, and also having similar behavior with PDOS of SrO phases. Near the Fermi level in valence band, the p-orbital of sulfur atoms shows major contribution, whereas the p-orbital of strontium atom shows lesser contribution for both the phases. On the other hand, in conduction band region, the s and p-orbital of surfer atoms and porbital of strontium atoms shows contributions in case of rock-salt phase, but has lower contribution in compare to the same as in VBM. In case of hexagonal monolayer, s and p-orbitals of sulfur atom and s-orbital of strontium shows major contributions. Overall, it appears from the PDOS analysis of SrS that the indirect energy band gap in both the considered phases arises due to the major contributions of p-orbital of sulfur and s- and p-orbital of strontium atoms.
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Fig. 7 The projected density of state (PDOS) of SrS for (a) rock-salt and (b) hexagonal monolayer phases.
3. Strontium Selenide (SrSe) The computed phonon dispersion spectra along the high symmetrical k-path for both the rock-salt and hexagonal monolayer phases of strontium selenide (SrSe) are depicted in Fig. 8(a) and (b), respectively. It may be noted that similar to SrO and SrS (Figs. 2 and 5), strontium selenide also shows positive acoustical branches in its allowed frequency domain. Also, in both the phases, available phononic modes are found to be six as also noticed in case of SrO and SrS. All the positive frequency domain of the acoustical branches confirms the dynamical stability for both the rock-salt and hexagonal monolayer phases of SrSe.
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Fig. 8 The phonon dispersion curves of SrSe for (a) rock-salt and (b) hexagonal monolayer phases.
The electronic properties of both the dynamically stable rock-salt and hexagonal monolayer phases at ambient conditions are further explored with their optimized lattice parameters, and presented in Fig. 9(a) and (b), respectively. The locations of valence band maximum (VBM) and the conduction band minimum (CBM) are found to be similar as that of SrO and SrS. The VBM lies at Γ point for rock-salt phase and at M point for hexagonal monolayer phase. The CBM lies at X for rock-salt phase and at Γ for hexagonal monolayer one. The band structures of both the rock-salt and monolayer phases of SrSe indicates their indirect nature of energy band gaps as 2.23 eV and 2.75 eV, respectively.
Fig. 9 The electronic band structures of SrSe for (a) rock-salt and (b) hexagonal monolayer phases.
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The projected density of state (PDOS) analysis of SrSe is reported in Fig. 10(a) and (b) for its rock-salt and hexagonal monolayer phases, respectively. It may be noted from the Fig. 10 that the orbital contributions in both the phases are quite similar to that of the SrO and SrS (Fig. 4 and Fig. 7). It is found that near the Fermi level in valence band of SrSe, the p-orbital of selenium atom shows major and p-orbital of strontium atom shows lower contributions in both the phases. In conduction band region, the s and p-orbitals of selenium atom and p-orbital of strontium atom shows major contributions for rock-salt phase. In case of hexagonal monolayer phase, the p-orbital of selenium atom and s-orbital of strontium shows major contributions. It may be concluded that the indirect energy band gap of SrSe arises due to the major contribution of p-orbitals of sulfur and strontium atoms for both the rock-salt and hexagonal monolayer phases.
Fig. 10 The projected density of states (PDOS) of SrSe for (a) rock-salt and (b) hexagonal monolayer phases. 4. Strontium Telluride (SrTe) The calculated phonon dispersion analysis along the high symmetrical k-path (at zero pressure and zero Kelvin) for both the rock-salt and hexagonal monolayer phases of strontium telluride (SrTe) are represented in Fig. 11(a) and (b), respectively. It may be noted that for both the phases of SrTe, all the acoustical modes are belongs to the positive frequency domain. However, in a previous work by Zheng at el. [18], the hexagonal monolayer phase of SrTe was reported to be unstable at a lower (LDA-pseudopotential based) level of calculations. In the present work, our considered higher level of calculation with ultra-soft pseudopotentials at the
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GGA-PBE level essentially reveal the hexagonal monolayer phase of SrTe as dynamically stable, with all of its acoustical modes as positive. Out of six phononic modes in both phases of SrTe, three of each belongs to acoustical and optical branches similar to the all other SrX (X=O, S and Se).
Fig. 11 The phonon dispersion curves of SrTe for (a) rock salt and (b) hexagonal monolayer phases. The electronic properties at ambient conditions with optimized lattice parameters for both rock-salt and hexagonal monolayer phases of SrTe are reported in Fig. 12(a) and (b), respectively. The VBM of SrTe is found to exist at Γ point for rock-salt phases, and at K point for hexagonal monolayer phase. Also, the CBM is found to exist at X point for rock-salt and at Γ point for hexagonal monolayer phases. Both the phases of SrTe are found to be indirect energy band gap semiconductors with energy gaps as 1.76 eV and 2.63 eV for the rock-salt and hexagonal monolayer structures, respectively.
Fig. 12 The electronic band structures of SrTe for (a) rock-salt and (b) hexagonal monolayer phases.
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The projected density of states (PDOS) of SrTe is reported in Fig. 13(a) and (b) for rocksalt and hexagonal monolayer phases, respectively. The orbital contributions in both the phases are found to be quite similar for VBM, and also having similar nature to the other SrX (X=O, S and Se). The p-orbital of Te atom shows major and p-orbital of Sr atom shows lower contributions near the Fermi level in VBM, for both the phases. In CBM region, s-orbital of Sr and Te atoms shows distinct contributions for rock-salt phase whereas for h-SrTe, the s and porbital of tellurium atom shows negligible contribution.
Fig. 13 The projected density of states (PDOS) of SrTe for (a) rock salt and (b) hexagonal monolayer phases.
In the present work, we have found all the considered strontium chalcogenides (SrX; X=O, S, Se and Te) as dynamically stable in both the rock-salt and hexagonal monolayer phases, and are indirect band gap semiconductors. The computed energy band gaps for all the considered phases along with the available values in literature by other researchers are presented in Table 2. It may be noted that our computed electronic band structures and energy gaps for all compounds are quite similar to that as reported by Khenata et al. [32] and Zheng et al. [18]. Also, a decreasing trend in energy band gap is noticed on increasing the size of chalcogenides atoms (Eg: SrO > SrS > SrSe > SrTe).
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Table 2 The calculated electronic band gaps of rock-salt and hexagonal monolayer phases of strontium chalcogenides (SrX; X=O, S, Se and Te) along with the same from other’s calculated values. Band Gap (Eg, eV)
Compounds
Phases
Direct
Indirect
SrO
rock-salt hexagonal rock-salt hexagonal rock-salt hexagonal rock-salt hexagonal
3.812 2.404 3.573 2.941 2.862 2.759 2.740 2.681
3.278 1.765 2.494 2.876 2.232 2.755 1.760 2.631
SrS SrSe SrTe
Other calc. (eV) Direct
Indirect
4.10 [34] 3.200 1.630 3.74 [32] 2.450 2.770 3.22 [32] 2.190 2.690 3.20 [32] 1.73 2.650
[34] [18] [32] [18] [32] [18] [32] [18]
Thermoelectric properties of SrX It may be noted that all the SrX phases are found to be wide and indirect band gap semiconductors (except for h-SrO and rs-SrTe), which motivate us to explore their possibilities in thermoelectrical applications especially generation of maximum thermoelectric power [35]. In a past work by Wickramaratne et al. [36] on thermoelectric investigation for layer based gallium and indium chalcogenides, it was noticed that single layer systems with wide energy gaps shows better thermoelectric properties compared to their multi-layers (of lower energy gaps) [36]. The present section provides a systematic study on the temperature dependent transport properties, viz. thermal conductivity (κ), electrical conductivity (σ), Seebeck coefficient (S) and figure of merit (ZT) for both the rock-salt and hexagonal monolayer phases of SrX, and represented in Fig. 14. The figure of merit (ZT) at a temperature T K of a material is defined as follows: ZT
S 2 T
(1)
Fig. 14(a) presents the response of thermal conductivity (κ) as a function of absolute temperature (T) for all the considered rock salt and monolayer phases of SrX compounds. The response of heat transport is recorded for a vast temperature range of 100-1200 K. The heat response behavior is mainly depends on the materials chemical compositions, structural
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symmetry, phase transition, grain size, temperature and pressure. In our present work, we have optimized the behavior of heat transport with respect to temperature and phases. It may be noted from the figure that the heat response in thermal conductivity is found to be larger in case of rock-salt phases in general compared to their hexagonal monolayer counterparts. The SrO in rock-salt phase shows larger thermal conductivity in the series, whereas the hexagonal monolayers of SrS and SrTe shows the minimum (also compared to their respective bulk counterparts). The electron transport response characteristics of materials in terms of electrical conductivity (σ) for both the rock-salt and hexagonal monolayer phases of SrX are presented in Fig. 14(b), for the temperature range of 100-1200 K. The electrical conductivity is primarily depends on the type of materials dimension, chemical composition and the stress states. The electrical conductivity for both the phases is noticed with slightly decreasing in nature with respect to the temperature rise. It may be noted that all the considered materials are having large electrical conductivities in which monolayer SrSe shows the maximum, and monolayers of SrS and SrTe shows the lowest in the series. Since electrical conductivity in a material depends on availability of charge carriers in wide band gap semiconductors, the presence of low amounts of charge carriers in the considered materials essentially leads a decreasing nature in σ with increase of temperature.
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Fig. 14 The calculated (a) thermal conductivity (κ), (b) electrical conductivity (σ), (c) Seebeck coefficient (S) and (d) figure of merit (ZT) for both the rock salt and hexagonal monolayer phases of SrX (X=O, S, Se and Te). The calculated Seebeck coefficient (thermoelectric power) with respect to temperature (range of 100-1200 K) for all the considered strontium chalcogenides (SrX) is reported in Fig. 14(c). It is understood that the temperature difference inside a material leads to the flows of charge carriers from hotter to colder side, resulting a potential difference known as thermoelectric voltage from which the Seebeck coefficients of SrX compounds are calculated. The sign of Seebeck coefficient does essentially decides the type of majority charge carriers in the system. Fig. 14(c) shows that both the types of carriers do exist in our considered materials, viz. (i) materials belongs in positive Seebeck coefficient region having the holes as majority charge carriers and (ii) materials lies in the negative Seebeck coefficient region has electrons as
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the majority charge carriers. It may be observed that monolayer SrS and SrSe as well as rock-salt SrO lies in the positive Seebeck region and the remaining appears in negative Seebeck region. Wickramaratne et al. [36] reported that the ring diameter of a monolayer plays significant role in thermoelectric properties of the materials. They have observed that the increase in ring diameter increases the Fermi energy resulting the modification in Seebeck coefficient. It may be noted from the present work that the maximum Seebeck coefficient in hexagonal monolayer of SrTe arises due to its maximum ring diameter compared to the other compounds in the SrX series. Finally, in order to check the efficiency of the considered thermoelectric materials we have computed the figure of merit (ZT) for both the rock-salt and hexagonal monolayer phases of SrX using Eqn. 1, and presented in Fig. 14(d). It may be noted from the Eqn. 1 that the figure of merit which essentially classifies the performance of a thermoelectric material depends on κ, σ and S at a given temperature. A good thermoelectric material should possess high Seebeck coefficient (S) and electrical conductivity (σ), and low thermal conductivity (κ). Fig. 14(d) shows that all the considered materials in both the rock-salt and monolayer phases has an increasing nature of ZT with respect to increasing temperature ranging between 100-1200 K. These results are quite similar to our previous study on calcium chacogenides in rock-salt and hexagonal monolayer phases [21]. It is heartening to note that all the considered materials possess good thermoelectric behaviors except for monolayers of SrO and SrSe. Overall, a couple of monolayer (h-SrTe and h-SrS) and rock salt phases (rs-SrO and rs-SrS) are found to be excellent thermoelectric materials with ZT > 0.8 for the temperature beyond 600 K, in which monolayers shows little better efficiency. This ZT value of these compounds are found to be comparable with the same to our previously reported CaS monolayer [21]. The strontium sulfide in both of its monolayer and rock salt phases reveal to be the best thermoelectric material in the considered SrX chalcogenides series.
Concluding Remarks In summary, detail investigation on the temperature dependent transport properties of rock-salt and hexagonal monolayer phases of strontium chalcogenides (SrX; X=O, S, Se and Te) is reported for the first time. It is heartening to note that under density functional GGA-PBE level of calculations, all of our considered strontium chalcogenides (SrX) in both of their rock-
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salt and monolayer phases are found to be dynamically stable, and therefore experimentally viable. Such observation overrules for few of these materials as reported to be unstable in past at a lower (DFT-LDA) level of calculation. The band characteristics are found to be similar for both the phases and all the SrX are found to be wide band (indirect) gap semiconductors, except for h-SrO and rs-SrTe. The calculated energy band gap for rock salt phase and monolayer phases are found to be in good agreement with available work by other researchers. PDOS analysis indicates that in both the rock-salt and monolayer phases, the p-orbitals of chalcogens atom near the Fermi level shows the major contribution in VBM region, whereas in CBM region the sorbital of strontium atom shows dominant contribution in general. The indirect energy band gap of all the considered SrX (in rock-salt and monolayer phases) may be understood due to the major contribution of p-orbital of chalcogens and p-orbital of strontium atoms. It is notable that couple of monolayer (h-SrS and h-SrTe) and rock salt phases (rs-SrO and rs-SrS) are reveal to be excellent thermoelectric materials with ZT > 0.8 (with a maximum of 1.44 for SrTe) for the temperature beyond 600 K. The strontium sulfide (in both of its monolayer and rock salt phases) reveals to be the best thermoelectric material in the considered series. The outcome of the present work will certainly help the experimentalist for their synthesis and relevant thermo power applications in future.
CRediT author statement: Kaptan Rajput: Methodology, Software, Investigation, Writing-Original Draft. Debesh R. Roy: Conceptualization, Supervision, Investigation, Funding Acquisition, Resources, WritingReviewing and Editing, Validation. Acknowledgements DRR is thankful to the SERB, New Delhi, Govt. of India for financial support (Grant No. EMR/2016/005830). KR is thankful to the SVNIT, Surat for his institute research fellowship (FIR-D17PH002). DRR and KR are also thankful for the High-Performance Computing facility at CDAC, Pune and IUAC, New Delhi. Conflict of Interest The authors declare that they have no conflict of interest.
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References [1] Pandey R, Sivaraman S (1991) Spectroscopic properties of defects in alkaline-earth sulfides. Journal of Physics and Chemistry of Solids 52:211–225 [2] Nakanishi Y, Ito T, Hatanaka Y, Shimaoka G (1993) Preparation and luminescent properties of SrSe: Ce thin films. Applied surface science 65:515–519 [3] Rao RP (1986) The preparation and thermoluminescence of alkaline earth sulphide phosphors. Journal of materials science 21:3357–3386 [4] Kaneko Y, Koda T (1988) New developments in IIa–VIb (alkaline-earth chalcogenide) binary semiconductors. Journal of Crystal Growth 86:72–78 [5] Asano S, Yamashita N, Nakao Y (1978) Luminescence of the Pb2+-Ion Dimer Center in CaS and CaSe Phosphors. Physica Status Solidi (b) 89:663–673 [6] Yamashita N, Ohira T, Mizuochi H, Asano S (1984) Luminescence of Pb2+ centers in SrS and SrSe phosphors. Journal of the Physical Society of Japan 53:419–426 [7] Luo H, Greene RG, Ruoff AL (1994) High-pressure phase transformation and the equation of state of SrSe. Physical Review B 49:15341 [8] Zimmer HG, Winzen H, Syassen K (1985) High-pressure phase transitions in CaTe and SrTe. Physical Review B 32:4066 [9] Labidi S, Meradji H, Labidi M, Ghemid S, Drablia S, Hassan FEH (2009) First principles calculations of structural, electronic and thermodynamic properties of SrS, SrSe, SrTe compounds and SrS1− xSex alloy. Physics Procedia 2:1205–1212 [10] Syassen K, Christensen NE, Winzen H, Fischer K, Evers J (1987) Optical response and band-structure calculations of alkaline-earth tellurides under pressure. Physical Review B 35:4052 [11] Dadsetani M, Pourghazi A (2006) Optical properties of strontium monochalcogenides from first principles. Physical Review B 73:195102 [12] Marinelli F, Dupin H, Lichanot A (2000) Comparison of elastic constants and electronic structures in the series of the alkaline-earth selenides: a quantum chemical approach. Journal of Physics and Chemistry of Solids 61:1707–1715 [13] Pandey R, Lepak P, Jaffe JE (1992) Electronic structure of alkaline-earth selenides. Physical Review B 46:4976 [14] Bhardwaj P, Singh S, Gaur NK (2009) Phase transition, mechanical properties and stability of strontium chalcogenides under high pressure. Journal of Molecular Structure: THEOCHEM 897:95–99 [15] Varshney D, Kaurav N, Kinge R, Singh RK (2008) High pressure structural (B1–B2) phase transition and elastic properties of II–VI semiconducting Srchalcogens. Computational Materials Science 41:529–537 [16] Xiao-Cui Y, Ai-Min H, Jie Y, Yong-Hao H, Gang P, Chun-Xiao G, Guang-Tian Z (2008) Theoretical prediction for structural stabilities and optical properties of SrS, SrSe and SrTe under high pressure. Chinese Physics Letters 25:1807 [17] Banu IS, Rajagopalan M, Palanivel B, Kalpana G, Shenbagaraman P (1998) Structural and electronic properties of SrS, SrSe, and SrTe under pressure. Journal of low temperature physics 112:211–226
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[18] Zheng H, Li X-B, Chen N-K, Xie S-Y, Tian WQ, Chen Y, Xia H, Zhang SB, Sun H-B (2015) Monolayer II-VI semiconductors: A first-principles prediction. Physical Review B 92:115307 [19] Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136:B864 [20] Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140:A1133 [21] Rajput K, Roy DR (2019) h-CaS and h-CaSenanosheets in CaX (X= O, S, Se and Te) series: promising thermoelectric materials under DFT investigation. Applied Nanoscience 1–12 [22] Madsen GK, Singh DJ (2006) BoltzTraP. A code for calculating band-structure dependent quantities. Computer Physics Communications 175:67–71 [23] Kresse G, Furthmüller J (1996) Software VASP, vienna (1999). Phys Rev B 54:169 [24] Kresse G, Joubert D (1999) Fromultrasoft pseudopotentials to the projector augmentedwave method. Physical Review B 59:1758 [25] Blöchl PE (1994) Projector augmented-wave method. Physical review B 50:17953 [26] Alfe D (2009) PHON: A program to calculate phonons using the small displacement method. Computer Physics Communications 180:2622–2633 [27] Philipsen PHT, Baerends EJ (1996) Cohesive energy of 3d transition metals: density functional theory atomic and bulk calculations. Physical Review B 54:5326 [28] Cortona P, Monteleone AV (1996) Ab initio calculations of cohesive and structural properties of the alkali-earth oxides. Journal of Physics: Condensed Matter 8:8983 [29] Ghebouli MA, Ghebouli B, Bouhemadou A, Fatmi M, Bouamama K (2011) Structural, electronic, optical and thermodynamic properties of SrxCa1− xO, BaxSr1− xO and BaxCa1− xO alloys. Journal of Alloys and Compounds 509:1440–1447 [30] Liu L, Bassett WA (1973) Changes of the crystal structure and the lattice parameter of SrO at high pressure. Journal of Geophysical Research 78:8470–8473 [31] Souadkia M, Bennecer B, Kalarasse F, Mellouki A (2011) Ab initio calculation of vibrational and thermodynamic properties of SrX (S, Se, Te) in the B1 (NaCl) and B2 (CsCl) structures. Computational Materials Science 50:1701–1710 [32] Khenata R, Baltache H, Rérat M, Driz M, Sahnoun M, Bouhafs B, Abbar B (2003) Firstprinciple study of structural, electronic and elastic properties of SrS, SrSe and SrTe under pressure. Physica B: Condensed Matter 339:208–215 [33] Syassen K (1985) Pressure‐Induced Structural Transition in SrS. physica status solidi (a) 91:11–15 [34] Kalpana G, Palanivel B, Rajagopalan M (1995) Electronic and structural properties of alkaline-earth oxides under high pressure. Physical Review B 52:4 [35] Khachai H, Khenata R, Haddou A, Bouhemadou A, Boukortt A, Soudini B, Boukabrine F, Abid H (2009) First-principles study of structural, electronic and elastic properties under pressure of calcium chalcogenides. Phys Proc 2:921–925 [36] Wickramaratne D, Zahid F, Lake RK (2015) Electronic and thermoelectric properties of van der Waals materials with ring-shaped valence bands. Journal of Applied Physics 118:075101
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Conflicts of interest The authors declare that they have no conflict of interest.
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CRediT author statement: Kaptan Rajput: Methodology, Software, Investigation, Writing-Original Draft. Debesh R. Roy: Conceptualization, Supervision, Investigation, Funding Acquisition, Resources, Writing-Reviewing and Editing, Validation.
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Highlights
Presents first report on the thermoelectric properties of strontium chalcogenides (SrX)
SrX (X=O, S, Se, Te) in rock salt and monolayer phases are found to be stable
All the SrX are found mostly to be indirect wide band gap semiconductors
SrS in both phases reveals as the best thermoelectric material (ZT~1) in the series