Electronic structure, optical and thermoelectric response of lead-free double perovskite BaMgLaBiO6: A first-principles study

doi:10.21203/rs.3.rs-1193686/v1

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Electronic structure, optical and thermoelectric response of lead-free double perovskite BaMgLaBiO6: A first-principles study

https://doi.org/10.21203/rs.3.rs-1193686/v1

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Electronic structure, optical and transport properties of double perovskite BaMgLaBiO₆ have been investigated theoretically with density functional theory (DFT) implemented in WIEN2k code. The structure is optimized to achieve the minimum energy at the ground state and the optimized lattice parameters. The calculated formation energy shows the stability of the compound, which confirms the possibility of synthesizing it. A band-gap of 2.7 eV is calculated with generalized gradient approximation (GGA) and further improvement, i.e., 3.8 eV is achieved with modified Becke-Johnson (mBJ) exchange potential. The electron density plots show both the covalent and ionic nature between the atoms. The calculated total density of states shows a good agreement with the band structure. The optical parameters are also calculated and a good optical conductivity is achieved in the selected energy range. The figure of merit is achieved up to 0.71 with mBJ which shows the suitability of the studied material for alternative energy devices. The overall response of the compound makes it a potential candidate for LED’s, lasers, power switching and thermoelectric applications.

Double perovskites

Density functional theory

Band-structure

Optoelectronics

Power Switching

The double perovskite oxides have attracted much attention because of their chemical flexibility and extensiveness of configurationally space spanning [1]. In the past few years, double perovskites have been studied extensively due to their extraordinary properties and promising technological applications [2–7]. They have obtained fundamental interest because of numerous interesting physical properties including spin-polarized half-metallic electrical conductivity, their unique electronic structure ranging from metallic to insulator [8–10], and superconductivity [11]. The perovskite structure with general formula ABX₃ (Space group Pm-3m) with cubic symmetry is formed by connecting BX₆ octahedral through corners (where A and B are cations). In the original perovskite, the charge on A and B cation may vary. Double perovskites are also the significant members of this family with different composition, structure and physical properties than the original perovskites. Double perovskites (general formula= A₂BB'X₆) are basically derived from perovskite have advanced technological applications in the field of magneto-dielectric, magneto-optics, half-metallic and spintronics [12, 13]. In double perovskites, A is a monovalent cation which is larger than monovalent B cation and halide ion X acts as potential alternatives [14]. The double perovskite halides have large carrier lifetimes in comparison with lead-based perovskites [15] and show high dispersed conduction and valence bands [16]. Recently, Ba₂ZnOsO₆ has been reported with a cubic structure having Fm-3m (225) space group [17]. A large number of perovskites, including double perovskites have been investigated for their physical properties [18–20]. Yun-Ping et al. [21] reported A₂CrMO₆ for half-metallic properties based on first-principles calculation. Mostly reported double perovskites have shown an indirect band-gap in the range of 2-5 eV. It limits the utilization of solar spectrum effectively [16]. The degradation of Cs₂AgBiBr₆ is observed on exposure to light and ambient air [16]. The composition space for merging different cations A and B by using monovalent halides restricts to achieve the required properties [22]. Recently, optoelectronic, magnetic and thermodynamic properties of double perovskite oxide have been studied [23–25]. The thermoelectric phenomenon is the process of refurbishing useless heat into useful electricity. The figure of merit (ZT) is the most important parameter while calculating the thermoelectric ability of the material [26]. The efficiency of any thermoelectric material can be enhanced with the improved ZT value [27]. The ZT value acceptable for real devices is still a challenge. To achieve a stable structure of perovskite and address the above-mentioned challenges, a new class of double perovskites with a general stoichiometry A'A''B'BiO₆ containing Bi³⁺ cations in the 3D octahedral framework is introduced [4]. The structures related to this class are widely studied and show good properties for practical devices [28–30]. In the present work, we have studied the lead-free BaLaMgBiO₆ double perovskite under the framework of density functional theory (DFT) using wien2k code. According to the author’s best knowledge, so far, no DFT-based study has been done on the said compound to explore its properties. We will calculate the structural, electronic, and optical properties of the BaLaMgBiO₆ compound to investigate its response for thermoelectric and optoelectronic applications.

Electronic structure and geometry optimization have been done with the full-potential linearized augmented plane wave (FPLAPW) method implemented in WIEN2k code [31]. Kohn-Sham equations are calculated with FPLAPW with the help of self-consistent method [32]. In Kohn-Sham DFT, the exchange correlation energy (EXC=EX+EC) as a functional of electron spin densities must be approximated. For slow varying densities, the famous functional have the appropriate form: the generalized gradient approximation (GGA). Perdew, Burke and Ernzerhof Generalized Gradient Approximation (PBE-GGA) [33] is used to solve the electron exchange and correlation potential. However, the utilization of GGA strongly depends upon the properties of studied materials. The results achieved with GGA for the band-gap of insulators and semiconductors are severely not in good agreement with the experimental results, e.g., it mostly underestimated the bad-gap or sometimes even absent [34]. To solve this problem and achieve more accuracy in band-gap, modified Becke-Johnson exchange potential (mBJ) [35] is used. The total Hamiltonian of the system is calculated accurately with mBJ approximation because it uses both GGA exchange and correlation potentials. As a result, the band-gap accuracy comparable with the experimental result is significantly improved [35]. GGA correlation with mBJ potential is used in our calculation for a more accurate band-gap. The values for selected muffin tin radii (a.u) of different atoms are Ba=2.50, La=2.50, Mg=1.83, Bi=2.01 and O=1.69. The integration is done with the tetrahedral method using 1000 k-points in the complete Brillouin zone. The plane wave expansion cutoff is set at RMT Kmax=7.0 to carry the expansion of wave function, where RMT = atomic sphere radius and Kmax = plane wave cutoff. The electron potential and electron density inside the muffin tin spheres are presented with spherical harmonics [36] is set to l_max=10. The self-consistency convergence criterion for energy is achieved up to 10⁻⁵ Ry.

Structural and Electronic Properties

BaMgLaBiO₆ has a cubic double perovskite structure (general formula ${\text{A}}^{{\prime }}{\text{A}}^{{\prime }{\prime }}{\text{B}}^{{\prime }}{\text{B}}^{{\prime }{\prime }}{\text{X}}_{6})$ with a space group of F-43m. It is the extension of perovskite structure ABX₃. The oxygen atoms (O₂) are bounded with Ba⁺² to form cuboctahedra BaO₁₂ and they share corners with other equivalent BaO₁₂. Similarly, the oxygen atoms (O₂) are bounded with Mg⁺², La⁺³, and Bi⁺⁵ to form cuboctahedra MgO₁₂, LaO₁₂, and BiO₁₂ that also share corners with other cubooctahedra. The tilt angle of corner-sharing octahedral is${0}^{0}$. The bond lengths for all Ba-O and Mg-O, La-O and Bi-O are 2.93 ${\text{A}}^{0}$, 2.05 ${\text{A}}^{0}$, 2.93 ${\text{A}}^{0}$ and 2.10 ${\text{A}}^{0}$ respectively. In a linear distorted geometry, O₂ is bounded to two Ba⁺², one Mg⁺², two La⁺³ and one Bi⁺⁵ atom. Figure 1(a) shows the crystallographic unit cell of double perovskite BaMgLaBiO₆.

The unit cell of BaMgLaBiO₆ has been optimized for the ground state stable atomic configuration and to achieve optimized lattice constants. The following Murnaghan’s equation of state is used to calculate the ground-state lattice parameters.

$\text{E}\left(\text{V}\right)={\text{E}}_{0}+\left[\frac{{\left(\frac{{\text{V}}_{0}}{\text{V}}\right)}^{{\text{B}}_{0}}}{{\text{B}}_{0}-1}+1\right]-\frac{\text{B}{\text{V}}_{0}}{{\text{B}}_{0}-1}$

(1)

where E₀ is the minimum energy and V₀ is the volume at T=0k. The bulk modulus is B and the pressure derivative of B is B₀ at the equilibrium volume. The optimization curve is presented in Fig. 1b. On the parabolic curve, the obtained minimum energy value shows the ground state energy and the corresponding volume is the ground state volume.

In addition, the formation energy is also calculated to check the possibility of synthesizing this compound. The formation energy is basically the difference between the energies of the stable phases of the elements and the total energy of the compound.

${\text{E}}_{\text{F}\text{E}}={\text{E}}_{\text{B}\text{a}\text{M}\text{g}\text{L}\text{a}\text{B}\text{i}{\text{O}}_{6}}-({\text{E}}_{\text{B}\text{a}}+{\text{E}}_{\text{M}\text{g}}+{\text{E}}_{\text{L}\text{a}}+{\text{E}}_{\text{B}\text{i}}+6{\text{E}}_{\text{O}})$

(2)

It can be seen from the calculated formation energy (Table 1) that the studied compound can be synthesized. The calculated lattice parameters, bulk modulus B(GPa), pressure derivative of B and ground state energy${\text{E}}_{0}\left(\text{R}\text{y}\right)$ are presented in Table 1.

Table 1

Optimized parameters of perovskite BaMgLaBiO₆
Lattice parameters$\text{a} \left({\text{A}}^{0}\right)$		Bulk modulus B(GPa)	${\text{B}}^{{\prime }}$	${\text{E}}_{0}\left(\text{R}\text{y}\right)$	Formation Energy
BaMgLaBiO₆	7.91	153.2	4.84	-7742.214	-4.11552

The band structure is the key factor in describing the electronic behavior of any compound. Figure 2 shows the band structure of BaMgLaBiO₆ perovskite calculated with generalized gradient approximation (GGA) and modified Becke-Johnson (mBJ) potentials along with the high symmetry points of 1st Brillouin zone.

The conduction band is observed above the Fermi level (0 eV) and the valence band below it. The energy band-gap lies between the maxima of valance and minima of the conduction band. A direct band-gap is observed and it increased from GGA to mBJ potential which confirms the semiconductor nature of this perovskite. The calculated values of band-gap are 2.7 eV and 3.8 eV with GGA and mBJ potential, respectively. The band-gap nature can be further investigated with the density of states (DOS) plots. The understanding of atomic/orbital contribution towards the band structure can be achieved with DOS. Figure 3 shows the total density of states as a function of energy. The selected energy range is from -15 eV to 15 eV. The conduction band is represented with a positive energy range and the negative energy range corresponds to the valence band. A clear band-gap is observed near the Fermi level in the plot of the total density of states with both potentials. The contribution of different states above Fermi level in the conduction band (CB) and below Fermi level in the valence band (VB) start from the energy band-gap. The Ba-d and La-d states show their main contributions in the conduction and valence band. The s and p states of Mg and Bi have contribution in valence and conduction bands, while the O-p state shows its major contribution valence band. The contribution of other states for all atoms is negligibly small.

Electron density plots reveal the bonding nature between the atoms in the compound. The electron density along the (110) plane for BaMgLaBiO₆ is shown in figure 4. A week covalent bonding is observed between the Ba, and La atoms. Oxygen (O) atoms show the ionic bonding nature along with the Bi atoms. A strong covalent bonding can be seen between the Bi and Mg atoms. The overall response is comprised of both ionic and covalent bonding.

The optical response of the compound is represented with dielectric function at photon’s energies (E=hc/λ). Figure 4a shows the real ɛ1 (ω) part of the dielectric function of BaMgLaBiO₆ with GGA and mBJ potentials. The selected energy range is 0 to 14 eV. The static frequency limit ɛ₁ (0) is 4.68 and 4.10 with GGA and mBJ potentials, respectively. As the band-gap increases from GGA to mBJ potential (Figure 2), ɛ1 (0) values decreases respectively, which shows an inverse relationship between static frequency and band-gap as depicted in the Penn model [37]. Beyond the static point, ɛ1 (ω) starts increasing and reaches a maximum value of 6.28 at 3.71 eV and 4.58 at 3.86 eV with GGA and mBJ, respectively. It can be seen from the main characteristic peaks that the compound falls in the visible range of energy in the electromagnetic spectrum. After the peaks, the plot observed a decrease and became negative at a certain range of energy. The negative values show complete attenuation of light and depict metallic behavior [38]. Figure 4b represents the imaginary ɛ2 (ω) part of the dielectric function, which shows the band-gap and absorptive behavior of the material. The imaginary part is also representative of inter-band transitions. The ɛ₂ (ω) has two sharp peaks at 4.7 and 6.2 eV with GGA and 4.0 and 4.5 eV with mBJ potential. Depending upon the information collected from both ɛ₁ (ω) and ɛ₂ (ω), the calculation of essential optical parameters such as absorption coefficient, extension coefficient, refractive index and optical conductivity become permissible.

The refractive index (n=c/v) is the dimensionless quantity that describes the behavior of light traveling through the given medium. The refractive index n(ω) and extinction coefficients k(ω) both relates to the interaction of light with the material. The refractive index n(ω) and extinction coefficient k(ω) as a function of energy are calculated with respective potentials and plotted in Fig. 5. Figure 5a shows the behavior of n(ω) which follow the same pattern as the imaginary part of the dielectric function. The static frequency n(0) values are 2.01 and 1.75 with GGA and mBJ potentials, respectively. It can be seen from the band structure (Fig. 2) that the band-gap is larger for mBJ potential, while n(0) (Fig. 5a) is smaller for mBJ potential, which confirms an inverse relation between them. Further increase in energy causes to increase the value of n(ω) and maximum values obtained at 3.75 eV (2.51) and 3.83 eV (2.15) with GGA and mBJ, respectively. There are also other peaks but a gradual decrease is observed with a further increase in energy.

The extinction coefficient k(ω) is basically the imaginary part of refractive index n(ω) and is plotted in figure 5b. It shows the absorbed radiation in an analogous way. The threshold energies of k(ω) are 2.1eV and 2.7eV with both potentials. The k(ω) values show an increase with the increase in energy and maximum values are observed at 8.5 and 9.6 eV for GGA and 10.1 and 11.0 eV for mBJ potential. The high peaks indicate the high absorption in the perovskite.

The optical conductivity spectra are calculated and plotted in figure 6a. It is revealed from the figure that optical conductivity starts from 2.7 eV and 3.8 eV and it is the band-gap calculated with GGA and mBJ potentials, respectively. After the band-gap values, the optical conductivity gradually increases and achieves the peak value at 8.4 eV and 9.9 eV with respective potentials. The optical conductivity spectra start decreasing after the peak values with multiple minor peaks.

The relationship between the energies of the incident photon and their per unit length absorption is illustrated with the absorption coefficient ${\alpha }\left({\omega }\right)$ spectrum as shown in figure 6b. A non-linear increase in ${\alpha }\left({\omega }\right)$ as the function of energy is observed. The abrupt increase in ${\alpha }\left({\omega }\right)$ corresponds to the highest absorption of incident radiations. Photon absorption is the property of semiconductors. The absorbed photon causes to excite and shift the electrons from the valence band to the conduction band.

The energy loss function represents the loss in energy of moving electrons with high velocity by colliding with other electrons while moving through the material.

Figure 7 shows the energy loss as a function of energy in BaMgLaBiO₆ perovskite. Several peaks are observed for energy loss function. The maximum values are obtained at 10.7 eV and 12.1 eV with GGA and mBJ, respectively.

The direct conversion of temperature difference into electricity is known as the thermoelectric effect, while the lattice vibrations are responsible for the heat conduction in a material known as thermal conductivity. A high electrical conductivity (σ) and low thermal conductivity (k) are required to develop good thermoelectric material. As the thermoelectric response of any compound depends on electrical and thermal conductivity, power factor, Seebeck coefficient and the figure of merit, so we have calculated these properties as a function of temperature difference up to 800K. The flow of free charge carriers in the material is measured through electrical conductivity. Electrical and thermal conductivities as a function of temperature are shown in figure 9. It can be seen that the electrical conductivity shows a constant increase with the rise in temperature. As the electrical conductivity and band-gap have an inverse relationship, an increase in the band gap from GGA to mBJ potential leads to the decrease in electrical conductivity shown in figure 9a.

The maximum value of σ is observed at 800k is $3.5⨯{10}^{19}(s/m)$ and $1.9⨯{10}^{19}(s/m)$ for GGA and mBJ potentials, respectively. For a good thermoelectric material, the temperature gradient should be maintained, which can be done with low thermal conductivity. Figure 9b shows the thermal conductivity as a function of temperature. The k values obtained with mBJ are higher than GGA potential because of the band-gap difference with both potentials. The maximum values of k obtained for BaMgLaBiO₆ are $9.7⨯{10}^{14}\left(W{K}^{-1}{m}^{-1}\right)$ and $1.13⨯{10}^{14}\left(W{K}^{-1}{m}^{-1}\right)$ with GGA and mBJ potentials, respectively.

Seebeck effect (S) is used to measure the magnitude of induced thermoelectric voltage in the response of temperature gradient. A high value of the Seebeck coefficient is one of the major factors in achieving high-performance thermoelectric devices [39]. Figure 10a shows the Seebeck factor as a function of the temperature gradient. The calculated value of S at 300K is $2.7⨯{10}^{-4}(V.{K}^{-1})$ and $1.6⨯{10}^{-4}(V.{K}^{-1})$ with GGA and mBJ potentials, respectively. A decrease in the value is observed with GGA by increasing the temperature and a value of $2.1⨯{10}^{-4}(V.{K}^{-1})$ is noted at 800K. There is no significant change observed with mBJ between 300k to 800k. Power factor is another fundamental factor in evaluating the performance of practical thermoelectric devices and it is the product of Seebeck coefficient (S) and the electrical conductivity (σ) (PF=S²σ) [1].

Power factor is presented in the figure 10b. A consistent increase can be seen from 100k to 800k with both potentials. A maximum value of 7.3$\times {10}^{14}\left(W.{m}^{-1}{K}^{-2}\right)$ and 7.2$\times {10}^{14}\left(W.{m}^{-1}{K}^{-2}\right)$ is obtained at 800K with GGA and mBJ potentials, respectively.

The most important factor in determining the performance of any thermoelectric material is its figure of merit ($zT=\sigma {S}^{2}T/k$). The figure of merit has a direct relationship with electrical conductivity (σ) and Seebeck coefficient (S), while having an inverse relationship with thermal conductivity (k). Materials with ZT values near or greater than unity are considered to be a potential candidate for thermoelectric devices [40, 41]. The value of ZT as a function of temperature is shown in figure 10c. It can be seen that the maximum value is obtained in the case of GGA potential, which is 0.81 at 300K while at the same temperature; the value achieved with mBJ is 0.7. The decrease in ZT values (in the case of mBJ) is because of the increase in the bandgap value for mBJ potential. A reasonable ZT value makes BaMgLaBiO₆ a potential candidate for thermoelectric devices. Due to the unavailability of theoretical and experimental results on the overall computed physical properties, the contrast or precision is not possible, but the calculated data may use as reference data and can provide valuable information to the forthcoming experimental and computational investigation.

The electronic structure, optical and thermoelectric properties of double perovskite BaMgLaBiO₆ is studied in the presented work. The full-potential linearized augmented plane wave (FP-LAPW) method is employed under the DFT framework via WIEN2k code. A semiconductor behavior is revealed from the electronic properties with GGA and mBJ potentials. The density of states also gives the same results as band structure. The electron density is also studied and presented in the contour plots. Different optical parameters are investigated which shows the potential of the compound for optoelectronic devices. The thermoelectric response is also calculated through different parameters and the obtained value of ZT in the suitable range confirmed its availability for renewable energy devices. The present results also reveal the potential of double perovskite BaMgLaBiO₆ for lasers and power switching and renewable energy applications.

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Conflict of Interest

The authors declare that they have no conflict of interest.

Data Availability

All data generated or analyzed during this study are included in this published article

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Electronic structure, optical and thermoelectric response of lead-free double perovskite BaMgLaBiO6: A first-principles study

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