Effect of Ca, Ba, Be, Mg, and Sr Substitution on Electronic and Optical Properties of XNb₂Bi₂O₉ for Energy Conversion Application Using Generalized Gradient Approximation–Perdew–Burke–Ernzerhof

Abstract

Bismuth layered structure ferroelectrics (BLSFs), also known as Aurivillius phase materials, are ideal for energy-efficient applications, particularly for solar cells. This work reports the first comprehensive detailed theoretical study on the fascinating structural, electronic, and optical properties of XNb₂Bi₂O₉ (X = Ca, Ba, Be, Mg, Sr). The Perdew–Burke–Ernzerhof approach and generalized gradient approximation (GGA) are implemented to thoroughly investigate the structural, bandgap, optical, and electronic properties of the compounds. The optical conductivity, band topologies, dielectric function, bandgap values, absorption coefficient, reflectivity, extinction coefficient, refractive index, and partial and total densities of states are thoroughly investigated from a photovoltaics standpoint. The material exhibits distinct behaviors, including significant optical anisotropy and an elevated absorption coefficient > 10⁵ cm⁻¹ in the region of visible; ultraviolet energy is observed, the elevated transparency lies in the visible and infrared regions for the imaginary portion of the dielectric function, and peaks in the optical spectra caused by inter-band transitions are detected. According to the data reported, it becomes obvious that XNb₂Bi₂O₉ (X = Ca, Ba, Be, Mg, and Sr) is a suitable candidate for implementation in solar energy conversion applications.

1. Introduction

In recent few years, research engineers and scientists have focused strongly on photovoltaic (PV) technology in terms of sustainability, scalability, and environmental impact to reduce the world’s reliance on fossil fuels for energy generation [1]. Photovoltaic technology supports power space satellites, electrical energy generation, large-scale utilities, and smaller scales like electric systems and home solar well. In solar desalination and solar car applications, various innovative inventions, including PV cells, have also been patented. Due to the technology’s proven benefits and numerous applications, scientists working in the field of renewable energy applications are encouraged to enhance and speed up the research on PV technology by seeking out new materials/methodologies to bring out the main advantages of the devices in the form of higher efficiency, while developing new structures/morphologies can also be beneficial to achieve interesting performances [2,3,4,5,6]. The emerging PV technology has attracted the interest of scientists, and are divided into the following families: perovskite solar cells [7], thin-film amorphous silicon solar cells [8], quantum dot solar cells [9], dye-sensitized solar cells [10], gallium copper indium selenide solar cells [11], cadmium telluride solar cells [12], organic solar cells [13], etc.

Recently, bismuth layered structural ferroelectrics (BLSFs) have exhibited strong activity under visible light, which has garnered significant attention, specifically for the Aurivillius family, which contains Bi as a component element. There are two factors that maintly express the importance of Bi existence in BLSFs [14]. Firstly, it increases the probability of visible light absorption by raising the valence band (VB) edge due to the hybridization of Bi-6s with O-2p orbitals. Secondly, the remarkable mobility of the photogenerated holes is caused by the widely dispersed Bi-6s and O-2p-hybridized VB [15].The Aurivillius family of oxides is renowned for being a type of layered perovskite that is created by a regular intergrowth of perovskite (A_n−1B_nO_3n+1)²⁻ blocks and fluorite-like (Bi₂O₂)²⁺ layers; n is the number of corner-connected octahedral layers. Bi₂WO₆ and Bi₂MoO₆ are the prominent examples of n = 1 members of the Aurivillius family that have been thoroughly investigated as visible-light-driven photocatalysts. A recent article outlined the performances of the five-layer Aurivillius phase (Bi₆Ti₃Fe₂O₁₈) to examine the impact of La substitution on the structure, phase formation, and photocatalysis. The study concluded that single-semiconductor oxide photocatalysts without heterojunction formation are higher-ordered Aurivillius-layered perovskites [16,17,18,19]. Cui et al. computed the Aurivillius family’s members Bi₄Ti₃O₁₂ (BTO) and Sr₂Bi₄Ti₅O₁₈ (SBT), which revealed that the BTO sample’s bandgap is 2.51 eV, whereas the SBT sample’s is 2.23 eV. These two materials enable the theoretical framework of the Aurivillius family to be utilized in sensor, optical, and random access memory applications [20]. Lardhi et al. showed a theoretical examination of compounds containing bismuth titanate (Bi₁₂TiO₂₀ and Bi₄Ti₃O₁₂ materials). Bi₁₂TiO₂₀ offered lower effective masses, a greater absorption coefficient, a band edge, and improved charge transport properties compared to Bi₄Ti₃O₁₂. Titanate is recognized for its strong optoelectronic properties, which should be used in the formation of perovskite-based photovoltaic or photocatalytic applications [21]. Werner et al. have reported structural and optical investigations of La_2.1Bi_2.9Ti₂O₁₁Cl. The electronic structure of La_2.1Bi_2.9Ti₂O₁₁Cl is comparable to that of other double-layered oxyhalides of the Sillén–Aurivillius type of compounds. Visible light sensitivity can be achieved by a narrow bandgap of 2.8 eV, which is mainly due to the contribution of Bi-6p orbitals to the conduction band. These orbitals are primarily located at the Bi site, and Bi is adjacent to the perovskite layer [22]. Liu et al. have designed the Aurivillius-type Sn-based halide perovskites Ba₂X₂[Cs_n−1Sn_nX_3n+1] with X = I/Br/Cl, where the air’s oxygen is blocked by the [Ba₂X₂] layer, enhancing the crystals’ inoxidizability. The direct bandgaps (0.84–2.20 eV) of Ba₂X₂[Cs_n−1Sn_nX_3n+1] meet the requirements for both single- and multi-junction perovskite solar cells (PSCs). With an ideal bandgap (1.26 eV), strong carrier mobility (135–173 cm₂ V⁻¹ s⁻¹), and an ideal absorption coefficient (~105 cm⁻¹), Ba₂Br₂[Cs₂Sn₃Br₁₀] was reported to be the best candidate for the optical applications [23]. Xu et al. analyzed the electronic structure, ferroelectricity, and optical characteristics of CaBi₂Ta₂O₉. Its indirect bandgap was reported to be 3.114 eV, and its numerous optical characteristics were outlined [24]. Stachiotti et al. reported the extremely accurate band structure calculations of SrBi₂Ta₂O₉ with a paraelectric structure and presented the presence of ferroelectricity in it [25]. Given the above, it is evident that Aurivillius phase materials are gaining the interest of researchers due to their intriguing photovoltaic properties. To achieve calculations of the electronic and optical properties of BLSF’s family with reasonable accuracy, different approaches based on DFT, such as the local density approximation (LDA), LDA-1/2, full potential linearized augmented plane wave (FP-LAPW), modified Becke–Johnson (mBJ), GGA, and the Heyd–Scuseria–Ernzerhof (HSE06) function, can be employed [26,27,28].

Inspired by the above innovative concepts relating to BLSF’s family, with relatively few theoretical studies on it in the literature, XNb₂Bi₂O₉ (X = Ca, Ba, Be, Mg, and Sr) has been selected to be comprehensively explored. Therefore, it is essential to thoroughly investigate the structural, electrical, and optical characteristics of XNb₂Bi₂O₉ (X = Ca, Ba, Be, Mg, and Sr) compounds using the FP-LAPW approach with the DFT. The primary goal of this study is to use PBE-GGA exchange correlation potentials to carry out a complementary and comparative analysis of the ground state characteristics of the compounds. Having applications in fields of physics, material sciences, and also in chemistry, DFT-based calculations are among the cheapest, environmentally friendly, and time-saving computational approaches for evaluating the electronic and optical characteristics of different compounds.

2. Methodology

A DFT-based simulation was performed to examine the electronic properties [bandgap, band structure, the density of states (DOS), and partial density of states (PDOS)] and optical properties [reflectivity, refractive index, extinction coefficient, absorption, dielectric function (real and imaginary), optical conductivity (real and imaginary), and loss function] of the Aurivillius phase materials by using a framework named CASTEP (Cambridge Sequential Total Energy Package) [29], a first-principle plane-wave pseudopotential code for quantum mechanics-based simulations on BIOVIA Material Studio.

We settled the exchange correlation functional, as GGA provides better information regarding electronic subsystems, with PBE (Perdew–Burke–Ernzerhof) acting as the default exchange correlation functional [30,31,32,33]. For optimization convergence tolerance, the value of energy used to be 2.0 × 10⁻⁵ with a maximum force of 0.05 eV atom⁻¹ and a maximum stress of 0.1 GPa, with a maximum displacement of 0.002 Å. For calculations, the OTFG ultrasoft pseudopotential for minimization of error concerning a fully converged all-electron, along with Koelling–Hamon as a relativistic treatment, were used. For the basic set, a parameter energy cut-off value of 1200 eV with 2 × 2 × 2 set of k-points of Brillouin zone was used, the SCF tolerance was set to be 2.0 × 10⁻⁶, with density mixing as an electronic minimizer being used for calculations of the electronic and optical properties of the given structures.

3. Results and Discussions

3.1. Structural Properties

The crystal structure of BLSFs possesses the conventional formula (Bi₂O₂)²⁺(A_n−1B_nO_3n+1)²⁻. From the side view of the structure, the layers of Bi atoms are visible, in between of which the A and B site atoms are present (Figure 1). There is a total of 4 A-site atoms which can be divalent, like Ca, Ba, Be, Mg, Sr, etc., and 8 B-site atoms which can be Nb and Bi atoms, and there is a total of 36 atoms of oxygen in this structure, with a total of 56 atom possessing the orthorhombic structure, with a = 5.64, b = 25.40, c = 5.68, and α = β = γ = 90°.

3.2. Electronic Properties

3.2.1. Band Structure and Density of State

The density of state (DOS) is used to acquire significant information regarding a material’s electronic movement within a certain orbital band, i.e., between the VB and conduction band (CB) orbits. The band structure and DOS determine the electronic orbital movement between energy levels for XNb₂Bi₂O₉, which is displayed in Figure 2 and Figure 3 along the high-symmetry directions of the irreducible brillion zone (IBZ). These are obtained by employing the GGA approximation within the energy range of −6.0 eV to 6.0 eV. The dashed line at the center of Figure 2 presents the Fermi level (EF) at 0 eV. The VB is placed below EF, whereas the CB lies above EF. Sharp peaks are visible around the Fermi level on the VB’s edge. The band edges for VB and CB lie at the Y and G points, respectively. The results from the bandgap and TDOS clearly show the direct bandgap nature of these compounds. Direct bandgap semiconductors are advantageous for optical and electronic applications, as phonons are included in electronic transitions with electrons, as in indirect semiconductors. The values of the energy bandgaps for MgNb₂Bi₂O₉, BaNb₂Bi₂O₉, SrNb₂Bi₂O₉, CaNb₂Bi₂O₉, and BeNb₂Bi₂O₉ are 2.501, 2.493, 2.493, 2.490, and 1.834 eV, respectively. Overall, all the compounds follow the same bandgap trend, which lies within the range of the semiconductor bandgap value. The bandgap investigation was performed using the CASTEP code governed by a set of Equations (1)–(3).

$${\psi }_{ki}\left(r\right)=\mathit{exp}\left[ik\cdot r\right]f_i\left(r\right)$$

(1)

$$f_i\left(r\right)={\sum }_G{G}_{i,G}\mathit{exp}\left[iG.r\right]$$

(2)

$${\sum }_{G^{\prime }}\left[{\displaystyle \frac{h^2}{2m}}{\left|k+G\right|}^2{\delta }_{GG\prime }+V_{ion}\left(G-G^{\prime }\right)+V_H\left(G-G\prime \right)\right]C_{i,k+G\prime }={\epsilon }_i{C}_{i,k+G}$$

(3)

where, in Equations (1)–(3), ψ represents the pseudo wave function, while the wave vector is denoted by k; R represents the displacement function; δ_GG represents the Kronecker delta function; the unique constant density function is represented by G; V_ion represents the ionic potential, while V_xc is the exchange correlation potential; and r is the radial distance in a spherical coordinate system for a point in space.

3.2.2. Partial Density of States (PDOS)

The PDOS of the compounds is determined by using BIOVIA and is presented in Figure 4 to illustrate the contribution of each atomic orbital in creating the band structure and the orbital contributions in adjusting the bandgap.

(a)

CaNb₂Bi₂O₉

Figure 4a shows that the VB is mostly influenced by the O and Ca atoms, with a little minute influence by the Nb atoms. To be more precise, the O-2p⁴, Ca-4d⁴, and Nb-3d¹⁰ states have a significant influence in this sub-band, while the Bi-5p⁶ state is also somewhat present. Bi and Nb have a significant influence on the VB’s second sub-band, whereas Ca also has a slight presence. After that, there is no electronic state between 0 and 2.9 eV, which is the material’s energy bandgap. The Ca and O atoms contribute very little to the CB of CaNb₂Bi₂O₉, which is mostly made up of Nb and Bi atoms. More precisely, the Bi-6s² and Nb-3d¹⁰ states demonstrate their contributions, while the Ca-4d⁴ and Bi-5p⁶ states also show little presence.

(b)

BaNb₂Bi₂O₉

From Figure 4b, it can be seen that VB mainly presents an outcome of the hybridization of the O-2p⁴, Ba-5p⁶, Ba-4d¹⁰, and Nb-4s² states, but Nb-4p⁶ shows minute presence. The Ba, Nb, and O atoms have a significant influence on the VB. The compound’s energy gap is found to lie between 0 and 2.8 eV, where no electronic state of any type exists. Nb and Bi have an influence on the CB of BaNb₂Bi₂O₉. Specifically, the states Bi-6s² and Nb-3d¹⁰ exert significant effects, whereas the Ba-4d¹⁰ state also exhibits minimal presence.

(c)

BeNb₂Bi₂O₉

Figure 4c shows that VB is significantly influenced by the Nb and O atoms. This sub-band is mostly composed of the O-2p⁴ state, with a minor proportion of Nb-4s² orbitals, according to PDOS. The material’s energy bandgap lies between 0 and 2.0 eV, where no more electronic states exist. The atoms that influence the CB of BeNb₂Bi₂O₉ are Bi, Be, and Nb. A tiny percentage of the Be-2s² and Bi-5p⁶ states hybridize with the Bi-6s², Nb-3d¹⁰, and Be-2p⁴ states to affect CB, according to the PDOS.

(d)

MgNb₂Bi₂O₉

Figure 4d shows that the O and Nb atoms have a significant influence on the VB. Based on the PDOS study, this sub-band consists primarily of O-2p⁴ and Nb-4s² states, with a small proportion of Bi-6s² orbitals. After that, electronic states do not exist between 0 and 2.4 eV, which is the compound’s energy bandgap. The Nb, Bi, and Mg atoms are the main contributors to the CB. As to the PDOS, the formation of CB arises from the hybridization of Mg-3s², Bi-6s², and Nb-3d¹⁰ states, along with a small proportion of Bi-5p⁶ states.

(e)

SrNb₂B_i2O₉

Figure 4e shows that Sr, O, and Nb atoms demonstrate a significant influence on VB. According to the PDOS study, Sr-3d¹⁰, O-2p⁴, and Nb-3d¹⁰ states contribute the majority of this sub-band’s formation. After that, no electronic states appear between 0 and 2.4 eV, which is the compound’s energy bandgap. The CB is mostly attributed to the Sr, Bi, and Nb atoms. The PDOS result indicates that a minor amount of the Bi-5p⁶ state combines with the Sr-3d¹⁰, Bi-6s², and Nb-3d¹⁰ states to generate CB.

3.3. Optical Properties

Significant and focused understanding about the refractive index n(ω) is required to assess the technical applications of optical materials in optical devices. Materials used in photovoltaic systems must have strong optical conductivity, high absorption coefficient, low emissivity, and a high refractive index. Using the relations provided for understanding the depth of the optical characteristics, the refractive index n(ω), reflectivity R(ω), absorption coefficient I(ω), and energy loss function L(ω) were computed by using BIOVIA Material Studio. Equations (4)–(9) are the expressions of these optical and electronic measurements:

$$n\left(\omega \right)={\left\{{\displaystyle \frac{{\epsilon }_1\left(w\right)}{2}}+{\displaystyle \frac{\sqrt{{\epsilon }_1^2\left(\omega \right)+{\epsilon }_2^2}\left(\omega \right)}{2}}\right\}}^{{\displaystyle \frac{1}{2}}}$$

(4)

$${\epsilon }_1\left(\omega \right)=1+{\displaystyle \frac{2}{\pi }}P{\int }_0^{\infty }{\displaystyle \frac{{\omega }^{\prime }{\epsilon }_2\left({\omega }^{\prime }\right)}{{{\omega }^{\prime }}^2-{\omega }^2}}d{\omega }^{\prime }$$

(5)

$${\epsilon }_2\left(\omega \right)={\displaystyle \frac{4{\pi }^2{e}^2}{m^2{\omega }^{2}V}}\sum {\int }_{Bz}{\left|⟨{\psi }_k^v\left|\overrightarrow{p_i}\right|{\psi }_k^C⟩\right|}^2\delta \left(E_{{\psi }_k^c}-E_{{\psi }_k^v}-\mathsf{ħ}\omega \right)$$

(6)

$$R\left(\omega \right)={\left|{\displaystyle \frac{\sqrt{\epsilon \left(\omega \right)}-1}{\sqrt{\epsilon \left(\omega \right)}+1}}\right|}^2$$

(7)

$$\mathrm{I}\left(\omega \right)={\left\{\sqrt{{\epsilon }_1^2\left(\omega \right)+{\epsilon }_2^2\left(\omega \right)}-{\epsilon }_1\left(w\right)\right\}}^{{\displaystyle \frac{1}{2}}}$$

(8)

$$L\left(\omega \right)=-\mathit{Im}\left({\displaystyle \frac{1}{\epsilon }}\right)={\displaystyle \frac{{\epsilon }_2\left(\omega \right)}{{\epsilon }_1^2\left(\omega \right)+{\epsilon }_2^2\left(\omega \right)}}$$

(9)

The expression $n’ \left(\omega \right)=n \left(\omega \right)+ik \left(\omega \right)$ describes the complex refractive index. This case indicates that the degree of transparency of a material is determined by the incoming electromagnetic radiations. Figure 5a shows the refractive index plots of XNb₂Bi₂O₉ with X = Ca, Ba, Be, Mg, and Sr, which have demonstrated static refractive indices (n) of 3.29, 3.31, 3.24, 3.33, and 3.29, respectively. The values of the refractive indices increase with the energy of the photon, and for XNb₂B_i2O₉, the largest peak is seen at 3.54 eV. The materials will be regarded as optically active if the value of n(ω) lies between 1.0 and 4.0 eV.

The threshold values of energy for the calculated spectra of K(ω) are presented in Figure 5b. The spectra of K(ω) initially show no peak, which is the known specific spectra for the threshold energy, and the values of this energy are approximately 2.48, 2.52, 2.57, 2.49, and 2.49 eV for XNb₂Bi₂O₉ with X = Ca, Ba, Be, Mg, and Sr, respectively. The main cause of the prominent peaks in the spectra of K(ω) is the transition of electrons from VB to CB.

Equations (10) and (11) provide the intensity of light I(x) expression at the distance x from the surface of the material, because the absorption coefficient (α) indicates the part of the energy of light that is lost by the light wave as it passes through the material [30].

$$I\left(x\right)=I\left(0\right)\mathit{exp}\left(-\alpha x\right)$$

(10)

$$\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e} \alpha ={\displaystyle \frac{2k\omega }{c}}$$

(11)

The penetration length of the incoming photon before its total absorption in the material is computed by using the absorption coefficient. The calculated spectra of α(ω) are shown in Figure 5c. All optical properties are measured for the energy range of 0–14 eV. Absorption is lowest for the material SrNb₂Bi₂O₉, with a value of 199,031 cm⁻¹, and greatest for CaNb₂Bi₂O₉, with a value of 218,645 cm⁻¹. The α(ω) spectrum demonstrates the highest peaks between 9.0 and 14.0 eV. These materials often behave as transparent in low-energy areas or in the infrared region; they may find suitable application in UV devices. The results show that these materials have the potential to be employed in solar devices.

The simulated reflectivity R(ω) spectra for XNb₂Bi₂O₉ with X = Ca, Ba, Be, Mg, and Sr in the energy range of 0–14 eV are presented in Figure 5d. The reflectivity R(ω) is the measure of the fraction of incident photons that are reflected at the interface. The static values of R(ω) that correspond to the zero-frequency limit for XNb₂Bi₂O₉ with X = Ca, Ba, Be, Mg, and Sr are 0.17, 0.187, 0.19, 0.20, and 0.18, respectively. Prominent peaks in the reflectivity spectra in the higher UV (2–6 eV) region indicate excited absorption. These materials can reflect more than 50% of incident light in the high UV range.

Figure 6a,b shows the Kramers–Kronig relation for the complex dielectric function $\epsilon \left(\omega \right)={\epsilon }_1\left(\omega \right)+i{\epsilon }_2\left(\omega \right)$, which can be used to describe the dielectric properties. Here, ε₁(ω) represents the real part that is useful for measuring light polarization and dispersion, and ε₂(ω) denotes the imaginary part that characterizes the material’s absorptive qualities [34]. The maximum values of ε₁(ω) for XNb₂Bi₂O₉ with X = Ca, Ba, Be, Mg, and Sr occur at 3.4, 3.35, 3.16, 3.39, and 3.38 eV, respectively. Following that, one may see a decline in the spectrum with rising energy. Direct optical transitions take place between VBs and CBs because the electronic band topologies show the direct bandgap. For these compounds, the static dielectric constants (a real component of the dielectric constant at zero energy) are 6.35 for (ε₁). These outcomes show how these materials develop an anisotropic dielectric function. The orthorhombic structure is responsible for the dielectric constants’ anisotropic nature. The total of all transitions from VBs to CBs is known as ε₂(ω). At an energy of 4.5 eV, the XNb₂Bi₂O₉ (X = Ca, Ba, Be, Mg, and Sr) structure exhibits a maximum value in ε₂(ω), occurring inside the visible light spectrum.

The shift in optical conductivity σ(ω) with photon energy is presented in Figure 6c. Initially, the compounds act as semiconductors, since the conductivity σ(ω) values are zero. As seen in Figure 6c, the critical energy point of ~1.8 eV is where the conductivity σ(ω) begins. With a comparable value of 5.3 fs⁻¹, the conductivity σ(ω) increases with an increase in photon energy up to ~4.8 eV in the visible range. The high absorption of the material is the cause of the increase in optical conductivity.

The electron energy loss (EEL) spectra of XNb₂Bi₂O₉ with X = Ca, Ba, Be, Mg, and Sr in the energy range of 0–14 eV are presented in Figure 6d. When attempting to distinguish between plasma resonance occurrences and regular inter-band transitions, the EEL approach can be helpful. Sharp peaks in the energy loss function are known to coincide with the roots of Re(ε) crossing the x = 0 line, which is related to plasma oscillations. The EEL spectra show only one major peak that is connected to plasma oscillations. The plasmon energy has the greatest peak value at 6.7 eV. It is evident that the Re(ε) passes through 0 at these energies.

4. Conclusions

For the first time, a detailed theoretical investigation has been conducted on the layered perovskites XNb₂Bi₂O₉ with X = Ca, Ba, Be, Mg, and Sr. The objective of this study is to analyze the optical and electronic characteristics of these materials to clarify their potential for optical and electronic applications. Since the observed bandgap lies between 1.8 and 2.6 eV for all compounds, these materials reveal a direct energy bandgap and are ideally suited for utilization in solar energy conversion applications. The optical parameters, such as the real part of the dielectric function, range from 10 to 10.6, which shows that these materials absorb the maximum number of incident photons in the visible region. The refractive index varies from 3.24 to 3.33, which proves that they are optically active. The optical conductivity, threshold energy of the extinction coefficient, absorption coefficient, and static value of reflectivity lie between 5.04 fs⁻¹ and 5.3 fs⁻¹, 2.4 and 2.6 eV, 192,000 cm⁻¹ and 219,000 cm⁻¹, and 0.33 and 0.35, respectively. Conversely, a low-range loss function of 0.351 to 0.545 has been reported. The above-discussed parameters show that XNb₂Bi₂O₉ is a potential candidate for photovoltaic applications.