The optimized lattice parameters for the studied hybrid double perovskites are listed in Table 1. These Sb-based hybrid inorganic and organic double perovskites show increasing trend in order from X = Cl, Br and I.
Table 1. Calculated lattice constants and bandgaps for hybrid double halide perovskites ANaBX6 (A = CsMA, (MA)2; B = Sb; X = Cl, Br, I).
From Table 1, it can be inferred that the bandgap energy increases with reducing lattice constants in accordance with the observation by (Greenman, Williams, & Kioupakis, 2019; Roknuzzaman et al., 2017) that the replacement of halogen atom (X) by a lighter and smaller halogen atom reduces the lattice parameter. Generally, the halogens increasing in atomic size down the group in Periodic Table (Kragh, 1963; Yao et al., 2021) and as such, increasing the halide concentration results in decrease of the bandgap energy.
The electronic band structures for the hybrid double perovskite compounds are shown in Figs. 1–3. These hybrid double perovskites were predicted to be of indirect band gap as their inorganic double perovskites, Cs2NaBX6(B = Bi, Sb; X = Cl, Br, I)(Shuai & Ma, 2016). The CBMs were shown to appear at the X point of the high symmetric path of the BZ with exception of (CsMA)NaSbI6, with its CBM at the R point of the BZ. On the other hand, the VBMs of these materials were found to be at the M point. The calculated band gap values are presented in Table 1 from which it can be inferred that the iodide hybrid double perovskite ( (CsMa)NaSbI6 (2.09 eV)) exhibit the smallest band gap value. These value are comparable with that of Cs2AgBiBr6 (2.19 eV by measurement)(McClure, Ball, Windl, & Woodward, 2016). Moreover, all the perovskites in the present method gave band gap values of (CsMA)NaSbI6 (2.09 eV), (CsMA)NaSbCl6 (3.05 eV), (CsMA)NaSbBr6 (2.55 eV). These values are comparable with that of (MA)2BiAgCl6 (2.7 eV) (Volonakis et al., 2016) within the same level of theory and MAPbCl3 (3.0eV) (McClure et al., 2016) apart from, (CsMA)NaSbCl6 (3.1 eV) in the present study which show slight deviations which could be attributed to its small value of lattice parameter as opined by (Greenman et al., 2019).
Moreover, the band gap of the investigated perovskites can be tuned by changing the halogen contents. This characteristic spurs usability in areas such as light emitting diode (LEDs) (Roknuzzaman et al., 2017, 2019).
In Figs. 4–6, the total and projected DOS of the considered hybrid double perovskites were calculated to investigate the band compositions of atomic orbital contribution towards electronic states at VBM and CBM. The result of the total and projected DOS of (CsMA)NaSbI6 perovskite in Fig. 4. It is shown that the contribution to the total DOS towards VBM is by the Sb-5p states and I-5p states. The contribution to the total DOS towards CBM is by the I-5p states while the Na-3s states gave a partial contribution to the total DOS towards VBM.
In Fig. 5, the total and projected DOS for (CsMA)NaSbCl6 perovskite is shown from which it can be seen that the contribution to the total DOS towards VBM is by the Sb-5p states and Cl-3p states. The only contribution to the total DOS towards CBM is by the Cl-3p states. The Na-3s states is seen to contribute only partly to the total DOS towards VBM. For the (CsMA)NaSbBr6 perovskite in Fig. 6, the main contribution to the total DOS towards VBM is by the Sb-5p states and Br-4p states. The Br-4p states is also seen to contribute to the total DOS towards CMB while the Na-3s states offers partial contribution to the total DOS towards VBM.
Looking at the results of the total and projected DOS in Figs. 4–6, it is evident that the halogen atoms contribute to the total DOS both towards VBM and CBM. This characteristic is pertinent to the observed change of band gap with the change of the halogen content in the hybrid double perovskites. Evidently for all the aforementioned hybrid double perovskites, it can be seen that the least contribution to the total DOS towards VBM is by the Na-3s states. This feature of the Na atom is also observed in the inorganic double perovskites, Cs2NaBX6(B = Bi, Sb; X = I,BR, Cl) investigated by (Shuai & Ma, 2016). The authors, observed that although the Na atom is important to the formation of the double perovskite crystal, the Na s orbital is not involved in the composition of VBM.
The calculated dielectric functions, absorption coefficients, real and imaginary parts of the refractive indices of ANaBX6 (A = CsMA, (MA)2; B = Bi, Sb; X = Cl, Br, I) are presented in Figs. 7–18.
The investigated optical properties of the considered hybrid double perovskites include, dielectric function, real and imaginary parts of the refractive index as well as the absorption coefficient. The dielectric function and refractive indices were observed for the photon energy from 0 to 30 eV while the absorption coefficients were observed for the wavelength from 0 to 800 nm. The (CsMA)NaSbI6 perovskite has the highest dielectric constant at higher energy region (2-4eV) function over the same energy region compared to the other hybrid double perovskites investigated.
Owing to the dependence of the absorptive behaviour of a material on the imaginary part of the dielectric function (Shuai & Ma, 2016), the imaginary parts of the dielectric function of the considered compounds were investigated. The material (CsMA)NaSbI6 depicts the highest value for the imaginary dielectric function of all the investigated compounds for solar radiation. This high value of the dielectric function of the (CsMA)NaSbI6 material for solar radiation suggests that it is a potential optoelectronic material. Moreover, due to the dependence of photovoltaic performance of a material on high dielectric constant or dielectric function at zero frequency, as materials with large dielectric constant can hold large amount of charge over a long period of time thus enhancing the photovoltaic performance. Among the investigated hybrid double perovskites, the highest value of the dielectric constant of 4.43 is obtained for the (CsMA)NaSbI6 material. This value shows closeness to the dielectric constant of MAPbI3 (Roknuzzaman et al., 2017), with value of 5.23. The discrepancy in value compared to the value of the dielectric constant for the (CsMA)NaSbI6 material in the present study is 0.8. This closeness shows that other optical properties of the hybrid double perovskite (CsMA)NaSbI6 material should ought to be similar to those of the hybrid perovskite MAPbI3.
The absorption coefficient of a material is a key determinant of its light harvesting capacity and plays a significant role in its application for solar energy conversion. The results showed that the investigated materials have high absorption coefficient with the highest absorption obtained with (CsMA)NaSbI6. This posits that the (CsMA)NaSbI6 hybrid double perovskite would be a suitable substitute to Pb-based hybrid perovskites for solar cell applications. Additionally, the refractive index for (CsMA)NaSbI6 in Fig. 8 showed the maximum peak (2.83) over a broad spectrum (2-4eV). Thus, the (CsMA)NaSbI6 material can be suitable in optoelectronic applications such as liquid crystal display (LCDs), organic-light emitting diode (OLED), quantum dot light emitting diode (QDLED) televisions which require materials with high refractive index (>1.50) (Garner, 2019).
Table 2. Calculated formation energy, H(kJ/mol) of of (CsMA)NaSbX6 (X = Cl, Br, I)
Looking at Table 2, the calculated formation energies of the considered hybrid double perovskites are presented. The formation energy of a material is the change of enthalpy when 1 mole of a compound is formed from its constituents elements. As opined by (Roknuzzaman et al., 2019), a negative formation energy of a material depicts the stability of the material. This stability increases with increasing negativity of the formation energy. As can be inferred from the results in Table 2, the formation energies of the I-based compounds show least negativity compared with that of Br or Cl-based compounds. In all, the results of the formation energies of the investigated compounds show that they are stable and can be utilized for different optoelectronic applications.