Introduction

Relatively high band-gap semiconductors are significantly used in various optoelectronic devices1,2,3. Although the energy band-gap of a wide band-gap semiconductor may exceed the Shockley–Queisser limit, it can still be utilized as a front UV filter4,5,6,7. A UV filter can be functionalized in optoelectronic devices, specifically solar cells and light harvesters, to protect the solar cells from high-energy photons8,9. For example, the new generation of solar cells, including but not limited to perovskite solar cells10, dye-sensitized solar cells11, and organic solar cells12, have shown severe degradation under UV emissions8. Accordingly, UV absorbers are commonly used as a protective layer6,13. Broad band-gap UV filters can be integrated into multifunction tandem cells as a front layer14,15.

BaTiO3 is considered one of the low-preparation cost alternatives for wide band-gap semiconductors16,17,18,19,20,21. Typically, the energy band gap of BaTiO3 is varied from 3.2 to 3.4 eV22,23,24,25. Attempts were introduced in the literature to modulate the band gap, seeking visible absorption23,24. However, the wide band-gap BaTiO3 is still very beneficial as a UV absorber26,27, especially in perovskite solar cells28,29, as reported in20. Another work utilized BaTiO3 in perovskite thin films but with Si-doping25 and other dopants30. Moreover, BaTiO3 recorded efficient integration in dye-sensitized solar cells, following data presented in16,18,31,32. Over and above, the UV absorption capability can be considered a credit in designing indoor light harvesters, where the UV portion in the light spectrum dominates33,34. In addition to the interesting optical properties of BaTiO3, it also showed exciting features in other applications, such as gas sensing17, water treatment35, and piezo-photoelectronic coupling18.

Recently, the optical and electrical properties of barium titanate (BaTiO3) have attracted a wide range of researchers, as demonstrated in the literature36,37,38,39,40,41,42. The impact of the synthesizing process on the optical properties of the BaTiO3 nano-structure is studied in37. Consequently, the optical band gap and the refractive index of the nanoparticles are well investigated in work reported in36,39. The influence of the compressive strain on the optical properties of BaTiO3 is tackled in43. The recorded data showed a variation in the refractive index from 1.55 to 1.6536. Sb–BaTiO3 and Y–BaTiO3 doped ceramics prepared by solid-state reaction were optically investigated in44. Another doped version of BaTiO3, Ce-Doped BaTiO3, was discussed optically and electronically in45 using first-principles calculations. Applying the same approach, the work in46 studied the Cr-doped BaTiO3. Alternatively, the utilization of density function theory (DFT) simulations glows up to accurately calculate the energy band-gap of the material47. Using hybrid HSE06 functional, the calculated band-gap values were 3.254, 3.894, 3.694, 3.519, and 3.388 eV, corresponding to the cubic, rhombohedral, and orthorhombic, respectively tetragonal, and hexagonal phase of BaTiO3 polymorphs47.

In the current investigation, BaTiO3 nano-powder has been prepared using a novel sonochemical-assisted solid-phase method and deposited over a BK7 glass substrate. The sonochemical-assisted solid-phase method overcomes the shortcomings of too high temperature in solid-phase separation. The adopted method is a simple, direct, and ultrasonic treatment to ensure the homogeneity of the suspension. For material characterization, the samples were characterized using X-ray diffraction (XRD), Fourier-transform infrared spectroscopy (FTIR), and atomic force microscopy (AFM). Optically, the diffuse reflectance spectroscopy (DRS) measurement was conducted for band-gap calculation, and UV–Vis-NIR spectrometer measurements were utilized to capture the optical transmission. The finite difference time domain solver was used to model the UV–Vis spectrum, whereas the density function theory model generated the optical permittivity as a complex wavelength-dependent function.

Experimental work

A novel sonochemical-assisted solid-phase method for the preparation of nano BaTiO3 is proposed in this manuscript to solve the shortcomings of ultra-high temperature in solid-phase preparation (see Fig. 1). BaCO3 was dispersed in water with TiO2 (molar ratio: TiO2:BaTiO3 = 1:1, as reported in48). Stirring was done at 35 °C for 30 min. More details about the TiO2 recipe can be accessed in our previous work49,50,51,52,53. After that, ultrasonic treatment was performed for 30 min, and the power was 160 W. Then, the formed powder was filtered and dried by heating at 80 °C for 8 h. After grinding, the BaTiO3 was prepared by sintering at 850 °C for 5 h, during which the heating rate was 5 °C per minute. BaTiO3 was formed according to the following chemical reactions by Beauger et al.54.

$${\text{BaCO}}_{{3}} \to {\text{ BaO }} + {\text{ CO}}_{{2}}$$
(1)
$${\text{2BaO}} + {\text{ TiO}}_{{2}} \to {\text{ Ba}}_{{2}} {\text{TiO}}_{{4}}$$
(2)
$${\text{Ba}}_{{2}} {\text{TiO}}_{{4}} + {\text{TiO}}_{{2}} \to {\text{ 2BaTiO}}_{{3}}$$
(3)
Figure 1
figure 1

Barium titanate powder preparation setup.

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For thin film deposition, about 0.5 gm of the TiO2 white powder in the mortar is mixed with 2–3 drops of the viscous colorless liquid carboxy methyl cellulose sodium salt (CMC) polymer slowly. The function of CMC is that it binds the BaTiO3 powder to the surface of the glass. Viscous CMC is prepared by dissolving 1 g of CMC powder in 250 mL distilled water in a beaker and placing this beaker on the magnetic stirrer for 4 h at 50 °C and 100 rpm. Grind and mix them with the pestle until a white paste is formed. On a non-conductive glass (5 cm × 1 cm), the substrate is fixed using a thin tape in order to have the thickness of the BaTiO3 paste layer at the same thickness. The used substrate is cleaned for 30 min with the water Labosol solution and then with distilled water, Followed by another 30 min in a Water–ethanol solution of NaOH, then distilled water again. Finally, dry the samples using the N2 stream. The screen printing is done by adding a few drops of BaTiO3 paste to the glass and spreading it evenly to the thickness of the tape using an automated glass rod screen printing machine, previously customized and reported in51. Finally, the glass substrate is placed on a hot plate for 6–8 min at 130 °C, removed, and left to cool down at room temperature. The complete process is illustrated in Fig. 2. Herein; repeatability is ensured as the printing process is managed automatically.

Figure 2
figure 2

(a) Barium titanate paste, (b) automatic screen printing deposition, and (c) BaTiO3 thin film on a glass substrate.

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Thin film deposition for the prepared BaTiO3 is conducted using our customized screen-printing tool51. In such a setup, the layer thickness can be roughly controlled through the motor biasing voltage, which reflects on the glass rod speed. The material charismatics of the prepared samples were measured using XRD (Empyrean Malver Panalytical), AFM (alpha300 Atomic Force Microscope from WITec GmbH), and Fourier Transform Infrared (FTIR) spectroscopy Burker Vertex70. Optically, the optical transmission spectra of the fabricated samples are measured through a V-770 UV–Vis.-NIR Spectrophotometer, Cary 5000, with a wavelength range from 190 to 2700 nm, and Diffuse reflection spectra (DRS) were used for band-gap calculations.

Consent to participate

All authors confirm their participation in this paper.

Computational model

Herein, we utilize the density function theory (DFT) to estimate the energy band gap for the BaTiO3, which can be experimentally verified using the DRS measurements. Utilizing the same VASP procedure as in50, four input files, INCAR, POTCAR, POSCAR, and K-POINTS, were inserted into the model. As outputs, the HOMO–LUMO gap was presented to estimate the material energy band gap. Moreover, the material permittivity as a complex wavelength-dependent function was obtained against wavelength using the DFT post-calculation, given by:

$$\upvarepsilon \left(\uplambda \right) =\upvarepsilon ^{\prime } \left(\uplambda \right) -\upvarepsilon ^{\prime \prime } \left(\uplambda \right)$$
(4)

where ε(λ) is the material permittivity as a function of wavelength λ, ε′(λ) is the real part of the material permittivity, used in calculating the real material refractive index \(n\), and ε″(λ) is the imaginary part of the material permittivity, exploring the optical extinction of the material.

Moving toward the thin film layer, an open-source, Linux-based Maxwell's equation solver, MEEP, was used to model the optical transmission spectrum using the finite difference time domain (FDTD) computational technique55. MEEP utilizes a scaled Maxwell's equations with a scaling factor of \(a\). For an input in the form of a gaussian beam of peak wavelength at 550 nm, the field at the end of the layer can be derived from a simple matrix operation given by:

$$\left[ {\begin{array}{*{20}c} {E_{1} } \\ {H_{1} } \\ \end{array} } \right] = M{ }\left[ {\begin{array}{*{20}c} {E_{2} } \\ {H_{2} } \\ \end{array} } \right]{ }$$
(5)

where \(E_{1}\) and \(H_{1}\) are the electric and magnetic field intensity in the input medium, \(E_{2}\), and \(H_{2}\) are the electric and magnetic field intensity in the output medium, and M is given by:

$$M = { }\left[ {\begin{array}{*{20}c} {\cos k_{o} h} & {i\sin k_{o} h/\gamma_{1} { }} \\ {\gamma_{1} { }i\sin k_{o} h} & {\cos k_{o} h} \\ \end{array} } \right]{ }$$
(6)

and \({ }\gamma_{1}\) is given by:

$$\gamma_{{1{ }}} = { }\sqrt {\frac{{\varepsilon_{o} }}{{\mu_{o} }}} \frac{{n_{1} }}{{\cos \theta_{i} }}$$
(7)

where \(k_{o}\) is the propagation coefficient (\(k_{o} = {2}\uppi /\uplambda\)), λ is the wavelength, h is the thin film thickness, \({\varepsilon }_{o}\) and \({\mu }_{o}\) are the air permittivity and permeability, \({n}_{1}\) is the refractive index of the thin film material and \({\theta }_{i}\) is the angle of incidence. The material dispersion and extinction spectra are inserted into MEPP using Lorentz–Drude (LD) coefficients55. These LD coefficients are the main link between the DFT and MEEP models. LD coefficients are extracted using the algorithm demonstrated in Fig. 3.

Figure 3
figure 3

LD fitting algorithm using FDTD MEEP simulator.

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Experimental results

This section demonstrates the experimental and numerical results for the material and optical properties of BaTiO3 thin film. Numerical investigations are integrated into this manuscript to provide a repeatable simulation parameter for BaTiO3 that can be useful for the research community in modeling BaTiO3 in various optical and optoelectronic devices. In addition, the proposed simulation model is verified in terms of band-gap for the DFT model and transmission spectra for the FDTD optical model concerning experimental measurements.

Material characterization

Initially, the BaTiO3 nano-powder was investigated using XRD. XRD is a powerful technique commonly utilized to characterize nanomaterials to investigate crystalline properties, including the crystalline phases, the corresponding planes, the average crystalline sizes, and many other parameters. XRD pattern is represented in Fig. 4. The peaks at 22.14°, 31.5°, 38.8°, 45°, 50.8°, 56.1°, and 66.1° were ascribed to (001), (110), (111), (002), (210), (211) and (202) plane respectively which corresponding to BaTiO3 (JCPDS No. 01-089-1428). The size of BaTiO3 crystallites recorded is estimated by the Debye–Scherrer56,57:

$${\text{t}} = \frac{{{\text{K}}\uplambda }}{{\upbeta \cos\uptheta }}$$
(8)

where \({\text{K}}\) is the Scherrer constant of 0.89, \({\uplambda }\) denotes the wavelength of the X-ray source, \({\beta }\) denotes the full width at half maxima (FWHM), and \({\uptheta }\) denotes the Bragg’s diffracted angle. The crystallite size was recorded at 59 nm, with the aid of the top five peaks in the XRD illustrated in Fig. 4. Herein, we utilize the first five peaks as these sharp and resolved peaks showed the best-fitting statistics obtained. The lattice parameters \(a\) and \(c\) are calculated using the equation56,57:

$$\frac{1}{{d^{2} \left( {hkl} \right)}} = \frac{4}{3} \left[ {\frac{{h^{2} + hk + l^{2} }}{{a^{2} }}} \right] + \frac{{l^{2} }}{{c^{2} }}$$
(9)
Figure 4
figure 4

X-ray diffraction pattern for barium titanate powder JCPDS No. 01-089-1428).

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This material crystallizes in a Tetragonal structure with lattice parameters a = 4.00 Å and c = 4.01 Å. The average lattice strain ε is determined by56,57:

$$\upvarepsilon = { }\frac{\beta }{4}\cos\uptheta$$
(10)

The average lattice strain showed ε = 0.202. The dislocation density δ is formulated by the equation58,59,60:

$$\updelta = \frac{{15\upbeta \cos\uptheta}}{4aD}$$
(11)

Consequently, the dislocation density was 1.76 × 109 cm-2. The determined dislocation density agrees with previously reported data in the literature61,62,63. The work in62 has reported a variation in the dislocation density of the BaTiO3 from 1.7 × 109 to 1.0 × 109 cm−2, while the data produced in63 recorded the same order of magnitude of 109 cm−2.

The X-ray diffraction pattern shows that the synthesized product is single-phase, well-crystallized, and tetragonal BaTiO3. Additionally, Fig. 5 shows the FTIR spectra of nano-structure BaTiO3. The low-frequency region of the spectrum at 988 cm−1 is attributed to O–H bonded to titanium. The same trend of the 988 cm−1 bands was obtained in the strong absorption peak of asymmetric stretching carbonates ion (BaCO3) at 1434 cm−1. Additionally, the powder SEM characterization was carried out in Fig. 6. The SEM results showed that the grains of BaTiO3 is irregularly polygonal in shape. EDX analysis of particles calcinated at 850 °C is given in Fig. 7 and confirms the accuracy of elemental composition. The particles are composed of Ba, Ti, and O elements. The experimental values of the BaTiO3 sample obtained from the spectrum of energy dispersive X-ray analysis (EDX) are shown in Table 1, and the corresponding element mapping is in Fig. 8. Finally, the thin film roughness was measured using an atomic force microscope (AFM), cf. Fig. 9. The experimental data recorded an acceptable roughness, with an average root-mean-square variation of around 1.50 nm in a (0.5 μm)2 region. Thin film is deposited on a BK7 glass substrate using screen printing, as introduced in “Experimental work” section. The recorded surface roughness showed significant improvement to the data in the literature as in64. We attribute this to the sonochemical-assisted solid-phase method to prepare nano BaTiO3. Additionally, the deposited samples were monitored several weeks after deposition, where no color changes were detected.

Figure 5
figure 5

\(FTIR\) of BaTiO3 powder, where the x-axis represents the wavenumber \(k\) in cm−1, and the y-axis indicates the transmittance in %.

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Figure 6
figure 6

SEM measurements for BaTiO3 powder (a)–(d).

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Figure 7
figure 7

Energy dispersive X-ray analysis (EDX) measurements for BaTiO3 powder. Herein the x-variation is for the energy in KeV. At the same time, the y-variation indicates the number of counts, which reflects the material weight in the composition, as highlighted in Table 1.

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Table 1 Experimental values for the Energy dispersive X-ray analysis (EDX) measurements for BaTiO3 powder.
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Figure 8
figure 8

Mapping measurements for BaTiO3 powder.

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Figure 9
figure 9

Roughness measurement of Barium Titanate Thin Film using atomic force microscope. The x–y axis represents the thin film coordinates in μm, while the color bar indicates the morphological surface roughness in nm.

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For the sake of thickness investigation, the SEM measurements in Fig. 10 (a demonstrated a top surface view, while b shows an edge view for thickness estimation) were conducted, showing an average film thickness of 178.45 μm, with the aid of the post-image processing technique and the correction factors introduced in our previous work in65. SEM measurement in Fig. 10a was also utilized to explore the porosity of the samples using a MATLAB image processing toolbox, as previously utilized in our work66. Herein, the processing showed a porosity of around 44.32%. Moreover, the SEM image in Fig. 10a is used to capture an estimated grain size of the BaTiO3 particles, where an adequate size of 23 nm is recognized. The image post-processing calculated grain size properly matches the one determined using the XRD in Fig. 4. We can attribute the slight mismatching to the aggregation effects associated with the solvent. All the obtained parameters in this section are listed in Table 2, where a comparison concerning literature is shown whenever possible.

Figure 10
figure 10

Thickness measurement of barium titanate thin film using SEM.

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Table 2 Experimentally obtained results for BaTiO3.
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Optical characterization

Principally, the diffuse reflection spectra (DRS) were measured to investigate the light absorbance profile of the prepared nanomaterial. Figure 11 shows the Tauc plot, where the Tauc relation is given by56,57:

$$\varepsilon^{^{\prime}} \left( {h\nu } \right) = C\left( {h\nu - E_{g} } \right)n$$
(12)

where C is a constant, \(\varepsilon^{^{\prime}} \left( {h\nu } \right)\) is the molar extinction coefficient, \(E_{g}\) is the average band gap of the material, and n depends on the type of transition. The band gap of prepared BaTiO3 nanoparticles was estimated to be 3.2 eV. Alternatively, DFT modeling is conducted, as mentioned in “Consent to participate” section. Perovskites are famous for the ABX3 structure, where a three-dimensional corner-sharing BX6 octahedron is formed. For simplicity, we consider only the cubic structure to explore the optoelectronic properties of BaTiO3. Firstly, the ABX3 structure is relaxed to calculate the lattice constant. Accordingly, the flexible structure is simulated to demonstrate the energy band diagram and the density of states (DOS) shown in Fig. 12. Knowing that the generalized gradient approximation (GGA) underestimates the band-gaps in DFT simulations, the hybrid nonlocal exchange–correlation functional (HSE) is used to calculate the band-gap of the BaTiO3 accurately. By observing the DOS, it can be concluded that BaTiO3 is an indirect band-gap material with a typical band-gap of 3.212 eV. This validates our simulation process, as it matches our experimental DRS measurements in Fig. 9 and reported data in the literature25,35,69,70.

Figure 11
figure 11

Tauc plot for barium titanate.

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Figure 12
figure 12

DOS and band structure for BaTiO3 outputted from the DFT VASP simulation model.

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Next, the imaginary part of the relative permittivity is simulated for BaTiO3 in Fig. 13. This spectrum reflects the extinction behavior of the materials in the optical region of interest from 200 to 550 nm. Herein, we can assume a dominating absorption effect over other scattering mechanisms. This can be easily proven due to the limited surface roughness measured by the AFM in Fig. 9. Thus, the surface scattering can be neglected. The real part of the permittivity is also extracted for refractive index estimation. The refractive index showed 1.595, which agrees with the reported data in36. Consequently, the data simulated in Fig. 13 can be directly converted to LD coefficients to be fed into the MEEP model.

Figure 13
figure 13

The imaginary permittivity component \((\varepsilon^{\prime \prime } ){ }\) for BaTiO3, as outputted from the DFT VASP simulation mode.

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Finally, the thin film of BaTiO3 prepared over a BK7 glass substrate is optically characterized using the Cary 5 UV–Vis spectrometer, see Fig. 14. Samples are measured against the BK7 substrate as a reference. In parallel, The FDTD was used to simulate a thin film of 178.45 μm thickness with two Gaussian beams centered at 550 nm, representing the TE and TM waves. As highlighted earlier, the material dispersion and extinction LD coefficients were captured from the DFT model. We utilize the same procedure as in50 for lithium titanate. The dispersion and extinction LD fitting coefficients were calculated to be: \({\upvarepsilon }_{\infty }\) = 1.595, \({\upsigma }_{1}\) = 1.5645 e + 41, \({\upomega }_{1}\) = 0.1254, \({\Gamma }_{1}\) = 0.05656, \({\upsigma }_{2}\) = 7.5565. \({\upomega }_{2}\) = 0.55128, \({\Gamma }_{2}\) = 1.9788, \({\upsigma }_{3}\) = 0.78155, \({\upomega }_{3}\) = 2.564578, \({\Gamma }_{3}\) = 2.2251, \({\upsigma }_{4}\) = 0.17521, \({\upomega }_{4}\) = 1.78215, \({\Gamma }_{4}\) = 0.95448 \({\upsigma }_{5}\) = 0.05551, \({\upomega }_{5}\) = 0.74158, and \({\Gamma }_{5}\) = 0.01452.

Figure 14
figure 14

The UV–Vis-NIR numerically simulated normalized transmission spectrum using MEEP for BaTiO3, with the experimentally measured spectrum for validation. The dispersion and extinction were inputted using LD fitting coefficients.

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For experimental validation, the T-λ FDTD simulated spectrum is demonstrated against the UV–Vis-NIR spectrometer measurement for our fabricated thin film. For accurate matching, the thin film scattering prefactor was considered the main free-fitting parameter with the given material thickness and refractive index (as a function of the permittivity previously simulated using DFT). A thin film of 178.45 μm thickness was reached. The comparison between the simulation data and the experimental measurements in Fig. 14 indicates an acceptable argument with an average root-mean-square error of 1.44%.

Conclusion

In conclusion, this paper introduces an experimentally validated FDTD numerical model to describe the optical properties of BaTiO3 as a potential layer in optoelectronic devices. Firstly, the DFT VASP model was used to estimate the energy band gap, nearly 3.21 eV, with DRS optical measurement agreement. The permittivity's real and imaginary parts of the permittivity were calculated, showing a refractive index of 1.595. Consequently, LD fitting parameters were used to input the complex permittivity of the BaTiO3 into the MEEP model. Less than 1.44% error was observed while the simulated MEEP spectrum was compared with the corresponding experimental spectrum. Experimentally, the manuscript provided a novel recipe to prepare and deposit a thin film of BaTiO3 with all essential morphological, physiochemical, and optical characteristics. A further investigation of other electrical properties, specifically the magnetic and the hall effect properties, can be part of future work.