1. Introduction

The uniqueness of hybrid perovskites of CH₃NH₃PbX₃ (where X is single or a mixture of Cl, Br, or I halides) in term of fabrication ease, large absorption coefficients, high carrier mobility, long carrier diffusion lengths and efficient light-electricity conversion have triggered research phenomena for solar cells recently [1–5]. Combined with additional material properties of high photoluminescence (PL) quantum yield and direct bandgap emission tunability within the visible spectrum, research of this material for other optical devices such as laser, light-emitting diode (LED) and photodetector (PD) are arising [3, 6]. Fundamentally, the information of optical constants whether in the form of an inter-related complex refractive index ($N=n-ik$ where $n$ is the refractive index (RI) and $k$ is the extinction coefficient) or complex dielectric function ($\epsilon ={\epsilon }_1-i{\epsilon }_2$ with ${\epsilon }_1=n^2-k^2$ and ${\epsilon }_2=2nk$) as function wavelength or energy are critical. This information will be useful in determining the electronic bandstructure of the perovskite, designing perovskite heterostructure or specific layer for waveguiding or light manipulation in laser, LED or tandem solar cells, and analyzing material properties such as carrier dynamic. To determine the optical constants of material, measurement using spectroscopic ellipsometry (SE), a precise and non-destructive technique for measuring optical properties, is widely used. By measuring the polarization shift from the reflected light off the sample surface and applying an appropriate optical dispersion model, the spectral dependent optical constants of a material can be empirically determined [7].

Numerous studies on optical constants of CH₃NH₃PbX₃ perovskites were reported recently [8–21]. However, mostly focused on hybrid perovskites of I and Cl halides (as single or as a mixture of halides). Only a few papers specifically reported the optical constants for the CH₃NH₃PbBr₃ perovskite [19–21], however all of these experiments were performed on single crystals. Typically, the optical constants of single crystal or bulk material are higher compared to thin films because of higher material densities and fewer defects from voids and surface inhomogeneity. Recent studies of CH₃NH₃PbI₃ perovskites have shown that the RI at 1.55 eV is approximately 2.45 for the single crystal, whereas for the thin films it is considerably lower at around 1.95 [21]. The discrepancy in RI can be detrimental for designing efficient device structures, or light manipulation layers for perovskite optical devices based on thin films. This can lead to poor light confinement, operating wavelength shifting and inefficient light reflection or absorption. Recently, several perovskite LEDs based on CH₃NH₃PbBr₃ thin film were reported [22–26], however the absence of optical constant information for this material in thin films form can delay the progress of efficient LED or laser demonstration.

Here, we report a comprehensive study on optical constants (complex RI and complex dielectric function) of CH₃NH₃PbBr₃ perovskite thin films deposited on FTO substrate with compact-TiO₂ (c-TiO₂) as an electron transport layer. The analysis is performed at room temperature (RT) using the phase modulated SE technique. The optical constants findings will be very useful for (1) quantifying the RI deviation between the CH₃NH₃PbBr₃ perovskite thin films and single crystals, (2) improving the CH₃NH₃PbBr₃ perovskite thin films fabrication, and (3) designing heterostructure for CH₃NH₃PbBr₃ perovskite-based laser, LED, PD and tandem solar cell devices. For these devices, the perovskite deposition using thin films approach is more relevant to form a thin multilayer structure.

2. Experiment

2.1 CH₃NH₃PbBr₃ thin films deposition and characterization

CH₃NH₃PbX₃ perovskites thin films can be fabricated using techniques of one-step precursor deposition (OSPD), sequential deposition method (SDM), dual-source vapor deposition (DSVD) and vapor assisted solution process (VASP). The details of fabrication steps and the advantages plus limitations for each technique are reviewed elsewhere [2, 4]. In this work, the CH₃NH₃PbBr₃ thin films were deposited using VASP method [27, 28]. This technique allows uniform films thickness, extensive films coverage and small surface roughness for the formation of high-quality perovskites thin films suited for multilayer devices. Initially, the FTO substrate was ultrasonically cleaned in detergent, DI water, acetone and IPA, then blow dried by N₂ and treated with O₂ plasma. Prior to CH₃NH₃PbBr₃ films deposition, the FTO substrate was spin coated with approximately 40 nm thickness of c-TiO₂ using mildly acidic titanium isopropoxide solution and heated at 500 °C for 15 min to smoothen the surface and to mimic as the electron transport layer deployed in mostly solar cells and LED devices. The 0.8M PbBr₂ solution in DMF was then spin coated and annealed at 100 °C for 10 min. After annealing, the films was treated by CH₃NH₃Br vapor at 145 °C for 1 hours in a closed petri dish with CH₃NH₃Br powder surrounding the substrate on a hot plate in a vacuum chamber and then rinsed with IPA.

Powder X-ray diffraction (XRD) for the deposited thin films was performed using Bruker AXS D8 diffractometer with Cu-K_α radiation. Surface roughness analysis were performed using Agilent Technologies 5400 atomic force microscope (AFM) under tapping mode operation for an area of $2.5\times 2.5$ and $5\times 5$ µm². The surface and cross-section microscopies were performed using FEI Quanta 3DFEG scanning electron microscope (SEM). The RT PL spectra were acquired using a Horiba Jobin Yvon Aramis UV spectrometer with a 473-nm excitation laser. All reflectance and transmittance spectra were measured with a Shimadzu UV3600 spectrophotometer equipped with integrating sphere and baselined to Al mirror.

2.2 Spectroscopic ellipsometry measurement

The SE measurement was performed using a phase modulated SE (Horiba Jobin Yvon UVISEL iHR320) at RT. Typically, SE data is measured in the form of ellipsometric angles of $\Psi$ and $\Delta$as a function of energy. However, for the phase modulated SE, the detected signals are in the form of the first and second harmonics (symbolized as $I_S$ and $I_C$) of the base modulation frequency of the polarized light upon reflection and can be extracted to determine $\Psi$ and $\Delta$ parameters [7, 14]. Measurements were performed at incident angles of 60, 65 and 70° for a spectral range between 1.5 to 5 eV with a 0.05 eV sampling step. The analysis of the SE data was performed using Horiba Jobin Yvon DeltaPsi2 software.

2.3 Optical dispersion model

After SE measurement, optical model fitting using appropriate dispersion model is performed to extract the optical constants, films thickness and surface morphology. A good fit to the measured data indicated by lowest mean squared error (MSE) is required across the entire spectral range. The Levenberg-Marquardt regression algorithm [7] was used for minimizing the MSE. We utilized Tauc-Lorentz (T-L) model [29], Drude-Lorentz (D-L) model [7], and New Amorphous model [14], for the CH₃NH₃PbBr₃ perovskite thin films, FTO substrate, and c-TiO₂ respectively. Except for the New Amorphous model, all of these models are Kramers-Kronig consistent. We applied T-L model since the similar model was used in the optical constant study of CH₃NH₃PbBr₃ single crystal [19], thus any deviation in our results can be assumed due to the sample (thin films versus crystal) and not owing to the disparity in SE modelling approach. The D-L dispersion model is commonly used for transparent conductive oxide films such as ITO and FTO [30–32].

2.4 Absorption coefficient spectra

The absorption coefficient ($\alpha$) spectra is calculated using equation of $\alpha =4\pi k/\lambda$ where $\lambda$ is the wavelength and $k$ is derived from the SE measurement. In addition to the PL and spectrophotometry measurements, the energy bandgap ($E_g$), is also calculated using the Tauc plot [33] of $\left(\alpha E\right)=A{\left(E-E_g\right)}^{1/2}$ where $\alpha$ is the absorption coefficient, $E$ is energy, and $A$ is a constant. The $E_g$ value is acquired by extrapolating the linear fit line back to the x-axis $\left(\alpha E=0\right)$.

3. Results and discussion

Material characterizations for the CH₃NH₃PbBr₃ perovskite thin films were performed to analyze the structural, morphology and optical properties. The XRD spectra shown in Fig. 1(a) verified the formation of the CH₃NH₃PbBr₃ films on the FTO/c-TiO₂ substrate. The peaks of the CH₃NH₃PbBr₃, c-TiO₂ and FTO were found consistent with the literature [34, 35]. The SEM and AFM microscopies indicate films morphology with grain sizes of 100-850 nm in diameter and vertical root-mean-square roughness (RMS) of 37.0 nm (Fig. 1(b) and the inset). The PL spectra shown in Fig. 1(c) exhibits $E_g$around 537 nm. The spectrophotometry spectra (Fig. 1(d)) indicate absorptance at wavelengths below the absorption edge (<537 nm).

 

Fig. 1 Material characterizations of CH₃NH₃PbBr₃ perovskite thin films deposited on FTO with c-TiO₂ buffering showing: (a) XRD spectra, (b) SEM top-view with 3D AFM topography inset, (c) PL spectra, and (d) spectrophotometry spectra.

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Due to the complexity of multilayer structure in our sample (CH₃NH₃PbBr₃ thin films/c-TiO₂ buffer layer/FTO substrate) plus the FTO substrate itself composed of 3 layers (typically 340 nm SnO₂:F, 25 nm SiO₂ and 30 nm SnO₂ layers coated on 2 mm glass [9]), we initially performed SE measurement for the bare substrate (glass pre-coated FTO). With this approach, we decoupled the complexity of the SE fitting which can arise from the multilayer interference during the measurement and coupling of optical model parameters during the SE modelling. This resulted in a good fitting agreement for the full sample analysis (shown later). Figure 2(a) shows the SE measured versus modelled spectra for the FTO substrate with good fitting acquired (MSE of 1.66) for the entire spectral range. The optical stack model shown in Fig. 2(b) represents the FTO substrate used for the SE modelling. Figure 2(c) depicts the extracted optical constants of $n$and $k$for the FTO substrate as a function of wavelength. The thickness of 429.5 nm and RMS of 18.0 nm (using effective medium approximation (EMA) of 55% SnO₂:F and 45% voids based on the Bruggeman theory [36]) obtained from the modelled FTO substrate are in good agreement with the measured SEM cross-section (425.7 nm) and RMS from AFM (18.7 nm) shown in Figs. 2(d) and 2(e), respectively. Additionally, we also performed SE measurement for the c-TiO₂ layer (spin coated on the bare FTO substrate). Figure 2(f) shows the extracted optical constants of $n$ and $k$ for the c-TiO₂ layer.

 

Fig. 2 Measurement and analysis for the FTO substrate showing: (a) fitting of measured and modelled SE spectra with MSE of 1.66, (b) schematic of the optical model, (c) wavelength-dependent optical constants, (d) cross-section SEM, and (e) 3D AFM topography. Measurement of SE is also conducted for c-TiO₂ layer to determine the wavelength-dependent optical constants, as shown in (f).

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Figure 3(a) shows the SE measured versus modelled spectra for the full sample comprised of CH₃NH₃PbBr₃ perovskite thin films coated on the glass pre-coated FTO substrate with a c-TiO₂ buffer in between. The spectra exhibit a good agreement across the entire spectral range. We obtained an MSE of approximately 1.54 (typically MSE <10 for a film with thickness >500 nm). From the spectra, several peaks were observed above the absorption edge (>2.31 eV) located at approximately 2.36, 3.58 and 4.55 eV. These peak points are consistent with previously reported spectra [19, 37]. To accommodate these peak points, the T-L model fit for the CH₃NH₃PbBr₃ perovskite thin films requires three oscillators. We also acquired reasonable spectral fitting for SE measurement at various angles of incidence (MSE of 1.94 for 65° and 2.17 for 60°, respectively), however we only show here for the best MSE obtained from the 70° incidence angle measurement. To minimize the MSE from the SE modelling, the films thickness and surface roughness of CH₃NH₃PbBr₃ perovskite thin films were treated as free fitting parameters whereas the thickness and surface roughness of the FTO substrate and c-TiO₂ layer were fixed using values obtained from the above SE analysis. The optical stack model deployed for this full sample SE analysis is shown in Fig. 3(b). For the CH₃NH₃PbBr₃ perovskite thin films, we employed two layers to model the main layer and the surface roughness. Besides voids consideration on the surface layer, we also considered voids presence in the main layer to reflect pin-holes existence. The modelled thickness for CH₃NH₃PbBr₃ perovskite thin films and c-TiO₂ layer are highly accurate (less than 4% and 10% deviations for the former and latter layers, respectively) in comparison with the SEM cross-section shown in Fig. 3(c). The modelled RMS of 33.5 nm with EMA of 84% CH₃NH₃PbBr₃ films and 16% voids for the surface layer is also in good agreement with the previously measured AFM (RMS of 37.0 nm in Fig. 1(b)). The SE modelling also indicated approximately 5% of voids exist (from pin-holes) in the main layer of the CH₃NH₃PbBr₃ perovskite thin films.

 

Fig. 3 Measurement and analysis of CH₃NH₃PbBr₃ perovskite thin films on glass pre-coated with FTO and a c-TiO₂ buffer layer showing (a) fitting of measured and modelled SE spectra with MSE of 1.54, (b) schematic of the optical model, and (c) angled SEM cross-section view (tilted at 52°) indicating the CH₃NH₃PbBr₃ films, c-TiO₂ buffer layer and FTO substrate.

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Figure 4(a) shows the extracted optical constants of $n$ and $k$ of CH₃NH₃PbBr₃ perovskite thin films as a function of wavelength. For comparison, we plotted the RI spectra of reported CH₃NH₃PbBr₃ perovskite single crystals using SE measurement with T-L model [19], SE measurement with a critical points-joint density of state model [21], and using spectrophotometry with nonlinear regression model [20]. It is observed that the RI of CH₃NH₃PbBr₃ perovskite thin films is lower than all single crystals counterpart. At 535 nm wavelength for example (Fig. 4(b)), the RI of CH₃NH₃PbBr₃ thin films is around 2.29 whereas all single crystals exhibit 2-8% higher RI. Higher RI of around 25% is also observed for the CH₃NH₃PbI₃ perovskite single crystals case compared to the equivalent thin films [21]. The disparities of RI values between all perovskite thin films and single crystals can induce weak guiding of light when designing heterostructure devices such as laser, LED and tandem solar cells. Moreover, if the heterostructure is based on perovskite with different halides (such as a combination of CH₃NH₃PbI₃/CH₃NH₃PbBr₃), the precise values of RI will become more crucial since the RI range is within proximity to each other. Figure 4(c) shows the dielectric functions of the CH₃NH₃PbBr₃ perovskite thin films. We obtained approximately 5.1 for the dielectric function near the absorption edge which is close to the reported value of 4.8 measured using spectrophotometry [37]. As for the $k$ and ${\epsilon }_2$ spectra, the absorption edge of around 2.309 eV is consistent with most reported values for CH₃NH₃PbBr₃ perovskite [11, 19, 21, 28]. Figure 4(d) shows the absorption coefficient spectra for the CH₃NH₃PbBr₃ perovskite thin films plotted together with the spectra of single crystals [19] for comparison. Both spectra exhibit almost similar absorption edges and peak positions. Using the Tauc plot (inset of Fig. 4(d)), the calculated $E_g$ of the CH₃NH₃PbBr₃ perovskite thin films is approximately 2.309 eV which is consistent with the PL emission wavelength (Fig. 1(c)) and absorption edge indicated using spectrophotometry (Fig. 1(d)). Although the Tauc plot from SE analysis exhibits good agreement with the PL and spectrophotometry measurements, careful consideration should be applied here because the calculated $E_g$could be imprecise [11] due to the excitonic effects near the band edge for hybrid perovskites [20].

 

Fig. 4 Spectra of CH₃NH₃PbBr₃ perovskite thin films showing (a) wavelength-dependent optical constants and comparison with single crystals, (b) comparison of RI values at specific wavelength for thin films and single crystals, (c) dielectric functions, (d) absorption coefficient and comparison with single crystals (inset showing the Tauc plot), (e) effect of voids on the RI spectra, and (f) effect of voids on the absorption spectra.

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The discrepancies of 2-8% in RI (refer Fig. 4(b)) and around one magnitude order in absorption coefficient (refer Fig. 4(d)) between CH₃NH₃PbBr₃ perovskite thin films and single crystals can be attributed to the dissimilarities of material densities (due to voids) and surface condition (roughness and homogeneity). It is well-known that perovskite thin films exhibit higher voids compared to single crystals since solution processing involved in most of the perovskite thin films deposition methods normally exhibit pin-holes [2, 4]. These voids can reduce the quality of the material, thus lowering the RI value as shown for CH₃NH₃PbI₃ perovskite case with voids included [11].To establish this argument for the CH₃NH₃PbBr₃ perovskite thin films, we modelled voids at the film’s surface. The voids were varied at 5, 10 and 20% at the surface using the EMA between CH₃NH₃PbBr₃ films and air. As for the main CH₃NH₃PbBr₃ perovskite layer, we used EMA of 95% CH₃NH₃PbBr₃ films and 5% voids as obtained for the best-fit SE spectra (MSE of 1.54 as shown in Fig. 3(a)). From various SEM cross-sections performed (results not shown here), we found that the voids (pin-holes effects) appeared mostly on the sample surface. Figures 4(e) and 4(f) show the increment of RI and absorption coefficient spectra, respectively as the percentage of voids decreased. The excitonic peaks of both spectra were also blue-shifted as the voids diminished. We also plotted the RI and absorption coefficient spectra from the actual sample measurement (dashed lines) for comparison. Although the DSVD deposition method [38] is claiming non-existence of pin-holes for perovskite thin films, substantial voids are still observable between the polycrystalline grains. Thus the voids existence could not be totally omitted in any of the existing thin films deposition methods (OSPD, SDM, DSVD or VASP) which are preferred for the fabrication of multistructure perovskite. Beside voids, other possible factors for the variance of RI can be attributed to the non-stoichiometry of the fabricated samples, mixture of crystalline and amorphous phases in the sample, scattering effect from the randomness of perovskite polycrystals in the thin films, accuracy in measurement method (such as SE modelling and SE versus spectrophotometry), and sample degradation over time.

4. Conclusion

In our study, we reported comprehensive optical constants and dielectric functions for CH₃NH₃PbBr₃ perovskite thin films using SE technique. We found that the RI of the thin films is around 8% less than the single crystals counterpart. We obtained approximately 5.1 for the dielectric function near the absorption edge for the CH₃NH₃PbBr₃ perovskite thin films. The$E_g$is around 2.309 eV as measured using the PL and spectrophotometry techniques, and calculated from the SE measurement. The lower RI observed for the CH₃NH₃PbBr₃ perovskite thin films compared to the single crystals counterpart signifies the importance of having precise optical constants database for thin films devices. This is because most of the perovskite based laser, LED, PD and tandem solar cells are relying on the thin films deposition approach in fabricating the heterostructure and multijunction structure. The knowledge of the optical constants will also help to quantify the RI deviation between thin films and single crystal, and improve the fabrications of CH₃NH₃PbBr₃ perovskite thin films.