Absorption Performance of Doped TiO2-Based Perovskite Solar Cell using FDTD Simulation

Department of Electrical Engineering Education, Universitas Pendidikan Indonesia, Bandung, 40154 Jawa Barat, Indonesia Department Physics Education, Universitas Pendidikan Indonesia, Bandung, 40154 Jawa Barat, Indonesia Engineering Physics, Institut Teknologi Bandung, Bandung, 40132 Jawa Barat, Indonesia Department of Mechanical Engineering Education, Universitas Pendidikan Indonesia, Bandung, 40154 Jawa Barat, Indonesia


Introduction
Concerns about the environment, particularly the repercussions of the greenhouse effect for future generations, have prompted the development of alternative energy sources such as solar, wind, and biomass in recent decades [1]. Solar energy is regarded as the most abundant, sustainable, and ecologically beneficial renewable energy source among these [2,3]. Because of their high efficiency of over 25%, perovskite solar cells (PSC) have attracted a lot of interest [4][5][6][7][8].
The development of PSC depends on several factors, including perovskite layer, the electron transport layer (ETL), and hole transport layer (HTL), as previously studied by Azri et al. and Hasanah et al. [11,12]. The ETL was functioned to extract and transport the photogenerated electron and suppress the charge recombination to blocking hole as one of the significant activities in solar cell devices [13]. Therefore, the ETL is required to have high charge mobility, sufficient energy level alignment, and related morphology and interfacial properties [14]. TiO 2 is a well-known material that has widely used in PSC due to its good alignment of conduction band to the lowest unoccupied molecular orbitals (LUMO) of active layers of perovskite [11]. However, TiO 2 havea low-coordinated Ti cation at the surface, which provided electron traps due to low-lying Ti 3d and this condition reduced the charge mobility [15]. The wide energy gap owned by TiO 2 limits the absorption only at the UV-light region, which can affect the PSC absorption performance [16].
The enhancement of TiO 2 properties is commonly obtained by doping with noble metal ions, transition metal, and rare metal [17]. The dopants are function to reduce the number of electron trap sites because they can replace the low-coordinated Ti cations. The charge mobility can be improved by certain amounts of dopants that trigger exciton separation [17]. TiO 2 is an n-type semiconductor, and dopants for TiO 2 are classified into two types. To begin, pentavalent cations (Nb, Ta, and so forth) increase electron conductivity in TiO 2 and thus the energy gap [18]. Second, divalent/trivalent cations (Cr, Fe, Ni, Co, and so forth) can be used to convert TiO 2 to a p-type and decrease the energy gap [19].
The absorption performance of PSC with MaPbI 3 was investigated in this study using different types of TiO 2 doping as ETL. Tantalum (Ta) at concentrations of 1.8% and 3.8% and iron (Fe) at concentrations of 0.11% and 0.32% were employed as dopant materials. The thickness of TiO 2based ETL was also simulated to investigate the effect of thin and thick ETL. The simulation was obtained using Finite-Difference Time-Domain (FDTD) methods, which use Maxwell's equations to calculate. The absorption spectra are characterized at wavelengths ranging from 300 to 1500 nm, and the results are presented as absorption percentages and indexes in arbitrary units. Finally, this research should provide the best parameters for doped TiO 2 -based ETL in PSC.

Methods
The optical model was utilized to examine the absorption performance of doped TiO 2 -based PSC in this study. Lumerical Ltd.'s Finite-Difference Time-Domain (FDTD) simulations use Maxwell's equations to represent the interaction between electromagnetic light waves and the solar cell structure. FDTD simulations have been widely employed in various applications, including photovoltaic (PV) research [20]. The incident light bandwidth employed in this work was 300-1500 nm, based on an AM1.5 spectrum with a resolution of 12 nm; photon flux was high in this bandwidth but low elsewhere [21]. Light absorption is expressed as AbsðλÞ for each wavelength and is formulated using P Abs ðλÞ is the power absorbed per unit volume for a given wavelength, and dV is the absorber volume, which may be calculated using where ω is the angular frequency of the light which corresponds to the wavelength and ε ″ is the imaginary part of the dielectric permittivity and j E * j 2 is the electric field strength.
The performance of solar cells was determined using the FDTD simulation with the refractive index as the fundamental material parameter. ITO, TiO 2 , MaPbI 3 , CuSCN, and Au were used as the front contact, electron transport layer (ETL), absorption/perovskite layer, hole transport layer (HTL), and back reflector, respectively, in the PSC structure shown in Figure 1. The earlier work [22][23][24] refers to these materials complex refractive index and thickness. Meanwhile, the ETL is optimized in this study by varying the doping materials and thickness. The dopants used are 1.8% and 3.8% tantalum (Ta) to produce Ta-TiO 2 and 0.11 and 0.32% iron (Fe) to produce Fe-TiO 2 . The thickness was also varied to 20 nm, 50 nm, 100 nm, 200 nm, and 500 nm. The refractive index of doped TiO 2 was calculated using the refractive index-bandgap relation obtained from Reddy and Ahammed [25,26].
The FDTD simulations are carried out in the PSC structure 2-dimensional mesh cells, with a mesh accuracy rate of 3. The light source was used in the y-axis plane-wave mode with amplitude and wavelength of 1 and 300-1500 nm, respectively. The y-axis was used with perfect matching layers (PML) and boundary conditions (BC) to maximize incident light trapping. Meanwhile, the periodic BC was applied in the x-axis, assuming the structure's infinite periodicity [27,28]. A 2D y-normal frequency-domain field and power monitor were clamped to the layer being studied to record the absorption. The general investigation of the structure was obtained by placed the monitor between ITO-TiO 2 and CuSCN-Au. The 3D frequency-domain field and power monitor were also used to record the electric field j E * j 2 profile to analyze the field distribution in the PSC structure. Finally, the absorption curve and E-field profile for the desired structure and layers can be generated by this simulation.

Contribution of PSC Layers to Absorption Performance.
As descibed in the methods,the PSC structure in this study, consists of five layers with varying materials and functions. According to Shockley-Quisser theory, the direct bandgap of MaPbI 3 is 1.5-1.6 eV [10]. The absorption coefficient of MaPbI 3 with a thickness of 280 nm was 80% of incident light in the sun-ray range [29]. As a result, these perovskite materials are an excellent candidate for absorption layer to produce high PSC performance. CuSCN with a bandgap of 3.4 eV was used in the HTL because it had the highest efficiency compared to other HTL materials such as P3HT, Spiro-OMeTAD, CuI, and NiO. The efficiency of CuSCN in HTL is supported by the excellentalignment of its highest occupied molecular orbital (HOMO) level of the CuSCN with the valence band of perovskite layer [11]. The TiO 2 with bandgap 3.2 eV used in the ETL is also used to enhance the PSC performance. Azri et al. reported that TiO 2 had obtained the best efficiency of 20.26% compared to ITO, PCBM, IGZO, and SnO 2 [11]. Similar to the HTL, the good ETL should have a sufficient conduction band alignment to the lowest unoccupied molecular orbitals (LUMO) of the perovskite active layers [11].
The absorption spectra for each material are simulated separately and displayed in Figure 2(a) to understand the contribution of each layer to the absorption performance of the proposed PSC structure. The gray shaded curve plane represents the absorption of the entire PSC structure, while the green, purple, red, and blue curve planes represent the absorption of each material layer, including ITO, TiO 2 , MaPbI 3 , and CuSCN. It can be seen that the MaPbI 3 layer contributes the most to absorption activity, which corresponds to its function as an active or absorption layer. The highest absorption reaches 0.92-0.95 at the 400-750 nm wavelength and then drops significantly to 0.1 at 800-1400 nm. On the other hand, ITO as a front contact has the lowest absorption of 0.04-0.20, indicating a suitable functionality because incident light is not trapped in the ITO and is transmitted to the active layer. TiO 2 and CuSCN have low absorption but produce a significant peak at specific wavelengths, with TiO 2 producing a peak at 312 nm and CuSCN producing a peak at 911 nm.
As can be seen, the absorption spectra collected in each layer support each other to construct the complete structural spectra. The total light absorbed by the structure reached 79.5% with an average absorption of 0.795 by examining the shorter wavelength range of 300-800 nm as shown in Figure 2(b) and assuming the white space as residual incident light from the reflectance loss. This reflectance loss is incident light that is not absorbed by the structure. We have shown in this section that TiO 2 contribution as an ETL layer is still minimal. The current study will optimize through doping and thickness modifications, and the enhancement effect will be studied by comparison in Figure 2.

Absorption Optimization using Doped TiO 2 -based ETL.
In this study, two contrasting characteristics of materials, namely, Ta and Fe, were used for doping variation. Ta is considered a pentavalent cation that can increase the electron conductivity in TiO 2 and robust n-type characteristics [18]. Therefore, Ta doping can be expanded the energy gap of TiO 2 , namely 3.5 eV and 3.7 eV, for 1.8% Ta-TiO 2 and 3.8% Ta-TiO 2 , respectively [30]. Meanwhile, Fe doping which includes divalent/trivalent cations functions to modify TiO 2 into a p-type. Fe-doped TiO 2 can decrease the bandgap from 3.2 eV to 2.76 eV and 2.68 eV for 0.11% Fe-TiO 2 and 0.32% Fe-TiO 2 , respectively [19]. In this section, to discover the effect of doping in ETL, the absorption spectra were compared to pure TiO 2 , as shown in Figure 3. ETL thickness was kept constant at 90 nm for each doping study.
According to Figure 3, absorption in the active layer was increased for all doping modifications. The most substantial improvement was recorded around 350 nm, 520 nm, and 911 nm. Around the wavelength of 520 nm, the doped TiO 2 -based ETL achieved an absorption of 0.98. When compared to TiO 2 -based ETL with 0.88 absorption, indicates 0.2 less to the maximum absorption of 1.0 and 0.1 enhancement. In terms of total light absorption, the doped ETL increased to 81.7% for Fe-TiO 2 and 81.2% for Ta-TiO 2 , respectively. This finding also revealed that Fe doping is slightly greater than Ta doping, with an average absorption of 0.816 and 0.810, respectively, between 300 nm and 800 nm. Higher Fe doping performance corresponds to a reduced bandgap, and decreasing TiO 2 bandgap extends the light absorption to visible light. Lower bandgap brings the material closer to the optimal bandgap for solar cells of 1.4-2.4 eV [31]. The absorption spectra differed only slightly because of the low doping concentration in Fe-TiO 2 . The results, however, showed that raising the doping concentration resulted in more significant gains.
The doping effect can also be observed from the E-field profile of PSC structure in the z-normal plane. In Figure 4, a comparison of the E-field profile for the PSC structure with ETL TiO 2 and 0.32% Fe-TiO 2 was shown. The profile in Figure 4 occurred at a certain wavelength optimum based on absorption spectra in Figure 3 including 370 nm, 516 nm, 768 nm, and 912 nm. Referring to Equation (2); the E-field j E * j 2 is proportional to the absorption power, P Abs . The color legend shows that the color shift from deep blue to red indicates a larger E-field. For each wavelength, the E-field intensity resulting by 0.32% Fe-TiO 2 -based PSC is higher than TiO 2 -based PSC. With 0.32% Fe-TiO 2 , the high E-field is more congregates on the front contact surface until it enters the active layer as the wavelength increases.

Modelling and Simulation in Engineering
Generally, the light absorption in PSC can be enhanced by modifying the ETL to lead the resonance and optical enhancement. The nanostructure such as photonic crystal has been reported to result the high-performance PSC [1,21]. Due to the strong absorption dependence on refractive index,thickness studies can also be a simple and efficient way to optimize the PSC. Tooghi et al. reported the influence of hole transport layer (HTL) thickness on the absorption, and it shows that the thinner the HTL, the better performance obtained [32]. Since the ETL was placed in front of the active layer, the thickness should not be too thick, which can block the incident light transmission nor should not be too thin to optimize the electron transport activity [32]. Several studies on PSC applied TiO 2 -based ETL with thickness in the range 10-700 nm [33][34][35][36][37]. In this study, the thickness of 0.32% Fe-TiO 2 -based ETL was varied by 20 nm, 50 nm, 100 nm, 200 nm, and 500 nm. The 500 nm ETL has a fluctuating absorption spectrum, as shown in Figure 5, indicating that incident light is reflected back into the air at certain wavelength. The thinner layer of ETL is resulting more stable absorption, but it has dropped at 650-700 nm of wavelength. The optimum absorption is provided by the 100 nm of thickness, the spectra were dropped around 750 nm, and the peak occurred around 911 nm. Finally, it can be concluded that the optimum thickness of Fe-TiO 2 -based ETL is around 100 nm, with light absorption around 81%.
Finally, the proposed PSC has demonstrated excellent absorption performance. As shown in Table 1, Ta and Fe-   5 Modelling and Simulation in Engineering doped TiO 2 have a higher absorption percentage than other dopants reported in previous studies. Because of the higher intensity of the solar spectrum in AM1.5 [38], the comparison is specified in a wavelength of 446 nm.

Conclusions
In this study, the absorption enhancement of PSC-doped TiO 2 has been successfully achieved by optimizing the dopant, concentration, and thickness of ETL. The FDTD methods were used to simulate the PSC, which consist of five layers, including ITO (front contact), TiO 2 (ETL), MaPbI3 (active/absorption layer), CuSCN (HTL), and Au (back contact). The applied Fe and Ta doping into TiO 2 resulted in the higher incident light absorption of 81.7% and 81.2%, respectively, while the pure TiO 2 obtained lower absorption of 79.5%. However, the effect of doping concentrations cannot be further studied due to the slight performance difference. In general, 0.32% Fe-TiO 2 was the optimum ETL layer for the proposed PSC structure due to its ability to reduce the bandgap. The thickness optimization revealed that the thicker the ETL, the more fluctuated the spectra, and the thinner the ETL, the more the spectra dropped at short wavelength. Finally, Fe-TiO 2 with a thickness of 100 nm was concluded as the optimized ETL layers in the studied PSC. The proposed design is expected to deliver high solar cell performance in short circuit current, open-circuit voltage, fill factor, and power conversion efficiency.

Data Availability
The parameter data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.