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Abstract
The perovskite solar cell (PSC) has the benefits of flexibility, inexpensiveness, and high efficiency, and has important prospective applications. However, serious optical losing and low solar energy-utilizing efficiency remain a challenge for the ultra-thin PSCs because of the interface reflection of traditional planar structure. In this study, a hierarchical pore structure with a confined resonant mode is introduced and optimized by electromagnetic theory to improve the solar energy absorbing and utilizing efficiency of ultra-thin PSCs. The large pores in the top layer that support a whispering gallery mode can focus and guide the incident light into the solar cell. The small pores in the bottom layer enable backward scattering of the unabsorbed light and can improve the effective absorption of active layer. The finite-difference time-domain method is employed to optimize the geometric parameters of hierarchical pore structure to improve the light absorption of PSCs. The proposed resonant hierarchical pore structure can greatly improve sunlight absorption of ultra-thin PSCs, and the effective light absorption and photocurrent of PSCs with a hierarchical pore structure is 20.7% higher than that of PSCs with traditional planar structure. This work can offer a beneficial guideline for improving solar energy utilizing efficiency of various thin-film solar cells.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Human society is confronting a huge problem of environmental and energy crises; hence, it is significant to develop clean energy and renewable energy technologies. [1–5] As a significant type of renewable energy, solar energy has brilliant future for environment protection, greenhouse effect alleviation and air pollution mitigation. [6–9] Recently, photochemistry, photoelectricity, and photothermal technologies have been developed significantly. [10–14] Among these technologies, photovoltaics (PV) is environmentally friendly, easy to implement, and highly efficient. [15–18] Perovskite solar cell (PSC) is an emerging type of solar cells, and it has aroused widespread research interests, because perovskite materials own the benefits of exceptional flexibility, ultra-high efficiency and low cost. [19–23]
The PSC is flexible because of its ultra-thin characteristic, and it holds broad market prospects. Nevertheless, the reduction of PSC thickness decreases the path length of sunlight, which would result in insufficient light absorption of PSC. [24–26] Besides, traditional planar PSC with a wavelength-scale thickness would generate interface reflection and constructive interference, resulting in serious optical loss. [27–29] Therefore, manipulating the incoming sunlight is necessary for an ultra-thin PSC, which would gain admirable light absorption enhancement in perovskite layer. Several photon management and light trapping schemes have been investigated to promote sunlight absorption for solar cells especially PSC, and these schemes essentially enhanced light absorption by providing strong anti-reflection property and manipulating the focusing, funneling and scattering of sunlight. [30–32] For example, randomly textured surface such as deposition gratings, antireflection coatings, nanodomes and nanocones have been extensively researched. [33–36] These textured surfaces are commonly employed methods, and could be easily manufactured by mature techniques, such as low-pressure deposition and wet etching. [37,38] Irandoost et al. [39] designed a PSC with ZnO nanorods and plasmonic nanoparticles, and investigated the influence of nanoparticles and nanorods on the performance of PSC. Schmager et al. [40] reported that nanostructured perovskite active layer could promote the photocurrent of PSC by 5–6%. Xuan et al. [41] reported that nano/micro-structured surfaces of solar cells could enhance the broadband sunlight absorptivity by ∼97%. For solar cells, the previously proposed textured structures would weaken broadband sunlight reflection so that enhance the total absorption. Nevertheless, texturing the active absorber layer would ineluctably enlarge the surface area and the density of surface traps in PSC, enhancing carrier recombination and eventually deteriorating the solar cell efficiency. [42–44] Thus, it is significant to explore an effective photon management scheme which can protect integrality of PSC active layer and circumvents increasing the carrier capture and recombination.
Recent progresses in photonics indicate possibilities to handle light efficiently and enable prominent broadband photon management without PSC active layer texturing. Among these photonic schemes, the wavelength-size dielectric resonant nanospheres supporting whispering gallery modes (WGM) have aroused extensive research interests, because these resonant nanospheres own the advantages of efficient anti-reflection and light trapping capability and structural simpleness. [45–47] However, the nanospheres on the top of solar cells may face the risk of falling off due to insufficient adhesion. in this case, pore structures in the top layer may be superior alternatives.
In present study, a hierarchical pore structure with confined resonant mode is investigated to enhance the solar energy absorbing and utilizing efficiency of ultra-thin PSCs. The large pores in the top layer supporting WGM can focus and guide the incident sunlight into the solar cell due to their unique geometric structures. This layer can serve as a waveguide to capture the sunlight and circumvent the interface reflection. The small pores in the bottom layer enable backward scattering of the unabsorbed light and can improve the effective absorption of active layer. To demonstrate its advancement, this light management scheme is comparative researched compared with the previous light management scheme adopting the wavelength-size dielectric resonant nanospheres. The influence of filling factor, ratio and radius of the hierarchical pore structure on the effective light absorptivity and photocurrent of PSCs was investigated through finite-difference time-domain (FDTD) method. An algorithm named particle swarm method is utilized to optimize the hierarchical pore structure in terms of optical solutions. The hierarchical pore structure in this work illustrates a low cost, simple, and durable photon management scheme, and could provide general guideline for improving solar energy absorbing and utilizing efficiency of ultra-thin PSCs.
2. Methodology
2.1 Design of PSC with hierarchical pore structure
The structure schematic diagram of a planar PSC usually consists of five layers (as displayed in Fig. 1(a)): a metal substrate as a rear electrode (Ag), a hole transport material layer (HTM, Spiro-OMeTAD), a perovskite absorber layer (CH3NH3PbI3), an electron transport material layer (ETM, TiO2), and front transparent conductive electrode layer (TCO, ITO (In2O3:SnO2)). Figure 1(b) presents the schematic diagram of a PSC with the hierarchical pore structure. The diameter of hemispherical pore located in the top layer is larger than the diameter of truncated spherical pore in the bottom layer. The thicknesses of Ag, perovskite, and ETM layer are 80 nm, 300 nm, and 50 nm, respectively. And the thicknesses of these layers are constant and set by referring to other literatures [12,30,40] and the author’s experience. The thicknesses of TCO and HTM layer depend on the diameters of large pores and small pores, which are optimized in this study. Specifically, the thickness of TCO layer is designed to be half the diameter of the large pore, and the thickness of HTM layer is designed to be two-thirds of the diameter of the small pore. For the TCO layer, this thickness design can maximize the opening area of the large pore, thereby capturing more incident sunlight. For the HTM layer, this thickness design can increase the contact area between the air in the small pore and the active layer, forming a strong refractive index contrast, thereby enhancing the backward scattering of the unabsorbed sunlight. Figure 1(c) and (d) present two types of hierarchical pore structure, which will be investigated thoroughly later. The hierarchical pores are arranged in hexagonal, and the distance between the centers of any two adjacent large pores (or small pores) is the same. Figure 1(e) presents the top view of the PSC with the hierarchical pore structure.
Fig. 1. Schematic diagrams: (a) the optical loss mechanism of planar structure; (b) the light absorption enhancement mechanism of hierarchical pore structure; two types of hierarchical pore structure: type A (c), type B (d); (e) top view of a PSC with the hierarchical pore structure: the pores are arranged in hexagonal; (f) simulation settings in this study.
The dimensionless factor (R) defines the ratio between the diameter of large pore and that of small pore, and it is expressed as follows:
where D is the diameter of the large pore located in the top layer, d is the diameter of the small pore located in the bottom layer. The dimensionless filling factor (F) defines the distance between two neighboring pores, which can be calculated as follows: where L is the distance between two neighboring large pores.The hierarchical pore structure owns three advantages: 1) the pore structure can be can be directly produced by the polystyrene (PS) microsphere templates, which is a mature technique [48]; 2): the hierarchical pore structure can protect the integrality of PSC active layer and circumvent increasing the carrier capture and surface recombination [49,50]; 3) the hierarchical pore structure can capture the sunlight efficiently and circumvent the interface reflection.
The photon management mechanisms of planar structure and hierarchical pore structure are illustrated in Fig. 1(a) and (b). Serious optical losing exists in the traditional planar structure because of the interface reflection. On the contrary, the hierarchical pore structure can address this problem effectively. The large pores in the top layer that support whispering gallery mode can focus and guide the incident light into the solar cell due to their unique geometric structures. This layer can serve as a waveguide to capture the sunlight and circumvent the interface reflection. At the location where the large pore contacts with the ETM, a light leakage channel is formed because the ETM layer (TiO2) can provide a high refractive index. [49] The light confined in the hemispherical pore structure can be coupled to the leakage channel and scattered to the active layer. Owning to a huge refractive index difference between the perovskite active layer and the air-filled small pores, there arises an impedance mismatch in the PSC, which enables backward scattering of the unabsorbed light and can enhance the effective absorption of active layer.
The PSC with hierarchical pore structure can be achieved through sacrificial polystyrene (PS) microsphere templates [48,51,52]. First, a variety of sizes of the PS microspheres can be synthesized in emulsifier-free systems. The perovskite film can be fabricated by spin-coating a precursor solution directly on a TiO2 compact layer (ETM). The PS monolayer can be fabricated by spin-coating PS colloid precursors on TiO2 layer at a certain rotate speed (reference value: 3000–5000 rpm) and dried at a certain temperature (reference value: 70–100 °C). The fabrication of TCO (In2O3:SnO2, ITO) layer on PS monolayer is achieved by spin-coating a precursor colloid solution and drying at a certain temperature, and the PS template can be removed by immersing the TCO film in toluene, and then annealed at a certain temperature (reference value: 130–150 °C). After the above steps, the porous TCO layer can be obtained. The porous HTM layer can be also fabricated on the other side of the perovskite film [51]. Finally, the Ag layer can be fabricated by magnetron sputtering [48]. The annealing and drying temperatures and rotate speed may be the factors that affect the performance during fabrication.
2.2 Numerical analysis description
The light absorption and electromagnetic field distribution of the proposed PSC with hierarchical pore structure can be analyzed utilizing the FDTD method, which is an advanced technique for solving 3D electromagnetic matters. [53] In the analysis process, the boundary conditions and source settings are illustrated in Fig. 1(f). The perfectly matched layer (PML) boundary condition is adopted in the incident direction (Z axis) of the plane wave light source. The periodic boundary condition is employed in the polarization direction (X and Y axis). The mesh size is set as 5 nm, which is sufficiently small compared with the simulated sunlight wavelength (400–1000 nm). The spectral absorption of PSC includes two portions: parasitic absorption and effective absorption. Effective absorption expresses the sunlight absorbed by the active layer, which can yield photocurrent. Parasitic absorption represents the sunlight absorbed by other layers, which cannot yield photocurrent. Based on electromagnetic field distribution, the spectral absorption of the PSC can be calculated by [54].
The Pabs(ω) is the absorbed power of the incident normalized power per unit volume, and it is calculated by
where ω is the angular frequency and k is the imaginary part of the complex refractive index. |E| is the electric field intensity. The photocurrent of the PSC is derived by3. Model validation
The optical properties (refractive index) adopted in this study are presented in Fig. 2(a) and (b). For verifying numerical calculation accurateness, the calculated results by FDTD method are in comparation with those predicted by another numerical method and experimental results, respectively. The light absorption of pure perovskite active layer (the thickness is 300 nm) computed by FDTD method is in comparation with that computed by transfer matrix (TM) method. Figure 2(c) presents the results of spectral absorptivity of the perovskite active layer calculated by TM method and FDTD method, respectively. As displayed in Fig. 2(c), the spectral absorptivity of perovskite active layer calculated by FDTD method can agree well with that computed by TM method. Another case is conducted by comparing the experimental results and the numerical results calculated by FDTD method of a radiative cooling glass studied in our previous work. [55] The spectral transmissivity of the radiative cooling glass is measured by a UV–VIS–NIR spectrophotometer (SolidSpec-3700, Shimadzu, Japan). As displayed in Fig. 2(d), the spectral absorptivity of the radiative cooling glass calculated by FDTD method can agree well with the experimental results.
Fig. 2. Model validation: (a) real part and (b) imaginary part of refractive index for ITO (TCO), TiO2 (ETM), perovskite, Sprio-OMeTAD (HTM); (c) light absorptivity calculated by TM method and FDTD method; (d) spectral transmissivity calculated by FDTD method and tested by experiment, inset is the measured glass sample
4. Results and discussions
4.1 Performance of PSC with hierarchical pore structure and planar structure
The influence of the hierarchical pore structure on effective sunlight absorption and photocurrent generation of PSC is explored. Figure 3(a) displays the spectral light absorptivity (parasitic absorptivity and effective absorptivity) of PSC with the hierarchical pore structure and planar structure. As presented in the figure, the spectral effective light absorptivity of PSC with the hierarchical pore structure is obviously higher than that of PSC with planar structure, and the parasitic absorptivity of PSC with the hierarchical pore structure is basically the same as that of PSC with planar structure. So, the hierarchical pore structure can greatly improve the effective light absorption of PSC while does not bring about increased parasitic absorption. The spectral absorptivity curve indicates that the short-wave absorptivity curve of the PSC with planar structure fluctuates greatly, while the short-wave absorptivity curve of the PSC with hierarchical pore structure is stable. As an explanation, the planar structure generates interface reflection and constructive interference, and the hierarchical pore structure can effectively avoid these negative effects. Figure 3(b) displays the photocurrent of PSC with hierarchical pore structure and planar structure. The photocurrent of PSC with a planar structure is 19.3 mA/cm2, and the photocurrent of PSC with a hierarchical pore structure is 23.3 mA/cm2. The photocurrent of PSC with a hierarchical pore structure is 20.7% higher than that of PSC with a planar structure.
Fig. 3. Comparison of hierarchical pore structure and planar structure: (a) spectral absorptivity of PSC with hierarchical pore structure and planar structure; (b) photocurrent of PSC with hierarchical pore structure and planar structure; electric field distribution (λ=550 nm, X-Z cross) of PSC with (c) hierarchical pore structure and (d) planar structure; electric field distribution (λ=930 nm) of PSC with (e) hierarchical pore structure and (f) planar structure
To explore the optical mechanism for the enhanced absorption of PSC with hierarchical pore structure, the X-Z cross sectional electric field profiles of PSC with the two structures at two representative wavelengths (λ=550 and 930 nm) are respectively presented in Fig. 3(c,d). The influences of confined resonant mode and leaky channel effect are demonstrated by the X-Z cross sectional electric field distribution of PSC with hierarchical pore structure (Fig. 3(c,e)). After entering the large pore, incident light becomes confined within the pore because of its hemispherical geometry. Internal reflections at the air/ITO interface guide light along the inner boundary of the pore. At the location where the large pore contacts with the ETM, a light leakage channel is formed and the light confined in the hemispherical pore structure can be coupled to the leakage channel and scattered to the active layer. The small pores in the bottom layer enable backward scattering of the unabsorbed light and enhance the electric field strength of perovskite layer. The influences of interface reflection and constructive interference are demonstrated by the X-Z cross sectional electric field distribution of PSC with planar structure (Fig. 3(d,f)). Besides, the influences of confined resonant mode and backward scattering are demonstrated by the X-Y cross sectional electric field distribution of PSC with hierarchical pore structure (Fig. 4). In Fig. 4, the electric field profiles at three representative wavelengths (λ=550, 800 nm and 930 nm) are selected, because the sunlight absorption of PSC with the hierarchical pore structure is significantly enhanced compared with that of PSC with planar structure at these representative wavelengths.
Fig. 4. Demonstration of confined resonant mode: (a)(b) electric field distribution (X-Y cross) demonstrating the confined resonant mode of the large pore, (a) λ=550 nm, (b) λ=930 nm; (c)(d) electric field distribution (X-Y cross) demonstrating the strong scattering of the small pore, (c) λ=800 nm, (d) λ=930 nm
4.2 Comparison of pore structure and nanoparticle structure
The performance of hierarchical pore structure in this work and hierarchical dielectric nanoparticles adopted in Ref. [49] on the effective sunlight absorption and photocurrent generation of PSC are comparatively investigated in this section. Two types of hierarchical pore structures are presented in Fig. 1(c) and (d). For type A, the small pores are located at the bottom of the perovskite layer; for type B, the small pores are located at the top of the perovskite layer. In addition, two types of hierarchical nanoparticle structures are presented in Fig. 5(a) and (b). For type C, both the large particles and small particles are made of SiO2 nanoparticle; for type D, the large particles are made of SiO2 nanoparticle and the small particles are made of TiO2 nanoparticle.
Fig. 5. Comparison of different hierarchical structures: two types of hierarchical nanoparticle structure: type C (a), type D (b); (c)-(e) spectral absorptivity of PSC with different hierarchical structures (c) type A & type B, (d) type A & type C, (e) type A & type D; (f) photocurrent of PSC with different hierarchical structures
The spectral light absorptivity (parasitic absorptivity and effective absorptivity) of PSC with these four types of hierarchical structures is comparatively presented in Fig. 5(c)-(e). As displayed in Fig. 5(c), the effective light absorptivity of PSC with the hierarchical pore structure (type A) is obviously higher than that of PSC with the hierarchical pore structure (type B). The wavelength ranges of 0.55–0.75 µm and 0.9–0.95 µm are being particularly absorbed better. As an explanation, the small pores in the bottom layer enable backward scattering of the unabsorbed light and can enhance the effective absorption of perovskite layer, while the small pores in the top layer reflect the incident light and reduce the effective absorption of perovskite layer. The backward scattering of small pores can be attributed to two reasons: a huge refractive index difference between the perovskite active layer and the air-filled small pores makes an impedance mismatch in the PSC; the sizes of pores are small enough, which makes the scattering phenomenon close to Rayleigh scattering, i.e., strong backward scattering. As displayed in Fig. 5(d) and (e), the effective light absorptivity of PSC with the hierarchical pore structure (type A) is higher than that of PSC with the hierarchical nanoparticle structures (type C and D). Although the WGM still exists in the hierarchical nanoparticle structures, the refractive index difference between the nanoparticle and air leads to additional reflection and optical loss. The photocurrents of PSC with these four types of hierarchical structures are displayed in Fig. 5(f), and PSC with the hierarchical pore structure (type A) owns the highest photocurrent. Table 1 summarizes the photocurrent enhancements of these four types of hierarchical structures compared with traditional planar structure. As a result, all these four types of hierarchical structures can improve the light absorption and photocurrent of PSCs compared with conventional planar structure, and hierarchical pore structure (type A) is the optimal structure to improve the sunlight absorption and solar energy utilizing efficiency of PSCs. This comparison demonstrates the advancement of the light management scheme in this work compared with the previous light management scheme in other work.
Table 1. The photocurrent enhancements of hierarchical structures compared with planar structure.
4.3 Effects of geometrical parameters on the performance of PSC
The influences of geometrical parameters (ratio, diameter and filling factor) of hierarchical pore structure on the performance of ultra-thin PSC are researched here. The ratio (R) defines the ratio between the diameter of large pore and that of small pore. The effects of ratio (R) on the effective light absorption and photocurrent of PSC with hierarchical pore structure are presented in Fig. 6(a) and (b), respectively. The photocurrents of PSCs with hierarchical pore structure with the ratio of 1:1, 1:2, 1:3, 1:4, 1:5 and 1:6 are 22.73, 22.61, 22.63, 23.31, 21.58 and 21.79 mA/cm2, respectively. Therefore, hierarchical pore structure with different ratio can promote the photocurrent of PSC with different enhancement. And the ratio of 1:4 is the optimal value among these ratios. As displayed in Fig. 6(b), when the ratio is 1:4, there is no significant improvement for the average parasitic absorptivity of the PSC with hierarchical pore structure.
Fig. 6. Effects of geometric parameters on performance of PSC: (a) effect of ratio on the photocurrent of PSC; (b) effects of the ratio on the average absorptivity of PSC; (c) effect of diameter on the photocurrent of PSC; (d) effects of the diameter on the average absorptivity of PSC; (e) effect of filling factor on the photocurrent of PSC; (f) effects of the filling factor on the average absorptivity of PSC
The influences of the diameter of large pore on the effective light absorption and photocurrent of PSC with hierarchical pore structure are presented in Fig. 6(c) and (d), respectively. The photocurrents of PSCs with hierarchical pore structure with the large pore diameter of 0.5, 0.6, 0.8, 1.0, 1.2, 1.4 and 1.6 µm are 22.17, 23.31, 21.54, 21.1, 20.88, 21.01 and 21.41 mA/cm2, respectively. As shown in Fig. 6(c), the optimal diameter value of large pore is around 0.6 µm. The average parasitic absorptivity of the PSC with hierarchical pore structure basically exhibits an increasing trend with the increase of diameter.
The filling factor (F) defines the distance between two neighboring pores. The effects of filling factor on the effective light absorption and photocurrent of PSC with hierarchical pore structure are presented in Fig. 6(e) and (f), respectively. The photocurrents of PSCs with hierarchical pore structure with the filling factor of 1, 1.05, 1.1, 1.15, 1.2, 1.25 and 1.3 are 23.31, 23.28, 23.36, 23.02, 21.74, 20.9 and 20.61 mA/cm2, respectively. As shown in Fig. 6(c), when the filling factor is beyond 1.1, the photocurrent decreases gradually with the increase of the filling factor. The average parasitic absorptivity of the PSC with hierarchical pore structure basically holds constant with the increase of filling factor.
4.4 Angular sensitivity of the hierarchical pore structure
In practical applications of PSCs, the incident sunlight may reach the PSC at any angle. Thus, we further investigate the photocurrent of PSC with the proposed hierarchical pore structure with incident light at different angles, and the results are presented in Fig. 7. The performance of PSC with the planar structure at incident angle of 0° is also presented for comparison. As displayed in Fig. 7, with the incident angle increases, the photocurrent of PSC with the proposed hierarchical pore structure would decrease to some extent. However, the performance of the hierarchical pore structure is consistently better than that of the planar structure. The parasitic absorptivity of PSC with hierarchical pore structure with incident light at different angles is basically constant, and it only increases slightly when the incident angle is bigger than 45°. The reflectivity of PSC is basically constant, and the increase in parasitic absorption mainly results in the decrease in effective absorption. Fortunately, the effect of incident angle on the decrease of effective absorption is limited. Overall, the proposed hierarchical pore structure can provide an omnidirectional light trapping scheme.
5. Conclusions
In summary, a hierarchical pore structure with confined resonant mode is introduced and optimized to improve the solar energy absorbing and utilizing efficiency of ultra-thin PSCs. The large pores in the top layer that support whispering gallery mode can focus and guide the incident light into the solar cell. The small pores in the bottom layer enable backward scattering of the unabsorbed light and can improve the effective absorption of perovskite layer. The analysis results demonstrate that the proposed hierarchical pore structure can increase the photocurrent of PSC by up to 20.7% compared with traditional planar structure. The performances of different hierarchical structures are comparatively investigated, and the results indicate that the hierarchical pore structure is superior to hierarchical nanoparticle structure. The hierarchical pore structure with small pores located at the bottom of the perovskite layer is demonstrated to be optimal structure between the studied four structures. Furthermore, the hierarchical pore structure can still play impacts at oblique incident angles, thereby providing an omnidirectional light trapping scheme. The geometrical parameters (R, D, F) of the hierarchical pore structure are optimized to improve the sunlight absorption of PSCs. It is believed that this proposed optical scheme for improving the solar energy utilizing efficiency of ultra-thin PSCs can provide valuable guidance for various ultra-thin solar cells.
Funding
National Natural Science Foundation of China (52076064, 52211530089); Fundamental Research Funds for the Central Universities (HIT.DZJJ.2023095); National Key Research and Development Program of China (2018YFA0702300).
Acknowledgments
This work was supported by National Natural Science Foundation of China, the Fundamental Research Funds for the Central Universities, National Key Research and Development Program of China, and Taishan Scholar Foundation of Shandong Province (tsqn201812105).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available on request from the corresponding author.
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