Numerical investigation of structural optimization and defect suppression for high-performance perovskite solar cells via SCAPS-1D

All the reagents were used as received without further purification. Methylamine iodide (MAI, > 99.99%), lead iodide (PbI₂, > 99.99%), 2,2',7,7'-tetrakis (N, N-di-p-methoxyphenylamine)-9,9'-spirobifluorene (Spiro-OMeTAD, >99.5%), tris (2-(1H-pyrazol-1-yl)-4-tert-butylpyridine)-cobalt (Ⅲ) tris (bis-(trifluoromethylsulphonyl) imide) (FK209, > 99%), bis(trifluoromethance) sulfonimide lithium salt (LiTFSI, > 99%) and 4-tert-butylpyridine (4-TBP, > 96%) were purchased from Tokyo Chemical Industry Co., Japan. The SnO₂ colloid solution (tin (Ⅳ) oxide) was obtained from Alfa Aesar. Other chemicals were provided by Wako Co., Japan.

Fluorine-doped tin oxide (FTO) conducting glass substrates (sheet resistance of 10 Ω sq⁻¹) were sequentially washed by ultrasonication in detergent solution, deionized water, ethyl alcohol, acetone and isopropanol for 20 min, respectively. The SnO₂ colloid solution (15%) was diluted with deionized water to the concentration of 5 wt%. Before ETLs deposition, the cleaned FTO substrates were dried with nitrogen and treated by UV-ozone for 30 min. The colloid precursor of SnO₂ was spin-coated onto FTO substrate at 3000 rpm for 20 s. The substrate was then annealed at 150 °C for 30 min to obtain the SnO₂ film.

After the preparation for ETLs, the substrates were moved into a glove box filled with N₂ for perovskite, HTL deposition and electrode evaporation. The MAPbI₃ perovskite layers were fabricated by a one-step method as reported. 553 mg PbI₂ and 190 mg MAI were dissolved in 1 ml mixed DMF/DMSO (4:1) solvent and stirred for one night at 50 °C. After that, 100 μl of the precursor was spin-coated onto the FTO/SnO₂ substrate at 1000 rpm for 12 s and 5000 rpm for 30 s, respectively. During the high-speed spin-coating process, 200 μl antisolvent was dripped on the perovskite film after 7 s to promote the perovskite crystallization. Subsequently, the substrates were annealed at 100 °C for 10 min to form uniform and compact films. For HTL, the mixture of 72 mg Spiro-OMeTAD, 14 μl FK209 (376 mg ml⁻¹ in acetonitrile), 17 μl Li-TFSI (520 mg ml⁻¹ in acetonitrile) and 29 μl 4-TBP dissolved in 1 ml CB was spin-coated onto perovskite film at 4000 rpm for 20 s. Finally, 100 nm gold (Au) was thermally evaporated on the top of films under vacuum (<5 × 10⁻⁴ Pa). The active area of all the solar cells was 0.09 cm². The J–V characteristic of all the devices was recorded using a solar simulator (WXS-155S-10: Wacom Denso Co., Japan) under AM 1.5 G illumination at 100 mW cm⁻² in air condition.

To investigate both bulk recombination and interface recombination, the Shockley Read Hall (SRH) model is utilized in this simulation. The trap-assisted SRH recombination is mainly acknowledged to be the dominant recombination mechanism in PSCs. ²⁹⁾ Owing to the undesired film quality such as poor crystallization and high surface defect in the absorber layer, the generated free electron and hole are of higher possibility to be captured and thus recombine in trap centers. This so-called trap-assisted SRH recombination has been widely used to assess the photoconversion loss in single absorber device, which can be described by Eq. (1). ³⁰⁾

$$\begin{eqnarray}&&{R}_{\mathrm{SRH}}=\displaystyle \frac{np-{n}_{i}^{2}}{\tau \left(p+n+2{n}_{i}\,\cos \,h\left(\tfrac{{E}_{i}-{E}_{t}}{KT}\right)\right)}\end{eqnarray} \tag{ 1 }$$

where the R_SRH is the SRH recombination rate, n and p are the concentration of electron and hole, respectively, n_i represents the intrinsic carrier density, τ represents the carrier lifetime, E_i and E_t refer to conduction/VB and trapping energy level, respectively. It is evident that the SRH recombination rate is determined by the carrier lifetime of the perovskite layer. On behalf of interpreting the critical dependency of defect density for recombination, Eq. (2) is utilized to show the relation between carrier lifetime and defect density. ³¹⁾

$$\begin{eqnarray}&&\tau =\displaystyle \frac{1}{\sigma \times {N}_{t}\times {v}_{\mathrm{th}}}\end{eqnarray} \tag{ 2 }$$

where τ represents the carrier lifetime, σ is the carrier capture cross section, N_t is the defect density and v_th refers to electron thermal velocity. According to the Eqs. (1) and (2), the defect density is inversely proportional to carrier lifetime owing to the constant parameters for σ and v_th at RT. Therefore, the SRH recombination rate is exclusively dependent on the defect density. Figure 3(a) demonstrates the SRH recombination rate as a function of film depth with varied defect density for the absorber layer. Within the defect density of 10¹⁴ cm⁻³, the recombination rates are at a lower level in the range of absorber from 0.25 to 0.5 μm. As the defect density increases from 10¹⁴ to 10¹⁶ cm⁻³, the recombination rate rises significantly in the perovskite layer. Notably, in a high defect density of 10¹⁶ cm⁻³, a much steeper curve is observed for higher depth regions indicative to near the ETL side for the absorber layer. Since the sunlight illuminates the front of the device by the FTO side, there are masses of generated carriers accumulated in the first interface of ETL/absorber rather than the second absorber/HTL due to the excellent absorption of MAPbI₃ perovskite. ³²⁾ The quantitative discrepancy for non-equilibrium carriers brings more trap states and recombination centers in the interface of ETL/absorber, and thus results in a rapidly increased recombination rate. As a result, Fig. 3(b) exhibits the J–V curves for varied defect densities from 10¹³ to 10¹⁷ cm⁻³. While the defect density increases from 10¹³ to 10¹⁵ cm⁻³, the device performance drops mainly attributed to the reduced V_oc from 1.116 V to 0.993 V. Simultaneously, the J_sc nearly remains at the same level. However, when the defect density increases up to 10¹⁶ cm⁻³ or even higher, the observably severe recombination leads to the degradation both in V_oc, J_sc and FF. Therefore, it is vital for PSCs to suppress the defect density within 10¹⁵ cm⁻³ in the absorber layer to obtain good PCE.

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As an excellent absorber material, MAPbI₃ perovskite possesses a high diffusion length, which is beneficial for carrier extraction and even the absorption property in the near-spectral region. ³³⁾ Some researchers also reported a long diffusion length of over 1 μm in the nanostructured MAPbI₃ perovskite. ³⁴⁾ Here we investigate the relation between diffusion length and bulk recombination to improve the device performance. Equation (3) describes the relation between carrier lifetime and diffusion length.

$$\begin{eqnarray}&&{L}_{D}=\sqrt{D\tau }\end{eqnarray} \tag{ 3 }$$

where D is the diffusion coefficient and is related to the carrier mobility. Therefore, the suppressed defect density leads to increased carrier lifetime and prolonged diffusion length, as summarized in Table II. Figure 4 demonstrates the variation in J–V characteristics as a function of the diffusion length. An impressive impact is observed mainly in V_oc and FF owing to the higher diffusion length, attributed to suppressed defect density. Meanwhile, the effect on J_sc is very tiny while L_D > 0.2 μm. Thus, the V_oc improvement is dominant to affect PCE in this case. With the increasing diffusion length over 1.0 μm, the improvement of PCE is getting slower as well as V_oc. According to the literature, the optimization for absorber quality such as additive doping and crystallization control is effective to improve the diffusion length of perovskite and obtain high performance. ³⁵⁾ Considering the actual experimental process in absorber deposition, the thickness of one-step MAPbI₃ film is commonly within 500 nm. Under suppressed defect density of 5 × 10¹³ cm⁻³, the suitable carrier diffusion length for the subsequent simulation is assumed to be 720 nm with a carrier lifetime of 100 ns. Therefore, the better PCE of 17.86% is achieved with improved V_oc of 1.097 V and FF of 79.8%, compared with the control device PCE of 15.68%. In addition, to avoid blocking the carrier extraction and transfer, the film thickness is preferable within 720 nm.

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In Sect. 4.2, the effect of absorber thickness is compared and analyzed from 150 nm to 500 nm. Generally, with regard to the PSCs, the sufficient absorber thickness contributes to better device performance due to the preferable J_sc. ³⁶⁾ However, the excessively grown thickness may introduce problems of film morphology control and an increase of defect centers, which lead to severe recombination and V_oc loss. ³⁷⁾ Figure 5 shows the J–V characteristics with varied MAPbI₃ thickness from 150 nm to 500 nm to demonstrate the effect of absorber thickness, as summarized in Table III. It is clear the thicker absorber layer from 150 nm to 400 nm is beneficial for optical absorption and results in dramatically improved J_sc from 15.63 to 22.27 mA cm⁻². Meanwhile, the V_oc and FF have slight declines. Therefore, the PCE rises to 16.60% instead of 13.09%. On the contrary, since the thickness grows, the V_oc reduces from 1.037 V to 0.992 V and FF reduces from 77.3% to 66.6% continuously because of the severe recombination. Additionally, the series resistance also has a potential impact on the declining performance, which we will discuss in detail hereinafter. Even though the absorption ability is getting better, the J_sc has gradually become saturated with sufficient thickness, inducing the PCE loss over the thickness of 400 nm. In summary, the desirable absorber thickness is around 400 nm to achieve optimized J_sc, proper V_oc and FF, leading to superior device performance.

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To investigate the effect of ETL/HTL thickness, the device performance is simulated with varied thickness of the transport layer, as shown in Fig. 6. As for ETL, we used colloid SnO₂ precursor for deposition, which is interpreted in experimental Sect. 2. According to the literature, the thickness of SnO₂ film is around 35 nm. ³⁸⁾ Thus, the varied thickness of ETL is set to be 20 to 100 nm in the simulation. Figure 6(a) shows the overall J–V characteristics, including FF, J_sc and V_oc. The photovoltaic parameters almost remain constant since the thickness of ETL increases, which indicates an excellent carrier extraction capacity and defect-state tolerance. As a result, there is a negligible effect on device PCE by varying the ETL thickness. Conversely, the HTL exhibits a declined PCE from 15.75% to 15.55%, attributed to the decrease in FF from 75.9% to 74.9%. Meanwhile, other parameters like V_oc and J_sc have no significant change, as shown in Fig. 6(b). The reason for the varied FF is that the Spiro-OMeTAD film with high resistivity leads to higher series resistance and poor conductivity which is harmful to charge transport and transfer, compared to the tiny impact from the relatively thin film of ETL with lower resistivity. ^39,40) As an organic small molecule material, thin Spiro-OMeTAD film is also likely to suppress defects and achieves higher efficiency, as reported in several studies. ^41,42) Therefore, the proper thickness of ETL and HTL is set to be 20 nm and 150 nm for the subsequent optimization.

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After the assumption for both the absorber layer and transport layer, the interfaces between these layers are also investigated in Sect. 4.4. To analyze the effect of interface recombination, the IDLs with a thickness of 10 nm are simulated as ETL/perovskite and perovskite/HTL, respectively. Figure 7(a) presents the overall recombination from HTL-interface to ETL-interface based on the varied interface defect density from 10¹⁶, 10¹⁸ and 10²⁰ cm⁻³, respectively. At the low interface defect density of 10¹⁶ cm⁻³, the dominant recombination is in the range of 0.15 μm to 0.57 μm, which refers to the majority of bulk region and the interface ETL/absorber, respectively. In particular, the recombination rate of the bulk region rises rapidly near the ETL side, indicative of the masses of carrier collection in interface ETL/absorber. Simultaneously, it shows a relatively minor peak for interface absorber/HTL. Figure 7(b) demonstrates the effect of interface defect density on device performance. With the interface defect density increased to 10¹⁸ cm⁻³ and even higher, the recombination rate of interface ETL/absorber emerges and becomes remarkably stronger. Therefore, the severely increased recombination restrains the electron extraction and collection efficiency in the FTO electrode, finally leading to heavy energy loss. The V_oc shifts from 1.093 V to 1.036 V whereas the J_sc and FF almost remain the same. Thus, it leads to an efficiency discrepancy of around only 1% since the defect density increases by several orders of magnitude. Similarly, the peak of the interface absorber/HTL exhibits a relatively lower intensity and has a minor impact on device performance when the interface defect density is gradually increased, as shown in Fig. 7(c). The summary of J–V variation in Table IV shows that the interface ETL/absorber plays a critical role in interface recombination, which is harmful to the overall device parameters under high defect density (>10¹⁸ cm⁻³). One of the explanations could derive from the more generated carriers collected and accumulated at the front side during light illumination than at the backside. This high carrier density causes an increase in traps at the recombination centers. Generally, the surface for perovskite growth, which indicates SnO₂ in this n-i-p structure, is of great significance for the formation of film morphology and interface defects. ⁴³⁾ Therefore, according to the J–V simulation, to get good carrier extraction and transfer, the defect density in interface ETL/absorber needs to be suppressed within 10¹⁷ cm⁻³.

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In Sect. 4.5, we investigate the effect of doping concentration, which is also of great relevance for the bulk and interface recombination, as shown in Fig. 8. It has been reported that the doping concentration of MAPbI₃ perovskite is a practical method, like cation doping, to improve the opto-electronic property. ⁴⁴⁾ Here we set a series of varied doping concentrations from 10¹³ to 10¹⁷ cm⁻³ to demonstrate the appropriate value for device performance. In the low concentration region within 10¹⁵ cm⁻³, the increased doping concentration obtains negligible change in recombination, as illustrated in Fig. 8(a). However, when it rises over 10¹⁵ cm⁻³, the recombination rate grows up by several orders of magnitude, especially approaching the side of interface ETL/absorber. Thus, it induces a larger amount of electrons accumulated in the interface ETL/absorber, especially for the concentration of 10¹⁷ cm⁻³, as shown in Fig. 8(b). While the doping concentration increases from 10¹⁵ cm⁻³ to 10¹⁶ cm⁻³, the electric field is reinforced and accelerates the separation of the photo-generated carriers, which contributes to a slightly enhanced V_oc, as shown in Fig. 8(c). Nevertheless, the increasing bulk and interface recombination ascribed to changed doping concentration aggravates the device PCE with gradually decreased J_sc. Therefore, the reasonable doping concentration of perovskite should be assumed to be 10¹⁵ cm⁻³.

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The effect of series resistance (R_s) is generally ascribed to the ohmic loss from bulk resistance and the electrode contact, especially at the interface contact of metal/semiconductor. ⁴⁵⁾ Basically, the origin of the shunt resistance (R_shunt) is from the leakage current, owing to the heavy defect states in the interface. ²⁸⁾ In PSCs, the introduced R_s commonly induces a severe energy loss compared to R_shunt. Therefore, here we evaluate the device performance with the varied R_s and R_shunt. ⁴⁶⁾ Figs. 9(a) and 9(b) depict the relations between device performance and R_s, in which the increased R_s aggravates the efficiency from 20.55% to 18.26%, mainly attributed to the accordingly declined FF from 80.3% to 71.4%. The photovoltaic parameters are summarized in Table V. The impact of the increased R_s can be approximately interpreted by Eq. (4), which is dependent synergistically on the internal absorber resistance and the contribution from electrodes. ⁴⁷⁾

$$\begin{eqnarray}&&{R}_{s}\cong \rho b+\displaystyle \frac{{\rho }_{s}{L}^{2}}{2}\end{eqnarray} \tag{ 4 }$$

where b is absorber thickness, L is substrate length, and ρ and ρ_s refer to the resistivity of the absorber layer and FTO sheet resistance, respectively. On account of the constant effect from the electrode material, we ought to control the perovskite thickness because of the contribution for increased R_s, even thicker film will lead to higher J_sc. Meanwhile, the effect on device performance is slightly enhanced with highly increased R_shunt, as shown in Fig. 9(c). As a result, the PCE gradually improved as well as FF with reduced R_s and increased R_shunt for our simulation structure. Therefore, the optimized device requires the R_s within 1 Ω and R_shunt over 3000 Ω to get better FF.

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According to the modification and improvement above, including the suitably increased absorber layer thickness of 400 nm, thinner carrier transport layer thicknesses of 20 nm for ETL and 150 nm for HTL, suppressed defect density of 5 × 10¹³ cm⁻³ for absorber and 10¹⁷ cm⁻³ for interfaces, a well-controlled doping concentration of 10¹⁵ cm⁻³, R_s within 1 Ω and R_shunt over 3000 Ω, we reconstruct the device structure and obtain improved device performance. Importantly, the thicker absorber thickness provides sufficient optical absorption, leading to higher J_sc. Meanwhile, the suppressed bulk and interface recombination by suppressed defect density is the key point to achieving high V_oc and PCE. As a result, Fig. 10 shows the optimized device achieves improved J–V characteristics with V_oc of 1.087 V, J_sc of 22.56 mA cm⁻², FF of 78.5%, and an encouraging PCE of 20.09%, compared to the control device with V_oc of 1.022 V, J_sc of 19.45 mA cm⁻², FF of 75.52% and PCE of 15.68%.

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