Absorber Enrichment and Its Implication on the Performance of Lead-free CsSnI₃ Perovskite Solar Cells (PSCs) - A 1D-SCAPS Study

1. Introduction

The conversion of sunlight into electricity through photovoltaic (PV) effect using solar cells stands out as a potential solution to the future global energy crisis and environmental pollution brought about by energy generation from fossil fuel and natural gas [1,2,3]. The capacity of globally installed PV devices has been increasing over the last two decades. In 2020, the globally installed PV capacity amounted to 788 GW, with 183 GW and 191GW of new PV capacity installed in 2021 and 2022 respectively. This would amount to 1.5 TW if over 350.6 GW were to be installed in 2023 [4,5]. This indicates that the first generation silicon solar cells and the second generation thin film technologies are not only widely accepted but have also dominated the global PV markets [5,6]. Although, these solar cells have power conversion efficiency (PCE) of more than 26% and a lifespan of about 25 years, they are however characterized by high cost and difficult preparation conditions [6,7]. Amongst the third generation solar cells, perovskite solar cells (PSCs) have attracted significant attention due to lower material costs and low-temperature solution processing. Thus, making their fabrication procedures easy and cost-effective [7]. A typical PSC consists of an absorber material sandwiched between an electron transport material (ETM) and a hole transport material (HTM). The ETMs that are most commonly used in PSCs are n-type semiconductors such as TiO₂, ZnO and PCBM [8,9,10,11] while the HTMs that are most commonly used are organic p-type polymers such as spiro-OMeTAD, PTAA, P3HT and PEDOT:PSS [10,12,13,14].

Reports have shown that PSCs offer PCE of 25.2% which is comparable to those of Si and thin-film solar cells [7,15,16]. The unique optical and electronic properties of perovskites are responsible for the improvement in their performance [17]. However, despite the large efficiencies recorded, the organic hole transport materials (HTMs) used in conjunction with the perovskite (absorber) are responsible for their instability and increased processing costs [18].

In addition, organic HTMs are also susceptible to degradation over time under humidity due to external doping usually done to guarantee optimum PCE in PSCs [19]. No doubt these shortcomings of organic HTMs pose as obstacle to large-scale commercialization of PSCs, as such the search for efficient and cost effective HTM calls for the use of inorganic HTMs to enhance the life time of PSCs and reduce the fabrication cost simultaneously. Prior reports showed that inorganic HTMs such as CuI and Cu₂O have exhibited good mechanical and chemical stabilities with encouraging stable PCEs [20,21,22]. However, copper thiocyanate (CuSCN) proved to be a better alternative inorganic HTM compared with CuI and Cu₂O as a result of its improved stability and distinct chemical robustness arising from its polymeric structure [23,24,25,26]. CuSCN is an inorganic p-type semi-conductor which exists in two forms as α-CuSCN and β-CuSCN with β-CuSCN being readily available and more thermally stable. In addition to these, it possesses compatible and easy solution processing ability, chemical stability, and high-optical transparency [27]. Comparative cost and performance analyses showed CuSCN to be the right replacement for organic HTMs amongst various HTMs according to [18]. Over the years the PCE for CuSCN-based PSCs have increased from 12.4% [28] through 17.0% for pristine absorber and CuSCN films obtained via spray deposition [29] to 18% for low temperature solution processed CuSCN [30]. To date, research efforts are in progress to take the PCE for PSCs up to and beyond the maximum theoretical limit of efficiency formulated by Shockley–Queisser [31,32]. Consequently, research efforts centered on theoretical modeling of CuSCN-based PSCs have been carried out to optimized their performance by varying the thickness, defect density, and effective valence band density of the absorber layer using SCAPS software [33,34,35,36]. Recently, the significance of shallow doping and diffusion length of absorber layer, valence band and conduction band offsets of the various active layers and interface defects was pointed out as being critical to the performance of PSCs. A thorough investigation vis-à-vis optimization of these critical factors was carried out with 1D-SCAPS leading to an optimized PCE of 25.20% for PSC using lead-based perovskite with CuSCN and TiO₂ as HTM and ETM respectively [18].

Due to environmental concerns and stringent conditions imposed on the use of lead material for electronic and PV devices, significant research efforts have been directed toward replacing lead with similar metals having comparable electronic and optical properties for the engineering of alternative metallic based halide perovskite [37,38]. Accordingly, Ag⁺, Bi³⁺, Sb³⁺, Ti⁴⁺, Ge²⁺, and Sn²⁺ have been proposed as replacement for lead because they are less toxic and possess comparable properties as lead [39,40,41,42,43]. Amongst the various alternatives, tin based organic halide perovskites such as CH₃NH₃SnI₃ (MASnI₃), HC(NH₂)₂SnI₃ (FASnI₃) have been considered more suitable for PSCs partly because tin belongs to the same group as lead and due to the record PCE reported for PSCs with tin based organic halide perovskites as absorber layers [28]. However, PSCs based on MASnI₃ and FASnI₃ have been found to be chemically unstable because the organic cations therein react with water molecules to form weak hydrogen bonds that degrade device upon longtime exposure to moisture, heat and light [44,45]. Recently, metallic based halide perovskites with Cs⁺ cation have been investigated and found to be nontoxic with improved optoelectronic properties [46,47]. Among the cesium based metallic halide perovskites, reports have shown CsSnI₃ to possess exceptional electrical and optical properties [48,49,50,51,52,53,54,55,56,57,58]. CsSnI₃ is a unique material that exhibits four polymorphs with two of them existing independently at room temperature. One of the room temperature phases is yellow (Y) with a one-dimensional double-chain structure and the other phase is black (B-γ) with a three-dimensional perovskite structure [59]. The black perovskite CsSnI₃ displays p-type metallic conductivity with unusually high conductivity when heat-treated and optical band gap of 1.3eV [49,59]. The ability of CsSnI₃ to emit strong near-infrared photoluminescence at room temperature has been attributed to the readily changing Sn vacancy centers in the structure [49]. This rare characteristic would present opportunity to discover visible and IR light-emitting materials at room temperature, suitable for achieving ground breaking applications in photovoltaics, radiation detectors, and light-emitting diodes because the perovskite structure can incorporate a broad range of elements [60].

In the light of the above and to eliminate the factors hindering the commercialization of PSCs, it is therefore of paramount importance to consider cesium tin iodide (CsSnI₃) as a replacement for lead-based perovskite in the engineering of PSCs with a strong focus on the optimization of critical physical factors that have direct influence on the PCE. The most urgent challenge of the CsSnI₃-based perovskite solar cell is their low V_OC, which is far behind the bandgap of CsSnI₃ perovskite (1.3eV). This is mainly due to the severe charge recombination and band alignment mismatch at the absorber layer and its interfaces with the transport layers. These limiting factors have been the main obstacle to the efficiency improvement of CsSnI₃-based perovskite solar cells. To further explore the photovoltaic potential of CsSnI₃-based perovskite solar cells, the most important task is to minimize charge carrier recombination by enriching the absorber layer. In this paper, a detailed and systematic investigation of a modeled PSC consisting of TiO₂ as ETM layer, CsSnI₃ as absorber layer and CuSCN as HTM layer has been carried out with emphasis on enrichment of absorber layer with a view to optimizing the device performance.

2. Theory

2.1. Theoretical Details

The transport of charge carriers through the perovskite absorber to the respective transport layers in a PSC is governed by the Poisson’s equation and the continuity equations for electrons and holes as is the case of semiconductor [61]. Under solar light irradiation with a power intensity of P_in, the photogenerated charge carriers will flow inside the PSC in accordance with the continuity equations and their dynamics is governed by the following rate equation:

$$\frac{dn}{dt}=G-U$$

(1)

where n is the concentration of charge carriers, G is the charge generation rate and U represents the overall recombination rate resulting from direct (band-to-band) and indirect (Shockley-Read-Hall) recombination.

At short-circuit condition, the total current density (J_SC) equals to the total charge collected with respect to the photon absorbed taking into account the losses due to various recombination mechanisms in the absorber and at the interfaces according to equation (2):

$$J_{SC}=J_0\left[\exp \left(\frac{q{V}_{OC}}{k_{B}T}\right)-1\right]$$

(2)

From equation (2), high absorption of incident photons is guaranteed if the energy of the photons is equivalent to the bandgap of the perovskite absorber and this ultimately leads to high V_OC. To sustain high V_OC, the perovskite absorber in the PSC should have low bulk and surface defects. The recombination current density (J₀) depends on the defect density, the charge carrier diffusion length and lifetime. As such, a minimum recombination rate is achievable with a reduced total defect density in the perovskite absorber layer, thus giving rise to longer lifetime (τ_n,p) and diffusion length (L) of charge carriers necessary to improve the efficiency of the PSC as specified in the following relations:

$${\tau }_{n,p}=\frac{1}{{\sigma }_{n,p}.{\nu }_{th}.N_t}$$

(3)

and

$$L_{n,p}=\sqrt{D_{n,p}\cdot {\tau }_{n,p}}$$

(4)

where σ_n,p is defect capture cross section for electrons and holes, v_th is thermal velocity of the charge carriers, N_t is the concentration of defects in the absorber layer and D is the diffusion coefficient indicating that diffusion length of charge carriers is proportional to their lifetimes. With a minimum recombination rate, the overall capability of a PSC specified by the fill factor (FF) in combination with enhanced V_OC will ultimately give rise to improved power conversion efficiency ($\eta$) usually quantified as follows:

$$\eta =\frac{FF.J_{SC}.V_{OC}}{P_{in}}$$

(5)

where the parameters (J_SC, V_OC and FF) determining the PCE (η) are extracted from the current density–voltage (J–V) curve of the PSC.

2.2. Cell Structure and Numerical Modeling

The n-i-p planar configuration was adopted for the PSC architecture and it comprises of five (5) layers which include FTO as the transparent conducting oxide layer (front contact), TiO₂ as the electron transport layer (ETM), CsSnI₃ as the absorber layer, CuSCN as the hole transport layer (HTM) and gold as the back metal contact. Figure 1(a) depicts the PSC architecture employed in this work while the corresponding band diagram for the components is shown in Figure 1(b).

The basic physical parameters for each layer are listed in Table 1, the optical reflectance at each interface was assumed to be zero and single distribution was adopted for the nature of the defect at the ETM/absorber and absorber/HTM interfaces respectively for the numerical simulation of the PSC. The absorption constant for the absorber is set as ${10}^{4}c{m}^{-1}$, Gaussian distribution was adopted for the nature of the defect in the absorber with characteristic energy as $0.1eV$ while the defect capture cross section for electrons and holes was set as $2\times {10}^{-14}c{m}^{-2}$. The simulation of the PSC was done under the standard conditions of irradiance of 1000 Wm^-2 with $AM1.5G$ and temperature of $300K$.

Solar Cell Capacitance Simulator (SCAPS-1D) was employed to numerically simulate the proposed PSC architecture. The program takes into account only Shockley-Read-Hall (SRH) recombination statistics for the simulation and solves Poisson’s equation together with the continuity equations for electrons and holes at each point in the proposed PSC subject to the imposed boundary conditions. To interpret the main limitations of the device current-voltage characteristics, the photovoltaic parameters of the cell were analyzed by varying the absorber layer thickness. Consequently, to deal with the recombination rate in the absorber layer, the defect density in the perovskite absorber was varied from 10¹¹ cm^-3 to 10¹⁷ cm^-3. Finally, optimization of these parameters was done to improve the PCE of the modeled PSC.

3.1. Initial PSC Simulation and Validation

The variation of the current density with applied voltage and the spectral response (quantum efficiency) of the simulated CsSnI₃ –based PSC are given as (J–V) and QE curves in Figures 2s(a) and 2(b) respectively. With the applied voltage being scanned from 0 to 1.2 V, charge carriers that are continuously generated with increasing intensity of the incident light during the simulation translated to nearly constant current density at lower voltages and at zero voltage it reaches a maximum value referred to as J_SC with a magnitude of 22.859 mA.cm^-2 as shown in Figure 2(a). However, as the applied voltage increases, the recombination of charge carriers in the absorber and at the n/i interface of the simulated CsSnI₃ –based PSC became significant thus limiting the values of V_OC to 0.915 V, as evident from Figure 2(a). The low V_OC is mainly due to charge recombination at the n/i interface and in the absorber of the simulated CsSnI₃ –based PSC as evident from high recombination rate in Figure 2(c). Also, the deviation of current-voltage characteristics of the simulated PSC from idealness brought about mainly by SRH recombination mechanism in the simulated device reduced the value of FF to 47.84%. Thus, the overall PCE of the simulated PSC was obtained to be 10.01%. The simulated QE curve revealed that virtually all the photons from the incident light were absorbed from 385 nm to 500 nm of the wavelength range yielding QE of approximately 87%. Beyond 500 nm, the QE gradually reduced from 87% to 50% at 821 nm and decreases sharply at about 950 nm, which corresponds to the band gap of CsSnI₃ thin film as a result of the competition between charge generation rate and charge recombination rate as evident from Figure 2(c). The strong optical absorption of the simulated CsSnI₃ –based PSC is attributed to the structural characteristics of CsSnI₃ perovskite layer thus making it highly desirable for application in photovoltaics [59]. The obtained photovoltaic parameters for the simulated CsSnI₃ –based PSC agree fairly well with recently obtained results in the literature [75,76,77,78,79]. Though, the FF, V_OC and J_SC are lower compared to the same CsSnI₃ –based PSC with Spiro-OMETAD HTM [79], but the overall results for the simulated CsSnI₃ –based PSC with CuSCN HTM using the input parameters in Table 1 are better and higher than those previously obtained for CsSnI₃ –based PSC with polymer HTMs [80,81,82,83,84,85,86]. For the initial CsSnI₃ –based PSC, 0.2 µm and 10¹⁷ cm^-3 have been employed for the thickness and defect density of the absorber respectively and the observed diffusion lengths (0.08 µm and 0.28 µm for electrons and holes respectively) are small due to high defect density in the absorber which ultimately limits charge carrier lifetime to 0.05ns and eventually increases the recombination rate in the bulk of the initial CsSnI₃ –based PSC.

To further explore the dynamics of charge carriers in the simulated CsSnI₃ –based PSC, the thickness of the absorber layer was varied from 0.1µm to 1.0 µm while maintaining the defect density at 10¹⁷ cm^-3 and the results obtained are presented in Figure 3. Accordingly, as more charge carriers are generated with increase in the absorber layer thickness, the rate of recombination charge carriers also increases due to reduced mobility brought about by high defect density as depicted in Figures 3(a) and 3(b). This is evident from the reduction in the V_OC and FF as the absorber thickness increases. This trend is depicted in Figure 3(c) and 3(d) respectively with the V_OC reducing from a maximum value of 0.885V for absorber thickness of 0.1µm to a minimum value of 0.746V for absorber thickness of 1.0µm while the FF reduces from 75.29% to 60.25%. Nevertheless, enhancement in the values of the J_SC and PCE were observed which are in agreement with previous works on CsSnI₃-based PSC [78,79]. The results are presented in Figures 3(e) and 3(f) with J_SC increasing from 16.62 mA.cm^-2 to 34.48 mA.cm^-2 for absorber thickness of 0.1µm and 1.0µm respectively while the PCE increases from 11.074% for absorber thickness of 0.1µm up to 16.793% for absorber thickness of 0.5µm followed by a gradual decrease to 15.506% for absorber thickness of 1.0µm.

3.2. Absorber Enrichment and Device Optimization

To minimize charge carrier recombination rate and enhance V_OC, there is the need for compromise between the thickness of the absorber and its defect density, so that the diffusion length and the lifetime of charge carriers in the absorber are within the range required for uninterrupted transport and collection.

To achieve this, the defect density was tuned from 10¹¹ cm^-3 to 10¹⁷ cm^-3 to gain an insight into the carrier transport dynamics with respect to the magnitude of enrichment of the absorber for real practical situations. With the results obtained from the variation of PCE with absorber thickness [Figure 3(f)], it was realized that it is pertinent to reduce the density of defects in the absorber of the simulated CsSnI₃-based PSC with thickness of 0.5µm and optimum PCE. The selected absorber thickness is in agreement with previous results obtained for simulated CsSnI₃–based PSCs using SCAPS software [78]. For selected thickness, the variation of the current density-voltage curves, the charge carrier recombination rate of the CsSnI₃-based PSC and the photovoltaic parameters (J_sc, V_oc, FF and PCE) with the absorber defect density are presented in Figure 4. The current density remained constant with an average value of 32.60 mA.cm^-2 for the defect density range of interest as evident from Figure 4(c). The carrier lifetime increases from 0.05 ns to 50,000 ns as the defect density drops from 10¹⁷ cm^-3 to 10¹¹ cm^-3 and this increment translates to diffusion lengths that are long enough to improve photovoltaic parameters and the PSC performance. Correspondingly, improved values were observed for V_OC, FF, and PCE as the absorber defect density decreases from 10¹⁷cm^-3 to 10¹¹ cm^-3. FF has an optimum value of 80.13% when the absorber defect density was reduced to 10¹³ cm^-3 with an equivalent V_OC of 1.055 V while the corresponding PCE value is 27.565%. The need to reduce the noticeable high recombination rate at the n/i interface and in the absorber as depicted in Figure 4(b) is necessary in order to improve the V_OC and the PCE of the simulated CsSnI₃ –based PSC beyond the Shockley-Queisser limit. Although, the initiative demonstrated above is one of the important strategies needed for the lead-free PSCs to gain entry into the global PV markets but in real practical situations, it is difficult to synthesize CsSnI₃ absorber with a concentration of defect less than 10¹³ cm^-3. This is because above room temperature, intrinsic defects are highly probable leading to the formation of significant concentration of Sn⁴⁺ vacancy (V_Sn) which in effect may promote recombination of holes with electrons in the stoichiometric CsSnI₃. Shallow doping of lead-free Sn-based perovskites using appropriate passivation additives (e.g., SnF₂, SnCl₂), reducing agents (hypophosphorous acid (HPA), hydrazine) and doping ions (Br⁻, PEA⁺, pn⁺, and TN⁺) have been reported in previous works to increase the formation energy of V_Sn and inhibit the oxidation of Sn²⁺ to Sn⁴⁺ [80,81,82,83,84,85,86]. In this work, it is therefore compelling to preserve the intrinsic properties and improve the stability of CsSnI₃ absorber layer through enrichment using a combination of SnCl₂ and Br⁻ with appropriate concentration as additive and dopant respectively. This strategy would ensure a reduced concentration of V_Sn and improve carrier lifetime beyond 0.05 ns as obtained for the initially simulated CsSnI₃–based PSC. For a fixed concentration of Sn⁺⁴ vacancy, if cesium iodide interstitials were filled with varying concentrations of Br^- and the bulk enriched with SnCl₂, then the formation energy of Sn⁺⁴ vacancy would increase and the oxidation of Sn⁺² to Sn⁺⁴ would be inhibited. For this work, a novel strategy was employed by fixing N_A=10¹⁴ cm^-3, while N_V varies over a range of 10¹² cm^-3 to 10¹⁵ cm^-3 and N_D also varies over a range of 10³ cm^-3 to 10⁶ cm^-3. Strategically, the equilibrium hole concentration in the enriched CsSnI₃ will decrease much more compared to that of the electron thereby making CsSnI₃ predominantly n-type. Thus, with N_C set to 10¹⁵ cm^-3 and the optimum values for absorber thickness and total defect density (N_t) set to 0.5µm and 10¹³ cm^-3 respectively, a reduced SRH recombination rate prevails leading to improved charge carrier collection efficiency and enhanced power conversion efficiency for the device. With these values, the J-V curves, QE curves and the photovoltaic parameters for the modified CsSnI₃-based PSC are given in Figure 5.

Figure 6 compares the results obtained for the initial CsSnI₃-based PSC with that obtained for the optimized CsSnI₃-based PSC. The overall quality and idealness of the optimized CsSnI₃-based PSC are more pronounced compared to the initial CsSnI₃-based PSC as evident from the high fill factor (FF), enhanced open circuit voltage (V_OC) and short-circuit current density (J_SC) that ultimately gave rise to improved power conversion efficiency (PCE). From the J-V curves for the optimized CsSnI₃-based PSC and that for the initial CsSnI₃–based PSC given in Figure 6, we observed that the improvement in V_OC and J_SC for the optimized CsSnI₃-based PSC are approximately 29% and 30% respectively higher compared to those for the initial CsSnI₃-based PSC and this confirms efficient charge carriers transport and collection with minimal recombination rate. Thus, the resulting optimized CsSnI₃–based PSC performance parameters are V_OC = 1.289 V, J_SC = 32.60 mA.cm^-2, FF = 83.56% and PCE = 35.12%.

4. Conclusions

A systematic investigation of a modeled CsSnI₃-based PSC consisting of TiO₂ as ETM layer, CsSnI₃ as absorber layer and CuSCN as HTM layer was carried out with emphasis on enrichment of absorber layer with a view to optimizing the device performance using Solar Cell Capacitance Simulator (SCAPS-1D). For the initial CsSnI₃–based PSC, 0.2 µm and 10¹⁷ cm^-3 were employed for the thickness and defect density of the absorber respectively and the observed photovoltaic parameters were marred by high recombination rate of charge carriers thus limiting the values of J_SC to 22.859 mA.cm^-2, V_OC to 0.915 V, FF to 47.84% and PCE to 10.01%. To interpret the main limitations to the initial device current-voltage characteristics, the photovoltaic parameters of the cell were analyzed by varying the absorber layer thickness. Accordingly, a reduction in the values of V_OC and FF as the absorber thickness increases was evident while an enhancement in the values of the J_SC and PCE was observed. The PCE value increases from 11.074% for absorber thickness of 0.1µm up to an optimum value of 16.793% for absorber thickness of 0.5µm and this was followed by a gradual decrease up to absorber thickness of 1.0µm. Subsequently, the defect density in the perovskite absorber was varied from 10¹¹ cm^-3 to 10¹⁷ cm^-3 to understand the recombination rate in the absorber layer. Correspondingly, improved values were observed for V_OC, FF, and PCE as the absorber defect density decreases from 10¹⁷cm^-3 to 10¹¹ cm^-3 while the current density remained constant with an average value of 32.60 mA.cm^-2 for the defect density range of interest. FF has optimum value of 80.13% when the absorber defect density was reduced to 10¹³ cm^-3 with an equivalent V_OC of 1.055 V while the corresponding PCE value is 27.565%. Finally, optimization of these parameters was done in conjunction with appropriate concentration of SnCl₂ and Br⁻ as additive and dopant respectively to improve the PCE of the modeled CsSnI₃-based PSC. This was achieved by fixing N_A=10¹⁴ cm^-3, while N_V varies over a range of 10¹² cm^-3 to 10¹⁵ cm^-3 and N_D also varies over a range of 10³ cm^-3 to 10⁶ cm^-3. Thus, with N_C set to 10¹⁵ cm^-3 and the optimum values for absorber thickness and total defect density (N_t) set to 0.5µm and 10¹³ cm^-3 respectively, the resulting optimized CsSnI₃–based PSC performance parameters are V_OC = 1.289 V, J_SC = 32.60 mA.cm^-2, FF = 83.56% and PCE = 35.12% which represents an improvement over the initial results and compares reasonably well with results obtained from literature [78,79,84].