Numerical Analysis on the Effect of the Conduction Band Offset in Dion–Jacobson Perovskite Solar Cells

Abstract

Benefiting from the advantages of a high absorption coefficient, a long charge diffusion length, excellent carrier mobility, and a tunable bandgap, three-dimensional (3D) metal halide perovskites exhibit great potential for application in solar cells. However, 3D perovskite solar cells (PSCs) often suffer from poor long-term stability against moisture, heat, and light. To address this issue, reducing the dimension of perovskite and forming two-dimensional (2D) perovskites can be effective in slowing down the oxidation of the perovskite film and significantly improving device stability. In this study, 2D PSCs were designed with glass/FTO/TiO₂/Dion–Jacobson (DJ) perovskite/NiOx/Au structures, based on the solar cell simulation software SCAPS. The absorption layers employed in the study included PeDAMA₂Pb₃I₁₀, PeDAMA₃Pb₄I₁₃, PeDAMA₄Pb₅I₁₆, and PeDAMA₅Pb₆I₁₉. The influence of the conduction band offset (CBO) variation in the range of −0.5 to 0.5 eV on cell performance was explored through a numerical simulation. The simulation results indicate that the open-circuit voltage and fill factor continue to increase, whereas the short-circuit current density remains almost unchanged when the CBO increases from −0.5 eV to 0 eV. The devices exhibit better performance when the value of the CBO is positive and within a small range. For DJ PSCs, controlling the CBO within 0.1–0.4 eV is conducive to better cell performance.

1. Introduction

As a research direction with great potential in the field of solar cells, the development of perovskite solar cells (PSCs) has experienced rapid growth. The power conversion efficiency (PCE) of PSCs has surged from only 3.8% in 2009 to an impressive 25.73% to 28.75% [1,2,3,4]. Three-dimensional (3D) metal halide perovskites demonstrate substantial promise for solar cell applications owing to their high absorption coefficient, long charge diffusion length, excellent carrier mobility, and tunable bandgap. However, the inherent drawback of 3D PSCs lies in their inferior long-term stability against moisture, heat, and light, limiting their commercial potential. Various strategies, including doping, component engineering, interfacial modification, the use of novel electron and hole transport materials, and encapsulation have been used to enhance the stability of PSCs. Recent studies suggest that reducing the dimension of perovskite and forming 2D perovskites by introducing hydrophobic organic cations [5,6,7] can effectively mitigate the oxidation of the perovskite film, significantly improving device stability. Dion–Jacobson (DJ) perovskite, characterized by a distinct stacked structure, is a common form of 2D perovskite. In DJ perovskites, neighboring inorganic slabs are bridged by diammonium spacers without van der Waals gaps [8]. DJ perovskite PSCs exhibit superior optoelectronic characteristics and enhanced durability [9,10]. Despite these advantages, DJ PSCs face challenges related to serious non-radiative recombination in the bulk [11] and interface, resulting in poor carrier extraction and collection compared to 3D PSCs. Consequently, DJ PSCs still exhibit lower PCEs than their 3D counterparts.

To enhance the performance of DJ perovskite PSCs, numerous strategies have been proposed to optimize film quality, including compositional engineering [11], solvent engineering [12], additive addition [13], and an annealing process [14]. In 2019, Zheng et al. achieved PCEs of 14.16% and 16.38% by employing 1.3-propanediammonium (PDA) and 1.4-butanediammonium (BDA) to construct DJ PSCs, respectively. Their experimental results demonstrated that by controlling the thickness of the quantum well barrier, they could obtain DJ phase perovskites with better orientation and a more uniform distribution, thereby boosting the performance of DJ PSCs [15]. In 2021, Chen and colleagues fabricated DJ PSCs with a gradient energy band alignment in 2021 by coating FABr onto the perovskite films, resulting in an increase in the PCE from 13.78% to 16.75% [16]. Chen et al. also utilized a novel annealing process, combining pre-annealing and merged annealing, to modify the interface at the perovskite and charge-transporting layer, promoting charge transport [17]. To suppress surface defect density, Zhang et al. proposed a secondary anti-solvent strategy for DJ perovskite films which proved effective in preparing highly efficient DJ PSCs [18]. Mohammed et al. demonstrated through a numerical simulation that DJ PSCs with pentamethylenediamine spacers were promising for photovoltaic applications [19]. They optimized different parameters to improve solar cell performance and achieved a PCE of 21.17% [20]. In 2023, Zhai and coworkers proposed that charge recombination could be suppressed, interfacial charge accumulation restricted, and charge transport promoted by introducing an interlayer of polyaspartic acid at the interface of a hole-transporting layer (HTL) and a perovskite layer. With this optimization strategy, the PCE of a DJ PSC increased from 15.03% to 17.34% [21].

Many reported studies have confirmed that the characteristics of the interface between the perovskite layer and carrier transport layers have a direct impact on cell performance. The conduction band offset (CBO) between the perovskite layer and the electron transport layer (ETL) is an important feature of the interface. Therefore, there is a correlation between the CBO and cell performance. A suitable ETL should exhibit proper band alignment with the perovskite layer, ensuring that the transport of electrons is promoted while holes are hindered [22,23,24]. In order to achieve good band alignment between the perovskite layer and ETL, researchers have proposed many methods for interface engineering [25,26], such as doping the ETL with other elements to reach the optimal band alignment with the perovskite layer [22,23], adjusting the band structure via gradient doping [27], inserting a buffer layer between the perovskite layer and the ETL [28], or adjusting the electron affinity of the ETL to achieve proper band matching [29].

DJ PSCs were fabricated by incorporating bulky organic ammonium spacer pentamethylenediamine (PeDA) into DJ perovskite films with four different layer numbers: 3, 4, 5, and 6. These layer numbers correspond to PeDAMA₂Pb₃I₁₀, PeDAMA₃Pb₄I₁₃, PeDAMA₄Pb₅I₁₆, and PeDAMA₅Pb₆I₁₉, respectively. In this study, DJ PSCs, including PeDA-DAMA₂Pb₃I₁₀-based PSCs, PeDAMA₃Pb₄I₁₃-based PSCs, PeDAMA₄Pb₅I₁₆-based PSCs, and PeDAMA₅Pb₆I₁₉-based PSCs, were constructed and simulated using a one-dimensional (1D) solar cell simulation program, SCAPS. The focus of this simulation was on assessing the impact of the conduction band offset (CBO) between the DJ perovskite layer and the electron transport layer (ETL). To understand the operation mechanism of the devices, the relationship between the CBO in the range of −0.5 eV to 0.5 eV and the performance of the DJ PSCs was analyzed. The evaluation indicators included the open-circuit voltage (V_oc), short-circuit current density (J_sc), fill factor (FF), PCE, recombination current, and recombination rate. The numerical simulation results presented in this article offer significant guidance for the development and manufacturing of highly efficient DJ PSCs and provide a solid foundation for future advancements in solar energy technology.

2. Methods and Materials

2.1. Numerical Research Method

Studying PSCs through a numerical simulation can mitigate the influence of unrelated external factors and help researchers analyze the internal physical mechanisms of PSCs. This approach promotes the development of PSCs in experimental preparation. Therefore, in this study, a 1D numerical simulation software, SCAPS, developed by Professor Burgelman of Gent University in Belgium [30], was adopted as the research tool. SCAPS is widely used for numerical simulations of solar cells. Based on the fundamental equations of semiconductor device physics, including the Poisson equation, hole continuity equations, and electron continuity equations (Equations (1)–(3)) [31,32], SCAPS can calculate the current density–voltage characteristics (J-V), spectral response, capacitance–frequency characteristics (C-F), capacitance–voltage characteristics (C-V) band structures, carrier concentration, and spectral response under specific boundary conditions and has been extensively employed in numerical analyses of perovskite solar cells [3,4,33]. Specific operating parameters such as bias voltage, frequency, and temperature are set in SCAPS before running the simulation model.

$$-\frac{\partial }{{\partial }_x}\left(\epsilon \left(x\right)\frac{\partial V}{{\partial }_x}\right)=q\left[p\left(x\right)n\left(x\right)+N_D^{+}\left(x\right)-N_A^{-}\left(x\right)+p_t\left(x\right)-n_t\left(x\right)\right]$$

(1)

$$\frac{{\partial }_p}{{\partial }_t}=\frac{1}{q}\frac{\partial J_p}{{\partial }_x}+G_p-R_p$$

(2)

$$\frac{{\partial }_n}{{\partial }_t}=\frac{1}{q}\frac{\partial J_n}{{\partial }_x}+G_n-R_n$$

(3)

In the equations above, q represents the electronic charge, ε is the dielectric constant, V stands for the potential, and p(x) and n(x) denote the concentrations of free holes and electrons, respectively. Additionally, $N_D^{+}$ and $N_A^{-}$ are the donor and acceptor densities, while p_t(x) and n_t(x) represent the concentrations of hole traps and electron traps, respectively. J_n and J_p correspond to the current density of electrons and the current density of holes, respectively, and G_n and G_p signify the generation rates of electrons and holes. R_n and R_p represent the recombination rates of electrons and holes, respectively. A previous study also presented advanced experimental tools for characterizing PSC performance [34].

2.2. Model Structure and Material Parameters

Using SCAPS, we designed an N-I-P PSC with the structure glass/FTO/ETL/DJ perovskite/HTL/Au, as shown in Figure 1a. In this figure, TiO₂ and NiO_X were employed as the ETL and HTL, respectively. FTO served as the front contact, while Au acted as the metal back electrode. The DJ perovskite, encompassing PeDAMA₂Pb₃I₁₀, PeDAMA₃Pb₄I₁₃, PeDAMA₄Pb₅I₁₆, and PeDAMA₅Pb₆I₁₉, functioned as the active layer. Figure 1b depicts the energy levels of different materials. Excitons are generated when perovskite materials absorb photons with energies exceeding their bandgaps. Subsequently, the excitons migrate to the interface between the perovskite layers and the carrier transport layers, forming free electrons and free holes. These free electrons and free holes then traverse the ETL and HTL, respectively, and are ultimately collected by the corresponding electrodes.

The material parameter settings for constructing the initial models [14,18,25,26] and the interface parameters of the NiOx/DJ perovskite and DJ perovskite/TiO₂ [19,27] were derived from authoritative studies to ensure the reliability of the simulation reference data sources. In Figure 2, J-V characteristic curves are presented for devices under the conditions of dark and light. Figure 2a–d correspond to PeDAMA₂Pb₃I₁₀, PeDAMA₃Pb₄I₁₃, PeDAMA₄Pb₅I₁₆, and PeDAMA₅Pb₆I₁₉, respectively. The diode rectification characteristics in all four initial models indicate the reliability of the structural design. Figure 3a demonstrates an improvement in the J-V characteristic curve when transitioning from PeDAMA₂Pb₃I₁₀ to PeDAMA₅Pb₆I₁₉. Figure 3b explains this phenomenon. Among the four types of perovskite materials, the bandgap order from large to small is PeDAMA₂Pb₃I₁₀ > PeDAMA₃Pb₄I₁₃ > PeDAMA₄Pb₅I₁₆ > PeDAMA₅Pb₆I₁₉. Consequently, the absorption of photons gradually improves from PeDAMA₂Pb₃I₁₀ to PeDAMA₅Pb₆I_19, indicating that PeDAMA₅Pb₆I₁₉ and PeDAMA₂Pb₃I₁₀ have the best and worst absorption of photons, respectively. Hence, PeDAMA₅Pb₆I₁₉-based solar cells have the optimal quantum efficiency (QE), while PeDAMA₂Pb₃I₁₀-based solar cells have the lowest QE. In general, all initial models exhibit good photon absorption below 780 nm, confirming their reliability. Therefore, the following section will explore the impact of the interface band offset between the ETL (TiO₂) and the perovskite layer on the cell performance based on these models.

Table 1. Basic parameters of the initial model.

Parameter	NiOx	PeDAMA2Pb3I10	PeDAMA3Pb4I13	PeDAMA4Pb5I16	PeDAMA5Pb6I19	TiO2
Thickness/nm	100	800	800	800	800	50
Band gap/eV	3.5	1.83	1.76	1.65	1.6	3.2
Electron affinity/eV	1.8	3.15	3.28	3.64	3.98	3.9
Dielectric permittivity	10.7	25	25	25	25	9
Electron mobility/cm2/V.s	12	1.4	1.4	1.4	1.4	20
Hole mobility/cm2/V.s	2.8	0.3	0.3	0.3	0.3	10
Acceptor concentration/cm−3	3.0 × 1018	0	0	0	0	0
Donor concentration/cm−3	0	0	0	0	0	1.0 × 10−16
CB effective density of states/cm−3	2.8 × 1019	7.5 × 1017	7.5 × 1017	7.5 × 1017	7.5 × 1017	1.0 × 1021
VB effective density of states/cm−3	1.0 × 1018	1.8 × 1018	1.8 × 1018	1.8 × 1018	1.8 × 1018	2.0 × 1020
Defect type	Neutral	Neutral	Neutral	Neutral	Neutral	Neutral
Capture cross-section for electrons/cm2	1.0 × 10−15	1.0 × 10−15	1.0 × 10−15	1.0 × 10−15	1.0 × 10−15	1.0 × 10−15
Capture cross-section for holes/cm2	1.0 × 10−15	1.0 × 10−15	1.0 × 10−15	1.0 × 10−15	1.0 × 10−15	1.0 × 10−15
Total defect density/cm−3	1.0 × 10−15	2.5 × 10−14	2.5 × 10−14	2.5 × 10−14	2.5 × 10−14	1.0 × 10−16

listed the basic parameters of the initial model while

Table 2. Interface parameter settings.

Parameter	NiOx/DJ Perovskite	DJ Perovskite/TiO2
Type of Defect	Neutral	Neutral
Cross-Section for Electron Capture/cm2	1.0 × 10−15	1.0 × 10−15
Cross-Section for Hole Capture/cm2	1.0 × 10−15	1.0 × 10−15
Distribution of Energies	single	single
Reference for Energy Level of Defect	Above the highest Ev	Above the highest Ev
Energy with Respect to Reference/eV	0.6	0.6
Total Density of Defects/cm−3	1.0 × 1010	1.0 × 1010

displays key interface parameter settings.

3. Results and Discussion

Figure 4 illustrates a schematic of the barrier structure at the interface between the perovskite layer and the ETL. The CBO, which stands for conduction band offset, quantifies the misalignment between the conduction band of the perovskite and the ETL. The CBO value is calculated by subtracting the conduction band level of the perovskite from that of the ETL. The magnitude of the CBO is closely related to the interface barrier. The CBO is negative when the conduction band level of the ETL is lower than that of the perovskite, and it is positive when the conduction band level of the ETL is higher. As depicted in Figure 4a, a negative CBO results in an energy cliff at the interface between the perovskite layer and the ETL. Conversely, in Figure 4b, a positive CBO leads to the formation of an energy spike at the same interface. The structural difference between a cliff and a spike is significant. An energy cliff does not impede the movement of photo-generated electrons, while an energy spike acts as an obstacle. Consequently, the energy required for a photo-generated electron to traverse these different barriers varies, leading to variations in the accumulation and interface recombination of carriers.

The CBO has a significant impact on interface recombination which is both theoretically supported [35,36,37] and experimentally demonstrated [38,39,40]. To analyze the relationship between the CBO and the performance of the DJ PSCs in this study, we maintained the CBO within the range of −0.5 to 0.5 eV. The simulation work adopted the control variable method. To control the value of the CBO, the electron affinity of the ETL was altered, while the other parameters of the materials listed in Table 1 remained unchanged. Figure 5 and Figure 6 display the simulation results. Figure 5 illustrates the trends in the cell output parameters (V_oc, J_sc, FF, and PCE) with different CBO values, while the corresponding J-V characteristic curves are presented in Figure 6.

In Figure 5, when CBO values are negative, the V_oc, FF, and PCE consistently increase from −0.5 eV to 0 eV, while the J_sc remains relatively unchanged. Conversely, positive CBO values in the range of 0.1–0.4 eV show less significant differences in output parameters which are larger than those observed in the negative range. However, with a further increase in the CBO, the cell performance rapidly declines. Similar trends are observed in Figure 6, in which J-V characteristic curves steadily increase as the CBO changes from −0.5 eV to 0 eV, almost overlapping and improving from 0.1–0.4 eV but exhibiting a severe S-shape when the CBO reaches 0.5 eV.

When the CBO is less than 0 eV, a cliff forms at the interface between the ETL and the perovskite. Conversely, when the CBO is positive, a spike forms, as depicted in Figure 7 and Figure 8, demonstrating a high degree of consistency between simulation results and theory. The activation energy for carrier recombination (E_a) assesses carrier recombination at the interface between the perovskite and the ETL. For positive CBO values, the E_a equals the band gap of the perovskite. In contrast, for a negative CBO, the E_a is defined by the difference between the band gap of the perovskite and the absolute value of the CBO. Consequently, negative CBO values increase the likelihood of interface recombination.

The formation of an energy cliff occurs as the CBO increases from −0.5 eV to 0 eV. This energy cliff, while not impending the movement of photo-generated electrons, results in a nearly unchanged J_sc. However, the activation energy E_a is smaller than the band gap of the perovskite, indicating that interface recombination predominantly influences the recombination mechanism [41,42,43]. Research has generally proven that V_oc is closely tied to carrier recombination. Low carrier recombination has a positive effect on promoting V_oc. The E_a measures the difficulty of carrier recombination. Carriers are more likely to recombine when the E_a is smaller. Therefore, it can be inferred that the E_a directly influences V_oc. As the CBO gradually increases from −0.5 eV to 0 eV, the E_a also increases, leading to a gradual reduction in the likelihood of carrier recombination. Consequently, the V_oc shows a continuous increase. Both Figure 9 and Figure 10 confirm that interface carrier recombination decreases gradually with an increase in the CBO from −0.5 eV to 0 eV. The decrease in carrier recombination signifies a reduction in the internal consumption of the device, contributing to a gradual increase in the FF. The concurrent increases in the V_oc and FF further promote an overall rise in the PCE.

When the CBO ranges from 0.1 eV to 0.4 eV, an energy spike is formed. At this point, the E_a remains constant and is equal to the band gap of the perovskite, resulting in minimal differences in interface carrier recombination. Figure 11 illustrates that when the CBO is within this range, the fluctuation of the interface recombination current is weak, indicating insignificant changes in interface carrier recombination. Consequently, the V_oc and FF almost remain unchanged. It has been demonstrated that a spike within this small range has a limited effect on the motion of photo-generated electrons [31]. As a result, J_sc experiences little change. The negligible variations in the V_oc, J_sc, and FF translate to insignificant changes in the PCE. However, if the CBO further increases to 0.5 eV, it may induce a double-diode-like curvature, leading to a rapid decrease in the FF. Consequently, the PCE experiences a significant decrease.

The cells perform better when the CBO is in the range of 0.1–0.4 eV than when the CBO is negative. A positive CBO leads to the formation of an energy spike, which acts as a barrier and impedes the transport and collection of photo-generated electrons. However, research has shown that a spike within a small range has less effect on the motion of photo-generated electrons but a greater impact on the carrier recombination rate [31]. In other words, PSCs may achieve better performance when an energy spike forms at the interface between the perovskite and the ETL. Therefore, the E_a has a stronger impact when a spike is formed, and the cell performance improves when the CBO is positive and there is a spike within a small range. Figure 5 and Figure 6 demonstrate that controlling the CBO within 0.1–0.4 eV is beneficial for the better performance of DJ PSCs.

4. Conclusions

The effects of the CBOs of DJ PSCs were analyzed using the 1D solar cell simulator SCAPS. The CBO is negative when the ETL has a lower conduction band level than the DJ perovskite and vice versa. An energy cliff is formed at the interface between the DJ perovskite and ETL when the CBO is negative, and an energy spike is generated when the CBO is positive. When the CBO is negative and a cliff is formed, the movement of electrons is not suppressed, so J_sc remains almost unchanged. However, the E_a gradually increases with an increase in the CBO, reducing the interface carrier recombination, leading to continuous increases with increases in the V_oc and FF. Thus, the PCE is improved. When the CBO is positive and a spike is generated, the E_a is equal to the band gap of the DJ perovskite, so the V_oc and FF remain almost unchanged. It has been proven that the E_a has a more significant impact on cell performance when the CBO is relatively small, and simulation results indicate that when the CBO is 0.1–0.4 eV, the performances of DJ PSCs improve. These numerical simulation results should provide important guidelines for designing efficient DJ PSCs.