Optoelectronic properties and interfacial interactions of two-dimensional Cs₂PbX₄–MSe₂ (M = Mo, W) heterostructures

Abstract

Constructing 2D inorganic perovskites and TMDs heterostructures is an effective method to design stable and high-performance perovskites optoelectronic applications. Here, we investigate the optoelectronic properties and interfacial interactions of Cs₂PbX₄–MSe₂ (X = Cl, Br, I; M = Mo, W) heterostructures using first-principles calculations. Firstly, six Cs₂PbX₄–MSe₂ interfaces remain stable in energy. With the halogen varying from Cl to I, the interlayer distances of Cs₂PbX₄–MSe₂ heterostructures increase rapidly. The CBM and VBM of monolayer Cs₂PbX₄ are all higher than that of monolayer MSe₂ and the charges transfer from Cs₂PbX₄ interfaces to MSe₂ interfaces when they contact. Both Cs₂PbX₄–MSe₂ heterostructures are type-II heterostructures, which can drive the photogenerated electrons and holes to move in opposite directions. What's more, Cs₂PbCl₄–MoSe₂ heterostructures exhibit the highest charge transport efficiency among Cs₂PbX₄–MoSe₂ heterostructures because Cs₂PbCl₄–MoSe₂ heterostructures have the lowest exciton binding energies among Cs₂PbX₄–MSe₂ heterostructures. In addition, the optical absorptions of all heterostructures are significantly higher than the corresponding Cs₂PbX₄ monolayers and MSe₂ monolayers. The construction of Cs₂PbX₄–MoSe₂ heterostructures is beneficial for improving the photoelectric performance of two-dimensional perovskite devices. Lastly, we found that the Cs₂PbI₄–WSe₂ heterostructure has the largest PCE (18%) among Cs₂PbX₄–MSe₂ heterostructures. The Cs₂PbCl₄–MoSe₂ heterostructure exhibits great potential application in photodetector devices and the Cs₂PbI₄–WSe₂ heterostructure has great potential application in solar cells.

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Introduction

Solar energy is a renewable and clean energy source that can be used in the field of solar cells. In the early years, perovskites were considered to be one of the most promising solar cell materials.¹ Three-dimensional (3D) lead halide perovskites have been innovatively applied in the field of solar cells with power conversion efficiency (PCE) up to 25.6%.² The high PCE of 3D lead halide perovskites is because of their excellent photoelectric properties, such as high carrier mobility, large light absorption coefficient, long carrier diffusion length and strong photoluminescence.^3,4 Although the three-dimensional lead halide perovskites have great photoelectric properties, their instability in air limits their widespread use for commercialization.^5,6 In recent years, two-dimensional (2D) inorganic halide perovskites with good moisture resistance and stability have attracted attention for optoelectronic applications.⁷ Currently, many theoretical studies and experiments on 2D perovskites have been conducted. For example, Ding et al. reported that the number of layers would affect the optical absorption and transport properties of 2D perovskite Cs₂PbI₄.⁸ In addition, Bala et al. also revealed the same laws that the band gap and optical properties of 2D Cs_n+1Pb_nX_3n+1 (X = Cl, Br, I) perovskite vary with layer number.⁹ In experiments, Song et al. fabricated 2D CsPbBr₃ nanosheets and used them to produce high-performance photodetectors.¹⁰ These studies found that the bandgaps of 2D monolayer lead halide perovskites are larger than 3D lead halide perovskites, which lead to lower electric properties, optical absorption and low performance of optoelectronic applications.

Fortunately, two-dimensional monolayer lead halide perovskites have a wide range of photoelectric properties adjustable by replacing halogens, changing layers, and working with other two-dimensional materials. In particular, the halide perovskites grown in the other 2D materials provides excellent ability to further adjust band gaps, transport properties, charge carrier dynamics, chemical stability and optical light absorption.¹¹ Therefore, a great deal of scientific researches of 2D halide perovskites and 2D materials interface engineering have been carried to achieve low-cost, high efficiency, stable heterostructures photoelectric devices. For instance, He et al. theoretically studied the effects of different terminals of heterojunctions and found that CsPbI₃/MoS₂ heterostructure had higher electric performances than CsPbI₃/WS₂.¹² The WS₂–CsPbBr₃ heterostructure was applied to perovskite solar cells (PSCs), which significantly improved PSCs stability under constant light and humidity (80%) attack over.¹³ While, the PCE of WS₂–CsPbBr₃ PSCs is only 10.65%.¹³ Recently, inverted perovskite solar cells with WS₂ interlayers had increased PCE up to 21.1%.¹⁴ As we can see, 2D lead halide perovskites applying for PSCs have high stability and can effectively improve PCE by coordinating with two-dimensional transition metal dichalcogenides (TMDs) such as WS₂, MoS₂ and so on.

MoSe₂ and WSe₂ as conventional materials of TMDs are widely used in interface engineering in experiments to improve optoelectronic properties of 2D organic halide perovskites. In experiments, Lu et al. fabricated a high-Performance WSe₂–CH₃NH₃PbI₃ perovskite photodetector.¹⁵ MoSe₂–CsPbBr₃ Mixed van der Waals nanohybrids shown higher photocurrent than pure CsPbBr₃ nanocrystals.¹⁶ Lee et al. found photoluminescence (PL) quenching occurred after the hybridization of perovskites with MoSe₂ and WSe₂ layers, which reflects the charge-transfer effect.¹⁷ The PCE of PEDOT:PSS perovskite solar cells with WSe₂-mediated and without WSe₂-mediated is 16.3% and 13.8%, respectively.¹⁸ These experiments observed the construction of TMDs and perovskite heterostructures can effectively improve the optoelectronic properties of halide perovskites. However, interface electronic transfer and band alignment of Cs₂PbX₄–MSe₂ heterostructures are not studied theoretically. It's worth revealing the effect of halide elements and MSe₂ (M = Mo, W) on Cs₂PbX₄–MSe₂ heterostructures, which can promote the development of 2D inorganic halide perovskite and TMDs optoelectronic applications.

Herein, we constructed the 2D inorganic halide perovskite Cs₂PbX₄ (X = Cl, Br, I) and monolayer MSe₂ heterostructures and discussed their stability, photoelectric properties and charge transfer mechanism through first-principles calculations. We studied electronic structures of the heterostructures with different halide elements and analysed the band alignment type for comparison. Next, we explore the charge transfers mechanism by calculating charge density difference. Finally, optical absorption coefficients of monolayer MSe₂, Cs₂PbX₄ and heterostructures Cs₂PbX₄–MSe₂ were calculated. Our results will be helpful to improve the application performance of two-dimensional lead halide perovskite and TMDs heterostructures.

Computational details

All the density functional theory calculations were performed with the Vienna Ab initial Simulation Package (VASP) code.^19,20 The projector-augmented wave (PAW) method was referred to electron–ion interactions.²¹ The structure-relaxation, interface binding energy and optoelectronic properties were computed by Perdew, Burke and Ernzerhof's (PBE) exchange correlation function within the generalized gradient approximation (GGA) formalism.^22–26 The band gaps of monolayer perovskites and TMDs were further corrected using the screened Heyd–Scuseria–Ernzerhof (HSE) hybrid density functional with the spin–orbital coupling (SOC). The plane wave basis set with a cutoff energy of 450 eV. The convergence criteria were 1 × 10⁻⁴ eV for the self-consistent field energy and 0.01 eV Å⁻¹ for the residual forces on each atom, respectively. A vacuum of 20 Å was considered along z direction to avoid artificial interlayer interactions. 3 × 6 × 1 k-sampling generated by the Monkhorst–Pack scheme for the Brillouin zone was adopted. The zero damping DFT-D3 method of Gimme is used to account for correcting the van der Waals interaction of Heterostructure.

The interface binding energy is calculated by the following formula:

E_b = (E_heter. − E_Cs2PbX4 − E_MSe2)/A (1)

where A represents the interfacial area of Cs₂PbX₄–MSe₂ heterostructures, E_heter., E_Cs2PbX4, E_MSe2 are the total energy of heterostructures Cs₂PbX₄–MSe₂, monolayer Cs₂PbX₄ and MSe₂, respectively.

The plane-averaged charge density difference Δρ is calculated as the followed equation:

Δρ(z) = ρ_heter. − ρ_Cs2PbX4 − ρ_MSe2 (2)

where ρ_heter., ρ_Cs2PbX4 and ρ_MSe2 correspond to the plane-averaged charge density of heterojunctions Cs₂PbX₄–MSe₂, monolayer Cs₂PbX₄ and MSe₂, respectively.

The 2D Mott–Wananier (MW) exciton binding energy (E_eb) equation is calculated as the followed equation:

where μ_ex is the effective exciton mass (μ_ex = m_em_h/(m_e + m_h)), m₀ is the electron mass, and ε is the static dielectric constant. The effective masses of electron (m_e) and hole (m_h) are determined by the curvature of the energy band extremum.

The optical absorption coefficients are obtained from dielectric function, as the followed equation represented:

ε(ω) = ε₁(ω) + iε₂(ω) (5)

where α, ω correspond to the optical absorption coefficient, the angular frequency and the dielectric function ε(ω) contains real part ε₁(ω) and imaginary part ε₂(ω).

Results and discussion

In recent years, the 2D inorganic perovskites Cs₂PbX₄ (X = Cl, Br, I) and monolayers MSe₂ (M = Mo, W) have been successfully synthesized, which attracted much attention due to its highly stable structures.^7,27,28 The unit cell of Cs₂PbX₄ perovskites belongs to cubic system and the optimized lattice parameters of monolayer Cs₂PbCl₄, Cs₂PbBr₄, Cs₂PbI₄ is 5.64 Å, 5.91 Å and 6.30 Å, respectively.²⁹ [CsI]⁰ interface exhibits more strongly charge transferring than [PbI₂]⁰.³⁰ Therefore the [CsI]⁰ plane of the monolayer Cs₂PbX₄ is used to form the heterojunctions. The optimized lattice parameters of monolayer MoSe₂, WSe₂ are 3.32 Å.^31–33 To minimize the lattice mismatch between the stacking blocks, the supercell of new Cs₂PbX₄–MSe₂ heterostructures are built by 3 × 1 cubic phases Cs₂PbCl₄ and MSe₂, cubic phases Cs₂PbBr₄ and MSe₂, and cubic phases Cs₂PbI₄ and MSe₂, respectively, as seen in Fig. 1 (Table 1).

Fig. 1 Top and side views of relaxed Cs₂PbX₄–MSe₂ (M = Mo, W) heterostructures. (a and b) Cs₂PbCl₄–MSe₂ heterostructure. (c and d) Cs₂PbBr₄–MSe₂ heterostructure. (e and f) Cs₂PbI₄–MSe₂ heterostructure.

Table 1 Optimized lattice parameters (a and b) and expanded cell lattice parameters (a₁ and b₁), lattice mismatch, interlayer distance ΔZ and interface binding energy E_b of the relaxed Cs₂PbX₄–WSe₂ heterostructures

Heterostructures	a (Å)	b (Å)	a1 (Å)	b1 (Å)	Mismatch (%)	ΔZ (Å)	Eb (meV Å^−2)
Cs2PbCl4–MoSe2	16.51	5.66	16.75	5.69	1.10%	3.09	−16.73
Cs2PbBr4–MoSe2	16.35	11.81	16.65	11.89	0.62%	3.12	−16.28
Cs2PbBr4–MoSe2	18.22	8.66	18.14	8.84	1.79%	3.16	−16.12
Cs2PbBr4–WSe2	16.41	5.67	16.75	5.69	1.02%	2.90	−17.09
Cs2PbBr4–WSe2	16.35	11.81	16.65	11.89	0.65%	3.18	−17.52
Cs2PbBr4–WSe2	18.21	8.66	18.20	8.67	1.82%	3.30	−15.56

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The lattice mismatches of Cs₂PbCl₄–MoSe₂, Cs₂PbBr₄–MoSe₂, Cs₂PbI₄–MoSe₂, Cs₂PbCl₄–WSe₂, Cs₂PbBr₄–WSe₂ and Cs₂PbI₄–WSe₂ heterostructures are less than 1.10%, 0.62%, 1.79%, 1.02%, 0.65% and 1.82%. The optimized vertical interlayer distances of Cs₂PbCl₄–MoSe₂, Cs₂PbBr₄–MoSe₂, Cs₂PbI₄–MoSe₂, Cs₂PbCl₄–WSe₂, Cs₂PbBr₄–WSe₂ and Cs₂PbI₄–WSe₂ interfaces are 3.07, 3.12, 3.16, 2.90, 3.18 and 3.30 Å, respectively, which increase gradually with the halogen varying from Cl to I. Interface binding energy of Cs₂PbCl₄–MoSe₂, Cs₂PbBr₄–MoSe₂ and Cs₂PbI₄–MoSe₂, Cs₂PbCl₄–WSe₂, Cs₂PbBr₄–WSe₂ and Cs₂PbI₄–WSe₂ interfaces is −16.73, −16.28 and −16.12, −17.09, −17.52 and −15.56 meV Å⁻², respectively. The small interface binding energy and the interlayer distance ranging from 2.9 Å to 3.3 Å indicate that 2D Cs₂PbX₄–MSe₂ heterostructures are formed by vdW contact.³³ These E_b values are comparable to E_b of InSe/GaSe (−18.25 meV Å⁻²), suggesting that Cs₂PbX₄–MSe₂ heterostructures are stable in energy.³⁴ ln addition, MoSe₂–CsPbBr₃ Mixed van der Waals nanohybrids also have been fabricated in experiments (Table 2).¹⁶

Table 2 The bandgaps of monolayer Cs₂PbX₄, MoSe₂ and WSe₂ by different calculation method

Functional	Cs2PbCl4	Cs2PbBr4	Cs2PbI4	MoSe2	WSe2
PBE	2.59	2.18	1.84	1.45	1.56
HSE	3.58	2.91	2.57	2.10	2.03
PBE + SOC	1.84	1.46	1.09	1.37	1.33
HSE + SOC	2.78	2.14	1.78	1.89	1.93
Experiment	3.01	2.32	1.86	1.48	1.60

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In order to study the band structures of Cs₂PbX₄–MSe₂ heterostructures, the band structures of 2D perovskites Cs₂PbX₄, monolayer WSe₂ and monolayer MoSe₂ were calculated by different functionals, including PBE, PBE with SOC (PBE + SOC), HSE, and HSE with SOC (HSE + SOC) functionals. Monolayer MoSe₂ and monolayer WSe₂ show a direct band gap of 1.45 eV and 1.56 eV using PBE functional. Monolayer Cs₂PbCl₄, Cs₂PbBr₄ and Cs₂PbI₄ possess a direct bandgap of 2.59 eV, 2.18 eV and 1.84 eV using PBE functional. We find that the bandgaps of Cs₂PbX₄ computed via PBE and HSE + SOC functionals are in good agreements with experiments and other theoretical results.^{9,10,27,28,35–38} The band gap calculated by HSE is larger than PBE and the band gap calculated by PBE + SOC is smaller than PBE. In addition, the band gap of MSe₂ calculated by HSE + SOC is larger than the related experimental data.^27,28 This is because the HSE functional usually overcorrects slightly the band gap of an intrinsic semiconductor.³⁹ Thus, in order to accurately and closely study the contact characteristics of Cs₂PbX₄–MSe₂ heterostructures, PBE is employed in the following heterostructures section. When monolayers Cs₂PbX₄ and MSe₂ (M = Mo, W) are contacted to make up Cs₂PbX₄–MSe₂ heterostructures, the electronic structures of Cs₂PbX₄–MSe₂ heterostructures are shown in Fig. 2. The Cs₂PbCl₄–MoSe₂, Cs₂PbBr₄–MoSe₂, Cs₂PbI₄–MoSe₂, Cs₂PbCl₄–WSe₂, Cs₂PbBr₄–WSe₂ and Cs₂PbI₄–WSe₂ heterostructures have an indirect bandgap with the value of 1.30 eV, 1.48 eV, 1.54 eV, 1.33 eV, 1.67 eV and 1.53 eV, which approach optimal bandgap (1.34 eV) for solar cells.⁴⁰ Moreover, the conduction band minimum (CBM) of Cs₂PbX₄–MSe₂ heterostructures are dominated by the MSe₂ layer and the valence band maximum (VBM) of Cs₂PbX₄–MSe₂ heterostructures are dominated by Cs₂PbX₄ part.

Fig. 2 Band structures of Cs₂PbX₄–MSe₂ heterostructures (a) X = Cl, M = Mo; (b) X = Br, M = Mo; (c) X = I, M = Mo; (d) X = Cl, M = W; (e) X = Br, M = W; (f) X = I, M = W. The red and blue lines correspond to Cs₂PbX₄ and MSe₂, respectively.

The analysis of energy level arrangement is of great significance to further study interface properties of Cs₂PbX₄–MSe₂ heterostructures. The vacuum energy level (E_v) is set to zero in the precontact state and the Fermi level (E_f) is set to zero in the contact state. In precontact state, the CBM and VBM of monolayer Cs₂PbX₄ are both higher than that of monolayer MSe₂ and both Cs₂PbX₄–MSe₂ are type-II heterostructures, as seen in Fig. 3(a). The electrons will diffuse from monolayers Cs₂PbX₄ to monolayers MSe₂ and the holes will move from monolayers MSe₂ monolayer to monolayers s₂PbX₄ when they contact. Correspondingly, the holes accumulate in Cs₂PbX₄ monolayers and the electrons accumulate in MSe₂ monolayers. Moreover, the difference between the vacuum level and the Fermi level is defined as the work function.³¹ The work function is the internal dynamics of electron flow. The computed work functions of monolayers Cs₂PbCl₄, Cs₂PbBr₄, Cs₂PbI₄, MoSe₂ and WSe₂ are 4.08 eV, 4.21 eV, 4.30 eV, 4.83 eV and 4.51 eV, respectively. The heterostructures are mainly related to the work function after contact. In order to maintain Fermi levels at the same level after contact, the Fermi level of all Cs₂PbX₄ perovskites moved down and the Fermi level of monolayer MSe₂ moved up after they contact each other.

Fig. 3 Energy level graphs of the monolayer MSe₂ and Cs₂PbX₄ in the precontact (a) and contact (b). Blue and gray rectangles represent the monolayer Cs₂PbX₄ and MSe₂. The bottom and top of rectangles correspond to VBM and CBM, respectively.

The energy level diagram of Cs₂PbX₄–MSe₂ heterostructures in contact states is given in Fig. 3(b). The Cs₂PbX₄–MSe₂ heterostructures are type-II heterostructures, which can drive the photogenerated holes and electrons to move in opposite directions, resulting in spatial separation of holes and electrons on different sides of heterostructures.³³ Thus, Cs₂PbX₄–MSe₂ heterostructures are beneficial for improving the photoelectric conversion efficiency of Cs₂PbX₄–MSe₂ optoelectronic applications. In these type-II heterostructures, the differences between the VBM of their components (valence band offset, Δv) are crucial for hole blocking and the differences between the CBM of their components (conduction band offset, Δc) are crucial for electron transport. The large Δv promotes hole extraction from TMDs layers to perovskite layers and the large Δc allows free electrons to move from perovskite to TMDs layers. It is shown that Cs₂PbCl₄–MSe₂ heterostructure have the largest Δc and Δv among Cs₂PbX₄–MSe₂ heterostructures.¹² Thus, the Cs₂PbCl₄–MoSe₂, and Cs₂PbCl₄–WSe₂ heterostructures may have the largest charge transport power and are more conducive to reducing the dark current. In addition, Cs₂PbX₄–MoSe₂ heterostructures have lager Δc and Δv than Cs₂PbX₄–WSe₂ heterostructures.

In addition, the Mott–Wananier theory has been used to approximate exciton binding energies in the vdW heterostructures.⁴¹ Table 3 lists the carrier masses and MW exciton binding energy of Cs₂PbX₄–MSe₂ heterostructures. The lower exciton binding energies usually facilitate the splitting of excitons into free charge carriers.³⁴ It is shown that Cs₂PbCl₄–MoSe₂ heterostructures exhibit the lowest exciton binding energies among Cs₂PbX₄–MoSe₂ heterostructures. Therefore, Cs₂PbCl₄–MoSe₂ heterostructures can effectively promotes the separation of excitons and exhibit the highest charge transport efficiency among Cs₂PbX₄–MSe₂ heterostructures.

Table 3 Carrier effective masses (m_e, m_h, and μ_ex), static dielectric constant (ε) and MW excitonic binding energies (E_eb)

Heterostructures	me (m0)	mh (m0)	μex (m0)	ε	Eeb (eV)
Cs2PbCl4–MoSe2	1.16	0.28	0.23	5.34	0.43
Cs2PbBr4–MoSe2	0.79	0.71	0.37	5.44	0.68
Cs2PbI4–MoSe2	1.39	0.67	0.45	5.24	1.00
Cs2PbCl4–WSe2	1.46	0.27	0.23	4.95	0.50
Cs2PbBr4–WSe2	0.75	0.66	0.35	5.08	0.74
Cs2PbI4–WSe2	1.03	0.61	0.38	5.26	0.76

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To clearly investigate the recombination rates of electron–hole pairs and transfer of charges between the Cs₂PbX₄ monolayers and MSe₂ monolayers across the interfaces, the plane-averaged charge density difference Δρ are calculated, as shown in Fig. 4. The results demonstrate that the holes mainly accumulated at the Cs₂PbX₄ interfaces and the charges accumulated at MSe₂ interfaces. Additionally, the charges transfer from Cs₂PbX₄ interfaces to MSe₂ interfaces while the holes move in the opposite direction. The direction of charge transfer is consistent with that of band alignment analysis, which shown type-II heterostructures are benefited to the separation of electrons and holes. What's more, detail charge transfers among interlayer spacing are used to quantitatively evaluate charge transferring of heterostructures. The Cs₂PbCl₄–MoSe₂, Cs₂PbBr₄–MoSe₂, Cs₂PbI₄–MoSe₂, Cs₂PbCl₄–WSe₂, Cs₂PbBr₄–WSe₂ and Cs₂PbI₄–WSe₂ heterostructures have charge transfers among interlayer spacing with the values of 0.18, 0.15, 0.16, 0.16, 0.10 and 0.14 × 10⁻³e. We find that the Cs₂PbCl₄–MSe₂ heterostructures have the highest charge transfers in the six Cs₂PbX₄–MSe₂ heterostructures among interlayer spacing. In addition, Cs₂PbX₄–MoSe₂ heterostructures have larger charge transfers than Cs₂PbX₄–WSe₂ heterostructures. It is because Cs₂PbX₄–MoSe₂ heterostructures have smaller exciton binding energies than Cs₂PbX₄–WSe₂ heterostructures.

Fig. 4 The planar-averaged differential charge density Δρ(z) of Cs₂PbX₄–MSe₂ heterostructures: (a and d) X = Cl; (b and e) X = Br; (c and f) X = I. Red and blue represent electron depletion and accumulation.

Except for the electronic structures and charge redistributions of heterostructures, the optical properties in vdW heterostructures have important effects on the performance of perovskite optoelectronic devices.⁴² In order to further study the optical properties of Cs₂PbX₄–MSe₂ heterostructures, the optical absorption coefficients were calculated, as shown in Fig. 5. The optical absorption coefficients of MSe₂ monolayers are higher than those of Cs₂PbX₄ monolayers. The optical absorption coefficients of all heterostructures are significantly higher than those of corresponding Cs₂PbX₄ monolayers and MSe₂ monolayers. This is because the bandgaps of 2D Cs₂PbX₄–MSe₂ heterostructures are smaller than the bandgaps of Cs₂PbX₄ monolayers. The bandgaps of Cs₂PbX₄–MSe₂ heterostructures approach optimal bandgap (1.34 eV) for solar cells.⁴⁰ Thus, the construction of Cs₂PbX₄–MSe₂ heterostructures is beneficial to improve the light absorption of optoelectronic devices.

Fig. 5 Optical absorption coefficients of (a and d) Cs₂PbCl₄–MSe₂, (b and e) Cs₂PbBr₄–MSe₂, and (c and f) Cs₂PbI₄–MSe₂ heterostructures. The blue, black and red lines represent optical absorption spectrum of heterostructures, monolayer MSe₂ and Cs₂PbX₄, respectively.

In addition, the light absorption of Cs₂PbX₄–MoSe₂ heterostructures is only slightly greater than that of Cs₂PbX₄–WSe₂ in the visible region because the light absorption of MoSe₂ is slightly greater than that of WSe₂ in the visible region. The light absorption coefficients of Cs₂PbX₄ increase rapidly in the visible region with the halogen varying from Cl to I. The light absorption coefficients of Cs₂PbX4–MSe₂ heterostructures increase rapidly in the visible region with the halogen varying from Cl to I. Therefore, the Cs₂PbI₄–MSe₂ heterostructure has great potential application in solar cells among Cs₂PbX₄–MSe₂ heterostructures.

In order to explore the application of Cs₂PbX₄–MSe₂ heterostructures in solar cells, we further calculated the power conversion efficiency of Cs₂PbX₄–MSe₂ heterostructures. The PCE depends on the donor band gap and conduction band offset.^43,44 The PCE of Cs₂PbX₄–MSe₂ heterostructures with type-II alignment is shown in Fig. 6 as a contour plot where the x- and y-axes are the donor band gap and conduction band offset, respectively. The PCE of Cs₂PbI₄–MoSe₂, Cs₂PbI₄–WSe₂ and Cs₂PbBr₄–WSe₂ heterostructures is 13%, 18% and 10%, which is greater than 10%. Three heterostructures can be used in solar cells. Cs₂PbI₄–WSe₂ heterostructure has the largest PCE (18%) among Cs₂PbX₄–MSe₂ heterostructures. The PCE of Cs₂PbI₄–WSe₂ heterostructure is larger than that of WS₂/CsPbBr₃ PSCs (10.65%) and WSe₂–mediated PSCs (16.3%).^13,18 With the halogen varying from Cl to I, the PCE of Cs₂PbX₄–WSe₂ heterostructures increase rapidly. The PCE variation trend is consistent with the absorption coefficients of Cs₂PbX₄–MSe₂ heterostructures varying from Cl to I. In addition, the PCE of Cs₂PbX₄–WSe₂ heterostructures is larger than the PCE of Cs₂PbX₄–MoSe₂ heterostructures. This is mainly because Cs₂PbX₄–WSe₂ heterostructures have smaller Δc than Cs₂PbX₄–MoSe₂ heterostructures. Therefore, Cs₂PbI₄–WSe₂ heterostructure has great potential application in solar cells.

Fig. 6 Contour plot showing the calculated PCE of Cs₂PbX₄–MSe₂ heterostructures according to the Cs₂PbX₄ donor band gap and conduction band offset Δc.

Conclusions

In summary, we have systematically studied the structural, stability, charge transfer and optoelectronic properties of 2D perovskite Cs₂PbX₄–MSe₂ heterostructures with different halide elements based on density functional calculations. All these six heterostructures are stable in energy and the interlayer distances increase gradually with the halogen varying from Cl to I. Electronic structures show Cs₂PbX₄–MSe₂ heterostructures belongs to type-II energy level shifts with narrower optical gap than monolayers Cs₂PbX₄. In addition, the Cs₂PbCl₄–MoSe₂, and Cs₂PbCl₄–WSe₂ heterostructures may have the largest charge transport power due to their larger band offset, which is beneficial to reduce dark current and improve open circuit voltage. Cs₂PbCl₄–MoSe₂ heterostructures can effectively promotes the separation of excitons and exhibit the highest charge transport efficiency among Cs₂PbX₄–MSe₂ heterostructures due to their lowest exciton binding energies. Cs₂PbCl₄–MoSe₂ heterostructure has the potential to be applied in photodetectors. Next, the charges transfer from Cs₂PbX₄ interfaces to MSe₂ interfaces while the holes move in the opposite direction. The holes mainly accumulated at the Cs₂PbX₄ interfaces and the charges accumulated at MSe₂ interfaces. Cs₂PbX₄–MoSe₂ heterostructures have larger charge transfers than Cs₂PbX₄–WSe₂ heterostructures. Finally, optical absorptions of six heterostructures are significantly higher than the corresponding Cs₂PbX₄ monolayers and MSe₂ monolayers. The PCE of Cs₂PbX₄–WSe₂ heterostructures is larger than the PCE of Cs₂PbX₄–MoSe₂ heterostructures. Cs₂PbI₄–WSe₂ heterostructure has the largest PCE (18%) among Cs₂PbX₄–MSe₂ heterostructures. In conclusion, Cs₂PbCl₄–MoSe₂ heterostructure exhibits great potential application in photodetectors devices and Cs₂PbI₄–WSe₂ heterostructure has great potential application in solar cells. Our findings provide insight into of Cs₂PbX₄–MSe₂ heterostructures can effectively improve the performance of perovskite optoelectronic devices.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work is supported by the Fund of State Key Laboratory of IPOC(BUPT) (no. IPOC2019ZZ04) and the Open-Foundation of Key Laboratory of Laser Device Technology, China North Industries Group Corporation Limited (Grant No. KLLDT202103). We thank for the helpful discussion with Prof. Pengfei Guan and the computational support from the Beijing Computational Science Research Center (CSRC). We also acknowledge the computation supported by High-performance Computing Platform of BUPT.

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