Two-dimensional transition metal dichalcogenides for lead halide perovskites-based photodetectors: band alignment investigation for the case of CsPbBr3/MoSe2

Le Huang; Nengjie Huo; Zhaoqiang Zheng; Huafeng Dong; Jingbo Li

doi:10.1088/1674-4926/41/5/052206

Abstract

The distinguished electronic and optical properties of lead halide perovskites (LHPs) make them good candidates for active layer in optoelectronic devices. Integrating LHPs and two-dimensional (2D) transition metal dichalcogenides (TMDs) provides opportunities for achieving increased performance in heterostructured LHPs/TMDs based optoelectronic devices. The electronic structures of LHPs/TMDs heterostructures, such as the band offsets and interfacial interaction, are of fundamental and technological interest. Here CsPbBr₃ and MoSe₂ are taken as prototypes of LHPs and 2D TMDs to investigate the band alignment and interfacial coupling between them. Our GGA-PBE and HSE06 calculations reveal an intrinsic type-II band alignment between CsPbBr₃ and MoSe₂. This type-II band alignment suggests that the performance of CsPbBr₃-based photodetectors can be improved by incorporating MoSe₂ monolayer. Furthermore, the absence of deep defect states at CsPbBr₃/MoSe₂ interfaces is also beneficial to the better performance of photodetectors based on CsPbBr₃/MoSe₂ heterostructure. This work not only offers insights into the improved performance of photodetectors based on LHPs/TMDs heterostructures but it also provides guidelines for designing high-efficiency optoelectronic devices based on LHPs/TMDs heterostructures.

1. Introduction

In recent years, lead halide perovskites have attracted enormous attention because of their promising applications in high-performance optoelectronic devices^[1-6]. Halide perovskites have high light absorption coefficient, long charge diffusion length, high carrier mobility and high defect tolerance^[7-12]. These superior properties make them good candidates for optoelectronic applications, such as solar cells^[13-16], photodetectors^[17-21] and light-emitting diodes^{[22, 23]}, etc. Despite the good performance, halide perovskites potential stability issue remains a major challenge for optoelectronic devices^[24-26]. To achieve stable, high-efficiency halide perovskite based optoelectronic devices, other functional layers such as interfacial layers and encapsulation films are required to work together with halide perovskites.

Two-dimensional (2D) materials, such as graphene, transition metal dichalcogenides (TMDs) and black phosphorus, and so on, have excellent electronic, optical, and thermal properties^[27-32]. However, atomically thin TMDs hardly absorb light to a sufficient extent for photodetecting and it is necessary to incorporate them with other semiconducting materials such as halide perovskites to improve the performance. To take advantages of the high light absorption of halide perovskites and the excellent carrier transport properties of 2D materials, many 2D materials have been integrated into optoelectronic devices based on halide perovskites to achieve novel electronic and optoelectronic devices with improved performance. For example, by integrating MoS₂ with CsPbBr₃ nanosheets, excellent performance has been achieved in the hybrid MoS₂/CsPbBr₃-based photodetectors^[33]. Cho and co-workers have fabricated hybrid perovskite-graphene photodetector and observed improved performances due to the reduced recombination rates and efficient electron transfer^[34]. Integration of MoS₂ with MAPbI₃ leads to substantial improvement in the quantum efficiency and the responsivity of the photodetector^{[35, 36]}. Heterostructured WS₂/MAPbI₃ is also demonstrated to have an enhanced photoresponse^[37].

An exact knowledge of electronic levels is a prerequisite to design optoelectronic devices with good performance and for understanding the device physics^{[38, 39]}. The electronic structures, especially the band alignments, of the hybrid perovskites/TMDs play a key role in the optoelectronic devices. Theoretically, heterostructures with type-II band alignments can facilitate the separation of light-generated electrons and holes. As a result, the carrier recombination can be reduced and their optoelectronic performance can be improved. While for heterostructures with type-I band alignments, both electrons and holes tend to concentrate on the same material, which may result in the carrier’s reduced lifetime.

A unified understanding of the band offsets in perovskites/TMDs is missing. Even the type of their band alignment (type-I or type-II) is under debate. Furthermore, spin-orbital coupling (SOC) has significant influence on the electronic structures of lead halide perovskites (LHPs) and TMDs^{[40, 41]}. Specifically, for TMDs, significant relativistic effect is observed in their valence band maximum (VBM). In the case of LHPs, very large SOC gaps appear at the conduction band minimum (CBM) in their electronic structures. The role of SOC in the band alignment is far from clear. On the other side, upon two semiconductors making contacts, band bending will occur due to the interfacial interaction. How are the interfacial properties influenced by the interfacial coupling? And, what is the role of SOC in interfacial coupling? These questions are far from being answered and a thorough investigation is required.

In this work, CsPbBr₃ and MoSe₂ are taken as prototypes of LHPs and 2D TMDs to investigate the band alignment and interfacial coupling between them. Insights into the SOC effects on the band offsets and interfacial coupling are provided. Our GGA-PBE and HSE06 calculations reveal an intrinsic type-II band alignment between CsPbBr₃ and MoSe₂ with both the VBM and CBM of MoSe₂ monolayer being lower in energy than those of CsPbBr₃. The conduction band offset is significantly reduced by the large spin-orbital coupling at the CBM of CsPbBr₃. Meanwhile, the valence band offset is reduced by Hartree-Fock exchange interaction. Consequently, an intrinsic type-I alignment is achieved. The type-II band alignment recovers upon CsPbBr₃ making contacts with MoSe₂ due to the interfacial interaction. Furthermore, no deep defect states are observed in the band gap of CsPbBr₃/MoSe₂ heterostructures. These results suggest that the performance of CsPbBr₃-based photodetectors can be improved by incorporating MoSe₂ monolayer.

2. Computational details

We perform our calculations within the projector augmented plane-wave method^[42-44] in the VASP code. The exchange correlation functional with partial core correction included is described by using the general gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE)^{[45, 46]}. The plane-wave cutoff energy is set as 450 eV in all the calculations. A vacuum larger than 20 Å along is used to eliminate the interaction between adjacent slabs. All the structures are fully relaxed with a force tolerance of 0.02 eV/Å. HSE06 functional with mixing 25% of screened Hartree-Fock exchange to the GGA-PBE exchange is used to obtain the accurate electronic structures of all of the systems used here^{[47, 48]}. Mixing percentage is adjusted to reproduce the experimental band gaps of MoSe₂ monolayer and CsPbBr₃ bulk. DFT-D3 method of Grimme^[49] is used to correct the van der Waals interaction at CsPbBr₃/MoSe₂ interface.

CsPbBr₃ in the γphase, which is proved to be the most stable phase^[41], is taken as an example of LHPs and MoSe₂ monolayer as a prototype of TMDs to investigate the electronic structures of LHPs/TMDs interfaces. To simulate the interfacial coupling between LHPs and TMDs, a periodic CsPbBr₃ slab with a vacuum layer more than 20 Å is constructed here. Since γ-CsPbBr₃ has a cubic crystal structure. Hence, a rectangle cell of MoSe₂ monolayer is constructed to minimize the lattice mismatch between CsPbBr₃ and MoSe₂ monolayer, as we did in our previous works^[50-52]. The CsPbBr₃/MoSe₂ interface model contains 1 × 3 × 4 unit cells of α-CsPbBr₃ and 1 × 5 × 1 rectangle cells of MoSe₂. (CsPbBr₃ in α phase is used here because of the limit on computing capability. We have demonstrated that the core levels of Br_1s changed little in α-CsPbBr₃ and γ-CsPbBr₃. Therefore, using α-CsPbBr₃ in the heterostructures here does not influence the validity of our results.) The lattice mismatches along a and b directions are smaller than 4%.

The calculation method for band offsets is illustrated in Fig. 1 and Refs. [53, 54]. Firstly, the energy differences between the core level and the VBM in bulk γ-CsPbBr₃ and MoSe₂ monolayer are calculated. Then we do the alignment of core levels in CsPbBr₃/MoSe₂ heterostructure. The valence band offset, ∆E_v, is calculated as

Figure 1.(Color online) Schematic procedure to calculate the valence band offsets for heterostructured CsPbBr₃/MoSe₂. (a) Step I, calculating the energy difference between the VBM and core level in γ-CsPbBr₃ and monolayer MoSe₂, respectively. (b) Step II, calculating the core levels of each layer in CsPbBr₃/MoSe₂ superlattice and doing core-level alignment. A superlattice of CsPbBr₃/MoSe₂ is constructed in (b) to do the core-level alignment.

$ \Delta {E_{\rm{v}}} = \Delta E_{{\rm{c}},{\rm{v}}}^{{\rm{CsPbBr}}_3} - \Delta E_{{\rm{c'}},{\rm{v'}}}^{{\rm{MoSe}}_2} + \Delta E_{{\rm{c}},{\rm{c'}}}, $  ()

where is the energy difference between the core level and the VBM of CsPbBr₃, is that of MoSe₂ monolayer. ∆E_c,c' is the energy difference in core levels of CsPbBr₃ and MoSe₂ in the CsPbBr₃/MoSe₂ heterostructure. The conduction band offset is calculated as

$ \Delta {E_{\rm{c}}} = E_{\rm{g}}^{{\rm{CIS}}} - E_{\rm g}^{{\rm{CdS}}} + \Delta {E_{\rm{v}}}. $  ()

Here Br_1s in CsPbBr₃ and Se_1s in MoSe₂ monolayer are taken as the core levels to do the alignment.

Relativistic first-principles calculations are performed to explore the SOC effect on the electronic structures of CsPbBr₃, MoSe₂ monolayer and CsPbBr₃/MoSe₂ interface and its interfacial coupling. To exclude the impact from other factor on the interfacial coupling, we used the heterostructured CsPbBr₃/MoSe₂ structures that optimized by GGA-PBE functional to explore the SOC effects. The interface coupling is characterized by the binding energy, E_b, between CsPbBr₃ slab and MoSe₂ monolayer, which is calculated as

$ {E_{\rm{b}}} = {E_{{\rm{hetero}}}} - {E_{{\rm{CsPbBr}}_3}} - {E_{{\rm{MoSe}}_2}}, $  ()

where E_hetero, and are the total energies of CsPbBr₃/MoSe₂ heterostructure, MoSe₂ monolayer and CsPbBr₃ slab, respectively.

3. Results and discussion

Fig. 1 shows the crystal structures of γ-CsPbBr₃ and monolayer MoSe₂, and the schematic alignment procedure to calculate the valence band offsets. The optimized lattice constants of γ-CsPbBr₃ are a = b = 8.33 Å, c = 11.91 Å. The lattice constants of monolayer MoSe₂ are a = b = 3.33 Å. To do the alignment of the core levels, a superlattice of α-CsPbBr₃/MoSe₂ is constructed (Fig. 1(b)). During the core level alignment calculations, the lattice constants of α-CsPbBr₃ are fixed and strains are applied to the monolayer MoSe₂.

At the first step of band offset calculation (Fig. 1(a)), we calculated the electronic structures of γ-CsPbBr₃ and MoSe₂ monolayer in Fig. 2. MoSe₂ monolayer shows a direct band gap of 1.43 eV by GGA-PBE functional and 1.88 eV by HSE06 functional. It has been demonstrated that SOC have significant influence on the VBM at K point in the electronic structures of TMDs. The calculated SOC gap here is 0.18 eV by GGA-PBE functional and 0.28 eV by HSE06 functional. These results agree well with previous works^[55]. In Fig. 2(b), the band structures of γ-CsPbBr₃ are calculated by PBE, PBE + SOC, HSE06 and HSE06 + SOC methods. γ-CsPbBr₃ shows a direct band gap at the Γ point regardless of the functionals. Previous works have demonstrated that the VBMs of LHPs are formed by an antibonding of Pb_s and p orbitals of halides. Their CBMs are dominated by Pb_6p orbitals. Due to the large relativistic effect of Pb_6p orbitals, the LHPs always exhibit an extremely large SOC gap at the CBMs. The band structures of γ-CsPbBr₃ in Fig. 2(b) show that an SOC splitting about 1 eV appears at the CBM. After including SOC, the band gap of γ-CsPbBr₃ is significantly reduced. The large SOC of γ-CsPbBr₃ may have significant influence on the band alignments of heterostructured γ-CsPbBr₃/TMDs.

Figure 2.(Color online) Band structures of (a) γ-CsPbBr₃ and (b) MoSe₂ monolayer by using PBE (brown lines) and HSE06 (blue lines) functionals. Band structures with and without SOC are both calculated to explore the influence of SOC on the electronic structures. The VBMs are taken as the reference in all the band structures. All of the band gaps are labeled.

In photodetectors based on LHPs/TMDs heterostructures, the band offsets at the interfaces play an important role in their optoelectronic performance. In Figs. 3(a) and 3(b), the band alignment of CsPbBr₃/MoSe₂ is calculated by using PBE and HSE06 functionals. A type-II band alignment is found for both functionals. Specifically, both the VBM and CBM of MoSe₂ are lower than those of CsPbBr₃, suggesting that electrons and holes will separate spontaneously with electrons concentrating in MoSe₂ layer and holes concentrating in CsPbBr₃. Therefore, in optoelectronic devices based on CsPbBr₃/MoSe₂, the recombination will be reduced and the efficiency can be improved. Comparing the results in Figs. 3(a) and 3(b), larger band gaps are obtained by HSE06 functional than PBE functional. It is found that HSE06 calculation obtains reduced conduction and valence band offsets than PBE results. It should be noted that PBE calculation underestimates the band gaps of CsPbBr₃ and monolayer MoSe₂ than their experimental values.

Figure 3.(Color online) Band alignment of CsPbBr₃ and MoSe₂ is calculated by using PBE and HSE06 functionals. Conduction and valence band offsets are labeled in black. Red-dashed lines in (d) are the corrected band edges of CsPbBr₃ and MoSe₂ monolayer with Hatree-Fock exchange percentage of 15% for MoSe₂ monolayer and 45% for CsPbBr₃. The corrected band gaps are labeled in blue. The conduction and valence band offsets are 0.26 and –0.13 eV, respectively.

It has been demonstrated in Fig. 2 that SOC has a significant influence on the band edges of CsPbBr₃ and MoSe₂ monolayer. Consequently, the band offsets between CsPbBr₃ and MoSe₂ monolayer can be changed accordingly. When SOC effect included, as shown in Figs. 3(c) and 3(d), our results indicate that the CBM of CsPbBr₃ shifts down because of the SOC splitting, resulting in a reduced band gap. Furthermore, the conduction band offset, ∆E_c, is much reduced due to the large SOC splitting at the CBM of CsPbBr₃. On the other hand, the influence of SOC on the valence band offset, ∆E_v, is rather weak. Additionally, HSE + SOC calculations indicate a type-I band alignment of CsPbBr₃/MoSe₂ with band edges of CsPbBr₃ encapsulated in that of MoSe₂ monolayer. This divergence with experimental results may result from their uncorrected band edges. To reproduce the experimental band gaps of CsPbBr₃ and MoSe₂ monolayer, we calculated their electronic structures by changing the mixing percentages of Hartree-Fock exchange (15% for MoSe₂ monolayer and 45% for CsPbBr₃) into the GGA-PBE exchange functional. Then, the MoSe₂ monolayer and 45% for CsPbBr₃ show corrected band gaps of 1.56 and 1.95 eV, respectively, which are in good consist with experimental values. The corrected band alignment is shown by the dashed lines in Fig. 3(d). Type-I band alignment of CsPbBr₃/MoSe₂ is maintained after corrections. What makes difference is that the VBM of CsPbBr₃ shifts downward to below that of MoSe₂ and its CBM shifts upward to higher than that of MoSe₂. In this case, both the photon-generated electrons and holes tend to concentrate in the MoSe₂ layer. As a result, the performance of photodetectors based on CsPbBr₃/MoSe₂ can be limited by the electron-hole recombination in MoSe₂ layer.

It has been demonstrated that the band offsets of a heterostructure can be modulated by interfacial interaction. In Fig. 4, we explored the interfacial interaction between MoSe₂ layer and CsPbBr₃ slabs with CsBr and PbBr terminated. Our results show that MoSe₂ layer exhibits a stronger binding to PbBr-terminated CsPbBr₃ slab (E_b= –1.907 eV per supercell) than to CsBr-terminated one (–1.699 eV). Additionally, SOC effect is revealed to have little influence on the interfacial coupling. (The binding energies become –1.900 and –1.701 eV for corresponding systems above when SOC effect included.) The results of charge difference in Fig. 4 suggest that charge transfer occurs at the CsPbBr₃/MoSe₂ interface. For both cases, a little negative charge (electrons) transfers from the interfacial metal atoms of CsPbBr₃ slab to Se atoms of MoSe₂ layer, suggesting a higher CBM of CsPbBr₃ slab than MoSe₂ monolayer.

Figure 4.(Color online) The charge difference at the interfaces between MoSe₂ monolayer and (a) CsBr-terminated, (b) PbBr-terminated CsPbBr₃ slab.

It is known that interfacial charge transfer has influence on the band offsets at interfaces. In Fig. 5, the projected band structures of CsPbBr₃/MoSe₂ interfaces are calculated to check their band alignments. The bands dominated by CsPbBr₃ and MoSe₂ are plotted by blue and red dots in Fig. 5. Our results indicate type-II band alignment in both CsPbBr₃/MoSe₂ interfaces with the CBM and VBM of CsPbBr₃ higher than those of MoSe₂ layer. Furthermore, there is no deep defect states appear in the band gaps of CsPbBr₃/MoSe₂ heterostructures, suggesting rather low density of non-radiative recombination center at the interface. This is attributed to the high defect tolerance of CsPbBr₃ and no dangling bonds of MoSe₂ layer. So, the performance of CsPbBr₃ based photodetectors can be improved by inserting a MoSe₂ layer to facilitate the separation of photo-generated electrons and holes.

Figure 5.(Color online) The projected band structures of CsPbBr₃/MoSe₂ heterostructures. (a) Interface between MoSe₂ and CsBr-terminated CsPbBr₃. (b) Interface between MoSe₂ and PbBr-terminated CsPbBr₃. The red and blue dots represent the bands dominated by MoSe₂ layer and CsPbBr₃, respectively.

It has been demonstrated that if we change the halide atom from Br to I, better light absorption usually can be obtained thanks to reduced band gaps that arise because of the CBM and the VBM approaches the Fermi level^[54]. Additionally, the VBM of MoS₂ monolayer is lower than that of MoSe₂ monolayer. Consequently, the downshift of the VBM of CsPbI₃ and the upshift of the VBM of MoS₂ will lead to a type-II band alignment in CsPbI₃/MoS₂, with a larger valence band offset than that in CsPbBr₃/MoSe₂. In this view, better performance can be obtained in photodetectors based on CsPbI₃/MoS₂ than those based on CsPbBr₃/MoSe₂. Our results in this work provide guidelines for designing high-performance optoelectronic devices based on hybrid LHPs and TMDs.

4. Conclusion

In summary, CsPbBr₃ and MoSe₂ are taken as prototypes of LHPs and 2D TMDs to investigate the band alignment between them. A type-II band alignment between CsPbBr₃ and MoSe₂ is manifested by our first-principles calculations by using GGA-PBE and HSE06 functionals. Both the VBM and CBM of MoSe₂ monolayer are lower in energy than those of CsPbBr₃. The conduction band offset is significantly reduced by the large spin-orbital coupling at the CBM of CsPbBr₃, resulting in an intrinsic type-I alignment between them by careful HSE06 + SOC calculations. Upon CsPbBr₃ making contacts with MoSe₂, the interfacial interaction leads to the upshift of the bands of CsPbBr₃ and downshift of the bands of MoSe₂, further resulting a type-II band alignment between them. This type-II band alignment suggests that the performance of CsPbBr₃-based photodetectors can be improved by incorporating MoSe₂ monolayer. Furthermore, the absence of deep defect states at CsPbBr₃/MoSe₂ interfaces is also beneficial to the better performance of photodetectors based on CsPbBr₃/MoSe₂ heterostructure. This work not only uncovers the mechanism of improved performance of photodetectors based on CsPbBr₃/MoSe₂ heterostructures but it also provide guidelines for designing high-efficiency optoelectronic devices based on LHPs/TMDs heterostructures.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Grants No. 11804058, 11674310, 61622406).

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