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 ? along is used to eliminate the interaction between adjacent slabs. All the structures are fully relaxed with a force tolerance of 0.02 eV/?. 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 γ phase, 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 ? 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, ?Ev, is calculated as
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Figure1.
(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.
$$Delta {E_{ m{v}}} = Delta E_{{ m{c}},{ m{v}}}^{{ m{CsPbBr}}_3} - Delta E_{{ m{c'}},{ m{v'}}}^{{ m{MoSe}}_2} + Delta E_{{ m{c}},{ m{c'}}},$$  |
where
m{c}},{
m{v}}}^{{
m{CsPbBr}}_3} $
m{c'}},{
m{v'}}}^{{
m{MoSe}}_2} $
$$Delta {E_{ m{c}}} = E_{ m{g}}^{{ m{CIS}}} - E_{ m g}^{{ m{CdS}}} + Delta {E_{ m{v}}}.$$  |
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, Eb, between CsPbBr3 slab and MoSe2 monolayer, which is calculated as
$${E_{ m{b}}} = {E_{{ m{hetero}}}} - {E_{{ m{CsPbBr}}_3}} - {E_{{ m{MoSe}}_2}},$$  |
where Ehetero,
m{MoSe}}_2}}$
m{CsPbBr}}_3}}$
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 ?, c = 11.91 ?. The lattice constants of monolayer MoSe2 are a = b = 3.33 ?. 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.
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Figure2.
(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.
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Figure3.
(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, ?Ec, 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, ?Ev
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 (Eb = –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.
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Figure4.
(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.
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Figure5.
(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).
