Theoretical Studies of Electronic and Optical Behaviors of All

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Theoretical Studies on Electronic and Optical Behaviors of AllInorganic CsPbI and Two-Dimensional MS (M=Mo, W) Heterostructures 3

2

Jian He, Jie Su, Zhenhua Lin, Siyu Zhang, Yu Qin, Jincheng Zhang, Jingjing Chang, and Yue Hao J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b12350 • Publication Date (Web): 06 Mar 2019 Downloaded from http://pubs.acs.org on March 6, 2019

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The Journal of Physical Chemistry

Theoretical Studies on Electronic and Optical Behaviors of All-Inorganic CsPbI3 and Two-Dimensional MS2 (M=Mo, W) Heterostructures

Jian He, Jie Su,* Zhenhua Lin, Siyu Zhang, Yu Qin, Jincheng Zhang, Jingjing Chang,* Yue Hao

State Key Discipline Laboratory of Wide Band Gap Semiconductor Tecchnology, Shaanxi Joint Key Laboratory of Graphene, School of Microelectronics, Xidian University, Xi’an, 710071, China.

Abstract: Two-dimensional (2D) transition metal dichalcogenides (TMDs) are not only promising optoelectronic materials, but also can improve the optoelectronic performances of perovskites by forming heterostructures. Here, the structural, electronic and optical properties of four kinds of CsPbI3/MS2 (M=Mo, W) heterostructures have been comprehensively investigated by density functional theory. No matter what the heterostructure structures, the electronic structure and excellent transport properties of both CsPbI3 surface and monolayer MS2 can be preserved in the CsPbI3/MS2 heterostructures. Moreover, CsPbI3/MS2 heterostructures show type-II band alignment with indirect band gaps and charge transfers, which separates electrons and holes spontaneously. The light absorptions of CsPbI3 surfaces in the infrared, visible and ultraviolet regions are enhanced upon forming heterostructures. Note that, the performances of heterostructures are strongly dependent on the heterostructure structure. Pb-I terminated CsPbI3/MS2 heterostructures exhibit lower tunneling barriers and larger band offsets which may lead to higher circuit voltages and lower dark currents, but they show lower stabilities compared with Cs-I terminated CsPbI3/MS2 heterostructures. Moreover, CsPbI3/MoS2 heterostructures demonstrate higher electric and optical performances than those of CsPbI3/WS2 heterostructures. Our findings provide a deep understanding of CsPbI3/MS2 heterostructures, and suggest an effective way to improve the performance of perovskite optoelectronic devices such as radiation detection.

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Introduction Perovskites, especially organic-inorganic hybrid perovskites, have attracted great attention because of their large optical absorption coefficient, low cost, simple preparation and low trap states, etc.1,2 Such properties make perovskites to be suitable for high performance photovoltaic and optoelectronic applications. For example, the power conversion efficiency (PCE) of organic-inorganic hybrid perovskite solar cells (PSCs) has reached up to 23.6 % in the past few years.3 Photodetectors based on organic-inorganic hybrid perovskites showed high external quantum efficiencies (up to 105)4, large carrier mobilities (2.5-1000 cm2v-1s-1) (0.08-4.5 µs)

7,8

5,6,

long carrier lifetimes

and diffusion lengths (2-175 µm)2,6,8,9. However, two important

issues hamper obtaining high performance and stable organic-inorganic hybrid perovskites devices. On one hand, organic-inorganic hybrid perovskites have poor stabilities due to hygroscopic and volatile nature of organic cations in organic-inorganic perovskites.10 On the other hand, perovskite optoelectronics often suffer from large electrical hysteresis, slow photoresponse, and low sensitivity.

11,12

Previous investigations have shown that replacing the organic cations by inorganic cesium (Cs) cations to form all-inorganic cesium lead halide (CsPbX3) is an effective way to improve the stability.13,14 Moreover, CsPbX3 also demonstrates excellent optoelectronic properties, such as direct optical band gaps, large optical absorption in the visible-light region, and high luminescence efficiency. 14,15 These properties make CsPbX3,

especially

photoluminescence, performances

of

CsPbI3,

promising

light-emitting all-inorganic

for

diodes,

CsPbI3

and

devices

solar

cells,

lasers.16,17 are

lower

photodetectors, However, than

some

those

of

organic-inorganic hybrid perovskites devices. For example, the highest PCE of CsPbI2Br PSCs is just over 17 %, far lower than 23.6%. 3, 18 Interface engineering has been regarded as an effective approach to improve the performances of perovskite devices. For instance, TiO2/perovskite and NiO/perovskite heterostructures have been shown to enhance the PCEs of MA1−yFAyPbI3−xClx perovskite solar cells with low electrical hysteresis to over 17.8 % and 20 %, respectively. 19-20 CH3NH3PbI3/graphene heterostructures not only have broadened the


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spectral photoresponsivity of CH3NH3PbI3 photodetectors, but also have increased the effective quantum efficiency to 5×104 % under an illumination power of 1µW.

21

CsPbI3/phosphorus heterostructures could improve the light absorption in the infrared region.

22

Inspired by these, forming perovskites/2D heterostructures is a promising

way to improve the performance of CsPbI3 perovskite optoelectronic devices. MS2 (M=Mo, W) as typical 2D TMDs have been intensively studied in the past decade due to their excellent properties, including tunable bandgaps, high mobilities, and high light absorption. 23 Such characters make them promising for optoelectronic applications. Recent studies have found that the responsivities and detectivities of MAPbI3 photodetectors were improved to be 60 mA·W-1 and 1012 Jones, respectively, by designing MoS2/MAPbI3 and WS2/MAPbI3 heterostructures.

11,12

Zeng et al.

24

demonstrated that the responsivity of MS2/CsPbBr3 heterostructure was 4.4 A·W-1 which was far higher than those of organic-inorganic perovskites and their heterostructures due to the efficient charge transfers at MS2/CsPbBr3 heterostructure 25.

Jiang et al.

26,27

reported that MS2/CsPbBr3 heterostructure strongly enhanced the

photoluminescence quantum yield of CsPbBr3 because MS2/CsPbBr3 heterostructure demonstrates ultrafast interfacial energy transfer and interlayer excitons. Inspired by these, designing CsPbX3/MS2 (M=Mo, W) heterostructures is an attractive way to improve the electrical and optical properties of CsPbX3 perovskites. However, it should be noted that charge transfers usually occur at type-II heterostructures while energy transfers commonly appear at type-I heterostructures. Such incompatible phenomena are observed simultaneously at CsPbX3/MS2 heterostructures. Note that, experimental energy diagram for heterostructures usually neglects the interface dipoles and interface interactions.

28

Moreover, the energy diagram is dependent of

the interfacial structures which are difficult to be accessed directly in experiments. A theoretical investigation in atomistic and electronic levels provides an effective strategy to understand the heterostructures. However, few studies have been focused on the CsPbI3/MS2 (M=Mo, W) heterostructures yet. Moreover, understanding the naturally physical properties of heterostructures is the fundamental for the application of CsPbI3/MS2 (M=Mo, W) heterostructures. Thus, structural, electronic and optical



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properties of CsPbI3/MS2 (M=Mo, W) heterostructures with different configurations have been studied by density functional theory in this work. Calculation methods All calculations were performed by using density functional theory on the basis of projector augmented wave method implemented in the VASP code

29,30.

The

cut-off energy was set to be 400 eV. The convergence criterions were 1×10-5 eV for the self-consistent field energy and 0.01 eV/Å for the residual forces on each atom, respectively. The structure relaxation, heterostructure binding energies, and electronic structures were calculated by Perdew-Burk-Ernzerhof (PBE) exchange-correlation functional with additional van der Waals (vdW) interactions correction (Grimme-D2) 31.

On the basis of PBE-optimized structures, the band gaps were further corrected

using the screened Heyd-Scuseria-Ernzerh (HSE) hybrid density functional with the spin-orbital coupling (SOC). A vacuum of 15 Å was considered along z-direction to avoid artificial interlayer interactions. A 5×1×1 k-sampling generated by the Monkhorst-Pack scheme for the Brillouin zone was adopted. As to cubic CsPbI3 perovskite, monolayer MoS2 and WS2, their lattice parameters and electronic structures (obtained by PBE and HSE functionals) are shown in Figure S1, and consistent with previous results. For the CsPbI3/MS2 (M=Mo, W) heterostructures, they were composed of 1×5 supercell of CsPbI3 (001) surface and 2√2×6 supercell of MS2 (001) surface. Two typical CsPbI3 (001) surfaces were considered: one is the Pb-I termination and the other is the Cs-I termination, as displayed in Figure 1. The average lattice mismatches of CsPbI3/MS2 heterostructures are less than 1.30 %. To obtain the stable CsPbI3/MS2 (M=Mo, W) heterostructures, the binding energies of CsPbI3/MS2 heterostructures were calculated using the formula (1)

𝐸𝑏 = (𝐸ℎ𝑒𝑡𝑒𝑟𝑜𝑗𝑢𝑛𝑐𝑡𝑖𝑜𝑛 ― 𝐸𝑝𝑒𝑟𝑜𝑣𝑠𝑘𝑖𝑡𝑒 ― 𝐸𝑀𝑆2)/𝑁 where 𝐸ℎ𝑒𝑡𝑒𝑟𝑜𝑗𝑢𝑛𝑐𝑡𝑖𝑜𝑛, 𝐸𝑝𝑒𝑟𝑜𝑣𝑠𝑘𝑖𝑡𝑒

and

𝐸𝑀𝑆2

represent

the

energies

of

heterostructures， corresponding to the CsPbI3 surface and isolated monolayer MS2. N represents the interfacial area of CsPbI3/MS2 heterostructures.


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The charge density difference along the Z direction (Z) was characterized as

(𝑍) = (𝑍)𝑡𝑜𝑡𝑎𝑙 ― (𝑍)𝑝𝑒𝑟𝑜𝑣𝑠𝑘𝑖𝑡𝑒 ― (𝑍)𝑀𝑆2 where

(𝑍)𝑡𝑜𝑡𝑎𝑙,

(𝑍)𝑝𝑒𝑟𝑜𝑣𝑠𝑘𝑖𝑡𝑒,

and

(𝑍)𝑀𝑆2

are

charge

(2) densities

of

heterostructures, isolated perovskite surface and monolayer MS2, respectively. Results and Discussion Geometric structures Figure 2 illustrates the binding energies of CsPbI3/MS2 (M=Mo, W) heterostructures as functions of the interlayer separation. When the interlayer separations of CsPbI3/MoS2 heterostructures with Pb-I and Cs-I terminations and CsPbI3/WS2 heterostructures with Pb-I and Cs-I terminations are 3.40 Å, 3.20 Å, 3.40 Å,

3.20

Å,

respectively,

binding

energies

of

corresponding

CsPbI3/MS2

heterostructures reach to the lowest negative values (-0.021, -0.043, -0.044, -0.067 eV/Å2). It suggests that CsPbI3/MS2 heterostructures with such interlayer separations are stable and equilibrium. Moreover, these four CsPbI3/MS2 heterostructures are possible to be fabricated in experiments. Thus, all electronic properties of CsPbI3/MS2 heterostructures are calculated through such equilibrium phases. In addition, the lowest binding energies of CsPbI3/MS2 heterostructures with Cs-I terminations are lower than those of CsPbI3/MS2 heterostructures with Pb-I terminations, suggesting that CsPbI3/MS2 heterostructures with Cs-I terminations are more stable. 3.2 Electronic structures Before investigating the electronic structures of CsPbI3/MS2 (M=Mo, W) heterostructures, electronic structures of their isolated surfaces and bulk CsPbI3 are calculated by HSE functional, as demonstrated in Figure S1 and S2. It can be found that the electronic structures of bulk CsPbI3, monolayer MoS2 and WS2 calculated by PBE and HSE functionals are similar, except for the band gaps. The conduction band minimum (CBM) and valence band minimum (VBM) of bulk CsPbI3 are dominated by Pb p-orbitals and I p-orbitals, respectively. Both the CBM and VBM of monolayer MS2 are mainly consisted of M d-orbitals. Such characters are consistent with previous reports

14, 32.

Moreover, the effective electron masses of monolayer MoS2



Page 6 of 21

and WS2, and effective hole masses of bulk CsPbI3 are 0.48 m0, 0.35 m0, and 0.23 m0, respectively, consistent with available values

33, 34.

However, the direct band gaps of

bulk CsPbI3, monolayer MoS2 and WS2 obtained by PBE functional are 1.66 eV, 1.73 eV, and 1.94 eV, respectively, which are lower than the corresponding experimental values due to the negligible many-body effects of PBE functional

34-35.

The direct

band gaps of bulk CsPbI3, monolayer MoS2 and WS2 obtained by HSE functional are 2.08 eV, 2.23 eV, 2.45 eV, respectively, which are larger than the related experimental data although SOC has been taken into account, since HSE functional is usually overcorrected slightly the band gap of an intrinsic semiconductor

34-35.

Thus,

in order to accurately investigate the contact properties of CsPbI3/MS2 heterostructures, both PBE and HSE functionals are employed in the following section. As to the isolated CsPbI3 surfaces with Pb-I terminations, they also show direct band gaps of about 1.68 eV (obtained by PBE functional) and 1.95 eV (obtained by HSE functional). Moreover, their effective hole masses are about 0.21 m0. Their CBM and VBM are dominated by Pb p-orbitals and I p-orbitals, respectively, as shown in Figure S2. These characters are close to those of bulk CsPbI3. In the case of isolated CsPbI3 surfaces with Cs-I terminations, similar phenomena are also observed (Figure S2). However, the band gaps and effective hole masses are slightly larger than those of isolated CsPbI3 surfaces with Pb-I terminations, as listed in Table 1. In general, the lower effective mass means the faster carrier transport. In other words, Pb-I terminated CsPbI3 surface and monolayer WS2 exhibit higher hole and electron mobilities, respectively. When CsPbI3 surface and MS2 (M=Mo, W) monolayer contact to form CsPbI3/MS2 (M=Mo, W) heterostructures, the electronic structures of heterostructures seem to be a simple sum of these surfaces, irrespective of heterostructure configurations, as demonstrated in Figure 3. Moreover, the direct band gaps of CsPbI3 part and MS2 part of heterostructures are highly similar to the individual surfaces, as listed in Table 1. For example, the band gaps of MoS2 in the Pb-I and Cs-I terminated CsPbI3/MoS2 heterostructures obtained by HSE functional (PBE functional) are 2.17


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eV (1.73 eV) and 2.18 eV (1.78 eV), respectively, close to that of isolated monolayer MoS2 of about 2.23 eV (1.73 eV). It is interesting that all the values of effective hole masses of CsPbI3/MS2 heterostructures are slightly lower than those of corresponding isolated CsPbI3 surfaces and isolated bulk CsPbI3, as listed in Table 1. Such characters reveal that forming CsPbI3/MS2 heterostructures not only can preserve the excellent electronic and transport properties of MS2 monolayer, but also can passivate the CsPbI3 surfaces to slightly improve its transport performance to surpass that of bulk CsPbI3. These enhanced hole transport properties of CsPbI3 part coupling the excellent electron mobilities of MS2 monolayers make CsPbI3/MS2 heterostructures great potential to improve the photoconductors and photo-detectivities of CsPbI3 based optoelectronics devices. In addition, it should be noted that all CsPbI3/MS2 heterostructures exhibit indirect band gaps which are desirable for radiation detection. Moreover, the CBM and VBM of CsPbI3/MS2 heterostructures are dominated by the MS2 layer and CsPbI3 part, respectively, indicating type-II characteristic for CsPbI3/MS2 heterostructures. It suggests that charge transfers rather than energy transfers dominate the CsPbI3/MS2 heterostructures, which is consistent with Zeng et al.24 experimental reports and different to Jiang et al.27 experimental results. One main reason may be that the band gap of CsPbI3 is enlarged upon forming quantum dots in the Jiang et al. experiment. In general, the type-II heterostructure can drive the photogenerated electrons and holes to move in opposite directions, resulting in spatial separation of electrons and holes on different sides of heterostructures. Thus, constructing CsPbI3/MS2 heterostructures would be an effective way to promote charge separation for improving the photoelectric conversion efficiency of CsPbI3 based photodetectors and other optoelectronic devices. In the type-II heterostructures, the differences between the CBMs of their components (viz. conduction band offset, Δc) are crucial for electron transport and the differences between the VBMs of their components (viz. valence band offset, Δv) are crucial for hole blocking. Hence, the band levels of CsPbI3/MS2 (M=Mo, W) heterostructures are explored in Figure 3. The detailed band offsets are listed in Table 2. The Δc (Δv) calculated by HSE functional are 0.66 (0.77), 0.24 (0.46), 0.23 (0.72),



and 0.02 (0.31) eV for CsPbI3/MoS2 heterostructures with Pb-I and Cs-I terminations, CsPbI3/WS2 heterostructures with Pb-I and Cs-I terminations, respectively. The large Δc allows free electron to move from perovskite to sulfide layers, and the large Δv promotes hole extracting from 2D layers to perovskite layers. Thus, compared to the Cs-I terminated CsPbI3/MS2 heterostructures, the Pb-I terminated CsPbI3/MS2 heterostructures may be particularly useful for decreasing dark current and improving open circuit voltage due to their larger Δc and Δv, although the Cs-I terminated CsPbI3/MS2 heterostructures are more stable than Pb-I terminated CsPbI3/MS2 heterostructures. In addition, among these heterostructures, the heterostructure constructed by monolayer MoS2 and Pb-I terminated CsPbI3 surface shows the greatest performance due to its largest Δc (0.60 eV) and Δv (0.77 eV), although monolayer WS2 shows higher transport properties than monolayer MoS2. Similar characters are observed for the Δc (Δv) calculated by PBE functional, except for the lower band offset values, as listed in Table 2. Such performance discrepancies can be further elucidated by charge density difference. As demonstrated in Figure 4, electrons are mainly accumulated at the MS2 parts and holes are primarily accumulated at the perovskite part, irrespective of terminations. Moreover, stronger charge transfers have been observed at the Pb-I terminated CsPbI3/MS2 heterostructures than Cs-I terminated CsPbI3/MS2 heterostructures. However, CsPbI3/WS2 heterostructures show more efficient charge transfers than those of CsPbI3/MoS2 heterostructures. This is because the electrostatic potential difference (ΔEP, marked in Figure 5) between CsPbI3 surface and monolayer WS2 is larger than that between CsPbI3 and monolayer MoS2, as demonstrated in Figure 5. Note that, there are obviously negative charges accumulating in the space charge region of these heterostructures, as displayed in Figure 4, which may result in evident interfacial tunnel barrier. The tunnel barrier heights (ΔTs) which determine the electron transport efficiency36 are marked in the electrostatic potential of CsPbI3/MS2 heterostructures, as exhibited in Figure 5. It shows that the Δ Ts of Pb-I terminated CsPbI3/MS2 heterostructures are lower than those of Cs-I terminated CsPbI3/MS2 heterostructures.


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Moreover, Pb-I terminated CsPbI3/MoS2 heterostructures exhibit lower ΔTs than Pb-I terminated CsPbI3/WS2 heterostructures. When the ΔT is lower, the electron transport efficiency is higher. In other words, Pb-I terminated CsPbI3/MoS2 heterostructures possess the highest electron transport efficiency. That is why Pb-I terminated CsPbI3/MoS2 heterostructures demonstrate higher performances than Pb-I terminated CsPbI3/WS2 heterostructures, although Pb-I terminated CsPbI3/MoS2 heterostructures have weaker charge transfer than Pb-I terminated CsPbI3/WS2 heterostructures, as above talked about. Thus, among these heterostructures, Pb-I terminated CsPbI3/MoS2 heterostructures are most advantageous to electronic transmission and diffusion. The detailed sketches of electron transport at these CsPbI3/MS2 heterostructures are displayed in Figure 6. 3.3 Optical properties Except for the electronic structures, the optical properties are important to the performance of perovskite photoelectric devices. According to the Bethe-Salpeter equation, the large difference between me and mh (as listed in Table 1) leads to a small exciton binding energy and suggests fast photo-induced carrier dissociation, which is crucial to the application in optoelectronics. Thus, Pb-I terminated CsPbI3/MS2 (M=Mo, W) heterostructures exhibit lower exciton binding energies and faster photo-induced carrier dissociations than those of Cs-I terminated CsPbI3/MS2 (M=Mo, W) heterostructures. To further investigate the optical properties of CsPbI3/MS2 heterostructures, Figure 7 demonstrates the absorption spectra of CsPbI3/MS2 heterostructures and corresponding isolated surfaces. The absorption coefficient of CsPbI3 surface is up to 105 cm-1, and higher than that of monolayer MS2. Pb-I terminated CsPbI3 surfaces show higher absorption coefficients than Cs-I terminated CsPbI3 surfaces in the infrared and visible regions, while an opposite character in the ultraviolet region. Upon forming CsPbI3/MS2 heterostructures, the absorption in the infrared region further increases, since an additional absorption can occur at the conduction band offset and valence band offset of heterostructure. Moreover, the absorption of Pb-I terminated CsPbI3/MS2 heterostructures is also



improved in the ultraviolet region, while that of Cs-I terminated CsPbI3/MS2 heterostructures is enhanced in the visible region. That is because the larger band offsets for Pb-I terminated CsPbI3/MS2 heterostructures lead to additional VBM of CsPbI3→CBM of MS2 and VBM of MS2→CBM of CsPbI3 absorption with high energies, while the relative smaller band offsets for Cs-I terminated CsPbI3/MS2 heterostructures lead to additional VBM of CsPbI3→CBM of MS2 and VBM of MS2→CBM of CsPbI3 absorption with low energies. Compared to CsPbI3/WS2 heterostructures, forming CsPbI3/MoS2 heterostructures has larger influences on the absorption of CsPbI3 surfaces because monolayer MoS2 shows a higher absorption than that of monolayer WS2. Therefore, monolayer MS2, especially MoS2, can effectively tune and improve the absorption of CsPbI3 surfaces by forming heterostructures.

Conclusion In summary, we systematically studied the structural, electronic and optical properties of CsPbI3/MS2 (M=Mo, W) heterostructures with different stackings, i.e., Cs-I and Pb-I terminations, via first-principles calculations. All these four heterostructures exhibit type-II band characters with charge transfers rather than energy transfers. The electronic structures and transport properties of both CsPbI3 surface and monolayer MS2 in the CsPbI3/MS2 heterostructures are consistent with those of isolated counterparts, irrespective of heterostructure structure. Note that, heterostructure structures have significant influences on the electronic and optical performance of CsPbI3 devices. Cs-I terminated CsPbI3/MS2 heterostructures are more stable than Pb-I terminated CsPbI3/MS2 heterostructures. However, Pb-I terminated CsPbI3/MS2 heterostructures show larger band offset, indicating larger open circuit voltage and lower dark current. Pb-I terminated CsPbI3/MS2 heterostructures can improve the light absorption in the infrared and ultraviolet regions, while Cs-I terminated CsPbI3/MS2 heterostructures can enhance the light absorption in the infrared and visible regions. In addition, although monolayer WS2 possesses more efficient electron transport, CsPbI3/MoS2 heterostructures demonstrate


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higher electronic and absorption performances than CsPbI3/WS2 heterostructures due to the larger electrostatic potential difference and lower tunneling barriers between CsPbI3 surface and monolayer MS2, and higher absorption of monolayer MoS2. Our findings provide a deep understanding of CsPbI3/MoS2 heterostructures, and suggest an effective way to improve the performance of perovskite photovoltaic and optoelectronic devices. ASSOCIATED CONTENT Supporting Information Additional Tables and Figures: Electronic structures of CsPbI3 bulk and surfaces, monolayer MoS2 and WS2 calculated by HSE and PBE functional. AUTHOR INFORMATION Corresponding Author *E-mail:

[email protected]; [email protected]

Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundation of China (Grant 61604119, 61704131, and 61804111); Natural Science Foundation of Shaanxi Province (Grant 2017JQ6002, and 2017JQ6031); Initiative Postdocs Supporting Program (Grant BX20180234); Project funded by China Postdoctoral Science Foundation (Grant 2018M643578); Fund of the State Key Laboratory of Solidification Processing in NWPU (Grant SKLSP201857, SKLSP201804). The numerical calculations in this paper have been done on the HPC system of Xidian University.

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Tables and Figures Table 1 Band gaps and effective masses of CsPbI3 and MS2 surfaces in CsPbI3/MS2 (M=Mo, W) heterostructures with different terminations obtained by HSE functional (values obtained by PBE functional are added in the parentheses). These values of corresponding isolated surfaces are added for comparison. PbI-MoS2

CsI-MoS2

PbI-WS2

CsI-WS2

heterostructure

heterostructure

heterostructure

heterostructure

Isolated surface Structures Pb-I

Cs-I

MoS2

WS2

Pb-I

MoS2

Cs-I

MoS2

Pb-I

WS2

Cs-I

WS2

1.95

1.99

2.23

2.45

2.06

2.17

1.96

2.18

1.90

2.39

2.04

2.33

(1.68)

(1.74)

(1.73)

(1.94)

(1.56)

(1.73)

(1.58)

(1.78)

(1.41)

(1.85)

(1.59)

(1.90)

me (m0)

-

-

0.48

0.35

-

0.48

-

0.46

-

0.34

-

0.32

mh (m0)

0.21

0.28

-

-

0.18

-

0.24

-

0.16

-

0.23

-

Band gaps (eV)

Table 2 Conduction band offset (Δc) and valence band offset (Δv) of CsPbI3/MoS2 heterostructures calculated by HSE and PBE functionals. HSE functional Δc (eV)

PBE functional

Δv (eV)

Δc (eV)

Δv (eV)

Pb-I terminated CsPbI3/MoS2

0.66

0.77

0.60

0.77

Cs-I terminated CsPbI3/MoS2

0.24

0.46

0.26

0.46

Pb-I terminated CsPbI3/WS2

0.23

0.72

0.21

0.65

Pb-I terminated CsPbI3/WS2

0.02

0.31

0.01

0.32


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Figure 1. (a)-(c) Top and side views of CsPbI3/MS2 (M=Mo, W) heterostructures with Pb-I termination. (b)-(d) Top and side views of CsPbI3/ MS2 heterostructures with Cs-I termination.

Figure 2. Binding energies of heterostructures as functions of the interlayer separations for CsPbI3/MS2 (M=Mo, W) heterostructures. Arrows indicate the positions of heterostructures with lowest binding energies.



(a)

(c)

(b)

(d)

Figure 3. Projected band structures of CsPbI3/MoS2 heterostructures with (a) Pb-I and (b) Cs-I terminations, and CsPbI3/WS2 heterostructures with (c) Pb-I and (d) Cs-I terminations. Green, blue, red and dark yellow points represent the contribution of Pb, I, Mo (W), and S atoms, respectively. The short lines in the right planes are the band edges of perovskite and MS2 parts of heterostructures.


Page 18 of 21

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(a)

(b)

(c)

(d)

Figure 4. Planar-averaged charge density differences of CsPbI3/MoS2 heterostructures with (a) Pb-I and (b) Cs-I terminations, CsPbI3/WS2 heterostructures with (c) Pb-I and (d) Cs-I terminations along the vertical z-direction normal to the heterostructures. The red and blue colors indicate electron accumulation and depletion, respectively. (a)

(b)

(c)

(d)

Figure 5. Planar-averaged electrostatic potentials of CsPbI3/MoS2 heterostructures with (a) Pb-I and (b) Cs-I terminations, and CsPbI3/WS2 heterostructures with (c) Pb-I and (d) Cs-I terminations along the vertical z-direction normal to the heterostructures. The work function differences between MS2 and CsPbI3 surfaces in the heterostructures are marked by the red arrows. The tunnel barrier heights of CsPbI3/MS2 heterostructures are marked by the black



arrows.

Figure 6. Transport diagrams of CsPbI3/MS2 (M=Mo, W) heterostructures with different configurations. The top and bottom of rectangles represent the values of CBM and VBM, respectively. The red and blue rectangles represent the energy level of CsPbI3 and MS2 parts of CsPbI3/MS2 heterostructures, respectively.

(a)

(b)

Figure 7. Calculated absorption coefficients of isolated CsPbI3 surfaces, isolated monolayer MS2 (M=Mo, W), and CsPbI3/MS2 heterostructures.


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TOC：


Theoretical Studies of Electronic and Optical Behaviors of All

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