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How the Structures and Properties of 2D Layered Perovskites MAPbI3 and CsPbI3 Vary with the Number of Layers Lei Zhang, and WanZhen Liang J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b03005 • Publication Date (Web): 16 Mar 2017 Downloaded from http://pubs.acs.org on March 17, 2017

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TheJournalofPhysicalChemistryLetters

How the Structures and Properties of 2D Layered Perovskites MAPbI3 and CsPbI3 Vary with the Number of Layers Lei Zhang and WanZhen Liang∗ State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, P. R. China E-mail: [email protected]

∗ To

whom correspondence should be addressed

1 ACSParagonPlusEnvironment


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Abstract This work aims at exploring the intrinsic properties of 2D-layered perovskites, (PEA)2 PbI4 (N) and Cs2 PbI4 (N), and demonstrating how their structures and properties vary with N. The results reveal that both (PEA)2 PbI4 (N) and Cs2 PbI4 (N) are direct bandgap semiconductors, their band/optical gaps and exciton-binding energies vary linearly with 1/N at N ≥ 3, and the effective masses slowly varies with N. Compared to the bulk phases, the structures of ultrathin (PEA)2 PbI4 (N) are more flexible and deformable than Cs2 PbI4 (N). The giant spin-coupling effect greatly decreases the band gaps of both 2D materials, however it only induces the spin splitting in the bands of (PEA)2 PbI4 (N). This work suggests that the ultrathin 2D materials can be a potential candidate for nano optoelectronic devices, and that the nanoplates with N ≥ 3 could have similar performances with bulk materials in the carrier migration and exciton separation so that they can be effectively applied in photovoltaic cells.


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Inspired by the high performance of graphene 1 and the methodology developed in preparing ultrathin atomic layer materials, 2 many other two-dimensional (2D) materials such as transition metal dichalcogenides, 3–5 and black phosphorus 6,7 have been synthesized and intensively studied. 2D materials, especially the 2D semiconductor materials, possess the fascinating electronic and optical properties and potential applications that emerge from 2D confinement. 8,9 Each layered material, when thinned to its physical limits, exhibits novel properties different from its bulk counterpart. Hybrid organic-inorganic perovskites, a kind of layered semiconductors with intriguing optoelectronic and charge-transport properties, can also be made into ultrathin 2D materials which have much stronger photoluminescent properties, 10–12 and better moisture stability than their bulk counterparts. 13–16 Besides, 2D-layered perovskites have many other excellent properties, such as the flexible and deformable structures and the tunable optical and electronic properties. Nowadays, many strategies have been proposed to fabricate 2D-layered perovskite materials. For example, Niu et al. 17 successfully produced ultrathin 2D perovskite flakes by using micromechanical exfoliation, Zhang and co-workers 18 reported a combined solution process and vaporphase conversion method to produce high quality perovskite nanoplates, and Xiong’s group 19 synthesized perovskite nanoplates by using chemical vapor deposition method as well. More recently, layered crystals of (C4 H9 NH3 )2 PbBr4 have been successfully synthesized by using a solutionprocessed method and have been exhibited to possess the photoluminescence internal quantum efficiency of 26%, much higher than that of bulk phase (< 1%) at room temperature. 10 Theoretical studies on ultrathin 2D-layered perovskites were mainly focused on the intrinsic properties and defect effects on the properties, or on designing new 2D materials through partially replacing the metal and cations in crystal structures so that the band structures, carrier migration and other related properties can satisfy the requirement of photoelectric applications. For example, Yakobson’s group 20 has systematically investigated the structural stabilities and electronic properties of 2D halide perovskites. It was found that 2D halide perovskites have better energetic stability than 3D halide perovskite and their bandgaps can be tuned by changing organic cations, central metal ions as well as different halogen. Pandey et al. 21 has studied the effect of differ-



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ent defects on the band structure of isolated monolayers of the organometallic halide perovskites (C4 H9 NH3 )2 MX2 Y2 and found that the most common defects only introduced shallow or no states in the band gap, indicating that these atomically thin 2D perovskites are likely to be defect tolerant. Liu and co-workers 22 has predicted unique properties of defects in 2D perovskites by first-principles calculations and argued that the line defects with fixed orientation could be tuned from electron acceptors to inactive sites by varying synthesis conditions. The 2D-layered perovskites are essentially natural quantum wells with charge carriers mainly confined in the 2D crystal planes, and they possess few interlayer electronic interactions. As the layer thickness varies, their structures and properties should change. It is that the dimensional effect of the materials should play a role on their intrinsic properties. Additionally, the thin 2D-layered perovskites normally have a tetragonal or orthorhombic structure and are inherently more flexible and deformable. The flexible and deformable geometries also influence their optical and electronic properties. To our best knowledge, so far, the tendency of structures/properties varied with the layer thickness, and the characteristic length scale for the transformation from a two-dimensional case to the three-dimensional limit are still unknown. In the present work, we performed a first-principles theoretical investigation on the intrinsic properties and the structureproperty relationships of 2D-layered perovskites with different layer thickness. This work aims at demonstrating the dependence of structures and properties on the number of layers N. One of our key interests is the characteristic length scale for the transformation from a two-dimensional case to the three-dimensional limit. Two types of 2D-layered perovskites MAPbI3 and CsPbI3 will be investigated. Hybrid perovskites are defined as any compound with the ABX3 crystal structure, consisting of corner-sharing BX6 octahedra with the A component neutralising total charge. A is a small cation such as organic cation or Cs+ . B is the metal ion such as Pb2+ or Sn2+ , and X is a halide anion (Cl− , Br− , or I− ). Generally, the A doesn’t directly play a major role in determining the band structure, but its size is important. A larger or smaller A cation can cause the whole lattice to expand or contract, and subsequently change the band structure. By incorporating large cations, one can


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transform 3D to 2D motifs. The 2D-layered materials have a general formula of (RNH3 )2 AN−1 BN X3N+1 . 13–16 R is a long-chain alkyl or aromatic group such as C6 H5 (CH2 )2 . The variable N indicates the number of the metal cation layers between two layers of the organic chains. And the two layers of organic cations cap both sides to balance the charge. At first, we constructed a series of hybrid organic-inorganic MAPbI3 layered compounds, (PEA)2 MAN−1 PbN I3N+1 (hereinafter referred to as (PEA)2 PbI4 (N)). (PEA)2 PbI4 (N), cut from the bulk tetragonal MAPbI3 crystal structure, expose the MAI-terminated surfaces (110). 23 The thicknesses of these slabs are varied from 1 to N inner layers, plus two symmetric organic layers on + both nanoplates sides by replacing MA cation (CH3 NH+ 3 ) with PEA cation (C6 H5 (CH2 )2 NH3 ).

Since the size of A cation in the ABX3 crystal structure plays a determining role in the optical and electronic properties of perovskites, CsPbI3 layered compounds, CsN+1 PbN I3N+1 (hereinafter referred to as Cs2 PbI4 (N)), have also been investigated. Cesium has a smaller effective ionic radius compared to MA. Recently, the experimental works 24–26 have found that adding a dash of cesium to the perovskite recipes can increase the chemical stability of perovskite-based solar cells and cesium-based perovskite may fortify next-generation solar cells. 27 Cs2 PbI4 (N) series, are the product of slicing the CsPbI3 crystal along the (001) plane, 28 where the vacuum layer thicknesses are set to 15 Å in order to eliminate the interaction between the surfaces. The schematic diagrams of 4-layered (PEA)2 PbI4 (N) and Cs2 PbI4 (N) are shown in Figure 1. Then, we calculated the band structures, density of states, optical absorption spectra, effective masses, exciton-binding energies, and the Rashba spin-splitting parameters, etc., by the firstprinciples approaches. The periodic electronic structure calculations were carried out within the projected augmented wave plane-wave basis implemented in the Vienna Ab-initio Simulation Package. 29–31 To account for the weak interactions of the layered perovskites, the zero damping DFTD3 of Grimme, 32 an approximate vdW correction method, was applied to optimize the geometries. An energy cutoff of 520 eV was employed. Compounds (PEA)2 PbI4 (N) with different layers of N = 1 − 2, 3 − 4, ∞, were modeled with 4 × 4 × 2 , 2 × 2 × 1 and 6 × 6 × 4 Γ-center grids for the κ -point sampling, respectively. Meanwhile, a 4 × 4 × 1 grid of κ -points was employed for



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Figure 1: The structure diagrams of 4-layered (PEA)2 PbI4 (4) cell (left) and Cs2 PbI4 (4) (right). the calculations of all Cs2 PbI4 (N = 1 − 5) slabs. The electronic and photoelectric properties of (PEA)2 PbI4 (N) at Γ-point of the Brillouin zone were carried out at the DFT level with the hybrid functional PBE0 with inclusion of the spin-orbit coupling (SOC) effect, which has been shown to have a significant effect on band gap of hybrid organic-inorganic lead halide perovskite, especially on the conduction band. 33 Moreover, the electronic and photoelectric properties of Cs2 PbI4 (N) were calculated at R-point of the Brillouin zone due to the minimum band gaps occurred at R, which is in agreement with previous theoretical study. 34 The PBE0 functional includes a fraction

α , of screened HF exchange to improve the derivative discontinuity of the Kohn-Sham potential for integer electron numbers. Here, we set α = 0.248 for (PEA)2 PbI4 (N) and α = 0.35 for Cs2 PbI4 (N) since those values can yield the experimentally-measured band gaps of 1.55 eV for MAPbI3 (I4CM) 35 and of 1.73 eV for CsPbI3 , 36 respectively. And the band structures of bulk MAPbI3 and CsPbI3 are shown in Figure S1 in detail. The geometries of (PEA)2 PbI4 (N=1-4) and Cs2 PbI4 (N=1-5) have been optimized, and the optimized structural parameters and lattice constants are shown in Table 1. It is observed that the cell phases of (PEA)2 PbI4 (N) change from monoclinic to orthorhombic phase as N increases, and the structures of quasi-2D-layered (PEA)2 PbI4 (N) are flexible and deformable. The optimized 2D structures exhibit a remarkable structure relaxation and lattice expansion in contrast to the bulk


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Table 1: The calculated and experimentally-measured lattice constants, Pb-I-Pb bond angles and Pb-I bond lengths. (PEA)2 PbI4 (N) MAPbI3

23

1-layer

2-layer

Cs2 PbI4 (N)

3-layer

4-layer

CsPbI3

a(Å)

8.85

12.22

12.41

12.55

12.70

b(Å)

8.85

12.51

12.65

12.62

12.78

c(Å)

12.64

20.01

26.20

32.88

38.47

α (◦ )

79.8

86.4

84.6

86.8

β (◦ )

86.1

88.0

84.8

91.4

90.7

89.4

89.7

89.70

γ (◦ )

90

28

1-layer

2-layer

3-layer

4-layer

5-layer

6.28

6.39

6.39

6.39

6.39

6.39

6.28

21.39

27.78

34.18

40.57

46.96

90.0

90.0

90.0

90.0

90.0

90.0

Pb-I(Å)

3.05-3.25

3.25

3.15-3.35

3.15-3.35

3.15-3.35

3.14

3.15

3.05-3.25

2.95-3.25

2.95-3.25

2.95-3.25

Pb-I-Pb(◦ )

163

143.33

147.66

150.41

156.34

180.0

180.0

180.0

180.0

180.0

180.0

phases, which could be responsible for the experimentally observed features, such as a shifted band edge emission. 10 It is also noted that the bond lengths of Pb-I in (PEA)2 PbI4 (N) are slightly larger than those in Cs2 PbI4 (N) because of the big size of organic cations. In (PEA)2 PbI4 (N), the organic cations MA+ can rotate freely in the cavities between [PbI6 ]4− octahedra and have larger size compared with Cs+ cations. The distribution of Pb-I bond length tends to be uniform for both (PEA)2 PbI4 (N) and Cs2 PbI4 (N) with the increase of N, which results in the band gap varying tardily with N when the layer thickness is large enough. The change of Pb-I-Pb bond angles in (PEA)2 PbI4 (N) is remarkable compared with those of bulk MAPbI3 , which reveals that the [PbI6 ]4− octahedra layers in layered structures are highly distorted, accounting for optical and electronic changes reported in hybrid perovskite systems. 37,38 Table 2: The bandgaps (in eV) of 2D-layered perovskites with different thickness by different DFT XC functionals with or without SOC effect, respectively. N PBE

PBE+SOC

PBE0+SOC

∞

1

2

3

4

5

6

7

(MA)2 PbI4

2.24

2.05

1.92

1.82

1.75

1.68

1.62

Cs2 PbI4 (N)

2.20

2.18

2.12

1.90

1.82

1.35

0.42

0.19

(MA)2 PbI4

1.52

1.28

1.06

1.00

Cs2 PbI4 (N)

0.92

0.76

0.59

0.50

(PEA)2 PbI4 (N)

2.60

2.40

2.21

2.00

Cs2 PbI4 (N)

2.82

2.53

2.31

2.10

1.50

0.57

1.50 1.98

1.57

The calculated band gaps of (PEA)2 PbI4 (N) and Cs2 PbI4 (N) based on different DFT XC func7 ACSParagonPlusEnvironment


tionals (PBE and PBE0) with and without inclusion of SOC effect were collected in Table 2. It is found that their band gaps decrease with the increase of N and approach to the band gaps of corresponding bulk phases, 35,36,39,40 in accord with experimental observations. 15 PBE0+SOC predicts that the band gaps of (PEA)2 PbI4 (N) and Cs2 PbI4 (N) vary from 2.60 (N = 1) to 1.50 eV (N → ∞) and from 2.82 to 1.57 eV, respectively. Since it is hardly possible to calculate the band gaps of (PEA)2 PbI4 (N > 4) by PBE0 because of the large computational costs, we calculated the band gaps of (PEA)2 PbI4 (N) by PBE functional. To have a clear dependent relationship between the band gaps and N, we plot the data in Figure 2. Obviously, the linear dependence of (E(N) − E(∞)) ∝ 1/N is hold for two types of layered materials except the nanoplates with N ≤ 2, which drastically deviate the straight lines, indicating that the ultrathin nanoplates with N ≤ 2 possess quite different geometric and electronic structures. These results verify that the energy gaps of photosensitive perovskite materials can be tuned through changing the layered thickness and the cation size. 2.3 2.2

(PEA)2PbI4(N) Cs2PbI4(N)

2.1 2.0

Bandgap (eV)

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1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2

0.0

0.1

0.2

1/N

0.3

0.4

0.5

Figure 2: The band gaps vary with 1/N for (PEA)2 PbI4 (N) (black line) and Cs2 PbI4 (N) (red line) calculated by PBE functional.

Figure 3 shows the calculated band structures of (PEA)2 PbI4 (N=1-4) by PBE+SOC. For the comparison, those of MAPbI3 based on PBE with and without SOC effect have been demonstrated, too. It is noted that the energy of uppermost valence band increases as N increases whereas the


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N=2

N=1

N=4

N=3

MAPbI3

MAPbI3

w/ soc

w/o soc

2.0

Energy(eV)

1.5

1.0

0.5

0.0

-0.5

-1.0

-1.5

X

X

Y

Y

Figure 3: The calculated band structures of (PEA)2 PbI4 (N=1-4) by PBE+SOC, and those of MAPbI3 by PBE with and without SOC.

N=1

N=2

N=3

N=4

N=5

CsPbI

CsPbI

3

3

2.0 1.5

Energy(eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.0 0.5 w/o soc

w/ soc

0.0

-0.5 -1.0 -1.5

X

R Y

R

R

R

R

R

X

R

Y

Figure 4: The calculated band structures of Cs2 PbI4 (N=1-4) by PBE+SOC, and those of CsPbI3 by PBE with and without SOC.



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energy of undermost conduction band reduces. The energy of valence band maximum(VBM) varies from −0.75(N = 1) to −0.5(N = 4) eV, and that of conduction band minimum (CBM) varies from 0.75 (N=1) to 0.5 eV (N=4), leading to the decrease of band gaps. Meanwhile, we observe that the bands near VBM become denser than those near CBM as N increases. A giant SOC effect appears in band structures of hybrid organic-inorganic perovskites, it significantly reduces the band gaps and splits both the valence and conduction bands. The band splitting can be explained by the Rashba-Dresselhaus effects. 41,42 Since the structures of hybrid organic perovskites don’t have the inversion symmetry, the spin degeneracy condition is no longer valid except for high symmetry point of the structure leading to a band splitting. Not like the bulk phase which has the same Rashba spin splitting along Γ→Y and Γ→X directions, for (PEA)2 PbI4 (N=1-4), Rashba spin splitting along the direction of Γ→Y is stronger than along Γ→X. By following the work of Even et al., 43 we calculated the Rashba parameter λR (defined as

ΔE 2κR ,

where κR is the momentum shift and

ΔE is the energy splitting) for the quasi-2D systems with a C2v symmetry. The calculated values are shown in Table S1. Along Γ→Y, λRV BM increases from 0.02 to 0.62 eV·Å, while λRCBM increases from 0.07 to 1.0 eV·Å , reflecting that the spin splitting increases as N increases and it is stronger in the conduction band than in the valence band. The unique spin-dependent properties of 2D-layered (PEA)2 PbI4 (N) provide potential applications in nanoelectronic devices 44 or spintronics. 45,46 Figure 4 shows the calculated band structures of Cs2 PbI4 (N)(N=1-5) with PBE+SOC. Compared to (PEA)2 PbI4 (N), the first appreciably difference is that there is no spin-spliting for all 2D-layered Cs2 PbI4 (N) because of their undestroyed high symmetry of D4h . The SOC effect only reduces the band gaps of Cs2 PbI4 (N). The other difference is that the positions of VBMs of Cs2 PbI4 (N) are hardly affected by the thickness and the layer thickness affects those of CBMs significantly. The bands near the CBM are quite steep in contrast to those near the VBM, indicating that the electrons in Cs2 PbI4 (N) can be transferred more quickly than the holes. The DOSs of (PEA)2 PbI4 (N=1-4) and Cs2 PbI4 (N=1-5) nanoplates have been calculated and shown in Figure 5(a) and Figure 5(b), respectively. It is found that the DOSs of (PEA)2 PbI4 (N) series whose CBM is mainly composed of Pb6p and VBM primarily consisted of I5p (see Figure S2)


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have the similar electronic structures, and the organic cations don’t play a major role in determining the band structure, which could further be proven by partial charge densities shown in Figure S3. Similarly, Cs2 PbI4 (N) series have the same pattern. As N increases, the DOS in the VBM increases remarkably but it changes slowly in the CBM, indicating that the thickness has a larger influence on VBM than on CBM for (PEA)2 PbI4 (N). And we found that the CBM of (PEA)2 PbI4 (N) is mainly composed of the inside Pb atoms of (PEA)2 PbI4 (N) whereas VBM is contributed by the surface atoms through analysis of partial charge densities, therefore, the layer number has a larger effect on VBM than CBM of (PEA)2 PbI4 (N). Furthermore, the layer number slightly affects the CBM and VBM of Cs2 PbI4 (N).

Figure 5: (a)/(b) The DOSs and (c)/(d) the absorption spectra of (PEA)2 PbI4 (N=14)/Cs2 PbI4 (N=1-5), respectively. All calculations were carried out based on PBE0+SOC. In addition, we have calculated absorption spectra of these 2D-layered perovskites to explore their optical properties (see Figure 5(c) and Figure 5(d)). It is observed that all (PEA)2 PbI4 (N) and Cs2 PbI4 (N) series have high extinction coefficients and good responses to solar spectrum, reflecting promising potentials in solar cells and other optoelectronic devices, such as perovskite light emitting diodes. 47,48 The optical gap of (PEA)2 PbI4 (1) was measured by Ishihara, 40 and it is 11 ACSParagonPlusEnvironment


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2.57 eV for a staggered arrangement, in accord with our calculation. Like the tendency of band gaps in terms of N, the optical gaps decrease with the increase of N and approach to the values of bulk phases at N → ∞.

Figure 6: (a) The calculated values of Rashba spin-splitting for (PEA)2 PbI4 (N), (b) effective electron and hole masses, (c) dielectric constants (ε∞ ), and (d) the exciton-binding energies Eb of (PEA)2 PbI4 (N=1-4) and Cs2 PbI4 (N=1-5), respectively. It is well-known that carrier mobilities are closely related to the effective masses of carriers. Next we calculated the effective masses of (PEA)2 PbI4 (N) (N=1-4) and Cs2 PbI4 (N) (N=15) series by fitting the energy dispersions of VBM and CBM to parabolic functions, 49,50 12 ACSParagonPlusEnvironment

1 m∗ii

=

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1 ∂ 2 En (κi ) h¯ 2 ∂ κi2

(i = x, y, z). Table S2 presents the calculated results of (PEA)2 PbI4 (N) by PBE+SOC,

where mxx , myy and mzz correspond to the components in Γ-X, Γ-Y and Γ-Z directions, respectively. Due to the existence of big organic phenethylamine layers, the carriers transfer along Zdirection is prohibited and thus the values of mzz are infinite. It is noted that bulk MAPbI3 has the smallest effective electron mass (mc ) of 0.16 and hole mass (mv ) of 0.17 , respectively, indicating the high mobility of photo-generated carriers in bulk phase. The average effective electron masses of (PEA)2 PbI4 (N) decrease from 0.221(N = 1) to 0.209(N = 4) and the effective hole masses change from 0.357(N = 1) to 0.268(N = 4), indicating that the carriers transfer slightly slowly in low dimensional perovskite materials compared with bulk phase. Moreover, it could be found that all mc are smaller than mv in layered perovskites, indicating that the electron transfer is faster than hole, in accord with the previous theoretical predications. 50–52 The calculated mc and mv of Cs2 PbI4 (N) are summarized in Table S3. It is found that the values of mxx and myy in Cs2 PbI4 (N) are same because Cs2 PbI4 (N) are isotropic. The tendency of effective masses versus N in Cs2 PbI4 (N) series is similar to that in (PEA)2 PbI4 (N) series as Figure 6 shows. The optoelectronic properties of the materials are reflected by the values of exciton-binding energies and dielectric constants. Lower exciton-binding energy leads to more effective exciton separation and higher PEC efficiency. In the end we calculated these two types of quantities. The exciton-binding energies were calculated by using a Wannier exciton model, 36 Eb = E1s · μ /ε∞2 . Here E1s is the energy of the fundamental state of hydrogen atoms, μ is the reduced exciton mass and ε∞ is the dielectric constant. The dielectric constants can be evaluated by using density functional perturbation theory. 53 Our calculated values together with the results from other works 54,55 are collected in Tables S2 and S3, respectively. It is observed that dielectric constants of both 2D-layered perovskite series have the similar varying patterns. They increase as N increases and gradually approach to the value of corresponding bulk phases. The larger the dielectric constants, the higher the conductivity for materials. And the insulativities become stronger when the 2D-layered perovskites become thinner. The calculated values of exciton-binding energies are controversial, which vary from 2 to 55 mev for bulk MAPbI3 . 56,57 Here, we obtained the binding



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energies of 5.5 and 85.4 meV for bulk MAPbI3 and (PEA)2 PbI4 (N=1), which closely matches the varied trend of experimental measurement, 55 although the absolute values of binding energies slightly deviate from experimental data. Due to the quantum confinement effect in the ultrathin 2D materials, the exciton-binding energy of (PEA)2 PbI4 (N=1) is the largest, which is in agreement with the experimental observation, 15 indicating a strongest PL emission in (PEA)2 PbI4 (N=1). The exciton-binding energies of Cs2 PbI4 (N) series change more dramatically than (PEA)2 PbI4 (N) series when N ≤ 3, and then they decrease gently with further increase of N, which indicates that the 2D-layered perovskites with N > 3 could have a similar properties with bulk materials to a certain extent. In summary, we have performed a first-principles study on the structures and properties of twotypes of 2D-layered perovskites (PEA)2 PbI4 (N) and Cs2 PbI4 (N), and demonstrated the tendency of structures and properties with the increase of layered thickness. The characteristic length scale for the transformation from a two-dimensional case to the three-dimensional limit is obtained. This work provides some full-scale insights into the correlation between the layered thickness and the structures/properties, and offers instructions to incorporate the 2D-layered materials with different thickness into the photoelectric devices. The following interesting conclusions can be achieved. (1) The structures of ultrathin quasi-2D hybrid organic-inorganic perovskites (PEA)2 PbI4 (N) are more flexible and deformable than Cs2 PbI4 (N). In Cs2 PbI4 (N), the high inverse symmetry of the structures can be well preserved so that the SOC effect only remarkably decreases the band gaps and no spin-splitting phenomenon appears on their band structures whereas in (PEA)2 PbI4 (N), the SOC effect not only appreciably reduces the band gaps but also leads to the spin-splitting in band structures. (2) Both types of 2D-layered perovskites are direct bandgap semiconductors, and their energy gaps increase with the decrease of the thickness, and the linear dependence of E ∝ 1/N is hold at N > 2. The energy gaps of ultrathin Cs2 PbI4 (N ≤ 2) drastically deviate the straight lines. (3) Both mc and mv diminish slowly as N increases, indicating that the effect of layer thickness on the mobility of photo-generated carriers of two types of 2D materials is not obvious and


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suggesting that the 2D-layered perovskites can be effectively used in photovoltaic cells. In both (PEA)2 PbI4 (N) and Cs2 PbI4 (N) series, mc is smaller than mv , indicating that electrons can be transferred more quickly than the holes in those 2D-layered perovskites. Besides, the mobilities of photo-generated carriers in Cs2 PbI4 (N) series are significantly higher than those in (PEA)2 PbI4 (N). (4) The dielectric constants of both types of 2D-layered perovskites increase greatly with the increase of N, leading to the exciton binding energy decreases as the layer thickness increases. The bulk phases of MAPbI3 and CsPbI3 have the smallest exciton binding energies, and thus possess the highest efficiency of carriers separation. The exciton-binding energies decrease dramatically as the N increases when N ≤ 3, they vary gently with further increase of N, indicating that Cs2 PbI4 (N=1) and (PEA)2 PbI4 (N=1) can be the best PL materials, and the 2D-layered perovskites with N > 3 could have a similar performance with bulk phases to a certain extent. The 2D-layered perovskites possess excellent structures and properties, and thus have promising potentials to be applied to nanoscale optoelectronic devices, whose optical and electronic properties can be tuned by changing the thicknesses of 2d-layered perovskites.

Supporting Information The calculated band structures of bulk MAPbI3 and CsPbI3 compounds, respectively. The PDOSs of 4-layered (PEA)2 PbI4 (N) and Cs2 PbI4 (N). The partial charge density for VBM−1, VBM, CBM and CBM+1 of (PEA)2 PbI4 (4) and Cs2 PbI4 (4). The calculated strength of the Rashba effect, λR (in units of eV·Å) for (PEA)2 PbI4 (N=1-4). The calculated effective masses (in units of the free electron mass), dielectric constants (ε∞ ) and exciton-binding energies (Eb (meV)) for (PEA)2 PbI4 (N=1-4, ∞) and Cs2 PbI4 (N=1-5, ∞), respectively.

Acknowledgement Financial supports from National Science Foundation of China (Grant Nos. 21290193, 21373163, and 21573177) are gratefully acknowledged.



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