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Electronic Supplementary Information for

Tin and Germanium Based Two-dimensional Ruddlesden−Popper Hybrid Perovskites for Potential Lead−Free

Photovoltaic and Photoelectronic Applications

Liang Ma,† Ming-Gang Ju,† Jun Dai,† and Xiao Cheng Zeng*,†,‡

†Department of Chemistry and Nebraska Center for Materials and Nanoscience, University

of Nebraska–Lincoln, Lincoln, Nebraska 68588, United States

‡Department of Chemical & Biomolecular Engineering and Department of Mechanical &

Materials Engineering, Lincoln, Nebraska 68588, United States

*Email: xzeng1@unl.edu

Electronic Supplementary Material (ESI) for Nanoscale.This journal is © The Royal Society of Chemistry 2018

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I. Computation Details

Structure relaxation and electronic structure calculations of the 2D hybrid perovskite BA2MAn-

1MnI3n+1 (M=Ge, Sn, Pb, n = 1–4) were performed with the Vienna Ab-initio Simulation Package

(VASP 5.4) package.1, 2 The exchange-correlation interactions were treated within the generalized

gradient approximation (GGA) parametrized by Perdew, Burke and Ernzerhof (PBE).3 The core–

electron interactions were described by the projected augmented wave (PAW) method.4, 5 The semi-

empirical Grimme’s DFT-D36 scheme was employed to describe the long-range dispersion

correction. It is found that the combination of PBE functional and Grimme’s D3 dispersion

correction is able to yield reasonable lattice constants of 2D hybrid perovskites, in good agreement

with the experimental lattice constants (Table S1).7, 8 To avoid the known bandgap underestimation

for semiconductors with using the GGA-PBE exchange correlation functional, more accurate but

computationally more expensive PBE0 hybrid functional was employed to compute the electronic

structures of Ge and Sn -based 2D hybrid perovskites, with the consideration of spin-orbit-coupling

(SOC) effect (see section II for details).9, 10 Orthorhombic cells were employed for all 2D hybrid

perovskites. Tetragonal cells were used for the bulk MAPbI3 and MASnI3,11 while a hexagonal cell

was chosen for the bulk MAGeI3 based on the experimental result.12 To minimize the interaction of

adjacent layers, a vacuum space of >14 Å was set along the c direction. A Gamma-centered 3×3×1

Monkhorst-Pack k-point sampling mesh was selected for hybrid functional calculation, while a much

denser mesh of 7×7×1 along with PBE functional were used for the structure relaxation and the

calculation of dielectric and optical properties.13 A 500 eV energy cutoff for the plane-wave basis

sets was chosen. The lattice constants and atomic positions were all relaxed until the maximum force

component was less than 0.01 eV/Å and the change of total energy was less than 10–5 eV.

Table S1. Computed lattice constants of 2D hybrid perovskites BA2MAn-1MnI3n+1 (M=Ge, Sn, Pb, n = 1–4) based on the PBE+D3 methods. The values in the brackets are taken from experimental data.

a Ref.7 b Ref.14

System BA2MAn-1GenI3n+1 BA2MAn-1SnnI3n+1 BA2MAn-1PbnI3n+1

Lattice constant a b a b a b

n=1 8.473 (8.722)a

8.168 (8.272)a

8.726 (8.837)a

8.500 (8.619)a

8.634 (8.863)a

8.617 (8.682)a

n=2 8.439 8.459 8.582 8.643 8.578 (8.947)b

8.721 (8.859)b

n=3 8.574 8.468 8.497 8.722 8.492 (8.928)b

8.819 (8.878)b

n=4 8.455 8.554 8.492 8.741 8.539 (8.927)b

8.839 (8.882)b

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II. Performance of Hybrid Functional on Electronic Structures Calculation of 2D

Hybrid Perovskites

We performed the PBE0 and HSE06 hybrid functional calculations to dertermine the bandgaps of

Ge- and Sn-based 2D hybrid perovskites for benchmark purpose. Here, the SOC effect was always

considered. For the Ge and Sn cases, the PBE0+SOC method can yield reasonable bandgaps of

MAGeI3 (2.04 eV) and MASnI3 (1.27 eV), both being in good agreement with the experimental

values, i.e., 1.9-2.0 eV12, 15 for MAGeI3 and 1.2–1.3 eV16-18 for MASnI3, respectively. While the

HSE06+SOC scheme computed ones, 1.44 eV for MAGeI3 and 0.77 eV for MASnI3, tend to

underestimate the corresponding experimental bandgaps. Thus, the PBE0+SOC scheme was chosen

to compute electronic structures of all Ge and Sn-based 2D hybrid perovskites (Tables S2-S3). Note

that a very recent experimental work reports the measured optical bandgaps of 2D BA2MAn-1SnnI3n+1

with 1.83 eV, 1.64 eV, 1.50 eV and 1.42 eV for n = 1-4, respectively.18 Considering the exciton

binding energies (in theory it is the energy difference between the electronic bandgap and the optical

bandgap), we roughly estimated that the exciton binding energies for the BA2MAn-1SnnI3n+1 (n = 1- 4)

are in the range of 300–100 meV, the PBE0+SOC calculated bandgaps, 2.04 eV, 1.97 eV, 1.87 eV

and 1.75 eV for n = 1 - 4, respectively, are in agreement with the experimental results.

The situations in Pb cases are slightly more complicated. As shown in Table S4, the bandgaps of

BA2PbI4 (1.96 eV) and MAPbI3 (1.17 eV), calculated based on the HSE06+SOC method,

underestimate the corresponding experimental values of 2.24 eV19 and 1.54 eV,11 respectively. On

the contrary, the PBE0+SOC scheme tends to overestimate the bandgaps of BA2PbI4 (2.57 eV) and

MAPbI3 (1.75 eV). As both the HSE06 and PBE0 functional are the Hartree-Fock type hybrid

functional with screening parameter µ of 0.2 Å–1 and 0, respectively. We adjusted the screening

parameter µ between 0.2 Å–1 and 0 and compared the calculated bandgap with the experimental

values. We found that the bandgaps of BA2MAn-1PbnI3n+1 (n = 1–4 and ∞) computed with µ = 0.1 Å–1

are consistent with the experimental report of Ref.19. While the ones calculated with µ = 0.05 Å–1 are

in agreement with the experimental values reported by the same group of Ref.14. This difference

stems from the fact that experimentally measured bandgaps can be influence by many factors, such

as hybrid phase, defect, impurities, encapsulation, transport layer materials, measurement method

and so on.19 We conclude that the hybrid functional with µ between 0.1 Å–1 and 0.05 Å–1 can give

reasonable estimation of the bandgap of Pb-based 2D hybrid perovskites. In the present work, we

chose the results associated with µ = 0.1 Å–1 for discussions.

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Table S2. Computed bandgaps of BA2MAn-1GenI3n+1 (n = 1–4 and ∞) based on the PBE, PBE+SOC,

HSE06+SOC, and PBE0+SOC methods, and bandgaps taken from experimental data.

Bandgap (eV)

Functional PBE PBE+SOC

HSE06+SOC

PBE0+SOC Exp.

BA2GeI4 1.38 1.25 1.74 2.35 N/A

BA2MAGe2I7 1.44 1.31 1.82 2.43 N/A

BA2MA2Ge3I10 1.36 1.24 1.73 2.34 N/A

BA2MA3Ge4I13 1.33 1.21 1.69 2.29 N/A

MAGeI3 1.12 1.00 1.44 2.04 1.9a

a Ref.12

Table S3. Computed bandgaps of BA2MAn-1SnnI3n+1 (n = 1–4 and ∞) based on the PBE, PBE+SOC,

HSE06+SOC, and PBE0+SOC methods, and bandgaps taken from experimental data.

Bandgap (eV)

Functional PBE PBE0+SOC

HSE06+SOC

PBE0+SOC Exp.

BA2SnI4 1.23 1.00 1.46 2.04 1.98a;1.83b

BA2MASn2I7 1.22 0.95 1.39 1.97 1.64b

BA2MA2Sn3I10 1.16 0.88 1.30 1.87 1.50b

BA2MA3Sn4I13 1.07 0.79 1.19 1.75 1.42b

β-MASnI3 0.68 0.43 0.77 1.27 1.3c; 1.23d;1.20b

a Ref.7 b Ref.18

c Ref.16

d Ref.17

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Table S4. Computed bandgaps of BA2MAn-1PbnI3n+1 (n=1–4 and ∞) based on the PBE, PBE+SOC,

hybrid functional with screening parameter µ=0.2 Å–1, 0.1 Å–1, 0.05 Å–1 and 0 plus SOC methods,

and bandgaps taken from experimental data.

Bandgap (eV)

Functional PBE PBE+SOC

µ=0.2 (HSE06) µ=0.1 µ=0.05 µ=0.0

(PBE0) Exp.

BA2PbI4 2.21 1.44 1.96 2.20 2.38 2.57 2.24a, 2.43b

BA2MAPb2I7 2.15 1.29 1.79 2.02 2.19 2.38 1.99a, 2.17b

BA2MA2Pb3I10 2.05 1.14 1.63 1.86 2.03 2.22 1.85a, 2.03b

BA2MA3Pb4I13 2.00 1.06 1.53 1.75 1.92 2.11 1.6a, 1.91b

MAPbI3 1.51 0.73 1.17 1.39 1.56 1.75 1.54c

a Ref.19

b Ref.14

c Ref.11

Table S5. The calculated effective masses of hole ( ) and electron ( ), the reduced effective 𝑚∗ℎ 𝑚 ∗

𝑒

mass (µ) of the exciton (hole-electron pair), the dielectric constant ε and the exciton binding energy

(Eb, in the unit of meV) of BA2MAn-1GenI3n+1 (n = 1–4), where the , , and µ are in the unit of 𝑚∗ℎ 𝑚 ∗

𝑒

the static mass of a free electron.𝑚𝑒

Thickness n ( )𝑚∗ℎ 𝑚𝑒 ( )𝑚∗

𝑒 𝑚𝑒 µ ( )𝑚𝑒 ε Eb (meV)

n=1 0.325 0.291 0.153 2.74 278

n=2 0.385 0.309 0.171 2.92 273

n=3 0.413 0.330 0.183 3.37 220

n=4 0.490 0.350 0.204 3.63 211

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Table S6. The calculated effective masses of hole ( ) and electron ( ), the reduced effective 𝑚∗ℎ 𝑚 ∗

𝑒

mass (µ) of the exciton (hole-electron pair), the dielectric constant ε and the exciton binding energy

(Eb, in the unit of meV) of BA2MAn-1SnnI3n+1 (n = 1–4), where the , , and µ are in the unit of 𝑚∗ℎ 𝑚 ∗

𝑒

the static mass of a free electron.𝑚𝑒

Thickness n ( )𝑚∗ℎ 𝑚𝑒 ( )𝑚∗

𝑒 𝑚𝑒 µ ( )𝑚𝑒 ε Eb (meV)

n=1 0.278 0.327 0.150 2.67 286

n=2 0.303 0.309 0.153 3.13 213

n=3 0.300 0.332 0.158 3.67 159

n=4 0.310 0.370 0.139 4.16 133

Table S7. The calculated effective masses of hole ( ) and electron ( ), the reduced effective 𝑚∗ℎ 𝑚 ∗

𝑒

mass (µ) of the exciton (hole-electron pair), the dielectric constant ε and the exciton binding energy

(Eb, in the unit of meV) of BA2MAn-1PbnI3n+1 (n= 1–4), where the , , and µ are in the unit of 𝑚∗ℎ 𝑚 ∗

𝑒

the static mass of a free electron.𝑚𝑒

Thickness n ( )𝑚∗ℎ 𝑚𝑒 ( )𝑚∗

𝑒 𝑚𝑒 µ ( )𝑚𝑒 ε Eb (meV)

n=1 0.566 0.436 0.246 2.27 650

n=2 0.591 0.465 0.260 2.64 508

n=3 0.596 0.488 0.268 2.93 425

n=4 0.585 0.478 0.263 3.40 310

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Fig. S1. a) Structure schemes of BA2MAn-1GenI3n+1 (n=1–4) and b) MAGeI3 (n∞). Example atomic view of the unit cell of BA2MA3Ge4I13 along c) c-axis, d) a-axis and e) b-axis, respectively (all hydrogen atoms are removed for clarity).

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Fig. S2. a) Structure schemes of BA2MAn-1PbnI3n+1 (n = 1–4) and b) MAPbI3 (n∞). Example atomic view of the unit cell of BA2MA3Pb4I13 along c) c-axis, d) a-axis and e) b-axis, respectively (all hydrogen atoms are removed for clarity).

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Fig. S3. Computed band structures of and BA2MAn-1MnI3n+1 (M=Ge, Sn, n = 1–2) based on the PBE0+SOC method, respectively. The G (0.0, 0.0, 0.0), X (0.5, 0.0, 0.0), and Y (0.0, 0.5, 0.0) are the high-symmetry special points in the first Brillouin zone, and the Fermi level is set to zero.

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Fig. S4. Computed band structures of BA2MAn-1PbnI3n+1 (n = 1–4) based on the hybrid functional with screening parameter µ = 0.1 Å–1, plus SOC method. The G(0.0, 0.0, 0.0), X(0.5, 0.0, 0.0), and Y(0.0, 0.5, 0.0) are the high-symmetry special points in the first Brillouin zone, and the Fermi level is set to zero.

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Fig. S5. Computed light absorption spectra of BA2MAn-1PbnI3n+1 for n = 2–4. The light-grey vertical bar denotes the photon energy range of visible light (wavelengths in ~390 nm–700 nm).

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III. Thermodynamic Stability of Sn- and Ge-based 2D Perovskites

To assess the thermodynamic stability of 2D perovskites BA2MAn–1MnI3n+1 (M=Ge, Sn, Pb), we

computed the decomposition enthalpy (ΔHdec), defined as the energy change from the decomposition

of the 2D perovskites. Negative ΔHdec means that the decomposition is endothermic and

thermodynamically unfavorable, whereas positive ΔHdec means that the decomposition is exothermic

and is thermodynamically favorable. One possible pathway (pathway 1) is simply given by20

BA2MAn−1MnI3n+1 2BAI + (n–1)MAI + nMI2 (S-1)

where M=Ge, Sn and Pb and n=1–4 and ∞ (3D). Since the Sn2+/Ge2+ can be readily oxidized into

Sn4+/Ge4+, another possible decomposition pathway (pathway 2) involving oxygen for the Sn- and

Ge-based 2D perovskites is given by

BA2MAn-1MnI3n+1 2BAI + (n–1)MAI + (n/2) MI4 + (n/2)MO2 – (n/2)O2 (S-2)

The computed decomposition enthalpy (per metal atom) of the corresponding pathways (1 for Ge,

Sn, Pb; and 2 for Ge and Sn) of 2D hybrid perovskites versus the thickness n are summarized in

Table S8 and presented in Figure 5.

Table S8. The calculated decomposition enthalpy (per metal atom) of the corresponding pathways (1

for Ge, Sn, Pb; and 2 for Ge and Sn) of 2D hybrid perovskites BA2MAn-1SnnI3n+1 (M= Ge, Sn, Pb, n

= 1–4 and ∞).

Thickness n n=1 n=2 n=3 n=4 n=∞

Ge -0.407 -0.233 -0.182 -0.135 -0.064

Sn -0.637 -0.422 -0.356 -0.326 -0.211pathway 1

Pb -0.529 -0.306 -0.247 -0.202 -0.085

Ge 1.552 1.727 1.778 1.825 1.896pathway 2

Sn 1.307 1.522 1.587 1.617 1.733

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