Defects in Halide Perovskites Does It Help to Switch from 3D to 2D Haibo XueZehua ChenShuxia Taoand Geert Brocks

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Defects in Halide Perovskites:

Does It Help to Switch from 3D to 2D?

Haibo Xue,†,‡Zehua Chen,†,‡Shuxia Tao,∗,†,‡and Geert Brocks∗,†,‡,¶

†Materials Simulation & Modelling, Department of Applied Physics, Eindhoven University

of Technology, P.O. Box 513, 5600MB Eindhoven, the Netherlands.

‡Center for Computational Energy Research, Department of Applied Physics, Eindhoven

University of Technology, P.O. Box 513, 5600MB Eindhoven, the Netherlands.

¶Computational Materials Science, Faculty of Science and Technology and MESA+

Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500AE Enschede, the

Netherlands.

E-mail: s.x.tao@tue.nl;g.h.l.a.brocks@utwente.nl

arXiv:2210.03415v1 [cond-mat.mtrl-sci] 7 Oct 2022

Abstract

Ruddlesden-Popper hybrid iodide 2D perovskites are put forward as stable alterna-

tives to their 3D counterparts. Using ﬁrst-principles calculations, we demonstrate that

equilibrium concentrations of point defects in the 2D perovskites PEA2PbI4, BA2PbI4,

and PEA2SnI4(PEA: phenethyl ammonium, BA: butylammonium), are much lower

than in comparable 3D perovskites. Bonding disruptions by defects are more detri-

mental in 2D than in 3D networks, making defect formation energetically more costly.

The stability of 2D Sn iodide perovskites can be further enhanced by alloying with Pb.

Should, however, point defects emerge in sizable concentrations as a result of nonequi-

librium growth conditions, for instance, then those defects hamper the optoelectronic

performance of the 2D perovskites, as they introduce deep traps. We suggest that trap

levels are responsible for the broad sub-bandgap emission in 2D perovskites observed

in experiments.

Hybrid organometal halide perovskites are materializing as candidate semiconductors for

new generations of optoelectronic devices such as solar cells and light-emitting diodes.1,2

Application of these materials, however, is severely hampered by their lack of long-term

stability.3–6One of the ﬁrst frequently studied compounds, MAPbI3, has favorable optical

and charge transport properties,7–10 but the MA+(methylammonium) ion is chemically not

suﬃciently stable, and suﬀers from degradation reactions.11,12 Replacing MA+by larger and

more stable cations, such as FA+(formamidinium)13 or GA+(guanidinium),14 suﬀers from

the perovskite structure becoming unstable, leading to a tendency to convert to diﬀerent

crystal structures that are much less optically active.15–17 This tendency can be suppressed to

a certain extent by mixing in smaller inorganic cations, such as Cs+,18,19 but the fundamental

issue remains that a stable 3D perovskite lattice requires the sizes of the constituting ions

to be of a certain proportion, as expressed by the Goldschmidt tolerance factor,2,20 and the

scale is set by the 3D network of metal halide octahedra in the perovskite.

In recent years, organometal halide perovskites with a Ruddlesden-Popper structure have

emerged as alternative materials.21 In these perovskites the metal halide octahedra form a

planar 2D network, and these 2D layers are separated by layers of organic cations, where

the interlayer interaction is typically Vanderwaals.22 Using organic ions with a quasi-linear

structure, such as PEA (phenethylammonium)23 or BA (butylammonium),24 the in-plane

tolerance factor for a stable crystal structure is easily obeyed, whereas the out-of-plane size

of the organic ion becomes relatively unimportant. Although the stability of such 2D per-

ovskites is markedly improved, as compared to their 3D counterparts, presently photoelectric

devices based upon 2D perovskites fail to reach the high eﬃciencies obtained with 3D per-

ovskites.22 In terms of this, defects can play an important role, whereas their concentrations

in 2D perovskites and resulting impacts on electronic properties are not yet clear.22

In this paper we explore the defect chemistry and physics of prominent 2D organometal

iodide perovskites, PEA2PbI4, BA2PbI4, and PEA2SnI4, and the alloy PEA2Sn0.5Pb0.5I4,

using ﬁrst-principles density functional theory (DFT) calculations. The ease with which

point defects can be created in a material is an indication for its stability. We therefore

focus on the defect formation energy (DFE) as it can be calculated assuming thermodynamic

equilibrium conditions. We use the same formalism as applied in our previous work on 3D

perovskites.25 A summary of the theory is given in the Supporting Information (SI), Sec. I.

The equilibrium chemical potentials of the diﬀerent elements are determined by considering

the phase diagram of the 2D perovskite, see the SI, Fig. S1. The defect formation energies

are calculated using iodine-medium conditions, which are the conditions most typically used.

Even if defects do not occur in large quantities under thermodynamic equilibrium condi-

tions, they may appear more prominently under nonequilibrium growth conditions, or under

operating conditions.26 If so, they can seriously aﬀect the electronic properties of the mate-

rial, as defect states with energy levels inside the semiconductor band gap can act as traps

for charge carriers, and as recombination centers for radiationless decay. We explore these

energy levels, called charge-state transition levels (CSTLs), associated with the most likely

point defects in the 2D materials listed above.

DFT calculations are performed on 2×2×1 supercells of 2D perovskites, with the Vienna

Ab Initio Simulation Package (VASP),27–29 employing the SCAN + rVV10 functional30 for

electronic calculations and geometry optimization. The SCAN+rVV10 functional is used

aiming at obtaining accurate defective structures and total energies, and therefore the DFEs,

which are the main focus of this work. Whereas the DFT band gap error may result in

incorrect band edges, the calculated CSTLs are suggested to be correct in a relative sense,

as discussed in our previous work Ref. 31. Detailed computational settings and structures are

discissed in the SI, Sec. I. We start with point defects in the most popular 2D perovskite,

PEA2PbI4, i.e, the PEA vacancy VPEA, the Pb vacancy VPb, and the iodine vacancy VI,

and the interstitials Pbiand Ii. The PEA interstitial is omitted because the structure

is too dense for additionally accommodating such an extra large-size organic cation. In

addition to these simple point defects, we also study the compound vacancies VPEAI and

VPbI2, representing missing units of the precursors PEAI and PbI2. The layered nature of

Figure 1: (a) Top and side views of a 2 ×2×2 PEA2PbI4supercell; optimized structures of

vacancies (b-g) and interstitials (h-j) in their most stable charge states in PEA2PbI4. The

positions of the defects are marked in red. The labels (in-plane) and (out-of-plane) refer to

positions of iodine vacancies and interstitials either within an PbI2plane or above/below it.

the 2D perovskite [Figure 1(a)], implies that iodine vacancies and interstitials in the central

PbI planes and those outside these planes can behave diﬀerently, and both conﬁgurations

are studied. Optimized structures of all defects in their most stable charge states are shown

in Figure 1(b-j).

The calculated DFEs of PEA2PbI4are shown in Figure 2(a). The intrinsic Fermi level

(E(i)

F= 0.67 eV with respect to the valence band maximum, VBM) is obtained from the

charge neutrality condition, see SI, Sec. I.3. At this condition, the vacancies VPEA

−and

VPb2−are easiest to form, and thereby are the most dominant defects, with formation energies

of 0.82 eV and 0.84 eV, respectively. This leads to equilibrium concentrations at room

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DefectsinHalidePerovskites:DoesItHelptoSwitchfrom3Dto2D?HaiboXue,y,zZehuaChen,y,zShuxiaTao,,y,zandGeertBrocks,y,z,{yMaterialsSimulation&Modelling,DepartmentofAppliedPhysics,EindhovenUniversityofTechnology,P.O.Box513,5600MBEindhoven,theNetherlands.zCenterforComputationalEnergyResearch,DepartmentofA...

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Defects in Halide Perovskites Does It Help to Switch from 3D to 2D Haibo XueZehua ChenShuxia Taoand Geert Brocks

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