Yevgeny Rakita1, Davide R. Ceratti1, Gary Hodes1, David Cahen1

Department of Materials and Interfaces Weizmann Institute of Science, 7610001, Rehovot, Israel ;

Halide Perovskites: a platform for

‘defect-tolerance’ & ‘self-healing’

Halide Perovskites (HaPs) have taken a unique place among functional semiconductors – at the bulk and the nanoscale. Surprisingly, their optoelectronically-relevant

defect/trap density is extremely low compared to traditional semiconductors made with similar methods. HaPs can be fabricated near RT, from solution, both as thin-films, and

as single crystals with ~1010 cm-3 defect/trap densities for single crystals and < ~1016 cm-3 for polycrystalline films. Usually, only very carefully fabricated semiconductors (e.g.,

MBE-grown GaAs) yield such values.

We show here that these results are due to ‘defect-tolerance’ and ‘self-healing’, intrinsic to HaPs, where the latter is basically “anneal” at RT. These properties directly

explain the phenomenal performance of HaP QDs and other HaP architectures. Thus, understanding HaPs can guide us to new materials with such properties.

• Materials with ‘defect-tolerating’ bands (=positive d’), such as HaPs and

other halide/lead-based materials, are also highly polarizable. Stability of

such systems is enhanced by entropy !

• Entropically stabilized systems mean: low enthalpy of: ∆HReaction

(material ⥄ ∑constituents) + low Eact.

• When at RT ∆GReaction + ∆Eact < ∆GForm(defect), RT annealing or ‘self-

healing’ should occur (and does for HaPs!).

• Other ‘soft’ and highly-polarizable (𝜀𝑠 > 2𝜀∞) materials, such as halide-

and Pb-based materials should possess similar properties.

In part, based on YR’s PhD thesis: arxiv.org/abs/1809.10949

(sections 3.3, 3.4 & chapter 4)

MA

Pb

I

CsP

bB

r

MA

Pb

Br

MA

Pb

Cl

TlC

l

TlB

r

Ag

Cl

Ag

Br

Ag

I

Pb

Te

Pb

Se

Pb

S

Cd

Te

Cd

Se

Cd

S

GaS

b

GaA

s

GaP

InS

b

InA

s

InP Si --

0

2

4

6

8

10

12

Chalcogenides

ab

so

lute

valu

e o

f d

', |

d'| ;

[

eV

]Si

III-V

Halides

HaP

Halide-based materials

have relatively low

absolute deformation

potential, |d’|

(≈ low mechanical stiffness)*

* ~scales with Madelung

(electrostatic) potential

MA

Pb

IC

sP

bB

rM

AP

bB

rM

AP

bC

lT

lCl

TlB

rA

gC

lA

gB

rA

gI

Pb

Te

Pb

Se

Pb

SC

dT

eC

dS

eC

dS

GaS

bG

aA

sG

aP

InS

bIn

As

InP Si -- --

-14

-12

-10

-8

-6

-4

-2

0

2

4

6

TlXPb

chalcogenides

defo

rma

tio

n p

ote

nti

al, d

'

; [e

V]

Si

III-V Cd

chalcogonides

AgX

APbX3

(HaP)

𝒅′ ≡ −𝑩 ∙∆𝐸𝑔

∆𝑃

B – bulk modulus∆𝐸𝑔- change in bandgap

∆𝑃 – change in pressure

Algebraic sign of the

‘deformation potential’,

d’, tells us about its

(valence) band-nature

-10 -8 -6 -4 -2 0 2 4 6

0.1

1

10

GaP

GaSb

InAs

GaAsInSb

CdTeCdSe

CdS

MAPbBr3

AgBr

CsPbBr3

AgCl

MAPbI3

TlBr

MAPbCl3

TlCl

PbTe

PbS

PbSe

'soft'

( e s

/ e

) -

1

d' [eV]

'rigid'

‘Defect-tolerant’

materials (halide-

/lead-based) possess

highly polarizable

structural bonds, i.e.,

𝜺𝒔 > 𝟐𝜺∞.

Bonds are easily

deformed !

Better

(configurational)

entropy

stabilization.

Calculated (ab initio) defects transition states – averaged picture of most

energetically-probable defects in Pb-chalcogenides and HaPs

Adopted from: Kovalenko et al., Science 358, 745–750 (2017)

Defect tolerant *(APbX3, PbX)

defect intolerant*GaAs, CdTe

* Shallow or intra-

band states

* mid-gap

states

Adopted from ref. 6

MAPbI3 ; MA=CH3NH3+)

Conduction band

Valence band

Adopted from ref. 7

shallow or intra-band defect transition states

• With low ‘deformation potential’ (~ soft material), strain fields can be tolerated.

For HaPs, |d’| ~ 1 eV, a strain energy of 1kTRT (= 26 meV) corresponds to ~2.5%

(volumetric) distortion.

• Most classical semiconductors will break under such strains.

Defects and their relaxation

1

Strain fields

Charge

1

2

• If defect is an ion (localized charge) ∆GForm(defect) >> kT

• In absence of kinetic stabilization (low ∆Eact) (can be assumed for low bond-energy

and highly polarizable systems) and if in given material

∆GReaction (material ⥄ ∑constituents) + ∆Eact. < ∆GForm(defect)

the material can decompose and reform to a defect-free state! anneal @ RT

2

Defect (can) create:

Based on calorimetric measurements1 and kinetic studies2 of HaP formation/ decomposition

of HaPs (MAPbX3) to their constituents (MAX+PbX2):

*∆GReaction {~0.1-0.2 eV}1,2+ ∆Eact. {~0.05 eV 2 - 0.45 eV} < # ∆GForm(defect) {~ 1.6 eV}

RT annealing / ‘self-healing’

‘defect tolerant’

* Dominant entropic stabilization! 1

‘deformation potential’ > 0 & ‘defect tolerance’ Easy deformation and entropic stabilization

We thank Omer Yaffe and Igor Lubomirsky for fruitfuldiscussions. We thank Weizmann Institute’s Sustainability andEnergy Research Initiative (SAERI)* and the Israel Ministry ofScience for partial support.

See: D. R. Ceratti, et al. Adv. Mater. 2018, 1706273

MAPbBr3 crystal is cleaved just

before experiment

• Similar results for other APbX3 compounds !

• Kinetic study (T-dependent) of ‘self-healing’, suggest

∆Eself-healing ~ 0.5 eV for MAPbBr3 and 1.2 eV for FAPbBr3

Even if defects exist, their influence on (opto)electronic

behavior will be small!

Conclusions # For Br-based HaPs. 1.6 eV is deduced from radioactive Br & Pb tracer diffusion in PbBr23 and comparison to

ionic diffusion Eact(ion) for different APbBr3 HaPs 4. ∆GForm(defect) for I-based HaPs (ab-initio) ~0.3-1.3 eV 6

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4. Kuku, et al., Solid State Ionics 34, (1989) 1417. Yin, W. et al., Appl. Phys.

Lett. 104, (2014) 0639036. Li et al., J. Phys. Condens. Matter 27, (2015) 355801

5. Bi et al, Nat Commun. 8, (2017) 15330