quantum and dielectric confinement effects in 3d ...€¦ · qd exciton fine structure : symmetry...

Quantum and dielectric confinement effects

in 3D nanocrystals and 2D layered perovskites

J. Even

FOTON , CNRS INSA Rennes, France

Opt. Telecom. / Silicon photonics (INSA/FOTON)

III-V/Si pseudosubstrate

GaP(N) lattice-matched on Si substrate

GaP(N)

Silicon

T. Quinci et al., J. Cryst. Growth. (2013)

12nm

GaAs/GaP 3% lattice mismatch : quantum dots

Cluster MBE/CVD

C. Robert, J.E. et al., Phys. Rev. B. (2016) electronic state

XSTM

Millions atoms TB

Rice Univ.

A. Mohite S.Tretiak

Northwestern Univ.

M. G. Kanatzidis

M. Kepenekian C. Katan L. Pedesseau

FOTON/ISCR CNRS team In Rennes

W. Nie C. C. Stoumpos

B. Traoré A. Rolland

Kaust

O. Bakr M. Kovalenko

ETH Zurich/EMPA

B. Lounis

Bordeaux Univ.

P. Tamarat J.C Blancon M. Bodnarchuk

Los Alamos Nat. Lab.

Stanford Univ.

H. Karunadasa

- DFT calculations : (Siesta/Vasp/Abinit…) - Empirical methods : TB, k.p, drift-diffusion models - Interpretation of exp. studies:

Optics/Diffraction/Devices (Solar cells, LEDs, …)

Introduction

Oxide perovskites ABO3 : CaTiO3, SrTiO3

ideal cubic structure

O2-

A=Ba2+, Sr2+, Ca2+

B=Ti4+

Ruddlesden-Popper

Dion-Jacobson(2) Double perovskites

n=1 n=2

source: https://www.princeton.edu/~cavalab/tutorials/public/structures/perovskites.html

n=2 n=2

Dion-Jacobson(1)

FAPbI3(@O. Bakr, KAUST)

and also since 2015, single crystals (for fundamental studies ….)

MAPbBr3(@S. Paofai, ISCR)

Low-cost thin-film deposition (glove box/spin coating and more elaborate methods ….)

From thin-films to monocrystals

MAPbI3

Inorganic or organic cation A= Cs+ Rb+ MA+ FA+

Halogen X= I- Br- Cl-

Metal B= Pb2+ Sn2+ Ge2+

Bulk 3D Halide Perovskites

Ideal cubic perovskite ABX3 crystal structure

Since 2009 for PV (Mysaka et al JACS2009), breakthrough in PV efficiency in 2012

Moller, Nature, 1958

First evidence of optoelectronic properties

The electronic band gap changes with X Eg,CsPbCl3 > Eg,CsPbBr3 > Eg,CsPbI3

First photovoltaic effect

Photovoltaic materials : a newcomer

NREL chart (June 2019)

Photovoltaic materials : a newcomer

Organic solar cells

Quantum dot … Perovskite

CIGS= Cu(In,Ga)Se2

Perovskite

Silicon Thin films

Silicon Polycristalline

Silicon

CdTe Now > 16%

Now > 24.2%

Perovskite/silicon tandem Now > 28%

GaAs

Recent Progress of OPV also:

(Armor Group in Nantes)

A strong optical absorption : thin films

Brenner et al, Nat. Mat. Rev. (2016)

Good carrier transport properties : defect tolerant

Tsai, J.E. et al, Adv. Mat. (2018)

Light emitting devices (LED) based on multilayered Ruddlesden-Popper Phases

(perovskite solar cells < 25mA/cm2)

A key factor for PV: abundant material ressource

To reach 12.5 TW (world total electricity consumption per year)

1000 years of Te

3 years of Si

500 years of Ga

400 years of In

A few days of Pb

Snaith, Nature Materials 2018

3D bulk halide perovskites

a

b

c

BX3-

J. Even et al, J. Phys. Chem. C (2014)

Simplified picture of the ABX3 crystal lattice

Constructing a prototype 3D band structure

Empty states

Occupied states

Constructing a prototype 3D band structure

I(p)

Pb(s)

𝐸𝑝𝑋

𝐸𝑠𝐵

Pb(p)

I(s)

𝐸𝑝𝐵

𝐸𝑠𝑋 x3

x3

Pb2+ atoms

I- atoms

J. Even et al, J. Phys. Chem. C (2014)

Empirical tight binding for cubic halide perovskites

Pb

I

s

s

p

p

VB CB

S. Boyer-Richard, J.E. et al. J. Phys. Chem. Lett. 2016

Volumetric band gap variation opposite to III-V

CBM and VBM: both antibonding states between s and p orbitals

J. Even et al. J. Phys. Chem. Lett. 2013 (DFT)

Giant spin-orbit coupling mandatory to analyse: - Electronic band gap - Effective masses - Optical absorption

Spin-orbit coupling and inversion sym. breaking

without SOC with SOC

When inversion symmetry is broken - Large spinor splittings -> Rashba/Dresselhaus - Various types of spin textures

M. Kepenekian, J. E. et al. ACS Nano 2015 (DFT and symmetry based k.p Hamiltonian)

J. Even et al. RRL 2014 (DFT, online oct 2013)

Anti-ferrodistorsive low-T Pnma phase

3D single crystal: Bound exciton / Wannier exciton

~ Free carriers

Wannier free exciton

Bound exciton

Ebx=50-100meV

Ebx=15meV

Ebx=5meV

CH3NH3PbI3 H. H. Fang, J. E. et al , Adv. Func. Mater. 2015

Zoom

below

50K

FE

FE

FC

BE

BE

H. Diab, J.E. et al J. Phys. Chem. Lett. 2016

Wannier free exciton Ebx=20meV

- Triplet of bright states

- Dark state Exciton fine structure : J. Even, J. Phys. Chem. Lett. 2015

QD excitonic properties

Akkerman et al nature mat 2018

Kovalenko et al science 2017

QD Exciton fine structure : symmetry breaking

M. Fu, J.E. et al, Nanoletters 2017 Ramade et al, Nanoscale 2018

Analysis :Bright triplet splitting affected by lattice antiferrodistortions Dark singlet below the bright triplet

D4h D2h

Triplet of bright states

Dark state

Oh

T1u+A1u

Doublet of bright states

Dark state

Eu+A2u+A1u

Bright state (singlet)

B1u+B2u+B3u+Au

Dark state Bright states (singlets)

Colloidal quantum dots of CsPbBr3

-Magneto PL

M.Nestoklon, S.V. Goupalov et al Phys. Rev. B 2018 B. Aich et al Phys. Rev. Mat. Appl. 2019

QD Exciton fine structure : symmetry breaking

shape anisotropy

Bright triplet splitting affected by shape anisotropy and long range exchange interaction

Becker et al, Nature 2018

CsPbX3 QD

QD Exciton fine structure : Rashba effect

Further symmetry breaking , Rashba effect : - the dark state is above the bright triplet - it explains the high brightness of QD

QD Exciton fine structure : emission lifetime

Canneson et al, Nanoletters 2017

CsPbBr3 QD

Chen et al, Nanoletters 2018

CsPbX3 alloys QD

Xu et al, J. Phys. Chem. C 2019

Mn-doped CsPbCl3 QD

QD Exciton fine structure : 2 optical-phonons process

M. Fu, J.E. et al Nature Comm. 2018

FAPbI3 QD

QD Exciton fine structure: dark state observation

FAPbBr3 QD Tamarat, J.E. et al Nature Materials 2019

QD Exciton fine structure : bright/dark states splitting


QD Exciton fine structure : 2 optical-phonons process


3D halide perovskites as ultrasoft semiconductors:

on the role of phonons

62/1 RE g

41

11 gg TA

62/1 RE u

CBVB

Cubic phase with spin-orbit coupling

J. Even et al, J. Phys. Chem. C 2014, J. Phys. Chem. Lett. 2015 A. Neukirch, Nanoletters 2016 W. Nie, Nature Comm. 2016

Electron/phonon coupling : symmetry analysis

Summary of electron coupling mechanisms

Si

CBM VBM

GaAs

CBM VBM

Hybrid perovskites

CBM VBM

Acoustic

phonons ADP ADP PZA, ADP PZA, ADP ADP (LA) ADP (LA)

Optical

Phonons - ODP FOP, ODP FOP, ODP FOP FOP

ADP : acoustic deformation potential

FOP : Fröhlich for optical phonons ODP : optical deformation potential

PZA : Piezoelectric for acoustic phonons

J. Even et al. Spie Proc. 2016, Nie, J.E. et al Nature Comm. 2016, Neukirch, J.E. et al, Nanoletters 2016

Exciton-phonon coupling in single FAPbI3 QD

- Exciton line-broadening in single FAPbI3 QD

Γ 𝑇 = Γ0 + 𝜎𝐴𝑐𝑇+Γ𝐿𝑂 exp 𝐸𝐿𝑂 𝑘𝐵𝑇 − 1

inhomogeneous Acoustic phonons Optical phonons

Below resolution

- Dominant Fröhlich interaction - Very weak acoustic def. pot. Interaction

Photoluminescence (PL)



- 3 LO phonon sidebands at 4K

- Fluctuating and energy dependent LO2 sideband

Photoluminescence (PL)

Exciton-phonon coupling in single FAPbI3 QD

lexc=488 nm 50 W.cm−2

Confocal image

Type-I (∼ 55% of the NCs) Type-II (∼ 45% of the NCs)

LO1 LO2

LO1 LO2

170 µeV

PL spectra of single CsPbBr3 NCs

2 K 2 K

Exciton-phonon coupling in single CsPbBr3 QD

M. Fu, J.E. et al Nano Lett. 2017

- Exciton line-broadening in single FAPbBr3 QD

Γ 𝑇 = Γ0 + 𝜎𝐴𝑐𝑇+Γ𝐿𝑂 exp 𝐸𝐿𝑂 𝑘𝐵𝑇 − 1

inhomogeneous Acoustic phonons Optical phonons

Below resolution

- Dominant Fröhlich interaction - Weak acoustic def. pot. interaction

Exciton-phonon coupling in single FAPbBr3 QD


Ultrasoft elastic constants

A. Ferreira, J.E. et al. Phys. Rev. Lett. 2018 C. Katan, J. E. et al, Nature Mat. 2018

- Very low resistance to shear stress (C44 small) - I-based materials softer - FA-based materials softer - FAPbI3 close to instability (Bulk modulus~0)

Multilayered halide perovskites

Why the solar cell performance still far from

3D perovskite?

X Karunadasa et al, Angew. Chem. Int. Ed. 2014

Kanatzidis et al., JACS 2015

Solar cell applications:

initial results

What happen if we can flip the crystal orientation?

Layered perovskite cells : Device challenges

(PEA)2(MA)n-1PbnI3n+1

(BA)2(MA)n-1PbnI3n+1

GIWAXS

Study

α

Layered perovskite solar cells

-10

-8

-6

-4

-2

0

2

4

Curr

en

t D

en

sity (

mA

/cm

2)

0.80.40.0Voltage (V)

Post Anneal n=4

-20

-15

-10

-5

0

5

Cu

rre

nt

De

nsi

ty (

mA

/cm

2)

0.80.40.0

Voc (V)

Hot-Cast n=4

PCE = 4.44% PCE = 12.51 %

(BA)2(MA)(n-1)PbnI(3n+1) n=3,4: crystal flipping and edge states

H. Tsai, J.E. et al. Nature 2016 J.C. Blancon, J.E. et al, Science 2017

Structure types Symmetry analysis

RP phases in halide perovskites

Another well-studied series:

MA=CH3NH3+

BA=C4H7NH3+

(BA)2(MA)n-1PbnI3n+1

C.C Stoumpos, J.E. et al Chem 2017

n=5

Shift (1/2,1/2)

L. Mao, J.E. et al. JACS 2018

Hybrid Dion−Jacobson Lead Iodide Perovskites

Alternative to RP phases : Dion Jacobson (DJ) phases

dications

Shift (0,0)

Alternative to RP phases : ACI phases

MA=CH3NH3+

GA=C (NH2)3+

C. Soe, J.E. et al J. Am. Chem. Soc. 2017

GA(MA)nPbnI3n+1 Alternating Cations in the Interlayer

Shift (1/2,0)

Quantum confinement (n layers) and reduced band gap (reduced octaedra tilts) (combined PL / DFT study)

Electronic properties Quantum confinement

Schematic Type I quantum well picture for monolayered perovskites

(D. Mitzi IBM 2001)

Review : L. Pedesseau, J.E. et al, ACS Nano 2016

without spin-orbit coupling with spin-orbit coupling

DFT : Quantum well-like band structure - No dispersion along the stacking axis - TE absorption

Giant spin-orbit coupling in the CB

k.p model and Bloch functions

Basic electronic properties of layered perovskites

DFT calculation for

J. Even et al. Phys. Rev. B 2012

Multilayered RP perovskites : quantum confinement

H. Tsai, J.E. et al. Nature 2016

n=1 n=3

RP halide perovskites (DFT calculations)

(BA)2(MA)(n-1)PbnI(3n+1)

- n sub-bands - lower band gap

J. Even et al. Chem. Phys. Chem. 2014

Quasi-composite picture

Quantitative assessment of the type-I confinement

≈ + Huge confinement potentials but ultrathin quantum wells !

Planar averages of A/B, A and B potentials

B. Traore, J.E. et al. ACS Nano 2018

Failure of the transverse effective mass model

J Even. et al. ChemPhysChem2014

(Tanaka et al Sci. Technol. Adv. Mater. 2003)

Transverse effective mass model: 2 major issues

Non-parabolicity

Superlattice electronic density of states

Excitonic effects Dielectric Confinement

Exciton : deviation from 2D Rydberg series for n=1 Tanaka. et al. PRB 2005

(C6H13NH3)2PbI4

Takagi. et al. PRB 2013

Yaffe et al. PRB 2015

(exfoliated (C4H9NH3)2PbI4 nanosheet)

Early work mentionning quantum and dielectric confinements: (Ishihara, Solid State Comm. 1989)

Deviations from Rydberg series as experimental proofs of dielectric confinement

Tuning the dielectric profile in (n=1) halide perovskites

M. Smith, J.E. et al. Chem. Sci. 2017

Exp.

DFT

RP halide perovskites : exciton properties

Deviation from the 2D excitonic Rydberg series for all n

J.C. Blancon, J.E. et al. Nature Comm 2018

𝑃𝑒ℎ 𝑘, 𝑘′, 𝐸 = 𝑃𝑒ℎ

0 𝑘, 𝑘′, 𝐸 − 𝑃𝑒ℎ0 𝑘, 𝑘′′, 𝐸

𝑘′′′𝑘′′

𝑉𝑠 𝑘′′ − 𝑘′′′ 𝑃𝑒ℎ 𝑘

′′′, 𝑘′, 𝐸


A semi-empirical model to solve the Bethe-Salpeter equation and compute the screened exciton Green function

Three new basic ingredients

1) Bloch states (spinors) from DFT 2) Dielectric profiles from DFT

3) Effective masses from the fit of exp. diamagnetic shifts

𝑃𝑒ℎ0 𝑘, 𝑘′, 𝐸 =

1

𝐸 − 𝐸𝐺 −ℏ2𝑘2

2𝜇+ 𝑖Γ𝛿𝑘,𝑘′ ,

Modified version of Schmitt-Rink’s model Z. Phys. B - Condensed Matter (1982)

J.C. Blancon, J.E. et al. Nature Comm 2018; C. Katan, J.E. et al Chem. Rev. 2019

𝜌𝑒 𝑧𝑒 for CB and 𝜌ℎ 𝑧ℎ for VB


𝜌𝑒 𝑧𝑒 for CB and 𝜌ℎ 𝑧ℎ for VB

From DFT

Bloch states (spinors)

Dielectric profiles

J.Even et al. PCCP 2014 D. Sapori, J.E. et al Nanoscale 2016

J.C. Blancon, J.E. et al. Nature Comm 2018

𝜓𝑒,𝑘𝑡 𝑟𝑡𝑒 , 𝑧𝑒 =𝑒𝑘𝑡.𝑟𝑡𝑒

𝐴𝑢𝑒,𝑘𝑡=0 𝑟𝑡𝑒 , 𝑧𝑒

𝜓ℎ,𝑘𝑡 𝑟𝑡ℎ, 𝑧ℎ =𝑒𝑘𝑡.𝑟𝑡ℎ

𝐴𝑢ℎ,𝑘𝑡=0 𝑟𝑡ℎ, 𝑧ℎ

𝑉s 𝑞t =−𝑒2

2휀w𝑞t 𝜌e 𝑧e 𝜌h 𝑧h 𝑒

−𝑞t 𝑧e−𝑧h + Δ𝜒 𝑒−𝑞t 𝑧e+𝑧h−𝑑 +𝑒−𝑞t 𝑧e+𝑧h+𝑑

𝑑2,𝑑2

−𝑑2 ,−𝑑2

+ Δ𝜒2 𝑒−𝑞t|𝑧e−𝑧h−2𝑑| +𝑒−𝑞t|𝑧h−𝑧e−2𝑑| 𝑑𝑧e𝑑𝑧h ,

𝑞t𝑑 ≪ 1

𝜌𝑒(𝑧𝑒) = 𝛿𝑧𝑒

𝜌ℎ(𝑧ℎ) = 𝛿𝑧ℎ

Ultrathin QW with no leakage of wavefunctions outside the well

휀w≫ 휀b = 1

In-plane Bohr radius larger than QW thickness

Large dielectric mismatch

Connection with Van der Waals heterostructrues

Conclusion

Take home messages : Perovskites are a new class of semiconductors with a specific electronic topology

Solid-state physics concepts may be applied, but unusual optoelectronic properties due to

• The exceptional softness of the lattice (acoustic phonons) • The strong anharmonicity and ionicity of the lattice (optical phonons) • The strong polarisability of the lattice leading eventually to spinor splitting

Layered perovskites are unusual quantum well superlattices

• Quantum confinement aspects are specific (breakdown of the envelope concept) • Dielectric confinement are dominant (deviation from exciton Rydberg series)

Quantum dots are affected by all the above phenomena and especially with:

• Long range exchange interaction: shape anisotropy and bright/dark exciton splitting

DRop-on demand flexible Optoelectronics & Photovoltaics by means of Lead-Free halide perovskITes

Figure 1. From Theory-Chemistry to Inkjet-printed optoelectronic & photonic devices on

flexible substrates.

Density Functional Theory:

• Screening of new generations of lead-free

perovskite compounds.

• Interfaces of perovskites with

ETM/HTM/passivation layers/2D perovskites

Perovskite group in Rennes at INSA (with FOTON and ISCR CNRS Labs)

“Postdoctoral research Position” (Starting in November 2019

for up to 33 months)

H2020 FETopen (8 Europeans partners)

Contact: [email protected]

quantum and dielectric confinement effects in 3d ...€¦ · qd exciton fine structure : symmetry...

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