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Quantum and dielectric confinement effects
in 3D nanocrystals and 2D layered perovskites
J. Even
FOTON , CNRS INSA Rennes, France
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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
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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, …)
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Introduction
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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)
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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
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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
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Moller, Nature, 1958
First evidence of optoelectronic properties
The electronic band gap changes with X Eg,CsPbCl3 > Eg,CsPbBr3 > Eg,CsPbI3
First photovoltaic effect
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Photovoltaic materials : a newcomer
NREL chart (June 2019)
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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)
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A strong optical absorption : thin films
Brenner et al, Nat. Mat. Rev. (2016)
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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)
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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
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3D bulk halide perovskites
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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
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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)
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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
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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
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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
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QD excitonic properties
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Akkerman et al nature mat 2018
Kovalenko et al science 2017
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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
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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
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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
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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
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QD Exciton fine structure : 2 optical-phonons process
M. Fu, J.E. et al Nature Comm. 2018
FAPbI3 QD
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QD Exciton fine structure: dark state observation
FAPbBr3 QD Tamarat, J.E. et al Nature Materials 2019
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QD Exciton fine structure : bright/dark states splitting
FAPbBr3 QD Tamarat, J.E. et al Nature Materials 2019
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QD Exciton fine structure : 2 optical-phonons process
FAPbBr3 QD Tamarat, J.E. et al Nature Materials 2019
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3D halide perovskites as ultrasoft semiconductors:
on the role of phonons
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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
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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
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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)
M. Fu, J.E. et al Nature Comm. 2018
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M. Fu, J.E. et al Nature Comm. 2018
- 3 LO phonon sidebands at 4K
- Fluctuating and energy dependent LO2 sideband
Photoluminescence (PL)
Exciton-phonon coupling in single FAPbI3 QD
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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
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- 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
FAPbBr3 QD Tamarat, J.E. et al Nature Materials 2019
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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)
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Multilayered halide perovskites
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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
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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
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Structure types Symmetry analysis
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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)
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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)
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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)
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Electronic properties Quantum confinement
Schematic Type I quantum well picture for monolayered perovskites
(D. Mitzi IBM 2001)
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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
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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
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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
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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
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Excitonic effects Dielectric Confinement
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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
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Tuning the dielectric profile in (n=1) halide perovskites
M. Smith, J.E. et al. Chem. Sci. 2017
Exp.
DFT
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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
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𝑃𝑒ℎ 𝑘, 𝑘′, 𝐸 = 𝑃𝑒ℎ
0 𝑘, 𝑘′, 𝐸 − 𝑃𝑒ℎ0 𝑘, 𝑘′′, 𝐸
𝑘′′′𝑘′′
𝑉𝑠 𝑘′′ − 𝑘′′′ 𝑃𝑒ℎ 𝑘
′′′, 𝑘′, 𝐸
RP halide perovskites : exciton properties
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
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RP halide perovskites : exciton properties
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
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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
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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
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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]