OPTICAL PROPERTIES OF
ADVANCED FERROELECTRIC HETEROSTRUCTURES
Marina Tyunina
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Microelectronics Research Unit, University of Oulu, Finland
Institute of Physics of the Czech Academy of Sciences, Prague
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Perovskite oxide ferroelectrics and related materials
Perovskite-type metal oxides
ABO3-type
perovskite-structure crystal
A
Boxygen
A B
a - valence of metal A-cation
b - valence of metal B-cation
a + b = 6
a = 3, b = 3: La3+Al3+O3
a = 2, b = 4: Ca2+Ti4+O3
a = 1, b = 5: Na1+Nb5+O3
Stability of perovskite structure is evaluated using
the Goldschmidt tolerance factor 0.7 < T < 1.1
rA, rB, rO – ionic radii of cations and oxygen OB
OA
rr
rrT
2
ideal cubic (T = 1); cubic, tetragonal (T = 0.9 – 1); orthorhombic, rhombohedral , monoclinic (T = 0.7 - 0.9); hexagonal, orthorhombic (T > 1); non-perovskite competing phases: pyrochlore, ilmenite, brownmillerite
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Perovskite oxide ferroelectrics
Natural: CaTiO3 (perovskite after L. A. Perovskii), SrTiO3 (tausonite after L. V. Tauson ) Best known: BaTiO3, PbTiO3, LiNbO3, solid solutions Pb(Zr,Ti)O3, (Ba,Sr)TiO3
Specific formula units: A(BIBII)O3 - PbMg1/3Nb2/3O3 ; (AIAII)BO3 - Na0.5Bi0.5TiO3
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-Pr
+Pr
+Ec
Po
lari
za
tio
n
Electric field
-Ps
+Ps
-Ec
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Re Ni O3
Other important perovskite oxides: spontaneous metal-insulator-transition materials
Resis
tivit
y (
log s
cale
)
Temperature
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La,Sr Mn O3
Other important perovskite oxides: metals-insulators with giant magnetoresistance
0
Resis
tivit
y
Magnetic field
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Re Mn O3
Other important perovskite oxides: magneto-electric multiferroics
Po
lari
za
tio
n
Magnetic field
Ma
gn
eti
za
tio
n
Electric field
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Ba,Sr Mn O3
Other important perovskite oxides: magneto-electric multiferroics
Po
lari
za
tio
n
Magnetic field
Ma
gn
eti
za
tio
n
Electric field
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Perovskite oxides represent excellent platform for achieving
dedicated response functions at will through cationic
variations.
Chemical and structural compatibility of different perovskite
oxides enables growth of EPITAXIAL HETEROSTRUCTURES
leading to novel functions and properties.
-Pr
+Pr
+Ec
Po
lari
za
tio
n
Electric field
-Ps
+Ps
-Ec
Resis
tivit
y (
log s
cale
)
Temperature0
Resis
tivit
y
Magnetic field
Po
lari
za
tio
n
Magnetic field
Ma
gn
eti
za
tio
n
Electric field
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Epitaxy
Two ancient Greek words, epi (epi, placed or resting upon) and taxiz (taxis, arrangement), are the root of the modern word epitaxy, which refers to extended single-crystal film formation on top of a crystalline substrate.
HOMOEPITAXY FILM and SUBSTRATE are of the SAME material. (Epilayer is freer of defects, purer than the substrate, and can be doped)
HETEROEPITAXY FILM and SUBSTRATE are of DIFFERENT materials. (Epitaxial heterostructures, superlattices, etc.)
SUBSTRATE
FILM
SUBSTRATE
FILM
Epitaxial pseudo-cubic perovskite films
a0
a
c
a0
a-Da c+D
c
film material epitaxial film
substrate substrate
x
y
z
c
cu
a
aauus
zz
yyxx
D
0
Biaxial in-plane misfit strain arises due to mismatch of the in-plane (parallel to the substrate surface) symmetry and/or lattice parameters of the film and substrate materials.
Misfit strain in cube-on-cube-type epitaxial film
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-4 0 4
200
400
600
cr
aa
T (
K)
s (10-3)
p
Strain–temperature s-T phase diagram
BaTiO3
200
400
600
T (
K)
CRYSTAL EPITAXIAL FILM
High-temperature paraelectric (PE) cubic phase transforms on cooling to ferroelectric (FE) tetragonal phase.
Transition temperature is higher than in crystal. FE phases differ from those in crystal. PE phase may not be metrically cubic.
PE PE
FE
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Our experimental studies
Epitaxial growth of perovskite oxides Pulsed laser deposition (PLD) Ferroelectrics (eventually any material) Conductors SrRuO3, (La,Sr)MnO3, (La,Sr)CoO3
Multiferroic manganites AMnO3
MIT nickelites ReNiO3
Microstructural and domain analyses X-ray diffraction and spectroscopy (XRD; EDXS); electron microscopies and diffraction (SEM, TEM, HRTEM, STEM, cBED, nBED); electron spectroscopies (XPS, XANES, XMCD, EELS); scanning probe microscopies (AFM, PFM, NSOM) Functional responses Impedance spectroscopy; Polarization; Magnetization; Resistivity Optical properties Variable angle spectroscopic ellipsometry (VASE)
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Ferroelectrics: unique functions
Dielectric e 103...105 [3.9 in SiO2] - capacitors
Tunable dielectric (E e) - varactors
Piezoelectric (s E or E s) d 102 – 103 pm/V [3 pm/V in quartz]
actuators, sensors, transducers, motors, MEMS, energy harvesters
Pyroelectric (DT E) p 103 C/(m2K) (energy harvesting)
Electro-caloric (E DT) (0.1- 1)10-6 (K m)/V (solid-state cooling)
Switchable polarization (E P) P (0.20 – 1) C/m2 (thin-film memories)
Temperature-dependent resistance (T r) - thermistors
Dielectric and piezoelectric applications are commercialized • Multibillion markets for applications of ceramics (PZT, BST) • Customized piezoelectric applications of crystals (PMN-PT) • Growing markets for integrated thin-film applications
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Ferroelectrics: optical properties
Wide bandgaps Eg > 3 eV (UV range)
Highly transparent in VIS range E < 3 eV
Large refractive index n (1.5 – 2.5) in VIS range
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Electronic energy band structure
Ener
gy
Wave vector
Conduction band is empty
Valence band
Mainly interband excitations are present. They correspond to absorption of light by electron (below the Fermi level) with a transition of electron to an unoccupied state in a higher band. They are intrinsically quantum mechanical processes.
Interband transitions in ferroelectrics
- VB state (u) and CB state (c) are coupled: momentum matrix elements <upc>2
- transitions are from occupied to unoccupied states (from below to above Fermi level)
- transitions are favored at specific critical points in the Brillouin zone
kdkEkEcW copt
32
3)(
8
22u
p
pu
probability of transitions per unit time
kdkEkEcc
3
3)(
8
2
pr uu
joint density of states
per unit energy
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theoretical calculations are satisfactory for paraelectric state
unknown
Ferroelectrics: especial optical properties
Electric-field dependent refractive index (E Dn):
linear electro-optic effect Dn E
quadratic electro-optic effect D(n-2) E2
Stress-dependent refractive index (s Dn): elasto-optic, piezo-optic, and acousto-optic effects
Temperature-dependent refractive index (T Dn ):
high-temperature thermo-optical behavior n T
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These properties are related to spontaneous or induced crystal polarization in ferroelectrics.
KNbO3
BaTiO3
PbTiO3
Slater mode Last mode
BO6-polarization A -polarization
Perovskite oxide ferroelectrics: polarization
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Electro-optic effect in BO6-ferroelectrics
quadratic EO coefficient (empirical knowledge):
g 0.15 m4/C2 in BO6-FEs (KNbO3, BaTiO3)
g 0.03 m4/C2 in A-FEs (PbTiO3)
Ener
gy
VB
O 2p
E g
CB
B d de
dg
Photon energy (eV) e
2
(4-5) eV
(8-9) eV
SEMI-EMPIRICAL MODEL
Crystal polarization P raises the de band. The main peak
blue-shifts by DE and refractive index n decreases. (NB tensor form of equations)
22
2
gPn
PE
D
D
g20
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Main effects electrooptic, elastooptic (acoustooptic) Main BULK materials crystals of LiNbO3 less often - crystals of K(Ta,Nb)O3, especial (Pb,La)(Zr,Ti)O3 ceramics Drawbacks of crystals • only a few compositions available, • demanding technology, • often poor chemical purity and high density of defects • difficult to integrate into micro- and nanodevices EPITAXIAL FILMS are attractive for integrated photonics applications
Ferroelectrics for photonics applications
Optical properties of ferroelectrics: open questions
What interband transitions are responsible for VIS refraction?
What mechanisms are responsible for electro-, piezo-, …-optical effects?
Why properties of BO6- and A-type ferroelectrics differ?
What are properties of solid solutions?
………………
Especially for thin films:
Are there effects of thickness, microstructure, epitaxy?
What are those effects?
What are their mechanisms?
……………….
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Our VASE studies
REFERENCE CRYSTALS SrTiO3 KTaO3 BaTiO3
KNbO3 NaNbO3 PbTiO3
FERROELECTRIC FILMS SrTiO3
KTaO3
BaTiO3
KNbO3 NaNbO3
PbTiO3
(Pb,Sr)TiO3
Pb(Zr,Ti)O3
(K,Na)NbO3
Pb(Sc,Nb)O3
(Pb,Sr)(Ti,Mn)O3
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SUBSTRATES SrTiO3 LaAlO3 DyScO3
(La,Sr)(Al,Ta)O3
MgAl2O4 MgO Si/SiO2
ELECTRODES SrRuO3 (La,Sr)MnO3 (La,Sr)CoO3
(In,Sn)Ox Pt/Ti
Variable angle spectroscopic ellipsometer
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Strain-induced changes in epitaxial films: n(VIS)
The out-of-plane strain s is expressed in 10-3 with reference to the tetragonal c-parameter of the bulk prototype (all are pseudo-tetragonal for simplicity).
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a b
c
bulk prototype
a b
a g 90o
(pseudo-tetragonal approximation)
(c+
Dc)
(c+
Dc)
strained films
s = Dc/c >0 s = Dc/c <0
Strain-induced changes in films: n(VIS)
1 2 3
2.5
3.0
n
E (eV)
crystal-5
-10
SrTiO3
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1 2 3
2.2
2.4
2.6
n
E (eV)
+2
-11
+7
NaNbO3
crystal
Epitaxial lattice strain has no or minor effect in films of antiferroelectric NaNbO3 and paraelectric SrTiO3.
Strain-induced changes in films: n(VIS)
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1 2 31.5
2.0
2.5
3.0
n
E (eV)
+7
0
(K,Na)NbO3
+12.5
1 2 3
2.0
2.5
3.0
E (eV)
n crystal
BaTiO3
+3
+8
+13
Epitaxial lattice strain has strong effect in films of BO6-type ferroelectric BaTiO3 and K0.5Na0.5NbO3.
Effective elasto-optic coefficient is (10…30) times larger than in bulk.
1 2 3 40
1
2
3
a (
10
5 c
m-1)
E (ev)
Strain-induced changes in BaTiO3
1 2 3
2.0
2.5
3.0
E (eV)
n
crystal
+13
+3
BaTiO3
+8
2 4 6 8
2
3
E (eV)
n
Decrease of n(VIS) is associated with the blue-shifts of the absorption edge and main peak, in good agreement with the semi-empirical model.
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Critical point analysis
gee iEEiAE 000 exp
2
0
2
2 exp
iEE
iA
dE
d e
CP’s parameters (A, , E0, and ) are impossible to directly extract from the spectra of dielectric functions. The second derivative is investigated
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(1) Dielectric function (e1, e2) is obtained using VASE (2) Spectra (e1, e2) are smoothed using Savitzky-Golay algorithm (3) Second derivatives are obtained numerically (4) CP’s parameters are extracted from spectra of second derivatives
assuming = 0, 0.5p, p, or 1.5p for simplicity (5) Energies E0 and phases of CPs in the films and crystals are compared
Critical points in KNbO3: film vs crystal
Cube-on-cube-type epitaxy of perovskite cell of KNaNbO3 on SrTiO3 (001). In-plane strain is compressive -2.8%.
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Critical points in KNbO3: film vs crystal
0
5
10
0
4
8
2 4 6 8
0
4
2 4 6 8
0
4
8
e1
c
CRYSTAL
e 1
a
FILM
E (eV)
e2
b
e2
E (eV)
d
VASE-measured room-temperature dielectric functions in the KNO film and crystal.
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-30
0
2 4 6 8
0
20
-100
0
2 4 6 8
-100
0
100
CRYSTAL
d2e 1
/dE
2
a
FILM
d2e 2
/dE
2
E (eV)
b
c
E (eV)
d
Critical points in KNbO3: film vs crystal
The derivative (a,c) d2e1/dE2 and (b,d) d2e2/dE2 as a function of photon energy E in (a,b) the epitaxial KNO film and (c,d) the KNO crystal. Solid lines show fits.
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Critical points in KNbO3: film vs crystal
epitaxial film
crystal
E0, eV , p A E0, eV , p A
3.56 0.02 1.5 0.40 0.05 0.20 0.02 4.00 0.02 1 1.5 0.10 0.28 0.02
4.23 0.01 0 1.60 0.03 0.23 0.01 4.41 0.01 0 6.0 0.20 0.21 0.01
4.80 0.02 0.5 1.05 0.05 0.27 0.03 4.72 0.02 1 1.5 0.10 0.20 0.02
6.92 0.02 1.5 0.80 0.05 0.40 0.03 5.60 0.03 0.5 0.6 0.10 0.24 0.02
7.24 0.03 1 0.40 0.05 0.40 0.03 5.90 0.03 1 1.8 0.10 0.20 0.03
8.42 0.02 0 0.80 0.02 0.40 0.02 8.20 0.01 0 1.5 0.10 0.22 0.02
E0, eV , p E0, eV , p
new 3.56 0.02 1.5 4.00 0.02 1
red-shift 4.23 0.01 0 4.41 0.01 0
new 4.80 0.02 0.5 4.72 0.02 1
new 6.92 0.02 1.5 5.60 0.03 0.5
new 7.24 0.03 1 5.90 0.03 1
blue-shift 8.42 0.02 0 8.20 0.01 0
Epitaxy produces dramatic changes of the energies and types of interband transitions!
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In brief:
Epitaxial ferroelectric heterostructures are attractive for
integrated photonics applications. Increased knowledge and better fundamental understanding of
optical properties of ferroelectric heterostructures should be achieved.
The state-of-the-art VASE instruments and methodology are capable of probing these optical properties.
Research progress demands expanded range of measurement conditions (spectral, thermal, temporal, etc) and extensive modeling.
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Acknowledgements
Grant Agency of the Czech Republic
Academy of Finland
Finnish Funding Agency for Innovation
Academy of Sciences of the Czech Republic
Graduate School (University of Oulu)
Graduate School (Czech Technical University in Prague)
ELI - Extreme Light Infrastructure
Our team
VASE studies
A. Dejneka, D. Chvostova, E. Chernova, C. D. Brooks
Epitaxial growth of perovskite oxides T. Kocourek, M. Jelinek Microstructural and domain analyses O. Pacherova, J. Peräntie, L. D. Yao, S. van Dijken, S. Saukko, M. Klinger, S. Cichoń, V. Cháb Functional responses M. Savinov, A. Stupakov, J. Pokorny, E. Tereshina Theory and modeling P. Yudin
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