OPTICAL PROPERTIES · Piezoelectric 2(s E or E s) d α 10 – 103 pm/V [3 pm/V in quartz]...

OPTICAL PROPERTIES OF

ADVANCED FERROELECTRIC HETEROSTRUCTURES

Marina Tyunina

ELI BEAMLINES 11.10.2017. 1

Microelectronics Research Unit, University of Oulu, Finland

Institute of Physics of the Czech Academy of Sciences, Prague


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


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


-Pr

+Pr

+Ec

Po

lari

za

tio

n

Electric field

-Ps

+Ps

-Ec


Re Ni O3

Other important perovskite oxides: spontaneous metal-insulator-transition materials

Resis

tivit

y (

log s

cale

)

Temperature


La,Sr Mn O3

Other important perovskite oxides: metals-insulators with giant magnetoresistance

0

Resis

tivit

y

Magnetic field


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


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


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


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


-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


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)


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


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


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


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


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


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



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?

……………….


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


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


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).


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


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)


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.


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


(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%.



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.


-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


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.



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!


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.



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


OPTICAL PROPERTIES · Piezoelectric 2(s E or E s) d α 10 – 103 pm/V [3 pm/V in quartz]...

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Transcript of OPTICAL PROPERTIES · Piezoelectric 2(s E or E s) d α 10 – 103 pm/V [3 pm/V in quartz]...