Size Effects on Polarization in Epitaxial
Ferroelectric Thin Films
H. Kohlstedt, N. A. Pertseva), Julio Rodríguez Contreras, J.Schubertb),
U Poppe,
U.
Poppe C.
C Jia,
Jia K.
K Szot,
Szot R.
R Waser,
Waser
and A. G. Zembilgotovc)
a)
b)
c)
FZ- Jülich, Institut für Festkörperforschung, Germany
A. F. Ioffe Physico-Technical Institute, St. Petersburg, Russia
FZ-Jülich, Institut für Schichten und Grenzflächen, Germany
State Technical University of St. Petersburg, Russia
Outline
1 Size-effects in ferroelectric materials (a short survey)
2
3
4
5
Electrical and mechanical boundary conditions
Epitaxial thin films
Mean-field theory on epitaxial films
Ferroelectric tunnel junctions (a „polar
polar switch
switch“?)
?)
6 Conclusions
FZJ R
Research
hC
Center
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Jülich
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h.h.kohlstedt@fz-juelich.de: MRS Fall 2001
1 Size-effects in ferroelectric materials
Lateral
L
t l 2D:
2D - individual
i di id l capacitors
it on substratesbt t
Top down, FIB 200 nm x 200 nm
Bottom up/top down
etch free fabrication
75 nm dots
Polarizatio
on
S. Tiedke, A. Roelofs,
T. Sc
Schmitz,
t , K. Prume,
u e,
T. Schneller, U. Kall,
C.S. Ganpule, A. Stanhishevsky,
R. Ramesh, and R. Waser, APL, 79 3678, 26 Nov. 2001
Bottom up: CSD-self assembled
70 nm
grain
M. Alexe et al. APL 75, 1793 (1999).
and APL 79,
79 242 (2001).
(2001)
Studyy of individual pproperties
p
In Powders: only averaging possible
A. Roelofs, T. Schneller, F. Schlaphof 2000
2
2
Pertsev
Ghosez and Rabe (PTO)
Abe (PZ
ZT);
Yoneda
a (BTO)
Li et al.
L
J. Scott
Symetrix (PZT)
10
Sayer (PZT)
100
Tyybell (PZT)
6
4
an (TGS)
Batra and Silverma
Thick
kness Lim
mit (nm)
1000
Bune (PVF2)
(nm)
8
Karasawa (P
PTO)
10
Marayuma (P
PZT)
Film Thickness:
historical survey – some milestones
Li et al.
L
1 Size-effects
Size effects in ferroelectric thin films
monolayer of oxide (0.4 nm)
0
1996
1997
1998
1999
2000
2001
1
1970 1975 1980 1985 1990 1995 2000
Year of Publication
??Whyy does this trend exists??
3
Boundaryy conditions
(for thin films)
Dead layer and/or
Surface layer
Top electrode
Ferroelectric film
Bottom electrode
S b t t
Substrate
A Electrical boundary
B Mechanical/compositional
boundary
Scaling: Interfaces become more important !!
4
A: Electrical Boundary Conditions
Milestones:
Polarization
P
Depolarization field
++++++++++++
ED
Batra and Silvermann,
Solid State Comm. 11, 291 (1972).
d > 400 nm due to depolarization
____________
R. Kretchmer and K. Binder,
Phys. Rev. B 20, 1065 (1979).
ρ = div P
inhomogeneous polarization distribution at interface
Tilley and Zêks, Solid State Comm., 49, 823 (1984)
Thomas-Fermi
Thomas
Fermi screening length
M_ _l _ _ _ _ _
_ _ _ _ _Metal
++++++++++++
ED
____________
++++++++++++
no
complete
compensation
Y. Watanabe, Phys. Rev. B 57, 789 (1998).
depolarization field vanishes
(ferroelectric has finite conductivity)
Metal
FZJ Research Center Jülich
5
B: Mechanical/Compositional Boundary Conditions
Device structure I
Noble metal electrodes
Dead layer formation, Pr = 0
High angle grain boundaries
High-angle
Device structure II
Epitaxial (single crystal) electrodes and Fe
Fe-Films
Films
on single crystal oxide substrates
Surface layer, Pr
Platinum/IrOx
SrRuO3
PZT, BTO
PZT, BTO
Platinum/IrOx
/
SrRuO3
Si-Substrate (CMOS)
SrTiO3
non-ideal situation, complicated,
difficult to reach by theory
approach for ideal situation,
may be accessible by theory
Best approach for application,
Combination
Co
b a o with CMOS
C OS Technology,
o ogy,
Good retention, fatigue and imprint data!!
P∞
Best approach to study
finite ssize effectss in
ferroelectric thin films
6
B: Mechanical/Compositional Boundary Conditions
Device structure II
Epitaxial (single crystal) electrodes and Fe-Films on
single crystal oxide substrates
Milestones:
(thin film deposition-devices)
R. Ramesh et al., Appl. Phys. Lett 59, 3542 (1991).
PbZr0.2Ti
0.803/YBaCuO/LaAlO3-Substrate
C. B. Eom et al. Science 258, 1766 (1993).
SrRuO3 as electrode on SrTiO3-Substrate
C. B. Eom et al. Appl. Phys. Lett. 63, 2570 (1993).
SrRuO3 /PbZr0.52Ti0.48 03/ SrRuO3 - Fe-Capacitors
Th. Tybell, C. H. Ahn, and J.-M. Triscone,
Apl.Phys. Lett. 75, 856 (1999).
4 nm PbZr0.2Ti0.803 on Nb:SrTiO3 are ferroelectric
7
The concept of extrapolation length
(free standing film)
R. Kretschmer and K. Binder, Phys. Rev. B20
B20,, 1065 (1979).
interface region
outer part
P
interface region
P
inner part
P∞
P∞
correlation
length ξ
ρ
extrapolation
t
l ti length
l
th
x
ρ > 0: P decreases at interface
x
ρ < 0: P increases at interface
8
I t i i effect
Intrinsic
ff t off fil
film surfaces
f
Mean fieldfield-theory + Concept of extrapolation length δ:
¾
¾
¾
¾
¾
R. Kretschmer and K. Binder, Phys. Rev. B20
B20,, 1065 (1979).
D. R. Tilley and B. Žekš, Solid State Comm.
Comm. 49
49,, 823 (1984).
J. F. Scott, H. M. Duiker, P. D. Beale, B. Pouligny, K. Dimmler, M.
Parris, D. Butler, and S. Eaton, Physica B150
B150,, 160 (1988).
W. L. Zhong, B. D. Qu, P. L. Zhang and Y. G. Wang, Phys. Rev.
Rev.
B50,, 12375 (1994).
B50
S Li
S.
Li, J.
J A
A. Eastman
Eastman, Z.
Z Li,
Li C.
C M.
M Foster,
Foster R.
R E.
E Newnham,
Newnham and L.
L E.
E
Cross, Phys. Lett.
Lett. A212
A212,, 341 (1996).
Free-standing films only!
Freeonly!
Substrate--induced strains in epifilms ignored!
Substrate
9
The concept of extrapolation length
(free film)
interface region
P
outer part
P∞
Substrate 2D-clamping,
compressive case
inner part
correlation
length ξ
ρ
extrapolation length
ρ > 0: P decreases at
interface
Unit cell of BaTiO3,
Pb (ZrTi) O3
x
Enhancement of P possible
Sm = (b – a0)/b
b = substrate
subst ate lattice
att ce pa
parameter
a ete
a0 = equiv. cubic cell constant of
free film, Prototypic cell
Sm: Misfit
f strain
10
EXTRINSIC SIZE EFFECT OF MECHANICAL ORIGIN
Lattice misfit between film and substrate
H ≤ H* :
⇒
Misfit strain Sm
Sm = (b – a0)/b – independent of film thickness H!
b = substrate lattice parameter
a0 = equivalent cubic cell constant of free standing film
H > H*:
Sm = (b* – a0)/b* - becomes thickness-dependent!
Substrate effective lattice parameter b*:
[J. S. Speck, W. Pompe, J. Appl. Phys. 76, 466 (1994)]
⎡ (b − a0 ) ⎛ H * ⎞⎤
b * ( H ) ≈ b ⎢1 −
⎜1 −
⎟
b ⎝
H ⎠⎥⎦
⎣
Polarization Ps = function of Sm
[N. A. Pertsev, A. G. Zembilgotov, A. K. Tagantsev, Phys. Rev. Lett. 80, 1988 (1998)]
⇒
Thickness dependence of Ps via Sm(H) at H > H*!
11
Ferroelectricity in ultrathin films on compressive substrates (I)
A. G. Zembilgotov, N. A. Pertsev, H. Kohlstedt, and R. Waser, cond
cond--mat/
mat/0111218;
0111218;
J. Appl
A l. Phys
Appl.
Ph . 89 (2002
Phys.
2002)) (in
(i press).
press)).
Total Helmholtz free energy of inhomogeneously polarized film
film::
H /2
ℑ/ A =
∫
F ( z )dz +
−H / 2
(
1
g11δ −1 P−2 + P+2
2
)
S m2
1 ⎛ dP ⎞
*
F ( z) =
+ a3* ( S m ) P 2 + a33
P 4 + a111 P 6 + g11 ⎜ ⎟
s11 + s12
2 ⎝ dz ⎠
2Q
Q12
a = a1 − S m
s11 + s12
*
3
2
Q122
a = a11 +
s11 + s12
*
33
Sm = misfit strain Q12 = electrostrictive constant sij = elastic compliances
12
Ferroelectricityy in ultrathin films on compressive
p
substrates ((II))
Polarization profile P(z) and mean
polarization via EulerEuler-Lagrange equation:
1.0
d 2P
*
P 3 + 6a111 P 5
g11 2 = 2a3* P + 4a33
dz
⇒ Size effect is governed by normalized
film thickness H/ξ* and ratio δ/ξ*!
|
Mean polariza
ation, P/Ps
0.8
0.6
0.4
0.2
ξ * = g11 / a3*
- modified correlation length
((function of misfit strain!))
0.0
0
2
4
6
8
10
12
14
*
Relative film thickness, H/ξ
Compare: ξ = g / a
11
1
= bulk correlation
length
13
The concept of extrapolation length
(free film)
o te pa
outer
partt
P∞
P
p g
Clamping
inne part
inner
pa t
correlation
length ξ
ρ
extrapolation length
x
ρ > 0: P decreases at
i t f
interface
negative surface effect
Polarization enhancement
14
Competition between surface and strain effects
620
40 nm
B TiO3
BaTiO
0.38
2
580
560
540
|
bulk
520
2 5 10 20
500
480
460
440
420
400
Mean polarizatio
M
on P, C/m
Tran
nsition temperatture Tc, °C
0.40
PbTiO3
600
thick film
0.36
0.34
12 nm
0 32
0.32
0.30
1
2.6
8.6
0.28
bulk
0.26
0.24
0.22
380
-5
-4
-3
-2
-1
0
-3
Misfit strain Sm, 10
Tc((film)) > Tc ((bulk)) even in ultrathin films!
(Numbers give the normalized thickness H/ξ0)
0.20
-30
-25
-20
-15
Misfit strain Sm, 10
-10
-5
-3
P(film) > P (bulk) even in ultrathin films!
Circles give remanent polarizations observed in
BaTiO3 films grown on SrRuO3 / SrTiO3
N. Yanase, K. Abe, N. Fukushima, T. Kawakubo,
Jpn. J. Appl. Phys. 38
38,, 5305 (1999).
15
Ultra-thin
Ultra
thin ferroelectric films
and
Quantum Mechanical Tunneling
The concept of Ferroelectric Tunnel Junctions: FTJs
SrRuO3
Ferroelectric-Film
SrRuO3
t < 6 nm
Quantum mechanical electron tunneling cannot be ignored !!
Large (tunneling) leakage current makes
measurements with Sawyer-Tower circuit difficult!!
16
E
Tunneling effect
-ikx
Ψ∝
e
k
Barrier
EB
Tunneling Propability:
⎛ 2 t
⎞
P( Ex ) = A ⋅ exp ⎜ − ∫ 2m ⎡⎣φ ( x,V ) − Ex ⎤⎦ dx ⎟
⎝ h 0
⎠
El
Electrode1
d 1
El
Electrode
d 2
0
t
Barrier
B
i
t
Tunneling Current:
I (V ) = ∫ ρ1 ( E ) ρ2 ( E − eV
V ) ⎡⎣ f ( E − eV
V ) − f ( E ) ⎤⎦ M ( E ) dE
2
FZJ Research Center Jülich
EF,1
φ0
eV
EF,2
17
Ferroelectric Tunnel Junctions
Motivation and first Results:
A polar switch?
Interplay between Tunneling and Polarization?
Metal
Pb2+
Tunnel current
± Pr
O2-
e-
Zr4+/Ti4+
Metal
P
Current
“1”
?
Vc
E
“0”
Vc
Voltage
Æ Itunneling = f (U, d, EB,A,… Ec, P) ???
18
Simplified band diagram of FTJ
c-axis
Ba
(1)
Ti
(2)
O
χ
Estimation: Ec = 200 kV/cm (thick film)
U (x)
E
EF1
φ1
φ2
eVbias
EF2
Eg
SrRuO3
SrRuO3
x
bottom electrode
BaTiO3
Barrier thickness t = 5 nm
Vc = 100 mV!!
(only correct if Ec is
thickness independent)
top electrode
t< 6 nm
19
Ferroelectric Tunnel Junctions
First Results:
High-Resolution TEM, C. Jia-FZ-Jülich
SrRuO3
PZT
SrRuO3
SrRuO3
4 nm PZT
SrRuO3
4 nm
SrTiO3
More details about layer deposition and tunnel junction fabrication are in:
C 6.5 /O5.8 this session at 4:15 pm by Julio Rodríguez Contreras
and
d
Poster Session: Today, 8:00 PM, Exhibition Hall D, O6.10/C8.10 by Jürgen Schubert
20
Ferroelectric Tunnel Junctions
First Results:
Tunnel junctions with oxides materials:
(other fields)
Superconducting tunnel junctions:
I Bosovic and J.
I.
J N.
N Eckstein
J. of Alloys and Compounds 251, 201 (1997).
(extremely difficult)
I+
FTJ
V-
ISiO2
V+
V
SRO
BaTiO3
SRO
Magnetic tunnel Junctions:
Y. Lu et al. Phys. Rev. B 54, 8357 (1996).
IBM Yorktown
LCMO
SrTiO
S
TiO3
LCMO
Note: the terms superconducting and magnetic
are related to electrode properties.
Whereas:
Ferroelectric (tunnel junction)
is related to a barrier property
21
Ferroelectric Tunnel Junctions
STO (substrate) SrRuO3/PbZr0.52Ti0.48(5nm)/Pt (top)
Typical virgin curve
Conductance vs
vs. V
Electric Field E (kV/cm)
-1000
1,5
0
1000
Asymmetric
barrier heights !
2000
1,75
#3 - 5 nm PZT FTJ 2/7
300 K
0,5
dI/dU (a.u.)
nt (mA)
Curren
1,0
A
0,0
,
RA= 760 Ω
-0,5
B
RB= 580 Ω
-1,0
B
1,50
A
start
-1,5
stop
-0,5
0,0
0,5
Voltage (V)
1,0
-0,1
0,0
0,1
Voltage U (V)
Watanabe et al. 1994 – 1998 (APL, PRB)
Explanations:
(a) electro migration
((b)Trapping/detrapping
) pp g/
pp g of carriers due to band bending
g
!! Two point measurement/100 nm and 200 nm ferroelectric films!!
22
Ferroelectric Tunnel Junctions
SrRuO3/BaTiO3(5nm)/SrRuO3
Ovonic device: based on
Chalcogenide alloys
Amorphous-crystalline transition
500 nm
Electric Field E (kV/cm)
-1000
0
1000
Currennt (mA)
1,0 #14 - 6 nm BTO FTJ 10/11
T = 300 K
Beck et al.
APL 77,, 139 (2000).
(
)
IBM-Zürich
Based on:
SRO/SrZrO3:Cr/SRO
Charging
g g and
decharching of traps
300 nm
4
5
0,5
3
00
0,0
2
Vs = 670 mV
6
-0,5
1
7
-1,0
-1000
-500
(resistive switching)
Stanford R. Ovshinsky,
Phys. Rev. Lett. 21, 1450 (1968)
I-V after poling: -1.2
-1 2 V,
V 500 ms
-2000
Other MIM structures
0
Voltage (mV)
500
Ferroelectric origin??
1000
L. Esaki et al.
IBM Technical Disclosure Bull.
Bull
13, 2161 (1971).
POLAR SWITCH
Nb/bismuth niobate/Bi
May be ferroelectric origin
23
Ferroelectric Origin of switching?
Es = 1000 kV/cm: switching fied
General tendency for critical field: t ⇓
Ec⇑
Thick film: 200 nm
Ec = 100 kV/cm
Thin film: 12 nm
Yanase et al
al.
Jpn. J. Appl. Phys. 38, 5305 (1999).
Ec = 600 kV/cm!
Ultra-thin film: 5 nm
Ec = 1000 kV/cm
Not unrealistic
24
Ferroelectric Origin of switching?
Butterfly curve
Piezoelectric effect?
Strain,
expansion z
Rtunneling ∼ exp (-t(V)...)
Electric Field E (kV/cm)
Field
-2000
-1000
0
1000
Current (mA))
C
1,0 #14 - 6 nm BTO FTJ 10/11
T = 300 K
Current
4
5
05
0,5
3
0,0
2
Vs = 670 mV
6
-0,5
1
Field
7
-1,0
-1000
1000
-500
500
0
500
1000
Voltage (mV)
25
Ult thi fil
Ultrathin
films under
d external
t
l electric
l t i field
fi ld
Metal
BaTiO3, PZT, or others
Metal
Tunnel current cannot be ignored
B. Meyer and D. Vanderbilt: Phys. Rev. B 63, 205426 (2001).
S. Tinte and M. G. Stachiotti, Phys. Rev. B 64, 235403 (2001).
A G.
A.
G Zembilgotov et al
al. cond
cond-mat/0111218,
mat/0111218 J.
J Appl.
Appl Phys.
Phys 89 (2002) in press.
press
26
Conclusions
•
The mean-field approach:
Expitaxial films down to 2 nm can be ferroelectric
•
At film thicknesses less than 6 nm
quantum
t
mechanical
h i l tunneling
t
li
can nott be
b ignored
i
d–
this is important for any theoretical and experimental consideration
•
Relation between Tunneling and Polarization?
•
First ferroelectric tunnel junctions were
prepared and I-V curves showed switching events.
•
It is not clear whether this switching
g events have a ferroelectric origin
g –
electromigration/creeping (or other effects) are may be present
Acknowledgement: This work is supported by the
Volkswagen Stiftung and the HGF-Strategiefonds “Piccolo”.
FZJ R
Research
hC
Center
t Jüli
Jülich
h
27