Transcript Document

Full first-principles simulations on 180º stripe
domains in realistic ferroelectric capacitors
Pablo Aguado-Puente
Javier Junquera
Technological applications: ABO3 perovskites
oxides, promising candidates for NV-FRAM
perovskite oxide
(PZT,BST)
metal
(SrTiO3-Nb, SrRuO3,Pt)
The use as a NV-FRAM depends on the existence of a
polar ground state …
… is there a fundamental limit?
Fundamental motivation: what’s the most stable
phase for epitaxial ferroelectric ultrathin films?
• Long time question.
1
1970 1975 1980 1985 1990 1995 2000
Year of Publication
?
Streiffer (PTO)
Streiffer (PTO)
Pertsev (PTO)
Tybell (PZT)
Marayuma (PZT)
Ghosez and Rabe (PTO)
2
Bune et al. (PVDF)
Yanase (PZT)
Yoneda (BTO)
Li (BTO)
Symetrix (PZT)
J. Scott (PZT)
10
Sayer (PZT)
100
Li et al. (PZT)
6
4
Batra and Silverman (TGS)
Thickness Limit (nm)
Courtesy of H. Kohlstedt
(nm)
8
Karasawa (PTO)
10
Junquera and Ghosez (BTO)
•Hot field.
0
1996 1997 1998 1999 2000 2001 2002 2003
PTO: PbTiO3
PZT: Pb(Zr,Ti)O3
BTO: BaTiO3
TGS: tryglycine sulphate
PVDF: Ferroelectric polymer
Ph. Ghosez and J. Junquera, First-Principles Modeling of Ferroelectric Oxide Nanostructures,
Handbook of Theoretical and Computational Nanotechnology, Vol. 9, Chap. 13, 623-728 (2006)
(http://xxx.lanl.gov/pdf/cond-mat/0605299)
and references therein.
Experimentally: small changes in boundary
conditions, great changes in ground state
a
d
d
PbTiO3
PbTiO3
SrTiO3
Nb-SrTiO3
(insulator)
(metal)
D. D. Fong et al. (2004)
S. K. Streiffer et al. (2002)
C. Lichtensteiger et al. (2005)
A. T. J. van Helvoort et al. (2005)
SrRuO3
d
PbTiO3
PbZr0.2Ti0.8O3
SrTiO3
SrRuO3
(insulator)
SrTiO3
D. D. Fong et al. (2005)
V. Nagarajan et al. (2006)
Many effects might alter the delicate balance
between long and short range forces
Surface
Defects
(vacancies, misfit
dislocations…)
Chemistry
Finite
conductivity
Mechanical
Experimental measures,
Electrostatic
global result
First-principles calculations allow to isolate their
respective influence
Surface
Defects
Chemistry
(vacancies, misfit
dislocations…)
Finite
conductivity
Mechanical
Electrostatic
Until today, monodomain studies, goal of this work:
ab initio multidomain simulations
real electrode
●
Uniform reduction of the polarization
Junquera and Ghosez, (2003)
Umeno et al. (2006)
bulk
Ed
P’
real electrode
real electrode
P
●
Break down into domains
Present work
• Full first-principles simulation using
• Explicitly included electrodes.
real electrode
Ferroelectric layer: fundamental parameters of the
simulations
FE layer: Nx repetitions in [100] direction and m cells in [001] direction
m = layer thickness
Nx = domain period
• Nx from 2 to 8 cells
• m from 2 to 4 cells
• FE layer made of BaTiO3.
• Domain wall in BaO and TiO2
Building the cell: the paraelectric unit cell
• Building the reference cell following the scheme of
Junquera and Ghosez (2003).
Sr
Short-circuit boundary
conditions
SrRuO3
Mirror symmetry plane
BaTiO3
[001]
SrRuO3
SrTiO3
[100]
a = aSrTiO3
Nat = 40 atoms
m = 2 unit cells
Ru
O
Ti
Ba
Building the cell: replicating the paraelectric
structure
• Nx repetitions in [100] direction.
• The energies of these cells as references.
Nat = Nx · 40 atoms
Building the cell: inducing a polarization by hand
• Chosing a domain wall.
• Inducing a polarization by hand in the FE layer displacing
the atoms a percentage of the bulk soft mode.
Nat = Nx · 40 atoms
Relaxing all the atomic coordinates coordinates,
both in the FE layer and the electrodes
Forces smaller than 0.01 eV/Å
No constraints impossed on the atomic positions
Results: multidomain phases more stable than
paraelectric structure for Nx > 4
2-unit-cells thick BaTiO3 layer
0.3
Ba-wall
( E -E para )/N x (meV)
0.2
Ti-wall
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
1
2
3
4
5
N cells
x
6
7
8
9
Results: multidomain phases more stable than
paraelectric structure for Nx > 4
Nx = 4
Nx = 4
0.3
Ba-wall
0.2
BaO domain walls
Ti-wall
0.1
0
( E -E
para
)/N
x
(meV)
BaO domain walls
-0.1
-0.2
-0.3
-0.4
-0.5
1
2
3
4
5
6
7
8
N cells
x
Ferromagnetic domains
C. Kittel (1971)
9
Results: multidomain phases more stable than
paraelectric structure for Nx > 4
Nx=4
BaO wall
2-unit-cells thick BaTiO3 layer
Nx=6
BaO wall
0.3
Ba-wall
Ti-wall
0.1
0
( E -E
para
)/N
x
(meV)
0.2
TiO2 wall
-0.1
-0.2
-0.3
TiO2 wall
-0.4
-0.5
1
2
3
4
5
N cells
x
6
7
8
9
Resulting phases show in-plane displacements and
small polarization
Nx = 4
BaO domain walls
Small polarization inside the
domains.
0.3

Sr
O
Ti
Ba
0.1
 (Bohr)
Ru
N =2
x
bulk
0.2

capacitor
0
-0.1
-0.2
-0.3
-10
-5
0
5
10
TiO -wall distance from domain wall (Bohr)
2
About 1/10 of bulk soft-mode polarization
In-plane displacements are essential to get
polarization domains
In-plane displacements: ON
In-plane displacements: OFF
0.3
0.3


N =2
x
bulk

0.1
capacitor
 (Bohr)
 (Bohr)
x
0.2
0.2
0.1
N =2
bulk
0
-0.1
-0.2
-0.2
-0.3
-0.3
-5
0
5
10
TiO -wall distance from domain wall (Bohr)
2
capacitor
0
-0.1
-10

-10
-5
0
5
10
TiO -wall distance from domain wall (Bohr)
2
When in-plane coordinates are fixed, structure goes back
to the paraelectric phase
Changing the electrode, the ground state of PbTiO3
changes from monodomain to polydomain
Lichtensteiger, et al.
Lichtensteiger, Triscone, Junquera, Ghosez.
Transition from vortices to standard 180º domains.
4-unit-cell thick layer, great increase in polarization
m = 4, Nx = 4
TiO2 domain walls
Sr
0.3

N =4
Ru
x
bulk
0.2
O
 (Bohr)
0.1
Ti
0

-0.1
Ba
capacitor
-0.2
-0.3
-15
-10
-5
0
5
10
15
TiO -wall distance from domain wall (Bohr)
2
(E-Epara)/Nx < -16.6 meV
Displacements 10 times bigger than in the 2-cells thick layer
Conclusions
• There are stable multidomain phases in ultrathin FE
films.
0.3
Ba-wall
Ti-wall
0.1
0
( E -E
para
)/N
x
(meV)
0.2
-0.1
0.3

-0.2
N =2
x
bulk
0.2
-0.3

0.1
 (Bohr)
-0.4
-0.5
1
2
3
4
5
6
7
8
9
N cells
capacitor
0
-0.1
x
-0.2
• The chemical interaction through the interface is an
essential factor since it affects the in-plane mobility of
the atoms.
-0.3
-10
-5
0
5
10
TiO -wall distance from domain wall (Bohr)
2
• Closure domains in FE capacitors are predicted.
Slides available at: http://personales.unican.es/junqueraj
Contact: [email protected]
[email protected]
More information …
Method: Computational details
First-principles calculations within
Kohn-Sham Density Functional Theory (DFT)
: Numerical Atomic Orbital DFT code.
http://www.uam.es/siesta
J. M. Soler et al., J. Phys. Condens. Matter 14, 2745 (2002)
Exchange-correlation functional : LDA, fit to Ceperley-Alder data
Norm conserving pseudopotentials: Ti, Sr, Ba, Ru: semicore in
valence
Basis set:
NAO: valence: Double- + Polarization ; semicore: Single-
Real-space grid cutoff : 400 Ry
k-point grid : equivalent to 12x12x12 for simple cubic perovskite
Supercell geometry
Very small energy differences, very accurate
simulations needed
m=2, Nx = 4
BaO domain walls
Structure
Total Energy (eV)
Paraelectric
-138326.083054
Multidomain
-138326.084463
(E-Epara)/Nx = -0.00035 eV