IMR, Tohoku UniversityTakeshi Nishimatsu

dielectricspiezoelectricspyroelectrics

ferroelectrics (switchable) Because BaTiO3 base and PbZrxTi1-xO3 (PZT) base ferroelectric materials has good properties for applications all above, there are many electronics devices using these materials. Traditionally, Japanese companies have high market shares in such ferroelectric ceramics industries.

High Symmetry Low

polarity

inversion

# of classes

crystal family

cubic hexagonaltetragonalrhombo hedral

ortho

mono

tri.

nonpolarcrystal (22)

yes(11) 11 Oh ThD6hC6hD4hC4hD3dC3iD2hC2hCi

no (21)

11O

T D6 D3h

C3hD4 D2d

S4 D3 D2Tdpolar （pyro）crystal (10)

10 C6vC6C4vC4C3vC3C2vC2 Cs

C1

white background: piezoelectric red letter: pyroelectric

}  Polarized by an applied external electric field

}  Switch-off electric field → polarization vanishes

} Application: multi-layer ceramics capacitor (MLCC) BaTiO3-base

} Application: electret microphone or capacitor microphone

Dielectrics

}  Piezoelectric effect: polarization developsin response to applied mechanical stress.

}  Inverse piezoelectric effect: strain develops in response of applied electric field.

}  Simple Td GaAs can have piezoelectricity. }  Applications: pressure sensor (Langasite,

La3Ga5SiO14), crystal oscillator (quartz SiO2) } Ceramics: piezoelectric speaker, ceramic oscillator, sonar, acceleration and gyro sensor, supersonic vibrator, etc., etc…..

Piezoelectrics

After catalog from muRata P82e.pdf 2011-06-30. Underlines by TN.

}  Polar crystals }  Polarization can be

slightly changed by IR. }  Application：IR sensor

}  Polarization can be switched by external electric field → ferroelectrics

PyroelectricsIR

IR sensor for lights (in IMR)

Phase transition of pyroelectrics.

}  Polarization can be switched by external electric field.

}  Spontaneouspolarization (Pr) remains at E=0.

}  Polarization can have some easy directions according to the crystal structure.

}  In finite systems, domain structures are formed to avoid depolarization field.

What are ferroelectrics?

}  Ferroelectric RAM is a random-access memory using a ferroelectric capacitor and its histeresis to achieve non-volatility.

}  Faster and lower voltage than Flash memory.

}  Down sizing →Higher Density →Replace DRAM → Normally-off Computing(Fast, Non-volatile, Without refresh)

What is electrocaloric effect?

Inverse effect of pyroelectric effect Application: Solid state cooling

Experimentally observed temperature dependence of lattice constants for BaTiO3. There are three first-order phase transitions. the cubic to tetragonal phase transition is nearly second-order one. After [H. E. Kay and P. Vousden: Philos. Mag. 40, 1019 (1949)]．

ferroelectric⇔paraelectric

After [Gen Shirane, Sadao Hoshino, and Kazuo Suzuki: Phys. Rev. 80, 1105 (1950)]

ferroelectric⇔paraelectric

}  Various applications of ferroelectric thin-films: multi-layer ceramics capacitors (MLCC), nonvolatile FeRAMs, nanoactuators, etc.

}  Down-sizing of FeRAMs (nano-capacitors of ferroelectric thin films) is highly demanded.

After [J. F. Scott: Ferroelectric Memories (Springer, 2000)]

}  Develope of fast molecular dynamics (MD) code which can simulate ferroelectric thin-film capacitors for a realistic system size (> 100 nm) and a realistic time span (> 100 ns).

}  Clarify the effect of dead layers between ferroelectrics and electrodes.

}  Predict properties of ferroelectrics ◦  dielectric constant ◦  domain structures ◦  effects of epitaxial strains ◦  pyroelectric effect ◦  electrocaloric effect ◦  etc, etc…

}  Parallelized with OpenMP http://OpenMP.org/ }  FFTW http://www.fftw.org/ }  Object Oriented Programming (OOP) with

Fortran 95/2003 }  GNU autotools (autoconf and automake) ◦  Easy to compile feram with ./configure && make ◦  Multi Platform using C preprocessor (CPP) ⇒ Available on PC Linux, Hitachi SR16000, Fujitsu FX10, etc.

}  Source code is version-controlled under Subversion in http://SourceForge.net/

}  It’s free software!

Home page of feram

Papers using feram

}  Investigate ferroelectric BaTiO3, PbTiO3, etc. with first-principles calculations and construct an effective Hamiltonian with 25 parameters ◦  Using ABINIT http://www.abinit.org/ �  Plane wave: Ecut=60 Hartree, on 8x8x8 k-points �  Pseudopotentials http://opium.sf.net/ (Rappe et al.) �  GGA (Wu and Cohen). LDA and GGA (PBE) do not work well. �  Basically, absolute 0 K properties.

}  MD: time evolution of the effective Hamiltonian ◦  Original feram http://loto.sf.net/feram/ ◦  realistic system size (> 100 nm) and a realistic time span

(> 100 ns) ◦  Temperature, pressure, strain, external electric field ◦  bulk and thin-film

After [T. Hashimoto, T. Nishimatsu et al.: Jpn. J. Appl. Phys. 43, 6785 (2004)]

electric polarization

(dipole)

Total-energy surface (can be calculated with first-principles calculations.)

BaTiO3 GGA (Wu and Cohen)

}  BaTiO3 has shallower total-energy surface.

}  Most stable direction: [111]

}  PbTiO3 has deeper total-energy surface.

}  Most stable direction: [001]

BaTiO3 vs. PbTiO3

GGA (Wu and Cohen)

Other many first-principles calculations required for determination of parameters

}  Lattice constants, elastic coefficients }  Inter-atomic force constant (IFC) matrix Φ(k)

for determination of shor-range interactions. }  etc. etc.

With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.

-- John von NeumannIt’s quite tough to determine 25

parameters only from first principles. -- Takeshi Nishimatsu :-)

http://www.lanl.gov/history/atomicbomb/images/NeumannL.GIF

}  Perovskite ABO3: 15N+6 degrees of freedom ◦  5 atoms in a unit cell ◦  each atom can move x, y, z 3 directions ◦  N unit cells in a super cell ◦  6 components of strain

}  Coarse-graining: 6N+6 degrees of freedom ◦  One dipole vector Z*u(R) on each unit cell ◦  One acoustic displacement vector w(R) on each u.c.

See [W. Zhong, D. Vanderbilt, and K. M. Rabe, Phys. Rev. B 52, 6301 (1995)].

Super cell calculations with array of dipoles (Periodic boundary condition)

Parameters for BaTiO3 [Takeshi Nishimatsu et al.: PRB 82, 134106 (2010)]

Simplified flow chart for calculating forces on u(R). FFT and IFFT enable rapid calculation of long-range dipole-dipole interactions. Real space: O(N2) Reciprocal space with FFT: O(NlogN)

See [U. V. Waghmare et al.: Ferroelectrics 291, 187 (2003)].

}  Only with long-range dipole-dipole interactions, the minimum is atM-point (antiferro).

}  Adding short-rang interactions, the minimumgoes to Γ-point.

Only with long-range dipole-dipole interactions

long-rang interactions + short-range interactions

M

Γ BaTiO3

3-dimentional simple cubic (sc) dipole lattice

M-point is the minimum.

Electrode can be considered as electrostatic mirrors

See Nishimatsu et al.: PRB 78, 104104 (2008)

RESULTS of MD SIMULATIONSBaTiO3 (from GGA (Wu & Cohen))

Experiment

} MD simulation

€

εαβ = (ε∞)αβ +V

ε0kBTPαPα − Pα Pα( )

-60

-40

-20

0

20

40

60

-300 -200 -100 0 100 200 300

P z [µ

C /

cm2 ]

E [kV/cm]

hysteresis loop

bulk 32×32×32, T = 360 Kbulk 32×32×32, T = 460 Kbulk 32×32×32, T = 560 K

T = 100 K

With dead layers, the z-polarized state is no longer the ground state for a ferroelectric capacitor [BaTiO3, 16x16x (l=63,d=1)]

Dead layer à

PbTiO3

Frozen ９０° degree domain structures of PbTiO3 (snapshot at 300 K)

JPSJ 81, 124702 (2012)

Experimentally observed ９０° degree domain structures of PbTiO3

PbTiO3の９０°ドメイン（２）

HAADF-STEM image around edge dislocations with an a-domain. After [T. Kiguchi et al.: Sci. Technol. Adv. Mater. 12 (2011) 034413]. 600℃成膜時ミスフィット大→室温a軸はミスフィット小→転移→aドメイン

PbTiO3 90°ドメインのドメイン壁の厚さ

厚さ→１〜２ユニットセル

}  BaTiO3, supercell of 96×96×96 unit cells }  Constant T canonical ensemble MD

calculation under external electric field Ez }  After that turn off Ez=0, constant energy

micro-canonical ensemble MD calculation (leap-frog method)

}  External electric field: Ez=0〜500 kV/cm}  Coarse graining → under estimate Cv →

over setimate ΔT → correction

Computational conditions of direct MD simulations of ECE

Results of 【direct】 MD calculations

Smaller super cell size, larger fluctuation of ΔT

BaTiO3-35

-30

-25

-20

-15

-10

-5

0

300 350 400 450 500 550 600 650 700

∆T

[K

]

T [K]

BaTiO3 160→60 kV/cm

indirectMD × 2/5optimization × 1/5MDoptimization

x 2/5 correction

x 1/5 correction

-50

-40

-30

-20

-10

0

10

20

0 100 200 300 400 500 600 700 800 900-10

-8

-6

-4

-2

0

2

4∆

T [

K]

∆T

corr

ecte

d [

K]

T [K]

BaTiO3 300→0 kV/cm

[001][110][111]

Anisotropic effect of E

Results of direct MD calculations of ECE

BaTiO3

-12

-10

-8

-6

-4

-2

0

300 400 500 600 700 800 900-60

-50

-40

-30

-20

-10

0

∆T

corr

ecte

d [

K]

∆T

[K

]

T [K]

5→0 kV/cm 50→0 kV/cm100→0 kV/cm200→0 kV/cm

300→0 kV/cm400→0 kV/cm500→0 kV/cm

Effective temperature rang is narrower for smaller E field.

}  We developed "feram", a fast simulator for perovskite-type ferroelectric bulks and thin films.

}  Molecular dynamics (MD) simulation withfirst-principles-based effective Hamiltonian.

}  Phase transitions of bulk BaTiO3 and PbTiO3. }  Thin-film capacitor with perfect and imperfect

short-circuited electrodes. }  Electrocaloric effect }  etc, etc…

Summary

feram is free software!!! You can freely get it from http://loto.sourceforge.net/feram/ .