Forschungszentrum Jülich

Ferroelectric Tunnel Junctions: A Theoretical Approach

H. Kohlstedt, A. Petraru, R. WaserForschungszentrum Jülich GmbH,

Institut für Festkörperforschung and CNI, the Center of Nanoelectronic Systems and Information Technology, Germany

N. A. PertsevA. F. Ioffe Physico-Technical Institute, St. Petersburg, Russia

Center ofNanoelectronic Systems Information Technology

Electron Tunneling through Insulators

EWpotW )(xφW )(xφ

xt0

k xikCΨxk real xk xk real

Re BΨ

xikB

xeB=Ψxik

CxeC=Ψimaginary

x

⎪⎫⎪⎧ t

xikxA −Ψ

Re AΨ

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧−= ∫ dxxmCT

t

0

)(22exp φh

AxeA=Ψ ⎭

Transmission coefficient

Electron tunneling: Current Transport Equation

Metal 1 Metal 2I

Fermi distributions of(occupied/unoccupied) states

Fermi distributions of( i d/ i d) t tj

j2-1(occupied/unoccupied) states

+ eVT

j1-2

dd

−− −=−=

jjjdirectionxdensitycurrentnvej x

1221

:

[ ] ⊥⊥

∞

⋅−= ∫∫⊥

⊥dkkTEfEfdEej

k

kE

max)(

),(213 )()(4 hπ o 04 hπ

Tunnel Junctions: A short Survey

Me I Me Su I Su Mag I Mag Semic I Me

Egg

I IΔR/R I

V V H V

Sommerfeld/Frenkel/Holm Giaever/Josephson Jullieré/Moodera/Parkin/(Sun/Fert for oxides)

Esaki

Ultra-thin Ferroelectric Films (Recent Results)

10

TO)

)

8

Gho

sez

(BT

ma

(PZT

)

ZT)

PTO

)

T)awa

(PTO

)

asur

ed

m)

6

O)

uera

and

G

(PTO

)

Mar

ayu

(PTO

)

Tybe

ll (P

Z

nd R

abe

(P

et a

l. (P

ZT

Kar

asa

cted

/mea

esss

(nm

2

4

treiff

er (P

T

Junq

u

Stre

iffer

Per

tsev

Gho

sez

anLi

um p

redi

c

thic

kne

1996 1997 1998 1999 2000 2001 2002 2003 20040

2 StG

Min

imu

one unit cell

Ferroelectricity exists down to a few number of unit cells!El t i l d h i l ( t i ) b d diti

1996 1997 1998 1999 2000 2001 2002 2003 2004

Electrical and mechanical (strain) boundary conditions are extremely important!

Ferroelectric Tunnel Junction

High-Resolution TEM

ASrRuO3

+ + + + + + + + + + + + + + + + + + + + + + + +e-

V10 unit cells PZT

+ + + + + + + + + + + + + + + + + + + + + + + +

P

4 nm

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

SrRuO3

Quantum Mechanical

⎪⎬⎫⎪

⎨⎧

∫ dCTx1

)(22 φ

Quantum Mechanical Electron TunnelingTunneling matrix element:

⎪⎭

⎪⎬

⎪⎩

⎪⎨−= ∫ dxxmCT

x0

)(2exp φh Polarization State of PZT

Superconducting -, Magnetic-, and Ferroelectric Tunnel Junctions

Dielectric Barrier

Superconductor Superconductor Magnet Magnet

[ ]dEEfeVEfEneVEnETAeVI )()()()()(2)( 21 −−⋅−= ∫∞

h

π∫∞−h

Metal Metal

Ferroelectric tunnel junction:

Cooperative phenomenon

Ferroelectric Barrier

is in the barrier !

Ferroelectric Tunnel Junction (preliminary Work)

13 2161 (1971)

Idea: Resistive switching caused by ferroelectricity! 13, 2161 (1971).by ferroelectricity!

European Patent:0 657936 A1, 1994R. M. Wolf and P. W. M. Blom, Philips Electronics, Eindhoven (NL).( )

Patent drawing Measurement

Influence of Ferroelectricity on Electron Tunneling y g

Volume effects Interface effects

S33 SrRuO3BaTiO3 +

VVc-Vc

-

Barrier thicknessLattice parameter:

Band structure

Polarization charge +/-Screening effectsDifferent structureBand structure

Effective mass Potential barrier

Strain: Volume effects I

t -t 0

VC-VC

a. Variation of barrier thickness

Voltage

b Shift of the conduction and valence band edges

Vdtt o 33+=

b. Shift of the conduction and valence band edges

dzEEhmCT

t

zC ⎟⎟⎠

⎞⎜⎜⎝

⎛−π−= ∫

0

0*24exp

( )02

*2

222

2 EEmk

kkk

zCz

z

−⋅=−

+= ⊥

h

⎠⎝ 0

( )333

0

2

SEE CC

zCz

κ+=h

Deformation Potential:Brooks 1955, Herring 1956, Kane 1970

3κ

c. Change of the electron effective mass

02* == km h** Vd∂∂

a: lattice parameter, Tight binding approx.

0,2 =Δ

= kEa

mC

0

33

33

*033

33

*0

*

tVd

SmmS

Smmm

∂∂

+=∂∂

+=

Strain: Volume effects II

T i i b bilit i WKB i ti ( b d d l)• Transmission probability in WKB approximation (one-band model)

dzEEmCTt

zc ⎟⎟⎞

⎜⎜⎛

−−= ∫*24exp π

• Influence of nonzero piezoelectric constant d33

hC zc ⎟

⎠⎜⎝

∫0

p π

⎪

⎪⎨⎧

±⎟⎟⎞

⎜⎜⎛

∂∂

±−= )(112

8exp)( 33033

*

*

*0 VdtVdm

hm

ET z π⎪⎩⎨ ⎟

⎠⎜⎝ ∂

)(23

p)( 330033

*0 tSmheVz

⎪⎫⎤⎡ ⎞⎛⎞⎛2/32/3

VV

⎪⎭

⎪⎬⎫

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−−±−⎟⎟

⎠

⎞⎜⎜⎝

⎛−±×

03333

0

03333

0zczc EeV

dVdEE

dVdE κκ

Strain: Volume effects III: I-V curves

4

2

3+Vc

106 A

/cm

2 ) 3

-V +Vance

, G/G

0

Symmetric I-V

0

1

Vnt d

ensi

ty (

2

-Vc+Vc

d co

nduc

ta

-2

-1 -Vc

Cur

ren

1Nor

mal

ize

-0.4 -0.2 0.0 0.2 0.4-4

-3 (a)

-0.4 -0.2 0.0 0.2 0.4

1(b)

Voltage (V) Voltage (V)

Parameter: d33 = 50pm/VCenter ofNanoelectronic Systems forInformation Technology

33 pBarrier height: 0.5 eVThickness t0 = 3 nm

Macroscopic Interface Effect I (non-perfect Screening)p ( p g)

Screening at top and bottom equivalent

M Dawber et al J Condens Matter 15 393 (2003)

PsV=0 V=0

----

++++

---

+++

M. Dawber et al., J. Condens. Matter, 15, 393 (2003).

Edep

V 0

Eel E l

-----

+++++

-----

+++++

Ferroelectricp

Electrode Electrode(a)

Eel-+--

++

Symmetric I V curveV

Same symmetry as in case of strain induced effects

Symmetric I-V curve

0 t/2 t x3

Macroscopic Interface Effect II (non-perfect Screening)p ( p g)

Screening at top and bottom not equivalent

Ps

---

Ps

+++

EEnfEdep

---

Edep

++++Δt

Enf

t

--

Δt ++

Δt Asymmetric I-V curce

V(x3)1 ( )ttEV dep Δ−+=21

x3

( )ttEV dep Δ−−=21

Symmetric and asymmetric Barrier Structures

tI

Symmetric barrier structure

φ

φ´1φ´2

φ1 φ2

t

t`

Vφ1 φ2

Electrode Ferroelectric Electrode S t i I VElectrode Ferroelectric Electrode

I

Asymmetric barrier structure

Symmetric I-V

I

φ´

2/)( ´21 φφφ +=a

2/)( φφφ +

fixedvariable

V

φ1 φ

22/)( 21 φφφ +=b

2

Asymmetric I-V

0.4

0.6

0.8 Φ2a

Φ1a = Φ1

b

(eV)

polarisation "a" polarisation "b"

0

1

2

3

4

A/cm

2 )

polarisation "a" polarisation "b"

20

30

(Ω-1cm

-1)

polarisation "a" polarisation "b"Extremely

Asymmetric

-5 0 5 10 15 20 25 30 35

0.0

0.2

Ym

Φ1b

Φ

x (A) -0.2 -0.1 0.0 0.1 0.2-4

-3

-2

-1J (A

U (V)-0.2 -0.1 0.0 0.1 0.2

0

10dJ/d

U (

U (V)

0.4

0.6

0.8 Φ2a

Φ1b

eV)

polarisation "a" polarisation "b"

0 00

0.05

0.10

0.15

0.20

/cm

2 )

polarisation "a" polarisation "b"

1 01.21.41.61.82.0

(Ω-1cm

-1)

polarisation "a" polarisation "b"

Reduced Asymmetry

-5 0 5 10 15 20 25 30 35

0.0

0.2

0.4

Ym

Φ2bΦ1

aΦ (

x (A) -0.2 -0.1 0.0 0.1 0.2

-0.15

-0.10

-0.05

0.00

J (A

/

U (V)-0.2 -0.1 0.0 0.1 0.2

0.00.20.40.60.81.0

dJ/d

U (

U (V)

Asymmetry

0.4

0.6

0.8 Φ2aΦ1

b

(eV)

polarisation "a" polarisation "b"

0 00

0.05

0.10

0.15

A/cm

2 )

polarisation "a" polarisation "b"

0 6

0.8

1.0

1.2

U (Ω

-1cm

-1)

polarisation "a" polarisation "b"

Crossingpoint CP

-5 0 5 10 15 20 25 30 35

0.0

0.2

Ym

Φ1bΦ1

a

Φ

x (A) -0.2 -0.1 0.0 0.1 0.2

-0.10

-0.05

0.00

J (A

U (V)

-0.2 -0.1 0.0 0.1 0.2

0.2

0.4

0.6

dJ/d

U

U (V)

pointCP: ΔR = 0@ -Vc

0.4

0.6

0.8 Φ2aΦ1

b

Φ (e

V)

polarisation state "a" polarisation state "b"

0.00

0.05

0.10

A/cm

2 )

polarisation "a" polarisation "b"

0 6

0.8

1.0

1.2

dU (Ω

-1cm

-1)

polarisation "a" polarisation "b"

S t i-5 0 5 10 15 20 25 30 35

0.0

0.2

Ym

Φ1bΦ1

a

Φ

x (A) -0.2 -0.1 0.0 0.1 0.2

-0.10

-0.05

J (A

U (V)

-0.2 -0.1 0.0 0.1 0.20.2

0.4

0.6

dJ/d

U (V)

Symmetric

Recent Work on Ferroelectric Tunnel Junctions

Nanoscale polarization manipulation and conductance switching in ultrathin films of a ferroelectric copolymerHongwei Qu et al APL 82 4322 (2003)Hongwei Qu,et al., APL 82 4322 (2003).

out-of plane

H. Kohlstedt, N. A. Pertsev, and R. Waser, in

J Rodríguez Contreras et al

, , ,Ferroelectric Thin Films X, MRS Symposia Proceedings, 688, 161 (2002).

E

J. Rodríguez Contreras, et al.,Appl. Phys. Lett. 83, 4595 (2003).x

t

GaN: an example! Resonant Electron Tunneling in GaN/Ga1-xAlxN strained structures with spontanous polarization and piezoeffect, Phys. Of the Solid State: 43, 529 (2001).

Outlook

Experimental realization of an FTJ p

S d t / S d t / New device structuresSuperconductor/Magnet

Superconductor/Magnet

New device structures

Ferroelectric Barrier

(IETS) Inelastic electron tunneling spectrocopy to study:(IETS)- Inelastic electron tunneling spectrocopy to study:

(1) Domain structures in nm thin ferroelectric materialsor(2) Phonon spectra in ultrathin ferroelectric barriers

AcknowledgementAcknowledgement

The work was supported by the HGF-Strategiefonds “Piccolo” and the V lk F d ti P j tVolkswagen-Foundation--Project

“Nano-sized ferroelectric hybrids” under contract number I/77 737.

DFG Project: „Displacive and Conductive Phenomena in Ferroelectric Thin Films:Scaling effects and switching properties“.

Center ofNanoelectronic Systems forInformation Technologygy