electronic properties ofelectronic properties of metal ... · electronic properties ofelectronic...

Electronic Properties ofElectronic Properties of Metal-Insulator Interfaces

Hermann Kohlstedt

Forschungszentrum JülichInstitut für Festkörperforschung

GermanyGermany

Tutorial September 2008 Barcelona_H. Kohlstedt1

Famous Comments about Surfaces and Interfaces

Wolfgang Pauli"God made solids but surfaces (and interfaces) were the work of the Devil "God made solids, but surfaces (and interfaces) were the work of the Devil.

This (very popular) quotation exists in a great variety of versions.

...in such a way the transition region or interface between the Herbert Kroemer

Nobel Lecture: Quasielectric fields and band offsets:

different materials plays an essential role in any device action. Often, it may be said that the interface is the device.

Nobel Lecture: Quasielectric fields and band offsets: teaching electrons new tricks, Rev. Mod. Phys. 73 (2001).


The MOSFET as an ExampleThe MOSFET as an Example

Others:Others:Laser Diode, Giant Magneto Resistance (GMR) DeviceMagnetic Tunnel Junctions, pn-Diode, Josephson junctions...


1 The MOSFET

Metal Oxide Semiconductor Field Effect Transistor


A Historical Remark

19261926MOSFET Patent: J. E. Lilienfeld, US Patent 1.745.173 (1930)

19461946Bipolar transistor?

1960First working MOSFETD Kahng and M M Atalla Pittsburgh 1960


D. Kahng and M.M. Atalla, Pittsburgh 1960

Computer: An Interface Story1959 first planar transistor

1961 first integrated circuit (IC)

1964 IC5 transistors

1968 IC array 180 Transistors

1978 CPU20000 transistors

1985 CPU 200000 transistors

2000 CPU - Pentium III 28.000.000 transistors

2008820 Millionen Transistors


The Metal Oxide Semiconductor Capacitor

MOS-Capacitor

Work functionGate metalSiO2

Work functionEnergy gapBand structure

Silicon (Si) Interface statesDefectsDevice fabricationDevice fabrication...

Why it took more than 30 years to realize a MOSFET?

...the MOS cap was a „hard nut“ - in preparation and in understanding!!


...the MOS cap was a „hard nut in preparation and in understanding!!

High Resolution TEM of Gate StackTEM: Transmission Electron Microscopy

Gate

SiO2

Channel


D. A. Buchanan, IBM J. Res. Develop. 43, 245 (1999)

Surface and Bulk Atoms

„Atom“1 nm

0.3 nm

1

1 nm0.3 nm

0.3 nm

1 nm

1 nm 1µm 1 mm

nVvolume atoms: 1 2 x 1010 2 x 1019

ns surface atoms: 26 5 x 107 5 x 1013

RelationnV/(nV+nS): 0.96 2 x 10-3 3 x 10-6


Corner Atoms: 8 8 8

Down scaling increase importancs of surface!!

Outline

Vacuum

Bulk Metal

Vacuum StepAdsorbate

Metal

Metal 2 Semiconductor Metal Ferromagnet

Metal 1

Metal 2

Metal

/Insulator

Metal

Ferroelectric

Ferromagnet

Ferroelectric

Metal Ferromagnet


Bulk MetalMetal


Energy Bands in Solids

Free electrons

ESchrödinger equation:

Ene

rgy

d2 ψ+

2 mψ [ E V( )] 0

V = V(x); only space dependence

ctro

n E

dx2 + h2

ψ [ E – V(x)] = 0

Ele

cSolution for V = 0: free electron

2 Wavevector k E = h2 k2

2 m


Confined Electron

En = h2 π 2

2 m L2n2

8 8

E Ψn=4

2 m LEigenenergies

rgy

E

E4

E

Ψ4

ergy

E

n=3

ectro

n en

e E3

E2

Ψ3

Ψ2ectro

n en

e

n=2

0 L

Ele

E1 Ψ1

2

Ele

n=1

0 L 0 L


Finite Barrier Height

Ψ, VV = V00

Outside the box due to

xquantum mechanical tunneling

n = 1


Kronig-Penny Model (1930)

A simple model to study the electron wave propagation in a crystal (1D)

V(x)V0

V(x) V(x) = V0 -b < x < 0

V(x) = 0 0 < x < a

x-b 0 a Atom

positions

Solution by solving the Schrödinger equation:

( )sin α a m: electron mass

positions

cos k a = cos α a + γ a ( )sin α aα a

γ =m V0 b α =

(2 m E)1/2

m: electron mass

h : Planck constant


γ = h2

α = h E: energy of the electron

Solutions of the Kronig-Penny Model

XX = cos α a + γ a ( )sin α a

α a2

1 allowed values

π 2 π 3 π 4 π

α a-1

of cos k a

-2γ a = π


Kronig-Penny Model: Formation of Energy Bands

Energybandsn

Ene

rgy E

bands

Ele

ctro

n

2π/a-2π/a π/a-π/ak

2π/a-2π/a π/a-π/a


Reduced Zone Representation

E

Ener

gy E

Elec

tron

Eg

k 2π/a-2π/a π/a-π/a π/a-π/a


Energy Band Structure of crystalline Solids

Evac

φ

EF

Eg

EF

Metal Semiconductor Insulator


Surface Science, K. W. Kolasinski. Wiley, 2004Fig. 1.9, p. 13

Energy Levels in Si vs. Interatomic Spacing

Fig 3 16 Petty p 84Fig. 3.16 Petty, p. 84


Metal-Vacuum Surface

Vacuum StepAdsorbate


Definitions:

Surface: „Region“ between a material and vacuum

Vacuum

Material

Interface: „Contact region“ between a material A and a material B

Material A

Material B


Vacuum

MetalMetal


Characteristic Length Scales

Example:Metal Surface

++++++++++ ++++- - -

Vacuum_

+Surface dipole layer ++++++++++ ++++

+++++++++++++ Metal

+dipole layer

Spill-out effect of electrons at the surfaceSpill out effect of electrons at the surface


The Jellium-Model

+++++-Metal Vaccuum

++++++ +-

- Spill-out effect of electrons at the surface

++++

Epot

Φpot

Work function : Energy to move an electronfrom bulk to vacuum (far away from the surface)

ΦEF

+ρ(x)

from bulk to vacuum (far away from the surface)

+ρ( )

Charge distribution


- Henzler/Göpel p. 217

Work function : Energy to move an electronΦWork function : Energy to move an electronfrom bulk to vacuum (far away from the surface)

Φ

EpotEvac

ΦEFEF

e-

Metal

x


Three characteristic Length Scales

+ρ(x)

1: Atomic: Dipol layer

2: Micron: Image PotentialF =e2

(2x)2

-

V(x) = -e2

( )

(0.1nm)

(1 µm)

V(x)

V(x) = - 1/x 3 x 6 10-4 µm eV

4x

(1 µm) ( ) µ

3: Macroscopic(several µm)

3: Macroscopic

Φ1

Φ2

Work function:


Work function:Move an electron several µm away from the surface

Electron density vs. Distance (Fermi wavelength)

Friedel Surface

sity

Friedeloscillations

Surface

ron

dens

B lk

Ele

ct Exponential decay into vacuum

Bulk

Distance (in the order of the Fermi wave length, i.e. A)

Lang and Kohn: Phys. Rev. B 1, 4555 (1970).


Surface Science, K. W. KolasinskiWiley, 2004, Fig. 1.10, p. 15

Electron density vs. Distance (Fermi wavelength)

Lang and Kohn: Phys Rev B 1 4555 (1970) H Hövel University of Dortmund GermanyLang and Kohn: Phys. Rev. B 1, 4555 (1970). H. Hövel, University of Dortmund, GermanyFriedel-Oscillations observed near a step (Grahit at 5 Kelvin)


Work Functions for various Metals

Dots: Experimental data

Dashed line: Theory, Jellium Model


Lang and Kohn: Phys. Rev. B 1, 4555 (1970).

Vacuum

Adsorbate(111)(110)


Work Function and Crystal Orientation

f f t d bi


fcc: face centered cubic

Adsorbate Layer on a clean Metal Surface

Adsorbate layer

Vacuum

- - - --++++++++++++++++++++++++++++++++++++++++++++

Metal


Adatom on a Surface

Evac

E3EF

φadsorbatΛ(E)

φclean

Γ

Evac

E2

Metal

( )

Metal

E1E s

Due to adatom on a surface:

x

-Shift of atomic levels-Broadening (Γ)-Shift of work function


Henzler/Göpel, p. 474

Work Function of Tungston vs. Crystal Orientation d Ab ti f Nitand Absorption of Nitrogen


D. L. Adams and L. H. Gremer, Surf. Sci. 27, 21 (1971).

Step


Electrostatic Potential at a Step

The smoothed electronic surface leads to a reduced dipol moment near the step (perpendicular to the surface).Th f th k f ti i l ll d d th t


M. D. Thompson and H. B. Huntington, Surf. Sci 116, 522 (1982).

Therefore the work function is locally reduced near the step.

Work function vs. Step Densityφ

(eV

)Δφ

Step density (106 / cm)


Step density (10 / cm)

K. Besocke, B. Krahl-Urban and H. Wagner, Surf. Sci. 68, 39 (1977).

Dispersion Relation for free and Bulk Electrons

Perodic potential (bulk)Perodic potential (bulk)

Free electron

n E

nerg

y EE

lect

ron

2π/a-2π/a π/a-π/ak

2π/a-2π/a π/a-π/a


Energy Levels: from Atoms to Solids

E

Atom Molecule Bulk (metal) crystal bulk and surface

Epot

EEss

EF

Eel

EF

kkπ/a π/a

Tutorial September 2008 Barcelona_H. Kohlstedt40From Henzler/Göpel p. 192

Surface States of a 3 D Crystal

Hypothetical electronic band structure of a crystal

E(k II) projected bulk band along k

Broken lines in the E(k II) plane indicate surface state bands in the gaps of the projected g p p jbulk-band structure, and surface resonances(degenerated with bulk states) –short doted lines


From: H. Lüth, Surfaces and Interfaces of Solids, Springer, p. 79

Bulk and Surface

EF

Ess

kπ/a


Semiconductor

Metal 1

Metal 2

Metal

Semiconductor/Insulator


Metal 2

Metal 1


Metal-Metal Interface

E M t l 1 M t l 2EVac

E

EF

eΦ1 eΦ2

Metal 1 Metal 2

EF

EVc = Φ2 - Φ1

Vc : Contact potential (Volta voltage)

EF

c p ( g )

Galvani voltage


Interface dipole layer

H. Lüth, Springer: Surfaces and Interfaces of Solids, 2001, p. 372

Dimension of the Interface Dipole Layer

EVc Screening of charge imbalanace:

Positive ion cores and free electroncs

EF

Positive ion cores and free electroncs

Coulomb potential of a point charge:

Metal 1 Metal 2

p p g

Φ(r) = C/r exp (-r/rTF) with rTF ≈ 0.5 (n/a0

3)-1/6rTF 0.5 (n/a0 )rTF ≈ 0.5 A for Cu: n = 8.5 x 1022 cm-3

a0: Bohr radiusInterface dipole layer

ESimpified representation

EF



Contact Voltage: Examples

Ag: 4.33 eVg

Cu: 4.49 eV Clean well defined UHV experiment

Au: 4.83 eV

Vc = Φ2 - Φ1 Au – Ag (0.50 eV)

Not correct: over simplified model

Work function changes due to: atomic structure changes after contact relaxation/reconstructionWork function changes due to: atomic structure changes after contact, relaxation/reconstructionDifferent situation before and after contact


Metal

Semiconductor


The Schottky Contact

EVeΦS χ*SC

n-typ SemiconductorMetal(high work function)

EFEF

EVac

eΦM

CEC

EF

EV

EVac

EC

n-type depletion ρ = -ε0ε d2V/dx2

Poisson EquationEF

EFC

EV

Poisson Equation



e-

The Schottky Barrier

EV

n-typ SemiconductorMetalEVac

χSC Schotty Barrier:Ideal case:E χ*SC

eΦBeΦM

Ideal case:eΦB = eΦM - χSC

eVB

EFEFS = -dΦB /d χ SCS = 1 (slope parameter)

Nonmatching bondsSpace charge layerx

n-type depletion region (≈10 nm -100 nm)Screening length in a semiconductor(l l t th i t l)

Nonmatching bonds, surface states, impurities etc.are not considered

Space charge layer


(less electrons than in a metal)

Schottky and Bardeen Model

High density of interface states

Schottky model (ideal case), too simpleW. Schottky, Z. Physik 113, 123 (1938).

What means Bardeen approach?Phys. Rev. 71, 717, (1947)

no interface states



Barrier heights of Si-Schottky contacts vs. work functions

Bardeen approach to explain the Barrier Height

EVac

n-typ SemiconductorMetal

Δ

χSCE

Δ Interface dipole energy

S = -dΦB /d χ SCS 0 ( l t )

EFEF

S = 0 (slope parameter)due to pinning of EFΦB

EFF

Interface states: EF pinning

Space charge layer10 nm – 100nm

5 A X (not to scale)


Surface states of clean semiconductor persists under metal overlayer (EF pinning)

Qualitative Explanation of Surface (Interface) States

ConductionAtom

A

Conduction band

Due to different bonding

Acceptor

Surface state

B

conditions to bulk atoms

Donor

Levels

ValenceValenceband

H. Lüth Solid Surfaces, Interfaces


,and Thin Films, p. 273, Springer 2001

Schottky, too simple: S = 1Schottky, too simple: S 1

Bardeen, too pessimistic approach: S = 0

Heine´s approach : MIGS (Metal Induced Gap States)V H i Ph R 138 A 1689 (1965)V. Heine Phys. Rev. 138, A 1689 (1965).

Metal Vacuum

Metal Semiconductor

Metal Semiconductor


Measurement of the Slope Parameter S

1) Schottky: Clean limit

2) Bardeen: Surface states at Semic. Surface

3) H i M t l I d d G St t (MIGS)3) Heine: Metal Induced Gap States (MIGS)

4) Real Interface structure and defects are important

S = 0.08 (slope parameter)(from experiment)


Mönch, Springer: Electronic Properties of Semiconductor Interfaces, 2001, p. 6

Wavefunctions of...

Metal Vacuum

... a (clean) metal surface

Metal Semiconductor

... a metal-semiconductor interface

... a surface state

Vacuum Semiconductor

Tutorial September 2008 Barcelona_H. Kohlstedt56Sketch from:

W. Mönch, Electr. Prop. of Semicond. Interf., p. 8

Extrinsic FactorsEVac

E

EFEF

Metal SemiconductorMetal Semiconductor

Reacted region

Interdiffuison region


L. J. Brillson, Surf. Sci. 299/300, 909 (1994).

Nonmatching bonds, surface states, impurities etc.are important to undertand Schottky contacts

The Metal Oxide Semiconductor Capacitor

MOS-Capacitor

Work functionGate metalSiO2

Work functionEnergy gapBand structure

Silicon (Si) Interface statesDefectsDevice fabricationDevice fabrication...

Why it took more than 30 years to realize a MOSFET?

...the MOS cap was a „hard nut“ - in preparation and in understanding!!


...the MOS cap was a „hard nut in preparation and in understanding!!

MOSFET and Interface Traps

Trap density:

Gate metal+ + + + + + + +

ap de s ty< 1012 /cm2/eVrequired

SiO - - TrapsSiO2

- --

- - -


Silicon (Si)

Complex Oxide Interfaces

F t

Ferroelectric

Metal

Ferroelectric

Ferromagnet

Metal Ferromagnet


ABO3 Complex Oxides (2 Examples)

Huge (remanent) surface charge SrRuO3: ConductorFerroelectric

Ba or Pb Sr

Ti

+P -P

O

Ru

Oc

Oa

PbZrxTi1-xO3

Tutorial September 2008 Barcelona_H. Kohlstedt

BaTiO3

Ferroelectric Hysteresis

“1” Pr

BaTiO

Metal

P zatio

n

BaTiO3

Metal

P

E

Pol

ariz

Electric Field

Ec“0”

Electric Field

Pr = 10 – 80 µC/cm2

Ec = 50 – 300 kV/cm2Comparison:

1 l t / f tThin Film Capacitor: t = 100 nm

1 electron/per surface atom:1015/cm2 x 1.6 x 10-19 C =160 µC/cm2

Tutorial September 2008 Barcelona_H. Kohlstedt62VC = 0.5 V - 2 V strong interface

effects expected!!

Metal-Ferroelectric Interfaces


J. F. Scott, Ferroelectric Memories p. 81, Fig. 4.1

Electrical Boundary Conditions

Screening by Electrons

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Metal

0⇒DE0=⋅∫ dsE+ + + + + + + + + + + + + + + + + + + + +

EDP (only for

f t i !!)

0⇒DE0∫ dsE

perfect screening!!)

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Metal

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

Potential

x

Tutorial September 2008 Barcelona_H. Kohlstedt64P. Würfel and I. P. Batra , Ferroelectrics 12, 55 (1976).

J. Juncquera and Ph. Ghosez, Nature 422, 506 (2003).

Layer Sequence of a Tunnel Junction

Top electrode(50 nm)

T l B iTunnel Barrier(1 nm – 3 nm)

Substrate

B ttBottom Electrode(50 nm)


Reaching the Tunneling Regime

Darrel Schlom & ChambersPenn State &Penn StateMBE grown oxidesJulio Rodriguez

&

SrRuO3S uO3

BaTiO3

21.5 nm2.1 nm

SrRuO380 nm

5 nm

Tutorial September 2008 Barcelona_H. Kohlstedt6620nm

Tunneleffect

real realRe

φxikxeB=ΨBΨ k k xkreal

imaginary

realB

eBΨB xk xk xk

xikC

xeC=Ψ

x

Re AΨ

xikA

xeA −=Ψ

Transmission coefficientTransmission coefficient

⎪

⎪⎬⎫

⎪⎪⎨⎧−= ∫ dxxmCT

t

)(22exp φ


⎪⎭⎬

⎪⎩⎨ ∫

0

)(ph

Frenkel, Phys. Rev. 36 (1930)

Electron Tunneling across a Ferroelectric

H K hl t dt t l Ph R B 72 125341 (2005)


H. Kohlstedt et al., Phys. Rev. B 72, 125341 (2005).E. Y. Tsymbal and H. Kohlstedt, Science 313, 181 (2006).

Superconducting -, Magnetic-, and Ferroelectric Tunnel Junctions

Dielectric Barrier Density of states effects

Superconductor Superconductor Magnet Magnet

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

h

π∫∞−h

Metal Metal

Ferroelectric tunnel junction:

Cooperative phenomenon

Tutorial September 2008 Barcelona_H. Kohlstedt69Ferroelectric Barrier

located in the barrier !

Alternative Screening Mechanism I

Fong, et al., Phys. Rev. B 71, 144112 (2005).Ionic Screening

Tutorial September 2008 Barcelona_H. Kohlstedt70Theoretically: G. Gerra et al., PRL (2006).

Rearrangements of Surface Atoms

Perfect/truncated bulkFew examples:

Relaxation Reconstruction Missing row reconstruction

c2

c1

cbulk


a

From: H. Lüth, Surfaces and Interfaces of Solids, Springer, p. 79

Alternative Screening Mechanism IImetal ferroelectric

Th F i i dThomas-Fermi screening andKretschmer-Binder effect

CTF CKB

B d h ti b fBond charge compensation by freecarriers in the ferroelectric

E t i f th i i l i tiExtension of the ionic polarizationinto the metal; Ionic distortion also in the metal


Sketch taken from G. Gerra et al.,PRL 96. 107603 (2006). Fig.1

Alternative Screening Mechanism

Ionic Screening

Fong, et al., Phys. Rev. B 71, 144112 (2005).

G. Gerra et al., PRL (2006).

1.5

2.0Electron Wave Interference

0.5

1.0

ER

GY

(eV

) M. Indlekofer and H. KohlstedtEurophysics Lett. 72, 282 (2005).Friedel Oscillations at interface;

-1.0

-0.5

0.0

EN

Tutorial September 2008 Barcelona_H. Kohlstedt

5 10 15 20 251.0

z (nm)

Pt/BaTiO3/Pt Tunnel Junctions


J. P. Velev et al., PRL 98, 137201 (2007)

F t

Ferroelectric

Ferromagnet

Ferromagnet


Magnetoelectric Interface Effect

Fe/BaTiO3

Interface between a ferromagnet and a ferroelectric

PPa ferromagnet and a ferroelectric

Top interface

DO

SMinority-spin charge density

Bottom interface

Tutorial September 2008 Barcelona_H. Kohlstedt76C.-G. Duan, S.S. Jaswal and E. Y. Tsymbal,

PRL 97, 047201 (2006).

EF

Multiferroic Materials: BiFeO3, BiMnO3 etc.Multiferroic Heterostructures: FE/FM/FE/FM/….

+ - + -

E+ - + -

P

MN S

ε M

H

ε

N. A. Spaldin and M. Fiebig, Science 309, 391 (2005). Sketch taken from Fig.1.

Hσ


W. Eerenstein, N. D. Mathur and J. F. ScottNature, 442, 759 (2006) and references therein

Fe/BaTiO3/Fe Tunnel Junctions


Julian P. Velev, et al., JOURNAL OF APPLIED PHYSICS 103, 07A701 2008

J.F. Scott, Nat. Mat. 6, 256 (2007).Mat Nat 6 296 (2007)


J.F. Scott, Nat. Mat. 6, 256 (2007).Mat. Nat. 6, 296 (2007).

Travelers undergo a lot

M l l d Ph El t Ph

(Inelastic) Electron Tunneling Spectroscopy

Molecule and Phonon Spectroscopy

Electron-Phonon Coupling α2 (ω,k)Magnons

P. Balk, JAP 1991 J. S. Moodera, PRL 1998 E. L. Wolf, PRB 1985,

n-Si/SiO2/Al Co/Al2O3/Ni80Fe20 Nb/MgO/Ag


Tunneling electrons are extremely sensitive to barrier and interface excitations!

An optimistic Outlook

Pyroelectric

Multiferroic Tunnel Junctions

P t- - -

FerroelectricAnti-ferroelectric

PyroelectricPiezoelectricDielectric

Paramagnet(Anti)-Ferromagnet

Superconductor

+ + +

- - -Multiferroic (Insulator)(Tunnel Barrier)

P, M

+ + +

(Tunnel Barrier)

MagneticAnti-ferromagnetic

Examples: -Cross correlation between magnetic and ferroelectric (piezoelectric) properties

Superconductor-Ferroelectric-Superconductor junction:- Joesphson coupling and screening charge?- Josephson (quasi particle) current and resistive state of the barrier?


Josephson (quasi particle) current and resistive state of the barrier?-Magnet-Ferroelectric-Magnet Junctions:-Spin dependent screening?

A few Milestones in Electron Tunneling

2010Experiments and theory on ferroelectric and multiferroictunnel junctionss

1990 Superconducting HTc tunnel junctions (not successful)First all-oxide magnetic tunnel junctiontunnel junctions

Oxi

des

Magnetic Tunnel Junctions

Supe co duct g c tu e ju ct o s ( ot success u )

1970

Superconducting Tunnel Junctions (LTc)

Magnetic Tunnel Junctions

Magnetic/Superconducting Hybrids, Spin Polarization

s

1950

Superconducting Tunnel Junctions (LTc)

Met

als

1950


1930 Theory and first experiments: Metal/Barrier/Metal

Literature

H. Lüth, Springer: Surfaces and Interfaces of Solids, 2001

Zangwill Cambridge: Physics at Surfaces 1988Zangwill, Cambridge: Physics at Surfaces, 1988

Desjonqueres, Springer: Concepts in Surface Physics

Feldmann/Mayer, North Holland: Fundamentals of Surface and Thin Film Analysis

Rudden/Wilson, Wiley: Elements of Solid State Physics

Mönch, Springer: Electronic Properties of Semiconductor Interfaces, p g p

H. Ibach and H. Lüth: Introd. to Solid State Physics, 1991Springer

J. F.Scott, Springer: Ferroelectric Memories, 2000


S. M. Sze, Wiley, Phys. of Semicond. Devices, 1981

pdf file: [email protected]

electronic properties ofelectronic properties of metal ... · electronic properties ofelectronic...

Documents