Quantum Confinement Of

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Quantum Confinement ofElectrons at Surfaces

Robert A. Bartynski

Department of Physics and AstronomyLaboratory for Surface Modification and NanoPhysics Lab

Rutgers University

Piscataway, NJ 08854NPL 203 [email protected] 732-445-5500 x4839

Surface/Interface Science Course (Phys 627/Chem 542)25 March2013

Laboratory for Nano Physics

Laborator

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


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Quantum Confinement Interference of Electron Waves

M.F. Crommie, C.P. Lutz, D.M. Eigler.Confinement of electrons to quantum corrals on a metal surface.Science 262, 218-220 (1993)

M.F. Crommie, C.P. Lutz, D.M. Eigler, E.J. Heller.Waves on a metal surface and quantum corrals.Surface Review and Letters 2 (1), 127-137 (1995)

STM rounds up electron waves at the QM corral. Physics Today 46 (11), 17-19 (1993).


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. . .. . .

Electronic Quantum Size Effects: Dimensionality

Electron density acquires nodal structure along confinement direction. Energy spectrum acquires discrete character.

2-d structure(thin film, quantum well)confinement in 1-d

0-d structure(cluster, quantum dot)confinement in 3-d

1-d structure(atomic chain, quantum wire)

confinement in 2-d

Y ( z

)

y ( z )

y ( z )

y ( x)

y ( x)


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Scanning Tunneling Microscopy/Spectroscopy


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VB

CLBCLS

hu 1

hu 2 > hu 1

EF

EV

KE

Intensity

KE

Intensity

Photoelectron Spectroscopy

Valence BandPhotoemission

Core levelPhotoemission

Auger ElectronEmission


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Complementary Spectroscopic Techniques

Inverse Photoemission (Unoccupied States)

e- e-Photoemission (Occupied States)

k

EF

EV

k

EF

EV

e- e-

PhotonCounts

EF

E f i n a

l

X X

ElectronCounts

EF

E i n i t i a

l

e-

e-

Vertical transitions in the reduced Brillioun Zone


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Angle Resolved Photoelectron Spectroscopy

Crystal Vacuum

Direct transition in solid in = o Periodicity in plane of surface || in = || out + G || || out = || o

k|| = ( 2 mE /h 2)1/2 sin q

Map E (k || )

For 2d systemobtain all informationabout energy bands

o

in

out

|| out

|| in

q

S u r

f a c e


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1-d confinement: Quantum Wells


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Metallic Quantum Well (MQW) States

C u(100) f c c F e

5 ML

C u

2 15ML

Cu(100) Fe/Cu(100) Cu/Fe/Cu(100)200 x 200 nm 200 x 200 nm 300 x 300 nm

Fe Cu Surf.


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k_parallel

k_perpendicular

Energy

k_parallel

k_perpendicular

Energy

k_parallel

k_perpendicular

Energy

k_parallelk_perpendicular

Energy


Energy


Energy


Energy

Effect of Confinement on Electronic States

1) Free electron bandsE k2

2) Continuous paraboloidshown as grid [ Dkx = 2 p /Na]

3) Confinement allows onlyfixed values of k

4) Projected on E axis:sub-bands

E(k || )= E n + h 2k|| 2/2m

For square well: E n = n2h2 / 8mL2


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Typical MQW Behavior: Cu/fccFe/Cu(100)

InversePhotoemission

(unoccupiedstates)

All spectra here obtained at k || = 0

MQW states disperse up with increasing Cu overlayer thickness!

CuFe

Energy above E F (eV) 4 3 2 1 0

3 ML

19 ML

q Cu

10 ML

CuFe

Photoemission

(occupied states)

@ALS w/ M. Hochstrasser, D. Arena, J. Tobin (LBL)

30 20 10 0 Thickness (ML)

1.0

0.8

0.6

0.4

0.2

B i n d i n g

E n e r g y

( e V ) 0.0


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ma (m + 1)a

n + 1

n

n + 1

n

n + 2

Since E = n 2h2/8mL 2 downwhen you increase the width of the well?

d d + D

n + 1

n

n + 1

n

u = (m n)

u - 1

u - 1

u

u + 1

they do, but by how much?


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Vin Cu Vin Fe

CuFe

But the Electrons are NOT in a Square Well

We must include the effect of the atomic potential

e -


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Bohr-Summerfeld Approx.(Phase Accumulation Model)

2k m a + Df c +D f s = n 2p 2k m a = n 2p - Df c - D f s

Quantum Well States in a Band

Phase accumulated in wellPhase shift on reflection from crystalPhase shift on reflection from vacuumExistence condition

Phase/2 p 0 5 10 15 20

u = m - n


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MQW states disperse up with increasing Cuoverlayer thickness

10

8

6

4

2

0

-2

-4

E l e c t r o n

E n e r g y

( e V )

k ^0 p /a

4

3

2

1

0

m ML

m+1 ML

n nodes

(n+1) nodes

Add a layer, add a node (MQW states are characterized

by the quantum number u = m - n )a

k p

a2

States near BZB


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n

n + 1

n

Sorting out n and n for MQW states of Ag/Fe(100)

n+1

T . C . C

h i a n g


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Yes, they move discretely!

T . C . C

h i a n g

Do MQW state disperse discretely or continuouslywith film thickness?


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Other System: Cu/fccNi/Cu(100)

But

-0.8

-0.6

-0.4

-0.2

0.0

B i n d i n

g E

n e r g y

( e V )

403020100Cu Thickness (ML)

Photoemission(occupied states)

B i n d i n g

E n e r g y

( e V )

Cu Thickness (ML)

Cu

Ni

-0.4

-0.2

0.0

-0.6

-0.8

0 10 20 4030

Anomalous behavior above E F

InversePhotoemission

(unoccupied states)

Energy Above E F (eV) 6 4 2 0

2 ML Cu

12 ML Cu

Cu

Ni

Similar to Cu/Ni(100)[Himpsel and Rader, APL 67, 1151 (1995)]


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Cu

C

d bands

Ni

C

d bands

Fe

C

d bandsEF

Behavior of electronic states depends on bandalignment

Cu 4sp Fe 3dNi 4 sp Cu 4 sp


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Dispersion with k ||

k || = (2 mE h 2)1/2 sin q


Energy

Energy

k ||Free electron-like dispersion

of sub-bands

T . C . C

h i a n g


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Energy (eV)

0 2 4 6

Dispersion with k ||

Nearly parabolicUpward dispersion

Flat dispersion !!

Downward dispersion !!

Projected bands ofCu and Co


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Mediate oscillatory magnetic coupling GMR

Quantum Size Effects and Materials Properties

MQW Intensity at E F (belly)

MXLD

Calculation

MQW Intensity at E F (neck)

Kawakami et al. PRL, 82 , 4098 (1999)

Low High


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Low T = 6 MLHigh T = 5 & 7 ML

Low T = 3 MLHigh T = 2 & 4 ML

MQW state-induced layer stability

Ag/Fe(100)

T . C . C

h i a n g

W ei t er i n g e t al .

Pb/Si(111)

Expt.

Theory

Theory

Quantum size effectsstabilize island height


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C O

C O

C O

C O

Quantization of Cu sp band results in MQW states

Cu sp electrons play a role in CO chemisorption (A. Nilsson et al.)

Changing Cu thickness modifies electronic levelswithout changing geometric structure

Corresponding modification in CO chemisorption?

Chemisorption on MQWs

C u(100) fccFe

5 ML

C u

2 15ML


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Measuring Bonding Strength

Mass Spec

Temperature Programmed Desorption (Bond Strength)

- C - O

- C - O

- C - O

M a s s

2 8 s i g n a

l ( A r b . U

n i t s )

300250200150Temperature (K)

TPD ofCO/Cu(100)

TP (th)


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CO TPD from MQWs

M a s s

2 8 I n t e n s

i t y ( A r b .

U n

i t s )

240200160120

Temperature (K)

Cu(100)

q Cu

CO /Cu/ fccCo /Cu(100) CO /Cu/ fccFe /Cu(100)

2.5 ML

5 ML

10 ML

15 ML

M a s s

2 8 I n t e n s i

t y ( A

r b .

U n

i t s )

240200160120Temperature (K)

2.5

5

10

13.75

qCu (ML)


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F

172

170

168

166

164

162

T d

( K )

20 10 0 Cu Film Thickness (ML)

I n t e n s

i t y a

t E F

( A r b .

U n

i t s

)

Cu(100)

CO/Cu/fccCo

Td IPE Intensity at E

IPE Intensity and Desorption Temperature

185

180

175

170

165

160

T d ( K )

30 20 10 0

Cu Film Thickness (ML)

I n t e n s

i t y a

t E F

( A r b .

U n

i t s

)

TdIPE Intensity at E F

CO/Cu/fccFe Cu(100)

F


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Weitering et al., Nature Physics (March 06)

Low Dimensionality and Hard Superconductivity


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2-d confinement: Quantum Wires


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How to make quantum wires (and dots)

(Himpsel et al.)

CaF/Sias

mask

Highly regularsteps on Si(111)


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Electronic structure of quantum wires

(Himpsel et al.)

Si(557) - Au

AuSi SiMetallic

Au wires

Semiconducting

Au film


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k_y

k_x

Energy

E_F

k xk y

EnergyEF

2D

1D

Fermi surface of quantum wires (and dots)


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N. Nilius, T. M. Wallis, and W. Ho, Science 97 , 1853-1856 (2002).

Other routes to quantum wires (and dots)

Atom-by-atom construction(Au/NiAl)

Self-assembly Ag/Cu(110)

S p r u n g e r ,

K u r

t z


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Scanning tunneling spectroscopy ofquantum wires (and dots)

dI/dV ~ N(E)

Y ( x) = S cnsin( np x/L)

W . H

o


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CDW within an atomic wire

Competing periodicities in fractionally filled one-dimensional bands, P.C. Snijders, S. Rogge, H.H. WeiteringPhysical Review Letters (February 24, 2006)

S


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Summary

Direct and Inverse Photoemission spectroscopies are powerfultechniques for exploring the electronic structure of nanometerscale structures.

2-d structures show discrete electronic structure to plane ofthe film, but band-like structure parallel to plane.

Square well model NOT sufficient, must take into accountelectronic structure of overlayer AND substrate to fully describe.

1-d structures can be fabricated and photoemission shows thatmetallic behavior is possible (undoubtedly owing to interaction withsubstrate).

Fermi surface mapping shows closed or open curves as expected

for 2-d and 1-d structures, respectively.

Scanning tunneling spectroscopy (STS) is powerful tool forfabricating and characterizing 1-d and 0-d structures.

Can use STS to map electronic states of small (i.e. several atom

l ) 1 d l di i i h l h

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Quantum Confinement Of