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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
k_parallelk_perpendicular
Energy
k_parallelk_perpendicular
Energy
k_parallelk_perpendicular
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
k_parallelk_perpendicular
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