The Electronic
T
Transport
in
i
Mesoscopic
p Structures
Nanostrukturphysik II
24.07.2012
Maurizio Micciché
24.07.2012
1
A
Agenda
d
„
„
„
„
„
Introduction
Electron--Electron Interaction and Quantum
Electron
Dots
Electron--Box
Electron
Two Terminal Setup
Single Electron Transistor (SET)
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2
I t d ti
Introduction
[1]
microscopic
[2]
mesoscopic
macroscopic
l
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3
Introduction:
I t d ti
Classical
Cl i l T
Transport
p t
„
Classical electronic transport characterized by
C d i i G
Conductivity
I
A
G=
„
U
=σ
L
Not applicable
pp
if:
„ l < λF
quantum nature dominates
„ l < lmfp
transport becomes
b
b
ballistic
lli i
„
24.07.2012
l < LΦ
qquantum mechanical interference
4
Introduction: The Landauer
Approach
„
„
„
„
Describes conductance of mesoscopic systems
Connectedd with
h macrosc. reservoirs (only
l µ and
d T ddep.)
Connection: ideal leads e.g.
g quantum
q
wires
Electrons are plane waves; no scattering
Conductivity described by scattering matrix
[4]
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Electron--Electron Interaction and
Electron
Quantum Dots
„
„
„
Electrons in Spherical Capacitor repel
each other but can always be further charged
In small dimensions Electron interaction
becomes more important
Charge Energy must be greater than CB
1
E~
R
C l bb
Coulomb
barrier
i (CB)
E(10nm) =
140 keV/cm
k V/
[4]
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[4]
6
El t -Box
ElectronElectron
B
„
„
Most simple oneone-Electron device
Gate
G Voltage
V l
controls
l the
h iislands
l d electrostatic
l
i E
Energy
[[4]]
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El t -Box
ElectronElectron
B
„
„
„
Electrons tunnel to
island
i l nd
Island charges rises by e
Temperature gives
additional energy
=> less sharp coulomb
steps
[4]
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T Terminal
Two
T
i l Setup
S t
„
„
Island connected with two tunnel barriers
Symmetrical design (back and forth possible)
e[4]
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T Terminal
Two
T
i l Setup
S t
[4]
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T Terminal
Two
T
i l Setup
S t p
„
„
„
„
UDS=0 no tunneling towards island Obvious?! No!
UDS↑ => ΔES→I ↓ => one e- tunnels to island => Ec ↑
Tunneling from island to Drain
⇒ Lowering ΔES→I
⇒ Constant current
by single electrons
Current dependent
on energy of the
electrons
l
andd the
h
[5]
charge energy Ec, which depend on…
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e[4]
11
T Terminal
Two
T
i l Setup
S t p
„
„
„
Energy of the electron: UDS and kBT
„ We want: energy mainly
l dependent
d
d on UDS
Charge
g Energy
gy Ec: size and charge
g of island
„ We want: Ec>> kBT
Ec↑ => Risland↓
kBT↓ => T ↓
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Risland
T
1 µm
4K
1 nm
300 K
12
Th Si
The
Single
l El
Electron
t
T
Transistor
i t
„
„
Combination of Electron Box and TTS
Current controlled by UGS and UDS
[4]
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[6]
13
Coulomb Barrier
Oscillations
[4]
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Th Si
The
Single
l El
Electron
t
T
Transistor
i t
[4]
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SET Wh
SET:
Why??
„
Conductance of SET changes strongly (several orders
off magnitude)
m nit d ) due
d to
t UGS
=> Amplification of quantum signal (e.g. quantum computer)
„
„
„
„
Conductance exhibits oscillations as a function of UGS
SET is also a tunable tunnel junction
Count e- with SET or create well defined currents
I=nef (n: number of electrons transferred per cycle; f: f of ac control voltage)
With small quantum dot ((~5nm)
5nm) single electron
tunneling can be observed at room temperature
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SET:
SET Wh
Whatt ffor??
„
Problems with MOSFET (in ~20 years):
Moore’s law (size ~ 20 nm)
„ High integration density =>
> too much heat
„ Quantum effects dominate, no classical description
„
„
SET:
Single electrons => low heat
„ Atomic dimensions => high integration density
„ Tunneling is fast => high switching frequencies
„
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SET F
SET:
Future
t
[7]
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Thank you for your
attention
tt ti
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Sources
Sources
„
„
„
„
„
„
„
1: Wikipedia: Tunneleffekt
2: fitamball.de
fitamball de
3: Wikipedia: Kugelkondensator
4: Der Einzelelektronentransistor; Andreas Klöber
5: archiexpo.de
6: Wikipedia: MOSFETMOSFET-Transistor
7: ucm.es/Quantum
ucm.es/Quantum_comuter
comuter
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