Page 1
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Note that 1µm = 10-6m = 10-4cm; 1nm = 10-9m = 10Å
A few relevant length scalesA few relevant length scales
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Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Electronic properties of the 2DEG in GaAs-AlGaAs and Si Electronic properties of the 2DEG in GaAs-AlGaAs and Si inversion layers. inversion layers.
Page 3
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Electron trajectories for the diffuse (l < W,L), quasi-ballistic (W < l < L) and ballistic (l > W,L) transport
regimes.
l
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Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Quantum Mechanical InterferenceQuantum Mechanical Interference
P1 = 1
P2 = 2
P12 = 1 + 2 2
Double Slit Interference
Page 5
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Quantum Mechanical Interference: Quantum Mechanical Interference: Experimental ResultsExperimental Results Au-Ring:Au-Ring:
Ø = 0.82 μm
50 nm thick
T = 32 mK
Rav = 29 Ω
g0 ↔
fluctuations within ring width
g1 ↔ h/q
g2 ↔ 2h/q
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Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
voltage
current
g0
fluctuations
g1 fluctuations
Page 7
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Increasing current density
Effect of current density & temperature on lEffect of current density & temperature on l
Page 8
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Weal Localization
The magneto-resistance of a thin Cu-film (d=80Å, resistance per square R=98Ω) at different temperatures. The mean free path is of the order of 10 Å so that classical magneto-resistance effects can be excluded.
Page 9
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Weal Localization
Cu
Page 10
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Weal Localization
Cu-particles
Page 11
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Weak LocalizationWeak Localization
2-d2-d GaAs-AlGaAs System: Length: 10 μm, Width: w
■ w = 1.5 μm
▲ w = 0.5 μm
Page 12
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Density of StatesDensity of States
Page 13
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Single Electron Transistor (SET)Single Electron Transistor (SET)An example for a new nanodevice
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Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
SET CharacteristicsSET Characteristics
Stability conditions:
Source junction:
n=0
-e/2Cd-[Cg/Cd ]Vg<
Vd<e/2Cd -[Cg/Cd]Vg
Source junction
Drain junction Drain junction:
n=0
e/2[Cs+Cg]+[Cg/[Cs+Cg] ]Vg>
Vd> -e/2[Cs+Cg]+[Cg/[Cs+Cg] ]Vg
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Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
The Coulomb Blockade
Charge transport through a metallic nanoisland
Equivalent circuit:
SOURCE
GATE
DRAIN
Single Electron Transistor (SET)
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Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Realization of Coulomb BlockadesRealization of Coulomb Blockades
Page 17
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Page 18
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Possible Applications:
• Low-power three-terminal devices• (Very) Very Large Scale Integration• Single electron logic• New standards for current and capacity
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Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Page 20
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Preparation and Characterization of Al2O3/Nb(110)/Al2O3(0001)
The Sapphire Substrate• Sapphire(0001): miscut < 0.1°• Annealed 1.5 h at 1100°C in O2
AFM:2 µm x 2 µm,z-scale: 1nmterrace width ~400nm → miscutstep height: 1/3 c 0.43nm
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Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
-3 -2 -1 0 1 2 3
-5 0
0
5 0
cu
rre
nt
[pA
]
energy [eV]
I-V characteristics on oxide
The Tunneling Barrier (Al2O3):• preparation by evaporation of 0.9nm Al at room temperature and subsequent oxidation in oxygen atmosphere.• verification of the oxidation by XPS.• characterization by STM:•STS: “Semiconductor” Gap of up to 3eV
STM:Al2O3/Nb(110)400nm x 400nmscale: 2.3nm
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Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
TEM: Au Nanoparticles/Al2O3/Nb(111)
10nm
1nm
STM:397nm x 397nmz scale: 6.58 nmInset: autocorrelation
TEM:Au Nanoparticle onAl2O3/Nb(110)
Nb(110)
Al2O3
Au
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Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Measurement setup:
• Prerequisite: C < e2/(2kBT) • C << 3aF at room temperature• r << 30nm for a free sphere
STM: (100nm)2
z scale 10nm2V/30pA
Equivalent circuit diagram:
C2C1
R1 R2
tip
particleNb(110)
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Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
-2 .0 -1 .5 -1 .0 -0 .5 0 .0 0 .5 1 .0 1 .5 2 .0-0 .1 0
-0 .0 8
-0 .0 6
-0 .0 4
-0 .0 2
0 .0 0
0 .0 2
0 .0 4
0 .0 6
0 .0 8
0 .1 0
cu
rre
nt
[nA
]
vo lta g e [V ]
m e a su re m e n t
th e o ry
C1 = 1.14×10-19 FC2 = 2.0×10-20 FR1 = 8.8×10+09 ΩR2 = 2.3×10+09 ΩQ0 = 3.4×10-02 eT = 300 K
-2 -1 0 1 2
-100
0
100
cu
rre
nt
[nA
]
vo ltag e [V ]
-1 0 10
50
100
150
200
dI/
dv
[n
S]
v o lta g e [V ]
increasing set current
Measured Coulomb Staircase on a Measured Coulomb Staircase on a Gold nanoparticleGold nanoparticle
Page 25
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Coulomb Staircases: Effect of TemperatureCoulomb Staircases: Effect of Temperature
Page 26
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Quantized ConductanceQuantized Conductance
Schematic cross-sectional view of a quantum point contact, defined in a high-mobility 2D electron gas at the interface of a GaAs-AlGaAs heterojunction. The point contact is formed when a negative voltage is applied to the gate electrodes on top of the AlGaAs layer. Transport measurements are made by employing contacts to the 2D electron gas at either side of the constriction.
Page 27
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Quantized ConductanceQuantized Conductance
Conductance quantization of a quantum point contact in units of 2e2/h. As the gate voltage defining the constriction is made less negative, the width of the point contact increases continuously, but the number of propagating modes at the Fermi level increases stepwise. The resulting conductance steps are smeared out when the thermal energy becomes comparable to the energy separation of the modes.
Page 28
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Quantized Conductance: Au-wire- vs – Au-FilmQuantized Conductance: Au-wire- vs – Au-FilmBy Laetitia G. Soukiassian
Purdue University
STM „Break Junction“
Page 29
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Naively expected behavior
Experimental result
Page 30
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
The k > 0 ProblemThe k > 0 Problem
Single Sub-Band Four Sub-Bands contributing
Page 31
Abteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of UlmAbteilung FestkörperphysikAbteilung Festkörperphysik
Solid State PhysicsSolid State Physics
University of UlmUniversity of Ulm
Statistics on a BreakjunctionStatistics on a Breakjunction