Lectures 8-11: Quantum transport and Single-electron tunneling · Lectures 8-11: Quantum transport...
Transcript of Lectures 8-11: Quantum transport and Single-electron tunneling · Lectures 8-11: Quantum transport...
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Nanoscience II spring 2009 1
Lectures 8-11: Quantum transport andSingle-electron tunneling
• Low-dimensional structures: 2-D, 1-D and 0-D, density-of states
• Magnetic field induced quantization: Landau levels
• Quantum conductance, quantum point contacts
• Single-electron tunneling
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Low-dimensional structures
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Nanoscience II spring 2009 3
High electron mobility transistor (HEMT)
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Nanoscience II spring 2009 4
Magnetic field induced quantization
Landau levels
Conductance oscillations:
Shubnikov - de Haas effect
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Quantum Hall effect
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QHE devices - edge channels
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Nanoscience II spring 2009 7
Quantum effects in 2D electron gases
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Ballistic transport
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Nanoscience II spring 2009 9
Quantized conductance
Ballistic transport (no scattering) in 1-dim. wires orquantum point contacts
Conductance quantum: 2e2/h (with spin degeneracy)
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Nanoscience II spring 2009 11
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Single-electron tunneling
Single-electron boxNecessary conditions for SET:
1. Charging energy EC = e2/2C >> kBT
2. Tunneling resistance RT >> h/e2
Coulomb blockade:voltage range for fixed n
n12
e
Cg<Vg < n+
12
e
Cg
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Grey fields: Coulomb blockade regime
Single-electron transistor
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Double junction: single-electron transistor
Figure 11.3. A schematic diagram of the single electron
transistor showing two small capacitance tunnel junctions
characterized by junction resistance R and capacitance C,
and also the capacitively coupled gate.
Figure 11.4. The Helmholtz free energy of the
system as a function of Qo/e for various charge
states n at V=0.
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SET: energy diagrams
Figure 11.5. (a) Energy diagram of a SET with
symmetric junction capacitances. Coulomb blockade
exists when the tunneling process is energetically
unfavorable.
Figure 11.5. (b) When bias voltage sources
provide enough energy to overcome the charging
energy barrier, single electron tunneling occurs.
Figure 11.5. (c) At Qo=e/2, the potential of the
island is lowered by EC so that Coulomb blockade
is absent at all bias voltages.
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Coulomb staircaseSingle-electron tunnelingthrough a quantum dot
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