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Lecture 14 - EEE 434/591Quantum Mechanics L14:1 Small...

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EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L14:1 EEE 434/591—Quantum Mechanics David K. Ferry Regents’ Professor Arizona State University Small resonant tunneling diode
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EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L14:2 Single-Electron Tunneling We have been talking earlier about the tunneling of electrons through a barrier, or two barriers, of many barriers in the case of a superlattice. When an electron crosses the tunnel barrier, the energy in the system must change by an amount eV , where V is the voltage across the barrier. Generally, we don’t worry about this energy change, as eV << k B T , so that the necessary energy comes from thermal noise fluctuations. What happens when eV > k B T ? This is an area known as Coulomb blockade .
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EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L14:3 C When the electron tunnels across the gap (through the dielectric insulator, as the thickness d is small enough for tunneling to occur), the energy changes by and the voltage changes by
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EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L14:4 At room temperature, this requires a capacitance that is small: But, when the capacitance IS this small, the tunneling cannot occur until the voltage is large enough to provide the tunneling energy. This blockage of the tunnel current until V = e/2C > k B T/e is the Coulomb blockade effect. e/2c -e/2c V I
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EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L14:5 Fulton and Dolan, Phys. Rev. Lett. 59, 109 (1987) Experiments carried out at low temperature (4.2 K):
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EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L14:6
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EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L14:7 Cross-section of an Al-AlO 2 -Al SET, fabricated at NIST in Boulder, Colorado.
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EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L14:8 If we take the small capacitor and force current through it, the voltage increases linearly, until a sufficient voltage is reached for tunneling to occur, then the voltage drops by e/C : V I t V -e/2c e/2c
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