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de Broglie wavelength

Regarding our discussion yesterday, you mentioned that DeBroglie wavelength in metals is approx. 1A. I understand the relation of phase and momentum relaxation lengths to the conductance. Also that particle’s momentum, respectively phase, is lost after the corresponding characteristic lengths, but I cannot relate the effect of DeBroglie wavelength . Kindly let me know of your opinion on this.

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    Supriyo Datta

    The number of modes in a conductor of cross-section S is ~ S / (DeBroglie wavelength)^2
    (please see slide#13, CQT Lecture 2)

    Note that DeBroglie wavelength changes with energy .. here we use the wavelength for electrons with energy Ef which for metals is ~ 5 eV, and for semiconductors is ~ 5 meV.

    I would expect the cross-sectional area to have significant effect on I-V if the number of modes is small, like ~ 10 but not if it is large like ~ 10,000 ..

    Makes sense?

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