You have learnt the lengthscale that an electron can propagate ballistically in a diffusive electronic system,...

 

 

Transcribed Image Text:

You have learnt the lengthscale that an electron can propagate ballistically in a diffusive electronic system, is the electron mean free path, 1 = VFT, related to the Fermi velocity VF and the time between subsequent scattering events. This has allowed to define an electron mobility 02D nse ² T (planar (2D) conductor). Here, n, is the 2D carrier density, m is the effective mass. Diffusive conduction in a large enough 2D electronic system would be descirbe by Ohm's law, m G = = 02D (1) a) From the classical Ohm's law, derive the famous Landauer formula for a transmission of electron wave functions, = G = W L' - 2e² - NT. h (2) b) Show that for a long conductor (L » Le), it has an effective transmission 2L, per mode. coefficient of T πι c) What the conductance be at L = 0? Is this result physical? = Hints: Remember the DeBroglie relationship ħkf = mvF, as well as the definition of the Fermi wave number kF. Also, the electron's Fermi wave length can be related to the carrier density F Finally, remember that the number of modes N can be estimated by comparing the DeBroglie wave length of electrons at the Fermi level with the conductor's lateral size. 2π ns You have learnt the lengthscale that an electron can propagate ballistically in a diffusive electronic system, is the electron mean free path, 1 = VFT, related to the Fermi velocity VF and the time between subsequent scattering events. This has allowed to define an electron mobility 02D nse ² T (planar (2D) conductor). Here, n, is the 2D carrier density, m is the effective mass. Diffusive conduction in a large enough 2D electronic system would be descirbe by Ohm's law, m G = = 02D (1) a) From the classical Ohm's law, derive the famous Landauer formula for a transmission of electron wave functions, = G = W L' - 2e² - NT. h (2) b) Show that for a long conductor (L » Le), it has an effective transmission 2L, per mode. coefficient of T πι c) What the conductance be at L = 0? Is this result physical? = Hints: Remember the DeBroglie relationship ħkf = mvF, as well as the definition of the Fermi wave number kF. Also, the electron's Fermi wave length can be related to the carrier density F Finally, remember that the number of modes N can be estimated by comparing the DeBroglie wave length of electrons at the Fermi level with the conductor's lateral size. 2π ns

Answer rating: 100% (QA)

a To derive the Landauer formula for a transmission of electron wave functions we start from the cla... View the full answer