Classical and quantum transport calculations for elastically scattered free electron gases in 2D nanostructures when B=0
The Boltzmann equation in the relaxation time approximation is used to calculate formal expressions for the local electrical, thermal and thermoelectric transport coefficients of a strictly 2D, elastically scattered, free electron gas. The terminal transport coefficients for the same gas confined in a quantum wire are also calculated using the Landauer-Buttiker formalism. Both calculations are valid in a quantum wire structure when its width w is much greater than the Fermi wavelength and its length l is much greater than the classical mean free path. Comparison shows that the sum of all the transmission coefficients through the system at the Fermi energy ɛ is therefore given by T(ɛ)=(w/l)ɛ/Δɛ where Δɛ=ħ/τ(ɛ) is the uncertainty in ɛ arising from the classical relaxation time τ(ɛ). A new way of calculating T(ɛ) using wave functions is outlined. Numerical results for both T(ɛ) and scattering wave functions are presented for two nanonstructures: (i) a quantum wire with one hard wall finger pushed in and (ii) a quantum wire with two hard wall fingers pushed in so as to create a quantum dot.
KeywordsWave Function Transmission Coefficient Quantum Wire Evanescent Mode Scatter Wave Function
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