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Computational Solid State Physics 計算物性学特論 第10回. 10. Transport properties II: Ballistic transport. Electron transport properties. l e : electronic mean free path l φ : phase coherence length λ F : Fermi wavelength. Tunneling transport. I L. Current in one-dimension.
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Computational Solid State Physics 計算物性学特論 第10回 10. Transport properties II: Ballistic transport
Electron transport properties le: electronic mean free path lφ: phase coherence length λF: Fermi wavelength
Current in one-dimension T(k): transmission coefficient
Low bias limit : conductance at low temperatures
Landauer’s formula I: current, V: bias :Conductance :transmission coefficient :Quantum conductance :Quantum resistance
Tow- and four- terminal measurement 2-terminal measurement 4-terminal measurement
Conductance of a quantum point contact Quantization of transverse motion Only one channel (n=1) is open. for n=1
Tunneling current via quantum dot :Lorentzian broadening of resonant tunneling through quantized energy EN of a dot :Thermal broadening
Resonant tunneling current :wave function :energy
Total resonant tunneling current Large bias and low temperature limit
Profile through a three-dimensional resonant tunneling diode Profile through a three-dimensional resonant-tunnelling diode. The bias increases from (a) to (d), giving rise to the I(V) characteristic shown in (e). The shaded areas on the left and right are the Fermi seas of electrons.
Calculate the density of states for free electrons in one, two and three dimensions. Calculate the ballistic current in two dimensions. Calculate the transmission coefficient for a square barrier potential. Calculate the transmission coefficient for a double square barrier potential. Problems 10