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Computational Solid State Physics 計算物性学特論　第１０回

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

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  1. Computational Solid State Physics 計算物性学特論　第１０回 10. Transport properties II: Ballistic transport

  2. Electron transport properties le: electronic mean free path lφ: phase coherence length λF: Fermi wavelength

  3. Tunneling transport I L

  4. Current in one-dimension T(k): transmission coefficient

  5. Total current in one-dimension

  6. Low bias limit : conductance at low temperatures

  7. Landauer’s formula I: current, V: bias ：Conductance ：transmission coefficient ：Quantum conductance ：Quantum resistance

  8. Two- and four- terminal measurements

  9. Tow- and four- terminal measurement 2-terminal measurement 4-terminal measurement

  10. Conductance of a quantum point contact

  11. Conductance of a quantum point contact Quantization of transverse motion Only one channel (n=1) is open. for n=1

  12. Nanowire of Au

  13. Nanowire of Au

  14. Nanowire of Au

  15. Mechanically Controllable Break Junction

  16. Histogram of conductance of a relay junction

  17. Conductance through a quantum dot

  18. Tunneling current via quantum dot :Lorentzian broadening of resonant tunneling through quantized energy EN of a dot :Thermal broadening

  19. A bound state and a resonant state

  20. Transmission coefficient for resonant tunneling IfTL=TR

  21. Transmission coefficient of a resonant-tunneling structure

  22. Characteristics of resonant tunneling diode

  23. Resonant tunneling current :wave function :energy

  24. Total resonant tunneling current Large bias and low temperature limit

  25. Transmission coefficient for resonant tunneling If TL=TR

  26. 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.

  27. 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

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