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Computational Solid State Physics 計算物性学特論　第９回

Computational Solid State Physics 計算物性学特論　第９回. 9. Transport properties I: Diffusive transport. Electron transport properties. l e : mean free path of electrons l φ : phase coherence length λ F : Fermi wavelength. Examples of quantum transport. key quantities.

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Computational Solid State Physics 計算物性学特論　第９回

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  1. Computational Solid State Physics 計算物性学特論　第９回 9. Transport properties I: Diffusive transport

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

  3. Examples of quantum transport key quantities le : mean free path of electrons lφ: phase coherence length λF: Fermi wavelength single electron charging

  4. Point contact: ballistic quantum conductance

  5. Aharanov Bohm effect: phase coherent quantum magnetic flux

  6. Quantum dot: single electron charging

  7. Shubnikov-de Haas oscillations and quantum Hall effect

  8. Diffusive transport

  9. Equation of motion for electrons k: wave vecot of Bloch electron Scattering Rate

  10. Relaxation time approximation for scattering Direct numerical solution: Monte Carlo simulation Boltzmann equation for distribution function of electrons How to solve equations of motion for electrons with scattering?

  11. Relaxation time approximation m: effective mass equation of motion E: electric field B: magnetic field current density n: electron concentration

  12. Drude model: B=0 : drift velocity conductivity

  13. Drude model: steady state solution in magnetic field : cyclotron frequency : B is assumed parallel to z. drift velocity

  14. Conductivity tensor in magnetic field

  15. Hall effect Hall effect no transverse magneto-resistance

  16. Scattering Drift Drift Scattering Monte Carlo simulation for electron motion

  17. Drift velocity as a function of time : current

  18. k r Boltzmann equation Motion of electrons in r-k space during infinitesimal time Interval Δt

  19. Equation of motion for distribution function equation of motion for electron distribution function fk(r,t).

  20. Boltzmann equation Steady state Boltzmann equation

  21. Electron scattering detailed balance condition for transition probability

  22. Scattering term assume: elastic scattering, spherical symmetry

  23. k’ Θkk’ k Transport scattering time Contribution of forward scattering is not efficient. Contribution of backward scattering is efficient.

  24. Linearized Boltzmann equation Fermi sphere is shifted by electric field.

  25. Current density and conductivity

  26. Electron mobility in GaAs

  27. Energy flux and thermal conductivity thermal conductivity

  28. Calculate both the conductivity and the resistivity tensors in the static magnetic fields, by solving the equation of motion in the relaxation time approximation. Study the temperature dependence of electron mobility in n-type Si. Calculate the electron mobility in n-type silicon for both impurity scattering and acoustic phonon scattering mechanisms, by using the linearized Boltzmann equation. Problems 9

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