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Graduate Lecture Series 29 June – 3 July, 2009 Prof Ngee-Pong Chang

Graduate Lecture Series 29 June – 3 July, 2009 Prof Ngee-Pong Chang. Lecture 2 Fermi Gas. Enrico Fermi 1901 - 1954. Paul Dirac 1902 - 1984. Band Theory of Metals. Start with isolated Sodium Atom. Ionisation Energy of Sodium 5.14 eV. Band Theory of Metals.

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Graduate Lecture Series 29 June – 3 July, 2009 Prof Ngee-Pong Chang

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  1. Graduate Lecture Series 29 June – 3 July, 2009 Prof Ngee-Pong Chang Lecture 2 Fermi Gas

  2. Enrico Fermi 1901 - 1954 Paul Dirac 1902 - 1984

  3. Band Theory of Metals Start with isolated Sodium Atom Ionisation Energy of Sodium 5.14 eV

  4. Band Theory of Metals Ionisation Energy of Sodium 5.14 eV

  5. Band Theory of Metals

  6. Band Theory of Metals Bring two Sodium Atoms together Splitting of 3s level with 2 Sodium atoms

  7. Band Theory of Metals Bring six Sodium Atoms together Splitting of 3s level with 6 Sodium atoms

  8. Band Theory of Metals Splitting of 3s levels with Sodium atoms in crystalline solid

  9. Band Theory of Metals

  10. Fermi-Dirac Distribution electrons holes

  11. Probability of Occupancy T=0 T > 0 1.0 0.0

  12. Probability of Occupancy

  13. ² F Filling up the Fermi Sea In One Dimensional Box 30 Energy in units 20 10

  14. 1-Dimensional Box

  15. 1-Dimensional Fermi Gas Sum Over Spins

  16. 1-Dimensional Fermi Gas Single Spin Orientation Fermi Surface dependence on number of electrons

  17. 2-Dimensional Fermi Gas Single Spin Orientation Fermi Surface dependence on number of electrons

  18. 3-Dimensional Fermi Gas Single Spin Orientation Fermi Surface dependence on number of electrons

  19. 1-Dimensional Fermi Gas Single Spin Orientation Total Energy

  20. 2-Dimensional Fermi Gas Single Spin Orientation Total Energy

  21. 3-Dimensional Fermi Gas Single Spin Orientation Total Energy

  22. 3-Dimensional Density of States

  23. 2-Dimensional Density of States

  24. http://upload.wikimedia.org/wikipedia/en/c/c5/DOS_multdim.jpghttp://upload.wikimedia.org/wikipedia/en/c/c5/DOS_multdim.jpg

  25. 3-Dimensional Fermi Gas Density of States

  26. 2-Dimensional Fermi Gas Density of States

  27. 1-Dimensional Fermi Gas Density of States

  28. Conduction Band Valence Band

  29. Woodward Yang harvard lecture notes

  30. CBO =conduction band offset

  31. 2-Dimensional Density of States

  32. Quantum Wire

  33. http://boulder.research.yale.edu/Boulder-2005/Lectures/Matveev/Boulder%20lecture.pdfhttp://boulder.research.yale.edu/Boulder-2005/Lectures/Matveev/Boulder%20lecture.pdf

  34. A graphene nanoribbon field-effect transistor (GNRFET). Here contacts A and B are at two different Fermi levels EF1 and . EF2

  35. Ballistic Conductor

  36. Landauer formula i t t’ i’ 1927 - 1999 Conductance

  37. µ Gas Pressure on the Wall A cos θ v δ t θ A

  38. Pressure due to Non-Relativistic Degenerate Fermi Gas Equation of state for Fermi Gas since at T = 0 We have for a metal

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