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ECE 874: Physical Electronics

ECE 874: Physical Electronics. Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu. Lecture 13, 11 Oct 12. Finite Potential Well:. (eV). Electron energy: E > U 0. Electron energy: E < U 0. (nm). Regions:. -∞ to 0. 0 to a.

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ECE 874: Physical Electronics

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  1. ECE 874:Physical Electronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

  2. Lecture 13, 11 Oct 12 VM Ayres, ECE874, F12

  3. Finite Potential Well: (eV) Electron energy: E > U0 Electron energy: E < U0 (nm) Regions: -∞ to 0 0 to a a to +∞ VM Ayres, ECE874, F12

  4. Last section of Chp. 02 is about the Finite Barrier: VM Ayres, ECE874, F12

  5. VM Ayres, ECE874, F12

  6. A last look at the finite well, for E > U0 too: VM Ayres, ECE874, F12

  7. Finite barrier Anderson, Modern Physics andQuantum Mechanics VM Ayres, ECE874, F12

  8. E > Anderson V0  Pierret U0 VM Ayres, ECE874, F12

  9. E > Anderson V0  Pierret U0 VM Ayres, ECE874, F12

  10. E < Anderson V0  Pierret U0 This is the expression for T that Pr. 2.8 is referring to. VM Ayres, ECE874, F12

  11. Which situation is this: to start? When part (a) is finished? cosh sinh VM Ayres, ECE874, F12

  12. To start: situation is: tunnelling through the barrier cosh sinh VM Ayres, ECE874, F12

  13. When part (a) is finished, situation being described is: transport “over” the barrier region, by using Pr. 2.9’s mathematical manipulations Starting description: E < U0 Finish description for: E > U0 VM Ayres, ECE874, F12

  14. Which situation is this? VM Ayres, ECE874, F12

  15. Transport “over” the barrier region: E > U0 with transmission coefficient T given by: VM Ayres, ECE874, F12

  16. Chapter 03: Energy band theory VM Ayres, ECE874, F12

  17. e- VM Ayres, ECE874, F12

  18. Describe e- as a wave: Next Unit cell VM Ayres, ECE874, F12

  19. e- described as a wave fitting into a periodic U0 situation.What happens? The Block theorem is the end result of boundary condition matching over multiple Unit cells. Result is: Only a phase shift when you get back to a repeat situation. The repeat situation is not the lattice constant unless you are moving in <100> direction. Variable “a” = the distance between atomic cores in a particulates transport direction. VM Ayres, ECE874, F12

  20. Another useful way to describe the same wave function for e-: This emphasizes that the e- is described by a travelling wave expikx that is being modulated by a repetitive environment. VM Ayres, ECE874, F12

  21. The two descriptions are equivalent. Equation (3.3) p. 54 VM Ayres, ECE874, F12

  22. Next Unit cell VM Ayres, ECE874, F12

  23. Kronig-Penney model: approximate the real U(x) due to a row of atomic cores (top) by a series of wells and finite barriers (bottom). VM Ayres, ECE874, F12

  24. Kronig-Penney model; VM Ayres, ECE874, F12

  25. Kronig-Penney model allowed energy levels: where LHS = RHS VM Ayres, ECE874, F12

  26. Graphical solution of 2.18b: VM Ayres, ECE874, F12

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