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

2. Lecture 13, 11 Oct 12
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3. Finite Potential Well:
(eV)
Electron energy: E > U0
Electron energy: E < U0
(nm)
Regions:
-∞ to 0
0 to a
a to +∞
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4. Last section of Chp. 02 is about the Finite Barrier:
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5. VM Ayres, ECE874, F12

6. A last look at the finite well, for E > U0 too:
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7. Finite barrier Anderson, Modern Physics and Quantum Mechanics
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8. E > Anderson V0
 Pierret U0
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9. E > Anderson V0
 Pierret U0
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10. This is the expression for T that Pr. 2.8 is referring to.
E < Anderson V0
 Pierret U0
This is the expression for T that Pr. 2.8 is referring to.
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11. Which situation is this: to start? When part (a) is finished?
cosh
sinh
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12. To start: situation is: tunnelling through the barrier
cosh
sinh
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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
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14. Which situation is this?
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15. Transport “over” the barrier region: E > U0 with transmission coefficient T given by:
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16. Chapter 03: Energy band theory
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17. e-
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18. Describe e- as a wave:
Next Unit cell
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19. e- described as a wave fitting into a periodic U0 situation
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.
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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.
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21. The two descriptions are equivalent.
Equation (3.3) p. 54
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22. Next Unit cell
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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).
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24. Kronig-Penney model;
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25. Kronig-Penney model allowed energy levels: where LHS = RHS
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26. Graphical solution of 2.18b:
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