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

2. Lecture 12, 09 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. Infinite Potential Well:
U (eV) = +∞
U (eV) = +∞
Electron energy: E < U0
(nm)
Regions:
-∞ to 0
0 to a
a to +∞
VM Ayres, ECE874, F12

5. For these two situations, found: - y(x) - En
VM Ayres, ECE874, F12

6. A) U0 = 0.7 eV = half the size of the bandgap
Lecture 11 Example problem: Find energy levels in a finite model for a SQW:
Consider a SQW of width a = 10 nm that is fabricated in GaAs that operates at 300K. The SQW is modelled as a finite well. How many energy levels for an e- exist for:
A) U0 = 0.7 eV = half the size of the bandgap
B) U0 = 1.4 eV = just under the size of the bandgap
C) What is the practical meaning of the limit: x = E/U0, 0 < x < 1?
VM Ayres, ECE874, F12

7. Finite Potential Well
Advantage is: you scale to important parameters: the height U0 and width a.
Note: Width a only affects the LHS: the number/spacing of tan curves.
Height U0 affects both sides but practical advantage on RHS plot..
VM Ayres, ECE874, F12

8. VM Ayres, ECE874, F12

9. VM Ayres, ECE874, F12

10. Discussion of Matlab solutions for:
ECE874_FiniteWellEnergyLevels_Lec11.m
Lecture 11 example problem: examples of two different well heights: U0 = 0.7 ev and U0 = 1.4 eV for a fixed well width and electron energy up to same value as U0
ECE874_FiniteWellEnergyLevels_ThreeVariables.m
General three variable set-up allows you to change:
well height U0
well width a
energy “of” electron compared to well height: z = E/U0
VM Ayres, ECE874, F12

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

12. VM Ayres, ECE874, F12

13. Finite barrier Anderson, Modern Physics and Quantum Mechanics
VM Ayres, ECE874, F12

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

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