ECE G201 H.W. #3, Due February 10, 2009

Note: Most of these problems are very quick. The last two are more challenging!

1. 1.10, text.

2. 1.11, text.

3. 1.12, text.

4. 1.21, text.

5. 2.1, text.

6. 2.4, text.

7. 2.5, text.

8. 2.6, text.

9. 2.7, text.

10. 2.11, text.

11. 2.13, text.

12. 2.15, text

13. 2.18, text

14. 2.22, text

15. 2.26, text

16. 2.29, text.

17. 2.34, text.

18. 2.37, text.

19. 2.44, text

20. S1B.2, text

21. For silicon doped with Phosphorus at 10¹⁴ cm^-3, at what temperature are half of the donors ionized. (This is easier than it appears!)

22. A particle of mass ma and fixed energy E is confined to a two-dimensional infinite potential well, as discussed in class. The x and y side lengths of the well are a and b (or Lx and Ly or ...), respectively. Also, the potential energy, Ep, is constant everywhere inside the well. Assuming the side-lengths of the box are large, derive an expression for the density of states (S(E)) for the particle. This problem is covered both in Pierret and in our text, Appendix D.

23. (4.3, Pierret - reference) Link Here a, b, and c are equivalent to Lx, Ly, and Lz in our text. Part a is refering to the form of the solution for the energy levels (and wavefunctions) for this problem - is it the same here or different? Obviously the numbers are different, but is the form of the equations the same? Part b. is referring to how you would count the solutions up. This will be a hybrid of the 2-D and 3-D solutions. In d. the idea is to plot both the 3-D and the "2.5-D" solutions on the same axes for comparison. What you should see is that the 2.5-D result will approach the 3-D result as the third dimension (c or Lz) increases.