1. ECE 875: Electronic Devices
Prof. Virginia Ayres
Electrical & Computer Engineering
Michigan State University

2. Lecture 22, 28 Feb 14
Chp. 02: pn junction and Chp 03: metal-semiconductor junction
About HW06 problems
VM Ayres, ECE875, S14

3. Pr. 2.04:
Assume: Si at 300 K

4. Remember this sequence in real research: find:
Charge Q and charge density r
Electric field E
Potential y
Energy barrier q y from y
Depletion region WD or equivalent local region from y
C-V to find concentration and ybi
I-V to find concentration and energy barrier
MODEL
MODEL
EXPERIMENT

5. Charge Q and charge density r Electric field E Potential y
Pr. 2.04:
Charge Q and charge density r
Electric field E
Potential y
Energy barrier q y from y
Depletion region WD or equivalent local region from y
C-V to find concentration and ybi
I-V to find concentration and energy barrier
MODEL

6. : r01 = qND01 = a constant (C/cm3)
: r02 = qND02 = another constant (C/cm3)
VM Ayres, ECE875, S14

7. VM Ayres, ECE875, S14

8. What are the two places that you know any E info for?
Answer: E 02 (x = WDn) = 0 E 01 (x = 0.2 mm) = E m-02
VM Ayres, ECE875, S14

9. Solve for E max-02
VM Ayres, ECE875, S14

10. E max-01 is in terms of WDn because E max-02 is in terms of WDn .
Solve for E max-01
E max-01 is in terms of WDn because E max-02 is in terms of WDn .
So need to find WDm (= Wm).
VM Ayres, ECE875, S14

11. Charge Q and charge density r Electric field E Potential y
Pr. 2.04:
Charge Q and charge density r
Electric field E
Potential y
Energy barrier q y from y
Depletion region WD or equivalent local region from y
C-V to find concentration and ybi
I-V to find concentration and energy barrier
MODEL

12. Find ybi (= potential V). Easiest way is graphically:
VM Ayres, ECE875, S14

13. Find ybi (= potential V). Easiest way is graphically:
VM Ayres, ECE875, S14

14. Find ybi (= potential V). Easiest way is graphically:
Now have an expression for ybi in terms of WDn.
If you had a value for ybi on the LHS, you could use the expression to solve for WDn.
VM Ayres, ECE875, S14

15. Find value of ybi:
VM Ayres, ECE875, S14

16. Find value of ybi:
qy1-2: + =
VM Ayres, ECE875, S14

17. Find value of ybi:
qy2-3: =
VM Ayres, ECE875, S14

18. Find value of ybi:
qy1-2 - qy2-3 = qybi =
VM Ayres, ECE875, S14

19. Put in value for ybi and solve for WDn:
Now have an expression for ybi in terms of WDn.
If you had a value for ybi on the LHS, you could use the expression to solve for WDn.
VM Ayres, ECE875, S14

20. Put in value for WDn and solve for E max-01
E max-01 is in terms of WDn because E max-02 is in terms of WDn .
So need to find WDm (= Wm).
VM Ayres, ECE875, S14

21. Pr. 3.01: Draw band-diagrams with the following values marked on it:
Barrier height on metal side: qfBn0 = 0.8 eV = given
Barrier height on semiconductor side: qybi
Barrier width W: primarily on n-side: WDn

24. Pr. 3.08:

28. W-Si example:

30. = 2.76 x 1019 cm-3
Too high

32. Too low

33. Pr. 3.08:
Use:
X 1/1010