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

2. Lecture 17, 17 Feb 14 Chp. 02: pn junction: Abrupt pn junction
Linearly graded pn junction
Both: Experimental measurements: C-V curves
Examples
VM Ayres, ECE875, S14

3. Remember this sequence in real research: find:
Charge Q and charge density r
Electric field E
Potential y
Energy barrier q y
Depletion region WD or equivalent local region
C-V
I-V

4. Abrupt junction:
Q and r = Constant values
E (x)
yi(x)
q yi(x)

5. An experimental measure for the Abrupt junction: C-V curve:
VM Ayres, ECE875, S14

6. Example: HW05: Sze Pr (a) find the slope and set up the calculation for N (b) find the intercept and set up the calculation for ybi
Slope ~ 1/N:
V = Vbattery

7. Realistic experimental result:
VM Ayres, ECE875, S14

8. Example:

9. Linearly graded junction: power of x raised by 1:
Achieve by co-doping
Q and r = linear = Constant x x
= a x
E (x)
yi(x)
q yi(x)

10. Linearly graded junction: power of x raised by 1:
r = linear = Constant “a” x x

11. An experimental measure for the linearly graded junction: C-V curve:
Missing 2kT/q in (38)
intercept
Experimentally sweep this
slope
VM Ayres, ECE875, S14

12. Example:

13. Excel (below) or Matlab:

15. Answer:
And given: it is an abrupt p+n junction

16. Example:

17. Slope
Intercept

18. Slope:

20. Given: p+n: N =

21. Intercept

22. Answer: 6 properties:

23. Given: p+n: WD

27. What is LD: the Debye length:

28. Debye length:

29. Debye length: 1. working definition of a good abrupt junction
2. watch out for circumstances that can create a small depletion width WD < LD

30. In Example: ✔

31. Lecture 17, 17 Feb 14 Chp. 02: pn junction: Abrupt pn junction
Linearly graded pn junction
Both: Experimental measurements: C-V curves
Examples
VM Ayres, ECE875, S14

32. Linearly graded junction: power of x raised by 1:
Achieve by co-doping
Q and r = linear = Constant x x
= a x
E (x)
yi(x)
q yi(x)

33. Steps 1-3:

34. E –field = E (x), and E max:

35. Potential yi(x), and ybi:

36. An experimental measure for the linearly graded junction: C-V curve:
Missing 2kT/q in (38)
intercept
Experimentally sweep this
slope
VM Ayres, ECE875, S14