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

2. Lecture 16, 14 Feb 14 HW 04: FRI: Pr. 2.07 Chp. 02: pn junction:
Experimental measurements for concentration:
Hall effect – Chp. 01: material:
measure VAB, and I, choose dimensions and Bext
C-V – Chp. 02: pn junction
Examples
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3. Which: are you in forward or reverse bias?
Jgen = ? OR
Jrec = ?
Which: are you in forward or reverse bias?
What happens to the depletion region WD?
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4. 1/tg = everything that’s left in U
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5. Jgen-rec = q U length Jgen-rec = tg is given = 1 x 10-5 sec
If: Assume: 300 K:

6. Vext = Vrev = -2 V

8. Lecture 16, 14 Feb 14 HW 04: FRI: Pr. 2.07 Chp. 02: pn junction:
Experimental measurements for concentration:
Hall effect – Chp. 01: material:
measure VAB, and I, choose dimensions and Bext
C-V – Chp. 02: pn junction
Examples
VM Ayres, ECE875, S14

9. 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

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

11. For Abrupt junction: find:
Charge Q and charge density r
Electric field E
Potential y
Energy barrier q y

12. Charge density r = all relevant concentrations:
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13. For Abrupt junction: find:
Charge Q and charge density r
Electric field E
Potential y
Energy barrier q y

14. Internal electric field E (x): must find separately on p-side and n-side:
Note: Linear:
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15. Internal electric field E (x): must find separately on p-side and n-side:
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16. Internal electric field E (x):
Note: Linear:
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17. Solve for maximum value of E –field:
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18. For Abrupt junction: find:
Charge Q and charge density r
Electric field E
Potential y
Energy barrier q y

19. Find: potential yi(x):
(Practical: you may be able to measure a potential drop: yi(x2) - yi(x1) ) +
Can integrate this!
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20. Potential yi(x): must find separately on p-side and n-side:
p-side of depletion region:
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21. Potential yi(x): must find separately on p-side and n-side:
n-side of depletion region:
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22. Example: find the potential drop across the p-side of the depletion region
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23. Answer: potential DROP:
Eq’n (15a)
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24. At least have an experimental estimate of E max
ybi is the potential drop across the whole depletion region – what you mainly measure.
At least have an experimental estimate of E max
Can we say anything about this factor
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25. ybi is the potential drop across the whole depletion region – what you mainly measure.
You know how you doped NA and ND – but could have hidden impurities or a bad doping process
WD =
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26. An experimental measure for the Abrupt junction: C-V curve:
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27. Useful parts on C-V graph: slope  concentration N
intercept  equilibrium potential ybi
V = Vbattery
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28. The 2 x kT/q correction factor:
Shielding by neutral region electrons
Shielding by neutral region holes
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29. Example: (a) find the slope and set up the calculation for N (b) find the intercept and set up the calculation for ybi
V = Vbattery

30. (a)

31. (b)

32. Example:

33. Linearly graded junction: power of x raised by 1:
Q and r = linear = Constant x x
E (x)
yi(x)
q yi(x)

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

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

37. Excel (below) or Matlab:

39. Answer:
Given: abrupt p+n junction