ECE 875: Electronic Devices

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

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 VM Ayres, ECE875, S14

3. Jgen = ? OR Jrec = ? Which: are you in forward or reverse bias? What happens to the depletion region WD? VM Ayres, ECE875, S14

4. 1/tg = everything that’s left in U VM Ayres, ECE875, S14

5. Jgen-rec = q U length Jgen-rec = tg is given = 1 x 10-5 sec If: Assume: Si @ 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: VM Ayres, ECE875, S14

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: VM Ayres, ECE875, S14

15. Internal electric field E (x): must find separately on p-side and n-side: VM Ayres, ECE875, S14

16. Internal electric field E (x): Note: Linear: VM Ayres, ECE875, S14

17. Solve for maximum value of E –field: VM Ayres, ECE875, S14

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! VM Ayres, ECE875, S14

20. Potential yi(x): must find separately on p-side and n-side: p-side of depletion region: VM Ayres, ECE875, S14

21. Potential yi(x): must find separately on p-side and n-side: n-side of depletion region: VM Ayres, ECE875, S14

22. Example: find the potential drop across the p-side of the depletion region VM Ayres, ECE875, S14

23. Answer: potential DROP: Eq’n (15a) VM Ayres, ECE875, S14

24. ybi is the potential drop across the whole depletion region – what you mainly measure. At least have an experimental estimate of Emax Can we say anything about this factor VM Ayres, ECE875, S14

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 = VM Ayres, ECE875, S14

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

27. Useful parts on C-V graph: slope  concentration N intercept  equilibrium potential ybi 0 V = Vbattery VM Ayres, ECE875, S14

28. The 2 x kT/q correction factor: Shielding by neutral region electrons Shielding by neutral region holes VM Ayres, ECE875, S14

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 VM Ayres, ECE875, S14

36. Example:

37. Excel (below) or Matlab:

39. Answer: Given: abrupt p+n junction