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ECE 875: Electronic Devices

ECE 875: Electronic Devices. Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu. Lecture 18, 19 Feb 14. Chp. 02: pn junction: C-V curves: About Pr. 2.02 Mixed linearly graded and abrupt pn junction: About Pr. 2.03 More about the Debye length.

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ECE 875: Electronic Devices

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

  2. Lecture 18, 19 Feb 14 • Chp. 02: pn junction: • C-V curves: About Pr. 2.02 • Mixed linearly graded and abrupt pn junction: About Pr. 2.03 • More about the Debye length VM Ayres, ECE875, S14

  3. VM Ayres, ECE875, S14

  4. Epitaxial layer: layer grown in front: n-layer grown on the p+ substrate “…formed IN an n-type epitaxial layer” As grown n-type epitaxial layer p+ substrate VM Ayres, ECE875, S14

  5. “…depletion capacitance ….formed IN an n-type epitaxial layer” means formation of a depletion region WD = WDp + WDn As grown n-type epitaxial layer p+ substrate VM Ayres, ECE875, S14 WDn = ? WDp = 0.07 mm

  6. Find the thickness of the depletion region WDn formed in the n-type epitaxial layer As grown n-type epitaxial layer p+ substrate VM Ayres, ECE875, S14 WDn = ? WDp = 0.07 mm

  7. Find the thickness of the depletion region WDn formed in the n-type epitaxial layer Under which bias condition? Vext = Reverse: -1 V As grown n-type epitaxial layer p+ substrate Equilibrium: 0 V Forward: + 0.95 V VM Ayres, ECE875, S14 WDn = ? WDp = 0.07 mm

  8. Find the thickness of the depletion region WDn formed in the n-type epitaxial layer Under bias condition: Vrev = -1 V, for which WD is biggest. Given WDp-max = 0.07 mm. Find WDn-max Vext = Reverse: -1 V As grown n-type epitaxial layer p+ substrate Equilibrium: 0 V Forward: + 0.95 V VM Ayres, ECE875, S14 WDn = ? WDp = 0.07 mm

  9. Two ways to finish: use Method 01: VM Ayres, ECE875, S14

  10. Use intercept:i VM Ayres, ECE875, S14

  11. Use slope VM Ayres, ECE875, S14

  12. Watch out for Units: VM Ayres, ECE875, S14

  13. VM Ayres, ECE875, S14

  14. Lecture 18, 19 Feb 14 • Chp. 02: pn junction: • C-V curves: About Pr. 2.02 • Mixed linearly graded and abrupt pn junction: About Pr. 2.03 • More about the Debye length VM Ayres, ECE875, S14

  15. VM Ayres, ECE875, S14

  16. For mixed type pn doping, find: WD ybi Emax NA-(x) and ND+(x) E (x) VM Ayres, ECE875, S14

  17. For mixed type pn doping, find: WD ybi Emax NA-(x) and ND+(x) E (x) 2nd easiest to find: Easiest to find: VM Ayres, ECE875, S14

  18. D D VM Ayres, ECE875, S14

  19. Find Emax “as if”: Solve for Em VM Ayres, ECE875, S14

  20. Next step: VM Ayres, ECE875, S14

  21. Relation of Emax to WDn “as if”: VM Ayres, ECE875, S14 Use Em. Solve for WDn

  22. For mixed type pn doping, find: WD ybi Emax NA-(x) and ND+(x) E (x) ✔ 2nd easiest to find: ✔ Easiest to find: VM Ayres, ECE875, S14

  23. For mixed type pn doping, find: WD ybi Emax NA-(x) and ND+(x) E (x) Find potential drop on p-side using correct yi(x) formula for linearly graded Find potential drop on n-side using correct yi(x) formula for linearly graded ybi = potential drop on p-side + potential drop on n-side ✔ ✔ VM Ayres, ECE875, S14

  24. For mixed type pn doping, find: WD ybi Emax NA-(x) and ND+(x) E (x) ✔ ✔ ✔ What do you expect the E (x) plot to look like? VM Ayres, ECE875, S14

  25. VM Ayres, ECE875, S14

  26. For mixed type pn doping, find: WD ybi Emax NA-(x) and ND+(x) E (x) ✔ ✔ ✔ What do you expect the doping(x) plot to look like? VM Ayres, ECE875, S14

  27. VM Ayres, ECE875, S14

  28. Lecture 18, 19 Feb 14 • Chp. 02: pn junction: • C-V curves: About Pr. 2.02 • Mixed linearly graded and abrupt pn junction: About Pr. 2.03 • More about the Debye length VM Ayres, ECE875, S14

  29. Debye length: p+n example on spring 2012 Midterm: VM Ayres, ECE875, S14

  30. Debye length: p+n example on spring 2012 Midterm: NA- NA- ND+ ND+ ND+ NA- NA- NA- NA- NA- NA- ND+ ND+ ND+ NA- NA- NA- NA- NA- NA- ND+ ND+ ND+ NA- NA- NA- NA- NA- NA- ND+ ND+ ND+ NA- NA- NA- NA- NA- NA- ND+ ND+ ND+ NA- NA- NA- NA- VM Ayres, ECE875, S14

  31. Debye length: p+n example on spring 2012 Midterm: LD = 41.2 nm NA- NA- ND+ ND+ ND+ NA- NA- NA- NA- NA- NA- ND+ ND+ ND+ NA- NA- NA- NA- NA- NA- ND+ ND+ ND+ NA- NA- NA- NA- NA- NA- ND+ ND+ ND+ NA- NA- NA- NA- NA- NA- ND+ ND+ ND+ NA- NA- NA- NA- VM Ayres, ECE875, S14

  32. Debye length LD pos-neg shielding length: “Debye shielding” LD = 41.2 nm NA- ND+ NA- ND+ NA- ND+ NA- ND+ NA- ND+ VM Ayres, ECE875, S14

  33. In Sze abrupt pn junction calculations for E (x) and yi(x): r Q+/WDn Area= ND+ Single type of charge. This is outside LD. NA- NA- ND+ ND+ ND+ NA- NA- NA- NA- NA- NA- ND+ ND+ ND+ NA- NA- NA- NA- NA- NA- ND+ ND+ ND+ NA- NA- NA- NA- NA- NA- ND+ ND+ ND+ NA- NA- NA- NA- NA- NA- ND+ ND+ ND+ NA- NA- NA- NA- VM Ayres, ECE875, S14

  34. Will see Debye shielding length LD again: Chp. 03: metal-semiconductor interface: develops special charge layer to achieve shielding Chp. 04 & Chp. 06: metal-insulator-semiconductor interface develops inversion layer (gate/channel region in a transistor) during operation VM Ayres, ECE875, S14

  35. Will see Debye shielding length LD again: Chp. 04, Fig. 4: Inversion region: e-s  surface charge Qs formed in a p-side VM Ayres, ECE875, S14

  36. Will see Debye shielding length LD again: Chp. 04, fig.4: Where: VM Ayres, ECE875, S14

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