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ECE 875: Electronic Devices

Explore the equilibrium of PN junctions, internal electric fields, potential drops, and experimental measurements in electronic devices. Learn about realistic configurations and built-in potentials for effective device design and analysis.

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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 15, 12 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 • Two realistic configurations beyond abrupt linear pn junction: • Linearly graded junction • Double layer junction: important, develops at interfaces VM Ayres, ECE875, S14

  3. Lecture 15, 12 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 • Two realistic configurations beyond abrupt linear pn junction: • Linearly graded junction • Double layer junction: important, develops at interfaces VM Ayres, ECE875, S14

  4. Example: Sweep the voltage Instrument reads out C typically in Farads

  5. Example: Sze Fig: V = Vbattery

  6. Where is C: depletion region of a pn junction: Can show equivalence to parallel plate capacitor: - Qtotal es + Qtotal

  7. Where is C: depletion region of a pn junction: CD =

  8. Where you measure: C-V = same as I-V: = SMU +Vext- Sweep the voltage p+ n WD = WDp + WDn

  9. Lecture 15, 12 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 VM Ayres, ECE875, S14

  10. pn junction at equilibrium: ECE 474: Streetman & Bannerjee p n p n VM Ayres, ECE875, S14

  11. pn junction at equilibrium: ECE 474: Streetman & Bannerjee p n Q = charge density r x Vol r = q with sign (ND+ or NA-) Poisson equation relates charge to electric field E : dE /dx = r/ese0 (material is not polarized or magnetic) VM Ayres, ECE875, S14

  12. Abrupt pn junction at equilibrium: ECE 875: Sze: Q = charge density r x Vol r = q with sign (ND+ or NA-) p n Poisson equation dE /dx = r/ese0 Solve for E Solve for built in potential ybi V0 Any potential: = Area VM Ayres, ECE875, S14

  13. Abrupt pn junction at equilibrium: Sze: names: p n Potential V0ybi Potential barrier qV0 qybi p-side: Ei – EF qyBp n-side: EF – Ei  qyBn p-side: EF – EV qfp n-side: EC – EF  qfn Potential drop across depletion region WD= Pot’l drop across p-side of WD + pot’l drop across n-side of WD : ybi = yp + |yn| Potential drop from 0 to x in WD: yi(x) VM Ayres, ECE875, S14

  14. Important questions are: What is the magnitude and direction of the internal electric field? What are the values of the various potential drops that matter? Can I get an experimental measure of anything? VM Ayres, ECE875, S14

  15. What is the magnitude and direction of the internal electric field?Can I get an experimental measure of anything? An antenna probe won’t work inside a solid -no direct experimental measure of E (x) -x E direction -WDp = = WDn VM Ayres, ECE875, S14

  16. What is the magnitude and direction of the internal electric field?Can I get an experimental measure of anything? -x E direction About the directions: E (x) direction = -x dx from/to direction = +x x is + from 0 to WDn x is – from –WDp to 0 E magnitude: f(x) -WDp = = WDn

  17. What are the values of the various potential drops that matter?Can I get an experimental measure of anything? Yes: can get an experimental measure of potential. The loop will include the built-in potential ybi and Vext and any IR drops. Total potential drop Vp-to-n is mainly across W ybi Vext VM Ayres, ECE875, S14 = SMU

  18. Potential energy barrier and built-in potential in terms of dopants: But what if doping concentrations are not what you think? VM Ayres, ECE875, S14

  19. Internal electric field E (x): in WD: VM Ayres, ECE875, S14

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

  21. Internal electric field E (x): Can solve for maximum value of E -field: VM Ayres, ECE875, S14

  22. Internal electric field E (x): VM Ayres, ECE875, S14

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

  24. Go from electric field E (x) to potential yi(x). Why: you may be able to measure a potential drop. + Can integrate this! = E0 x + C VM Ayres, ECE875, S14

  25. Must separate this into p-side and n-side of depletion region answers: p-side of depletion region: VM Ayres, ECE875, S14

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