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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 34, 04 Apr 14. Chp 06: MOSFETs Channel Current I DS (n-channel p-substrate) Finish theory Examples Goal: I DS in charge sheet constant mobility model,

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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 34, 04 Apr 14 • Chp 06: MOSFETs • Channel Current IDS (n-channel p-substrate) • Finish theory • Examples • Goal: IDS in charge sheet constant mobility model, • good for both linear and saturation I-V regimes VM Ayres, ECE875, S14

  3. Goal: IDS in charge sheet constant mobility model, good for both linear and saturation I-V regimes VM Ayres, ECE875, S14

  4. Why this is the Charge sheet model: Note that Qn = Qn(y) ≠ Qn(x,y). That means neglecting “thickness of Qn near the Source L z Width = Z y: S to D SiO2 x VM Ayres, ECE875, S14

  5. Why this is the Charge sheet model: Charge Qn(y) does vary in y-direction: Lots of e-s near source end of channel Few e-s in pinch near drain end of channel when VDS in ON L z Width = Z y: S to D SiO2 x VM Ayres, ECE875, S14

  6. Write Qn(y) in terms of VDS: Why do it this way: because VDS is something you actually know: Means: when y = L Means: when y = L VM Ayres, ECE875, S14

  7. Approximate the change that happens along y when VDS is ON as rise over run: d Dyi(y) / dy. The Dyi(y) part = the rise. See how it changes along y: nergy (y) VM Ayres, ECE875, S14

  8. Also: Dyi(y) is a potential in volts.Potentials can be related to E –fieldsE –fields can be related to that charges Q that cause them VM Ayres, ECE875, S14

  9. E –fields are related to charge Qn(y) as shown in (14) The E –fields in the oxide (constant value) and semiconductor are: Substitute (17) and (18) into (14) to get the expression for Qn(y): VM Ayres, ECE875, S14

  10. Now get IDS: recall Lec 32, our Units-based guess: Z ✔ cm Ccm = C = Amps cm2 s s Need vel. vel = average drift velocity <vel>. This is related to the mobility and the E –field along transport direction: VM Ayres, ECE875, S14

  11. Constant mobility model: Mobility is average particle drift velocity per unit electric field Assume that E = E (y) but that m is constant. Then: VM Ayres, ECE875, S14

  12. Therefore: Channel current IDS is: Blue is 0 < dy < L Red is VS - VS =0 volts < Dyi(y) < VD – VS = VDS volts Need to put one in terms of the other to finish the integral VM Ayres, ECE875, S14

  13. Start: Finish. It really is an easy integral. VM Ayres, ECE875, S14

  14. Goal: IDS in charge sheet constant mobility model, good for both linear and saturation I-V regimes Achieved goal: IDS in (23) is good for any combination of VG and VDS VM Ayres, ECE875, S14

  15. Behavior regimes Saturation: VD ≈ VG - VT Linear: VD < VG - VT VM Ayres, ECE875, S14

  16. Lecture 34, 04 Apr 14 • Chp 06: MOSFETs • Channel Current IDS (n-channel p-substrate) • Finish theory • Examples • Goal: IDS in charge sheet constant mobility model, • good for both linear and saturation I-V regimes VM Ayres, ECE875, S14

  17. Example: What regime?

  18. Answer: VD ? What relation to? VG - VT 0.1 V < 1V – 0.5V = 0.5V Linear Use linear regime approximate equation for ID Conductance g = dID/dVD

  19. Example: What regime?

  20. Answer: Only VG is given, little about VD and nothing about VT But Saturation regime is stated

  21. ox ox ox

  22. Easy to solve for VT Note that you are reading two VG curves at some VD in saturation VG = 3 V 200 mA VG = 1 V 50 mA

  23. Example: What regime?

  24. Answer: Not clear but not needed. VT is a requirement that is fixed by the materials properties of the semiconductor and the insulator (oxide)

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