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

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 D yi(y) / dy. The D yi(y) part = the rise. See how it changes along y:
nergy
(y)
VM Ayres, ECE875, S14

8. Also: D yi(y) is a potential in volts
Also: D yi(y) is a potential in volts. Potentials can be related to E –fields E –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 C cm = 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. It really is an easy integral.
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)