1. Penn ESE370 Fall2011 -- DeHon 1 ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 10: September 28, 2011 MOS Transistor Basics

2. Today MOS Transistor Topology Threshold Operating Regions –Resistive –Saturation –Velocity Saturation –Subthreshold Penn ESE370 Fall2011 -- DeHon 2

3. Last Time Penn ESE370 Fall2011 -- DeHon 3

4. Depletion region  excess carriers depleted Penn ESE370 Fall2011 -- DeHon 4 Refinement

5. Body Contact Fourth terminal Also effects fields Usually common across transistors Penn ESE370 Fall2011 -- DeHon 5

6. No Field V GS =0, V DS =0 Penn ESE370 Fall2011 -- DeHon 6

7. Apply V GS >0 Accumulate negative charge –Repel holes (fill holes) Penn ESE370 Fall2011 -- DeHon 7 + + + + - - - - - - - - -

8. Channel Evolution Increasing Vgs Penn ESE370 Fall2010 -- DeHon 8

9. Gate Capacitance Penn ESE370 Fall2010 -- DeHon 9 Changes based on operating region. Happy if you treat as parallel plate Capacitor for HW3.

10. Inversion Surface builds electrons –Inverts to n-type –Draws electrons from n + source Penn ESE370 Fall2011 -- DeHon 10

11. Threshold Voltage where strong inversion occurs  threshold voltage –Around 2 ϕ F –Engineer by controlling doping (N A ) Penn ESE370 Fall2011 -- DeHon 11

12. Resistive Region V GS >V T, V DS small Penn ESE370 Fall2011 -- DeHon 12

13. Resistive Region V GS >V T, V DS small V GS fixed  looks like resistor –Current linear in V DS Penn ESE370 Fall2011 -- DeHon 13

14. Linear or Resistive Region Penn ESE370 Fall2011 -- DeHon 14

15. Penn ESE370 Fall2011 -- DeHon 15 Dimensions Channel Length (L) Channel Width (W) Oxide Thickness (T ox )

16. Preclass Ids for identical transistors in parallel? Penn ESE370 Fall2011 -- DeHon 16

17. Preclass Ids for identical transistors in series? –(Vds small) Penn ESE370 Fall2011 -- DeHon 17

18. Transistor Strength (W/L) Penn ESE370 Fall2011 -- DeHon 18 S D

19. Transistor Strength (W/L) Shape dependence match Resistance intuition –Wider = parallel resistors  decrease R –Longer = series resistors  increase R Penn ESE370 Fall2011 -- DeHon 19 S D

20. L drawn vs. L effective Doping not perfectly straight Spreads under gate Effective L smaller than draw gate width Penn ESE370 Fall2011 -- DeHon 20

21. Channel Voltage Voltage varies along channel Think of channel as resistor Penn ESE370 Fall2011 -- DeHon 21

22. Preclass 2 What is voltage in the middle of a resistive medium? –(halfway between terminals) Penn ESE370 Fall2011 -- DeHon 22

23. Voltage in Channel Think of channel as resistive medium –Length = L –Area = Width * Depth(inversion) What is voltage in the middle of the channel? –L/2 from S and D ? Penn ESE370 Fall2011 -- DeHon 23

24. Channel Voltage Voltage varies along channel If think of channel as resistor –Serves as a voltage divider between V S and V D Penn ESE370 Fall2011 -- DeHon 24

25. Impact on Inversion What happens when –Vgs=2Vth ? –Vds=2Vth? What is Vmiddle (Vmiddle-Vs)? Penn ESE370 Fall2011 -- DeHon 25

26. Channel Field When voltage gap V G -V x drops below V T, drops out of inversion –Occurs when: V GS -V DS < V T –What does this mean about conduction? Penn ESE370 Fall2011 -- DeHon 26

27. Channel Field When voltage gap V G -V x drops below V T, drops out of inversion –Occurs when: V GS -V DS < V T –What is voltage at Vmiddle if conduction stop? –What does that mean about conduction? Penn ESE370 Fall2011 -- DeHon 27

28. Channel Field When voltage gap V G -V x drops below V T, drops out of inversion –Occurs when: V GS -V DS < V T –Channel is “pinched off” Penn ESE370 Fall2011 -- DeHon 28

29. Pinch Off When voltage drops below V T, drops out of inversion –Occurs when: V GS -V DS < V T Conclusion: –current cannot increase with V DS once V DS > V GS -V T –If current dropped to zero, then would invert and conduct again… Penn ESE370 Fall2011 -- DeHon 29

30. Saturation In saturation, V DS-effecitve =V x = V GS -V T Becomes: Penn ESE370 Fall2011 -- DeHon 30

31. Saturation V DS > V GS -V T Penn ESE370 Fall2011 -- DeHon 31

32. Saturation Region Penn ESE370 Fall2011 -- DeHon 32

33. Preclass 3 What is electrical field in channel? –L eff =25nm, V DS =1V –Field = V DS /L Velocity: v=F*μ –Electron mobility: μ n = 500 cm 2 /V What is electron velocity? Penn ESE370 Fall2011 -- DeHon 33

34. Short Channel Model assumes carrier velocity increases with field –Increases with voltage There is a limit to how fast carriers can move –Limited by scattering to 10 5 m/s How relate to preclass 3 velocity? Encounter when channel short –Modern processes, L is short enough Penn ESE370 Fall2011 -- DeHon 34 S D

35. Velocity Saturation Once velocity saturates: Penn ESE370 Fall2011 -- DeHon 35

36. Velocity Saturation Penn ESE370 Fall2011 -- DeHon 36

37. Below Threshold Transition from insulating to conducting is non-linear, but not abrupt Current does flow –But exponentially dependent on V GS Penn ESE370 Fall2011 -- DeHon 37

38. Subthreshold Penn ESE370 Fall2011 -- DeHon 38

39. Subthreshold W/L dependence follow from resistor behavior (parallel, series) –Not shown explicitly in text λ is a channel width modulation effect Penn ESE370 Fall2011 -- DeHon 39 S D

40. Subthreshold Slope Exponent in V GS determines how steep the turnoff is –Every S Volts –Divide I DS by 10 Penn ESE370 Fall2011 -- DeHon 40

41. Subthreshold Slope Exponent in V GS determines how steep the turnoff is –Every S Volts ( S not related to source ) –Divide I DS by 10 n – depends on electrostatics –n=1  S=60mV at Room Temp. (ideal) –n=1.5  S=90mV –Single gate structure showing S=90-110mV Penn ESE370 Fall2011 -- DeHon 41

42. I DS vs. V GS Penn ESE370 Fall2011 -- DeHon 42

43. Admin Text 3.3.2 – highly recommend read –Second half on Friday HW3 due Friday Intel Talk: Raisler lounge at 4pm –Be there! Penn ESE370 Fall2011 -- DeHon 43

44. Big Idea 3 Regions of operation for MOSFET –Subthreshold –Resistive –Saturation Pinch Off Velocity Saturation –Short channel Penn ESE370 Fall2011 -- DeHon 44