1. Penn ESE370 Fall2014 -- DeHon 1 ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 11: September 22, 2014 MOS Transistor Operating Regions Part 2

2. Today Operating Regions (continued) –Resistive –Saturation –Velocity Saturation –Subthreshold Drain Induced Barrier Lowering Penn ESE370 Fall2014 -- DeHon 2

3. Last Time… Penn ESE370 Fall2014 -- DeHon 3

4. Channel Evolution Increasing Vgs Penn ESE370 Fall2014 -- DeHon 4

5. Threshold Voltage where strong inversion occurs  threshold voltage –Around 2 ϕ F –Engineer by controlling doping (N A ) Penn ESE370 Fall2014 -- DeHon 5

6. Resistive Region V GS >V T, V DS small Penn ESE370 Fall2014 -- DeHon 6

7. 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” –Current will flow, but cannot increase any further Penn ESE370 Fall2014 -- DeHon 7

8. Saturation V DS > V GS -V T Penn ESE370 Fall2014 -- DeHon 8

9. 9 Blue curve marks transition from Linear to Saturation Saturation Region

10. New Stuff Penn ESE370 Fall2014 -- DeHon 10

11. Preclass 1 What is electrical field in channel? –L eff =25nm, V DS =1V –Field = V DS /L eff Velocity: v=F*μ –Electron mobility: μ n = 500 cm 2 /(V  s) What is electron velocity? Penn ESE370 Fall2014 -- DeHon 11

12. Same Phenomena I = (1/R) × V I increases linearly in V What’s I? –  Q/  t –Speed at which charge moves F=V/L v=  ×F=(  /L) ×V Velocity increases linearly in V What’s a moving electron? Penn ESE370 Fall2014 -- DeHon 12

13. Short Channel Model assumes carrier velocity increases with field –Increases with voltage Are there limits to how fast things (including electrons) can move? Penn ESE370 Fall2014 -- DeHon 13 S D

14. 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 < speed-of-light How relate to preclass 1b velocity? Encounter when channel short –Modern processes, L is short enough Penn ESE370 Fall2014 -- DeHon 14 S D

15. Velocity Saturation At what voltage do we hit the speed limit? (preclass 1c) This is V dsat –The voltage at which velocity (current) saturates Penn ESE370 Fall2014 -- DeHon 15

16. Velocity Saturation Once velocity saturates: Penn ESE370 Fall2014 -- DeHon 16

17. Velocity Saturation Once velocity saturates: Can still increase current with parallelism –W – make it wider –V gs -V t – make it deeper Penn ESE370 Fall2014 -- DeHon 17 S D

18. Velocity Saturation How does this V dsat compare to the threshold we have been using? Penn ESE370 Fall2014 -- DeHon 18

19. Velocity Saturation Penn ESE370 Fall2014 -- DeHon 19

20. Subthreshold Penn ESE370 Fall2014 -- DeHon 20

21. Below Threshold Transition from insulating to conducting is non-linear, but not abrupt Current does flow –But exponentially dependent on V GS Penn ESE370 Fall2014 -- DeHon 21

22. Subthreshold Penn ESE370 Fall2014 -- DeHon 22

23. Subthreshold W/L dependence follow from resistor behavior (parallel, series) –Not shown explicitly in text λ is a channel width modulation effect Penn ESE370 Fall2014 -- DeHon 23 S D

24. Steady State What current flows in steady state? What causes (and determines) the magnitude of current flow? Which device? Penn ESE370 Fall2014 -- DeHon 24

25. Leakage Call this steady-state current flow leakage Ids leak Penn ESE370 Fall2014 -- DeHon 25

26. Subthreshold Slope Exponent in V GS determines how steep the turnoff is –Every S Volts –Divide I DS by 10 Penn ESE370 Fall2014 -- DeHon 26

27. 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 Fall2014 -- DeHon 27

28. I DS vs. V GS Penn ESE370 Fall2014 -- DeHon 28

29. Subthreshold Slope If S=100mV and V th =300mV, what is Ids(Vgs=300mV)/Ids(Vgs=0V) ? What if S=60mV? Penn ESE370 Fall2014 -- DeHon 29

30. Threshold Penn ESE370 Fall2014 -- DeHon 30

31. Threshold Describe V T as a constant Induce enough electron collection to invert channel Penn ESE370 Fall2014 -- DeHon 31

32. V DS impact In practice, V DS impacts state of channel Penn ESE370 Fall2014 -- DeHon 32

33. V DS impact Increasing V DS, already depletes portions of channel Penn ESE370 Fall2014 -- DeHon 33

34. V DS impact Increasing V DS, already depletes portions of channel Need less charge, less voltage to invert Penn ESE370 Fall2014 -- DeHon 34

35. Drain-Induced Barrier Lowering (DIBL) Penn ESE370 Fall2014 -- DeHon 35 VTVT V DS

36. DIBL Impact Penn ESE370 Fall2014 -- DeHon 36

37. In a Gate? What does it impact most? –Which device, has large Vds? Vin=Vdd ? Vin=Gnd ? –How effect operation? Speed of switching? Leakage? Penn ESE370 Fall2014 -- DeHon 37

38. In a Gate V DS largest for off device –Easier to turn on Penn ESE370 Fall2014 -- DeHon 38

39. In a Gate V DS largest for off device –Easier to turn on –Leak more Penn ESE370 Fall2014 -- DeHon 39

40. PMOS Similar phenomena to NMOS Signs different –Negative V th –turn on when less than this Reason based on carriers Penn ESE370 Fall2014 -- DeHon 40

41. Approach Identify Region Drives governing equations Use to understand operation Penn ESE370 Fall2014 -- DeHon 41

42. Big Idea 3 Regions of operation for MOSFET –Subthreshold –Resistive –Saturation Pinch Off Velocity Saturation –Short channel Penn ESE370 Fall2014 -- DeHon 42

43. Admin Text 3.3.2 – highly recommend read –Finish it up on Wednesday Office Hours: M, T, W HW4 due Thursday Midterm 1 next Monday –Midterms from 2010, 2011, 2012, 2013 All online … both with and without answers Suggest start without answers Penn ESE370 Fall2014 -- DeHon 43