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

2. VM Ayres, ECE875, S14 Lecture 38, 14 Apr 14 Chp 06: MOSFETs Aspects of realistic MOSFET operation (n-channel p-substrate) Comment on 2D mobility  Use of field oxide in CMOS Short channel effects on ON operation: high E (y) => velocity saturation => lower I DS micron-scale = worst nano-scale = better (ECE 802: Nanoelectronics) another quantum mechanical trick: Current over-drive constant field and constant voltage scaling

3. VM Ayres, ECE875, S14 Long channel L:

4. VM Ayres, ECE875, S14 Long channel L: :

5. VM Ayres, ECE875, S14 Short channel L: due to velocity saturation:

6. VM Ayres, ECE875, S14 Short channel L: due to velocity saturation: ~ sub-  : 10 -7 m: in moderately doped Si at 300K: Limit is set by the linear regime

7. E cn E cn  n = 1: under-estimate Over-estimate VM Ayres, ECE875, S14 E cn-2-piece linear approx actual

8. VM Ayres, ECE875, S14 Short channel L: in current over-drive (Sze: “ballistic” regime):

9. VM Ayres, ECE875, S14 Short channel L: in current over-drive (Sze: “ballistic” regime): Due to high V G, charge sheet Q n = “injection charge” fills all available low energy levels. Charge sheet = already a 2DEG = a potential well. In a potential well, the higher the energy, the wider the energy level separation: noticeable E n separation Solve for Q n Sze quotes Ref. 25

10. VM Ayres, ECE875, S14 Short channel L: in current over-drive (Sze: “ballistic” regime): This approach has been superseded by nanoelectronics in graphene, CNTs, NWs, SETs using split gates, etc.

11. VM Ayres, ECE875, S14 Lecture 38, 14 Apr 14 Chp 06: MOSFETs Aspects of realistic MOSFET operation (n-channel p-substrate) Comment on 2D mobility  Use of field oxide in CMOS Short channel effects on ON operation: high E (y) => velocity saturation => lower I DS micron-scale = worst nano-scale = better (ECE 802: Nanoelectronics) another quantum mechanical trick: Current over-drive constant field and constant voltage scaling

12. 0.5  m 0.54  m 0.5  m 1.51  m n+ I G, + V G 0.47  m L V Drain = +6 VV S = gnd How to tell short versus long channel: consider depletion regions: Example: Lec 34: Si @ 300 K, N A = 4 x 10 15 cm -3 : channel ON: VM Ayres, ECE875, S14

13. 0.5  m 0.54  m 0.5  m 1.51  m n+ I G, - V G L V Drain = +6 VV S = gnd How to tell short versus long channel: consider depletion regions: Example: Lec 34: Si @ 300 K, N A = 4 x 10 15 cm -3 : channel OFF: Want to leave V DS = Sze V D = (6-0) volts ON permanently and achieve MOSFET ON/OFF using V G VM Ayres, ECE875, S14

14. 0.5  m 0.54  m 0.5  m 1.51  m n+ I G, - V G L = 5.08  m V Drain = +6 VV S = gnd How to tell short versus long channel: consider depletion regions: Open region in channel: 5.08 – 0.54 – 1.51  m = 3.03  m VM Ayres, ECE875, S14

15. 0.5  m 0.54  m 0.5  m 1.51  m n+ I G, - V G L = 3.38  m V Drain = +6 VV S = gnd How to tell short versus long channel: consider depletion regions: Scale length by 1/  where  = 1.5 Kappa  is called the “scaling factor” Open region in channel: 3.38 – 0.54 – 1.51  m = 1.33  m VM Ayres, ECE875, S14

16. 0.5  m 0.54  m 0.5  m 1.51  m n+ I G, - V G L = 2.032  m V Drain = +6 VV S = gnd How to tell short versus long channel: consider depletion regions: Scale length by 1/  where  = 2.5 No open region in channel: 2.032 – 0.54 – 1.51  m = negative: punch through V G cannot control the channel VM Ayres, ECE875, S14

17. 0.5  m 0.54  m 0.5  m 1.51  m n+ I G, - V G L = 2.54  m V Drain = +6 VV S = gnd Back off to here: Scale length by 1/  where  = 2 Open region in channel: 2.54 – 0.54 – 1.51  m = 0.49  m = 490 nm VM Ayres, ECE875, S14

18. Electric field is proportional to distance: closer to charge source = stronger field. Stronger field E (y) => v sat (y) negatively impacts device performance. Goal: shrink L/device but keep E (y) max the same value. Scaling issue: VM Ayres, ECE875, S14

19. Goal: shrink L/device but keep E (y) max the same value. Scaling issue: VM Ayres, ECE875, S14 Depends on doping and V DS Depends on doping and surface potential

20. Goal: shrink L/device but keep E (y) max the same value. Scaling issue: VM Ayres, ECE875, S14 Depends on doping and surface potential

21. Adjust device parameters to keep E field constant: Shrink physical parameters by 1/  Shrink all batteries by 1/  Increase substrate doping by  to adjust surface potential VM Ayres, ECE875, S14 Constant field scaling:

22. and V G VM Ayres, ECE875, S14

23. and V G Table 2 in the electronic book is just for Constant field scaling: VM Ayres, ECE875, S14

24. Table 2 in the hardcopy book is for Constant field & Constant voltage scaling: And V G Needed to do HW09: Table 2 in the hardcopy VM Ayres, ECE875, S14

26. Goal: shrink L/device but keep  s (y) max the same value. Constant voltage: VM Ayres, ECE875, S14 Depends on doping

27. What is the starting point relationship?

28. Starting point relationship is:

29. Make comparison 2 x’s

30. = 1 x 10 7 cm/s in Si at room temp, Sze p.307