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

2. Lecture 37, 11 Apr 14 Chp 06: MOSFETs
Aspects of realistic MOSFET operation (n-channel p-substrate)
Comment on 2D mobility m
Use of field oxide in CMOS
Short channel effects on ON operation:
high E (y) => velocity saturation => lower IDS
micron-scale = worst
nano-scale = not so bad
scaling
Good test for future ON/OFF operation: sub-threshold (not fully ON) swing
VM Ayres, ECE875, S14

3. Problem: if you reduce just L while keeping all other fabrication and operating parameters the same: performance degrades: RHS:
VM Ayres, ECE875, S14

4. Diagnose the problem: assuming that Z is still effectively the same, that leaves Qn(y) and <vel> as possible causes:
Lec 36: we noted that <vel> has a saturation effect at high E
Also: expect higher E (y) when same VDS is applied across a shorter length.
Check this possibility out

5. Previous steps leading to eq’n (23) for ID:
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6. No restrictions on E (y): can go all the way up to pinch-VDsat / L:
Result:
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7. Repeat with new <vel>: much more complicated mathematically:
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8. E (y) that increases along L
Simpler mathematics: for n-channel in Si: using green line or blue line approximation for realistic red line to get simpler v(E ):
<vel>
E (y) that increases along L
VM Ayres, ECE875, S14

9. Goal: find new VDsat. Then draw ID as in saturation after that point.
Simpler mathematics:
Goal: find new VDsat. Then draw ID as in saturation after that point.
Up to new lower VDsat continue to use:
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10. Also: replace Qn eq’n 20 with something simpler: eq’n (32):
Simpler mathematics:
Also: replace Qn eq’n 20 with something simpler: eq’n (32):
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11. But goal was: find new VDsat
Find ID:
But goal was: find new VDsat
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12. Find ID  E (y) = E critical where velocity saturation becomes a problem:
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13. Dyi (y = L) = (VatD – VatS) – (VatS – VatS) = VDS = Sze VD
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14. VM Ayres, ECE875, S14

15. Accomplished goal in terms of E c
E c for Si is pretty well known: 1 x 107 cm/s

16. Compare: With Constant mobility assumption: Pinch-
With field dependent mobility assumption in the two-piece linear approximation:
Velocity saturation-
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17. Velocity saturation-VDsat
Pinch-VDsat > Velocity saturation-VDsat
Therefore:
Pinch-ID > Velocity saturation-ID
Pinch-VDsat
Velocity saturation-VDsat
VM Ayres, ECE875, S14