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

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

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

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

Previous steps leading to eq’n (23) for ID: VM Ayres, ECE875, S14

No restrictions on E (y): can go all the way up to pinch-VDsat / L: Result: VM Ayres, ECE875, S14

Repeat with new <vel>: much more complicated mathematically: VM Ayres, ECE875, S14

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

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: VM Ayres, ECE875, S14

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): VM Ayres, ECE875, S14

But goal was: find new VDsat Find ID: But goal was: find new VDsat VM Ayres, ECE875, S14

Find ID  E (y) = E critical where velocity saturation becomes a problem: VM Ayres, ECE875, S14

Dyi (y = L) = (VatD – VatS) – (VatS – VatS) = VDS = Sze VD VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

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

Compare: With Constant mobility assumption: Pinch- With field dependent mobility assumption in the two-piece linear approximation: Velocity saturation- VM Ayres, ECE875, S14

Velocity saturation-VDsat Pinch-VDsat > Velocity saturation-VDsat Therefore: Pinch-ID > Velocity saturation-ID Pinch-VDsat Velocity saturation-VDsat VM Ayres, ECE875, S14