Brad Noble

1
Early Voltage in MOSFETs

• Due to channel length modulation

2
Saturation Voltage

• Vpinchoff VDS,sat VGS VTH
• Separates resistive from saturation region
• The drain current is given by
• Solving for VDS,sat
• Good to solve for quiescent voltage-current.

3
Ex Find VDS,sat for an NFET
4
Variations in VTH Across Channel

• We assume VTH is constant across channel
• THIS IS NOT TRUE!
• Depletion region is thick at S and thin at D.

5
Notes on PFETs

• PFETs typically have a shape factor 3 or 4 times
  larger than NFETs
• Body effect can be eliminated in PFETs by tying
  the n-well to VDD
• Need 6?m spacing between n-wells to isolate.
• Dr. Engel always does this on input devices, not
  always elsewhere.

6
Weak Inversion

• What really happens if VGS lt VTN?
• In digital design, IDS 0.
• We call it weak inversion or W.I.
• IDS is primarily due to Idrift in strong
  inversion and Idiffusion in weak inversion.

7
Modes of Inversion

• IDS Idrift Idiffusion
• If VGS gt VTN the channel has been inverted.
• To be more precise, we can say the channel has
  been strongly inverted (S.I.) due to an
  abundance of carriers in the channel.
• Inversion is independent of whether the FET is in
  the linear or saturation region.

8
Weak Inversion Idiffusion

• Drain is more reverse biased than source
• To find Idiff, compute gradient
• Because no carriers are lost as they travel from
  S to D, current is the same for all x and
  gradient is not a function of x.
• Note This is not really true due to
  recombination, but its close!

9
W.I. Surface Potential
10
Deriving Weak Inversion IDS
11
W.I. FET As Exp. Law Dev.

• S must be big for device to be useful.
• If VDS 100mV, can be neglected.
• For W.I. vDS,Sat ? 100mV
• Looks like a BJT

12
Inversion Coefficient

• Let
• Shape factor as a function of ?
• Lets you chose shape to match inversion mode.

13
Ex. Using Inversion Coeff.
14
Small Signal Analysis
15
Ex Quiescent Point
Question How many digits are significant?
16
Small Signal Model Limits

• Suppose the previous circuit is the input device
  of an amplifier.
• Small-signal model holds as long as the
  deviations are small

17
Taylor Series Expansion

• Taking a Taylor expansion of one variable

18
Small Signal Model Params
19
Example Small Signal Analysis
20
Small Signal Low-Freq Model
21
Ex Find gm and rO
22
Transconductance W.I. M.I.

• What is gm for a weakly inverted FET?
• What is gm for a moderately inverted FET?

Not in textbooks!