Brad Noble

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Cross Sectional View of FET
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FET I-V Characteristic
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Saturation Voltage

• Vpinchoff VDS,sat VGS VTH
• Separates resistive from saturation region
• The drain current is given by
• Solving for VDS,sat

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Early Voltage Function of Length
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Early Voltage in MOSFETs

• Due to channel length modulation
• Good to solve for quiescent voltage-current.

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Ex Find VDS,sat for an NFET
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Body Effect
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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.

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Small Signal Equivalent Ckt
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Parasitic Capacitance
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Capacitance Equivalent Circuit
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Variation in Capacitance
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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.

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Subthreshold Conduction
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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.

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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.

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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!

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W.I. Surface Potential
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Deriving Weak Inversion IDS
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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

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Inversion Coefficient

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

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Ex. Using Inversion Coeff.
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Small Signal Analysis
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Ex Quiescent Point
Question How many digits are significant?
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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

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Taylor Series Expansion

• Taking a Taylor expansion of one variable

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Small Signal Model Params
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Example Small Signal Analysis
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Small Signal Low-Freq Model
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Ex Find gm and rO
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Transconductance W.I. M.I.

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

Not in textbooks!