OUTLINE

1
Lecture 40

• OUTLINE
• The MOSFET
• Velocity saturation
• Reading Chapter 19.1

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Velocity Saturation

• Velocity saturation limits IDSsat in modern
  MOSFETS
• Simple model
• esat is the electric field at velocity saturation

for e lt e sat
for e ? esat
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MOSFET I-V with Velocity Saturation
In the linear region
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Drain Saturation Voltage VDSsat

• If esatL gtgt VGS-VT then the MOSFET is considered
  long-channel. This condition can be satisfied
  when
• L is large, or
• VGS is close to VT

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EXAMPLE Drain Saturation Voltage
Question For VGS 1.8 V, find the VDSsat of
an NFET with Toxe 3 nm, VT 0.25 V, and WT
45 nm, if L (a) 10 mm, (b) 1 um, (c) 0.1 mm,
and (d) 0.05 mm
Solution From VGS , VT, and Toxe , mn is 200
cm2V-1s-1. esat 2vsat / mn
8 ?104 V/cm m 1 3Toxe/WT 1.2
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(a) L 10 mm VDSsat (1/1.3V 1/80V)-1
1.3 V (b) L 1 mm VDSsat (1/1.3V
1/8V)-1 1.1 V (c) L 0.1 mm VDSsat
(1/1.3V 1/.8V)-1 0.5 V (d) L 0.05 mm
VDSsat (1/1.3V 1/.4V)-1 0.3 V
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IDSsat with Velocity Saturation

Substituting VDSsat for VDS in the linear-region
IDS eqn. gives
For very short channel length

• IDSsat is proportional to VGSVT rather than
  (VGS VT)2
• IDSsat is not dependent on L

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Short- vs. Long-Channel MOSFET

• Short-channel MOSFET
• IDsat is proportional to VGS-VTn rather than
  (VGS-VTn)2
• VDsat is lower than for long-channel MOSFET
• Channel-length modulation is apparent

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Velocity Overshoot

• When L is comparable to or less than the mean
  free path, some of the electrons travel through
  the channel without experiencing a single
  scattering event
• ? projectile-like motion (ballistic
  transport)
• The average velocity of carriers exceeds vsat
• e.g. 35 for L 0.12 mm NMOSFET
• Effectively, vsat and esat increase when L is
  very small

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Summary NMOSFET I-V

• Linear region
• Saturation region

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PMOSFET I-V with Velocity Saturation

• Linear region
• Saturation region