1. Lecture #40 OUTLINE The MOSFET: Velocity saturation
Reading: Chapter 19.1
EE130 Lecture 40, Slide 1

2. esat is the electric field at velocity saturation:
Velocity saturation limits IDSsat in modern MOSFETS
Simple model:
esat is the electric field at velocity saturation:
for e < e sat
for e  esat
EE130 Lecture 40, Slide 2

3. MOSFET I-V with Velocity Saturation
In the linear region:
EE130 Lecture 40, Slide 3

4. Drain Saturation Voltage VDSsat
If esatL >> VGS-VT then the MOSFET is considered “long-channel”. This condition can be satisfied when
L is large, or
VGS is close to VT
EE130 Lecture 40, Slide 4

5. 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
EE130 Lecture 40, Slide 5

6. (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
EE130 Lecture 40, Slide 6

7. IDSsat with Velocity Saturation
Substituting VDSsat for VDS in the linear-region IDS eq’n. gives:
For very short channel length:
IDSsat is proportional to VGS–VT rather than (VGS – VT)2
IDSsat is not dependent on L
EE130 Lecture 40, Slide 7

8. 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
EE130 Lecture 40, Slide 8

9. 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
EE130 Lecture 40, Slide 9

10. Summary: NMOSFET I-V Linear region: Saturation region:
EE130 Lecture 40, Slide 10

11. PMOSFET I-V with Velocity Saturation
Linear region:
Saturation region:
EE130 Lecture 40, Slide 11