Transcript Lecture #40 OUTLINE The MOSFET: • Velocity saturation Reading: Chapter 19.1 Spring 2007 EE130 Lecture 40, Slide 1

Lecture #40
OUTLINE
The MOSFET:
• Velocity saturation
Reading: Chapter 19.1
Spring 2007
EE130 Lecture 40, Slide 1
Velocity Saturation
Velocity saturation limits IDSsat in modern MOSFETS
Simple model:
v
e
e
1
e
sat
v  vsat
for e < e
sat
for e  esat
esat is the electric field at velocity saturation:
vsat
Spring 2007
8 106 cm/s for electrons in Si

6
6

10
cm/s for holesin Si

EE130 Lecture 40, Slide 2
e
sat

2vsat

MOSFET I-V with Velocity Saturation
In the linear region:
I DS
W
m


Coxe  eff VGS  VT  VDS VDS
L
2



VDS
1
e sat L
I DS
Spring 2007
long  channelI DS

VDS
1
e sat L
EE130 Lecture 40, Slide 3
Drain Saturation Voltage VDSsat
1
VDSsat
m
1


VGS  VT e sat L
e
sat

• 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
Spring 2007
EE130 Lecture 40, Slide 4
2vsat

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 m, (b) 1 um, (c) 0.1 m, and (d) 0.05 m
Solution: From VGS , VT, and Toxe , n is 200 cm2V-1s-1.
esat= 2vsat / n
= 8 104 V/cm
m = 1 + 3Toxe/WT = 1.2
VDSsat
Spring 2007
 m
1 

 

 VGS  VT e sat L 
EE130 Lecture 40, Slide 5
1
VDSsat
 m
1 

 

 VGS  VT e sat L 
1
(a) L = 10 m:
VDSsat= (1/1.3V + 1/80V)-1 = 1.3 V
(b) L = 1 m:
VDSsat= (1/1.3V + 1/8V)-1 = 1.1 V
(c) L = 0.1 m: VDSsat= (1/1.3V + 1/.8V)-1 = 0.5 V
(d) L = 0.05 m: VDSsat= (1/1.3V + 1/.4V)-1 = 0.3 V
Spring 2007
EE130 Lecture 40, Slide 6
IDSsat with Velocity Saturation
Substituting VDSsat for VDS in the linear-region IDS eq’n. gives:
I DSsat
W
2


Coxe eff VGS  VT
long channelI DSsat
2
m
L


VGS  VT
VGS  VT
1
1
e sat L
e sat L
For very short channel length:
I DSsat
e
sat
L  VGS  VT
W
W

e
vsat Coxe VGS  VT 
sat Coxe  eff VGS  VT  
2m
m
• IDSsat is proportional to VGS–VT rather than (VGS – VT)2
• IDSsat is not dependent on L
Spring 2007
EE130 Lecture 40, Slide 7
V gs = 1.0V
0.0
0
1
V ds (V)
Short- vs. Long-Channel MOSFET
0.4
L = 0.15 m
I ds (mA/m)
L = 2.0 m
V gs = 2.5V
Vt = 0.4 V
2.5
0.03
(b)
Vgs = 2.5 V
Vt = 0.7 V
0.3
0.02
Ids (A/m)
(a)
2
V gs = 2.0V
0.2
V gs = 1.5V
0.1
Vgs = 2.0 V
0.01
Vgs = 1.5 V
V gs = 1.0V
Vgs = 1.0 V
0.0
0.0
0
1
2
2.5
V ds (V)
Short-channel
MOSFET:
0.03
• IDsat
VVGS-VTn rather than (VGS-VTn)2
Vgsto
= 2.5
L =is
2.0 proportional
m
Vt = 0.7
• VDsat
is Vlower than for long-channel MOSFET
• Channel-length modulation is apparent
0.02
/m)
(b)
Vds (V)
Spring 2007
Vgs Lecture
= 2.0 V 40, Slide 8
EE130
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 m NMOSFET
 Effectively, vsat and esat increase when L is
very small
Spring 2007
EE130 Lecture 40, Slide 9
Summary: NMOSFET I-V
• Linear region:
W
m


Coxe  eff ,n VGS  VTn  VDS VDS
L
2


I DS 
VDS
1
sat L
e
• Saturation region:
W
2
Coxe eff ,n VGS  VT 
I DS  I DSsat  2m L
VGS  VT
1
sat L
e
Spring 2007
EE130 Lecture 40, Slide 10
e
sat

2vsat

vsat  8 106 cm/s
for electrons in Si
PMOSFET I-V with Velocity Saturation
• Linear region:
W
m


 Coxe eff , p VGS  VTp  VDS VDS
L
2


I DS 
VDS
1
sat L
• Saturation region:
W
2

Coxe eff , p VGS  VTp
I DS  I DSsat  2m L
VGS  VTp
1
sat L
e

e
Spring 2007
EE130 Lecture 40, Slide 11
