Lecture 3:
CMOS
Transistor
Theory
CMOS VLSI DesignCMOS VLSI Design
4th Ed.
3: CMOS Transistor Theory 2
Outline
 Introduction
 MOS Capacitor
 nMOS I-V Characteristics
 pMOS I-V Characteristics
 Gate and Diffusion Capacitance
CMOS VLSI DesignCMOS VLSI Design
4th Ed.
3: CMOS Transistor Theory 3
Introduction
 So far, we have treated transistors as ideal switches
 An ON transistor passes a finite amount of current
– Depends on terminal voltages
– Derive current-voltage (I-V) relationships
 Transistor gate, source, drain all have capacitance
– I = C (∆V/∆t) -> ∆t = (C/I) ∆V
– Capacitance and current determine speed
CMOS VLSI DesignCMOS VLSI Design
4th Ed.
3: CMOS Transistor Theory 4
polysilicon gate
(a)
silicon dioxide insulator
p-type body

4th Ed.
3: CMOS Transistor Theory 5
Terminal Voltages
 Mode of operation depends on V
g
, V
d
, V
s
– V
gs
= V
g
– V
s
– V
gd
= V
g
– V
d
– V
ds
= V
d
– V
s
= V
gs
- V

4th Ed.
3: CMOS Transistor Theory 6
nMOS Cutoff
 No channel
 I
ds
≈ 0
+
-
V
gs
= 0
n+ n+
+
-
V
gd
p-type body
b
g
s
d
CMOS VLSI DesignCMOS VLSI Design
4th Ed.
3: CMOS Transistor Theory 7
nMOS Linear
 Channel forms
 Current flows from d to s
– e
-

> V
gd
> V
t
V
ds
= 0
0 < V
ds
< V
gs
-V
t
p-type body
p-type body
b
g
s
d
b
g
s
d
I
ds
CMOS VLSI DesignCMOS VLSI Design
4th Ed.
3: CMOS Transistor Theory 8
nMOS Saturation
 Channel pinches off

I
ds
CMOS VLSI DesignCMOS VLSI Design
4th Ed.
3: CMOS Transistor Theory 9
I-V Characteristics
 In Linear region, I
ds
depends on
– How much charge is in the channel?
– How fast is the charge moving?
CMOS VLSI DesignCMOS VLSI Design
4th Ed.
3: CMOS Transistor Theory 10
Channel Charge
 MOS structure looks like parallel plate capacitor
while operating in inversions
– Gate – oxide – channel
 Q
channel
= CV
 C = C
g
= ε
ox
WL/t
ox
= C
ox
WL

s
V
d
C
g
n+ n+
p-type body
W
L
t
ox
SiO
2
gate oxide
(good insulator, ε
ox
= 3.9)
polysilicon
gate
C
ox
= ε
ox
/ t
ox
CMOS VLSI DesignCMOS VLSI Design
4th Ed.
3: CMOS Transistor Theory 11
Carrier velocity
 Charge is carried by e-

W
V
C VV V
L
V
VV V
µ
β
=

= −−



= −−


ox
=
W
C
L
βµ
CMOS VLSI DesignCMOS VLSI Design
4th Ed.
3: CMOS Transistor Theory 13
nMOS Saturation I-V
 If V
gd
< V

3: CMOS Transistor Theory 14
nMOS I-V Summary
( )
2
cutoff
linear
saturatio
0
2
2
n
gs t
ds
ds gs t ds ds dsat
gs t ds dsat
VV
V
I VV VVV
VV VV
β
β


<



= −− <



= 0, 1, 2, 3, 4, 5
– Use W/L = 4/2 λ
( )
14
2
8
3.9 8.85 10
350 120μA/V
100 10
ox
W WW
C
L LL
βµ
−
−

×⋅

= = =


⋅


0 1
2
3
4 5
0

– Source is the more positive terminal
 Mobility µ
p
is determined by holes
– Typically 2-3x lower than that of electrons µ
n
– 120 cm
2
/V•s in AMI 0.6 µm process
 Thus pMOS must be wider to
provide same current
– In this class, assume
µ
n
/ µ
p
= 2
-5 -4 -3
-2 -1 0
-0.8
-0.6
-0.4
-0.2
0
I
ds
(mA)
V
gs
= -5

 Approximate channel as connected to source
 C
gs
= ε
ox
WL/t
ox
= C
ox
WL = C
permicron
W
 C
permicron
is typically about 2 fF/µm
n+ n+
p-type body
W
L
t
ox
SiO
2
gate oxide
(good insulator, ε
ox
= 3.9ε
0
)
polysilicon