Introduction to
CMOS VLSI
Design
Lecture 3:
CMOS Transistor Theory
David Harris
Harvey Mudd College
Spring 2004
Outline







Introduction
MOS Capacitor
nMOS I-V Characteristics
pMOS I-V Characteristics
Gate and Diffusion Capacitance
Pass Transistors
RC Delay Models
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 2
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 (DV/Dt) -> Dt = (C/I) DV
– Capacitance and current determine speed
 Also explore what a “degraded level” really means
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 3
MOS Capacitor
 Gate and body form MOS capacitor
 Operating modes
– Accumulation
– Depletion
– Inversion
Vg < 0
+
-
polysilicon gate
silicon dioxide insulator
p-type body
(a)
0 < V g < Vt
+
-
depletion region
(b)
V g > Vt
+
-
inversion region
depletion region
(c)
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 4
Terminal Voltages
Vg
 Mode of operation depends on Vg, Vd, Vs
+
+
– Vgs = Vg – Vs
Vgs
Vgd
– Vgd = Vg – Vd
Vs
Vd
– Vds = Vd – Vs = Vgs - Vgd
+
Vds
 Source and drain are symmetric diffusion terminals
– By convention, source is terminal at lower voltage
– Hence Vds  0
 nMOS body is grounded. First assume source is 0 too.
 Three regions of operation
– Cutoff
– Linear
– Saturation
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 5
nMOS Cutoff
 No channel
 Ids = 0
Vgs = 0
+
-
g
+
-
s
d
n+
n+
Vgd
p-type body
b
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 6
nMOS Linear
 Channel forms
 Current flows from d to s
V
– e from s to d
 Ids increases with Vds
 Similar to linear resistor
gs
> Vt
+
-
g
+
-
s
d
n+
n+
Vgd = Vgs
Vds = 0
p-type body
b
Vgs > Vt
+
-
g
s
+
d
n+
n+
Vgs > Vgd > Vt
Ids
0 < Vds < Vgs-Vt
p-type body
b
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 7
nMOS Saturation




Channel pinches off
Ids independent of Vds
We say current saturates
Similar to current source
Vgs > Vt
+
-
g
+
-
Vgd < Vt
d Ids
s
n+
n+
Vds > Vgs-Vt
p-type body
b
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 8
I-V Characteristics
 In Linear region, Ids depends on
– How much charge is in the channel?
– How fast is the charge moving?
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 9
Channel Charge
 MOS structure looks like parallel plate capacitor
while operating in inversion
– Gate – oxide – channel
 Qchannel =
gate
Vg
polysilicon
gate
W
tox
n+
L
n+
SiO2 gate oxide
(good insulator, ox = 3.9)
+
+
Cg Vgd drain
source Vgs
Vs
Vd
channel
+
n+
n+
Vds
p-type body
p-type body
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 10
Channel Charge
 MOS structure looks like parallel plate capacitor
while operating in inversion
– Gate – oxide – channel
 Qchannel = CV
 C=
gate
Vg
polysilicon
gate
W
tox
n+
L
n+
SiO2 gate oxide
(good insulator, ox = 3.9)
+
+
Cg Vgd drain
source Vgs
Vs
Vd
channel
+
n+
n+
Vds
p-type body
p-type body
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 11
Channel Charge
 MOS structure looks like parallel plate capacitor
while operating in inversion
– Gate – oxide – channel
 Qchannel = CV
Cox = ox / tox
 C = Cg = oxWL/tox = CoxWL
 V=
gate
Vg
polysilicon
gate
W
tox
n+
L
n+
SiO2 gate oxide
(good insulator, ox = 3.9)
+
+
Cg Vgd drain
source Vgs
Vs
Vd
channel
+
n+
n+
Vds
p-type body
p-type body
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 12
Channel Charge
 MOS structure looks like parallel plate capacitor
while operating in inversion
– Gate – oxide – channel
 Qchannel = CV
Cox = ox / tox
 C = Cg = oxWL/tox = CoxWL
 V = Vgc – Vt = (Vgs – Vds/2) – Vt
gate
Vg
polysilicon
gate
W
tox
n+
L
n+
SiO2 gate oxide
(good insulator, ox = 3.9)
+
+
Cg Vgd drain
source Vgs
Vs
Vd
channel
+
n+
n+
Vds
p-type body
p-type body
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 13
Carrier velocity
 Charge is carried by e Carrier velocity v proportional to lateral E-field
between source and drain
 v=
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 14
Carrier velocity
 Charge is carried by e Carrier velocity v proportional to lateral E-field
between source and drain
 v = mE
m called mobility
 E=
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 15
Carrier velocity
 Charge is carried by e Carrier velocity v proportional to lateral E-field
between source and drain
 v = mE
m called mobility
 E = Vds/L
 Time for carrier to cross channel:
– t=
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 16
Carrier velocity
 Charge is carried by e Carrier velocity v proportional to lateral E-field
between source and drain
 v = mE
m called mobility
 E = Vds/L
 Time for carrier to cross channel:
– t=L/v
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 17
nMOS Linear I-V
 Now we know
– How much charge Qchannel is in the channel
– How much time t each carrier takes to cross
I ds 
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 18
nMOS Linear I-V
 Now we know
– How much charge Qchannel is in the channel
– How much time t each carrier takes to cross
Qchannel
I ds 
t

3: CMOS Transistor Theory
CMOS VLSI Design
Slide 19
nMOS Linear I-V
 Now we know
– How much charge Qchannel is in the channel
– How much time t each carrier takes to cross
Qchannel
I ds 
t
W
 mCox
L
V  V  Vds
 gs t
2

V
  Vgs  Vt  ds Vds
2

3: CMOS Transistor Theory
V
 ds

CMOS VLSI Design
W
 = mCox
L
Slide 20
nMOS Saturation I-V
 If Vgd < Vt, channel pinches off near drain
– When Vds > Vdsat = Vgs – Vt
 Now drain voltage no longer increases current
I ds 
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 21
nMOS Saturation I-V
 If Vgd < Vt, channel pinches off near drain
– When Vds > Vdsat = Vgs – Vt
 Now drain voltage no longer increases current
V
I ds   Vgs  Vt  dsat Vdsat
2

3: CMOS Transistor Theory
CMOS VLSI Design
Slide 22
nMOS Saturation I-V
 If Vgd < Vt, channel pinches off near drain
– When Vds > Vdsat = Vgs – Vt
 Now drain voltage no longer increases current
Vdsat

I ds   Vgs  Vt 
2



V

2
gs
 Vt 
3: CMOS Transistor Theory
V
 dsat

2
CMOS VLSI Design
Slide 23
nMOS I-V Summary
 Shockley 1st order transistor models


0

 
Vds
I ds    Vgs  Vt 
2


2


Vgs  Vt 


2
3: CMOS Transistor Theory
Vgs  Vt
V V  V
 ds
ds
dsat

Vds  Vdsat
CMOS VLSI Design
cutoff
linear
saturation
Slide 24
Example
 We will be using a 0.6 mm process for your project
– From AMI Semiconductor
– tox = 100 Å
2.5
V =5
2
– m = 350 cm /V*s
2
– Vt = 0.7 V
1.5
V =4
 Plot Ids vs. Vds
1
V =3
– Vgs = 0, 1, 2, 3, 4, 5
0.5
V =2
– Use W/L = 4/2 l
V =1
0
Ids (mA)
gs
gs
gs
gs
gs
0
 3.9  8.85  1014   W 
W
W
  mCox   350 

120
m A /V 2
 

8
L
L
 100  10
 L 
3: CMOS Transistor Theory
CMOS VLSI Design
1
2
3
4
5
Vds
Slide 25
pMOS I-V
 All dopings and voltages are inverted for pMOS
 Mobility mp is determined by holes
– Typically 2-3x lower than that of electrons mn
– 120 cm2/V*s in AMI 0.6 mm process
 Thus pMOS must be wider to provide same current
– In this class, assume mn / mp = 2
– *** plot I-V here
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 26
Capacitance
 Any two conductors separated by an insulator have
capacitance
 Gate to channel capacitor is very important
– Creates channel charge necessary for operation
 Source and drain have capacitance to body
– Across reverse-biased diodes
– Called diffusion capacitance because it is
associated with source/drain diffusion
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 27
Gate Capacitance
 Approximate channel as connected to source
 Cgs = oxWL/tox = CoxWL = CpermicronW
 Cpermicron is typically about 2 fF/mm
polysilicon
gate
W
tox
n+
L
n+
SiO2 gate oxide
(good insulator, ox = 3.90)
p-type body
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 28
Diffusion Capacitance
 Csb, Cdb
 Undesirable, called parasitic capacitance
 Capacitance depends on area and perimeter
– Use small diffusion nodes
– Comparable to Cg
for contacted diff
– ½ Cg for uncontacted
– Varies with process
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 29
Pass Transistors
 We have assumed source is grounded
 What if source > 0?
VDD
– e.g. pass transistor passing VDD
VDD
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 30
Pass Transistors
 We have assumed source is grounded
 What if source > 0?
VDD
– e.g. pass transistor passing VDD
VDD
 Vg = VDD
– If Vs > VDD-Vt, Vgs < Vt
– Hence transistor would turn itself off
 nMOS pass transistors pull no higher than VDD-Vtn
– Called a degraded “1”
– Approach degraded value slowly (low Ids)
 pMOS pass transistors pull no lower than Vtp
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 31
Pass Transistor Ckts
VDD
VDD
VDD
VDD
VDD
VDD
VDD
VDD
VSS
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 32
Pass Transistor Ckts
VDD
VDD
VDD
VDD
VDD
VDD
Vs = VDD-Vtn
Vs = |Vtp|
VDD-Vtn VDD-Vtn
VDD
VDD-Vtn
VDD-Vtn
VDD
VDD-2Vtn
VSS
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 33
Effective Resistance
 Shockley models have limited value
– Not accurate enough for modern transistors
– Too complicated for much hand analysis
 Simplification: treat transistor as resistor
– Replace Ids(Vds, Vgs) with effective resistance R
• Ids = Vds/R
– R averaged across switching of digital gate
 Too inaccurate to predict current at any given time
– But good enough to predict RC delay
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 34
RC Delay Model
 Use equivalent circuits for MOS transistors
– Ideal switch + capacitance and ON resistance
– Unit nMOS has resistance R, capacitance C
– Unit pMOS has resistance 2R, capacitance C
 Capacitance proportional to width
 Resistance inversely proportional to width
d
g
d
k
s
s
kC
R/k
2R/k
g
g
kC
kC
s
3: CMOS Transistor Theory
kC
d
k
s
kC
g
kC
d
CMOS VLSI Design
Slide 35
RC Values
 Capacitance
– C = Cg = Cs = Cd = 2 fF/mm of gate width
– Values similar across many processes
 Resistance
– R  6 KW*mm in 0.6um process
– Improves with shorter channel lengths
 Unit transistors
– May refer to minimum contacted device (4/2 l)
– Or maybe 1 mm wide device
– Doesn’t matter as long as you are consistent
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 36
Inverter Delay Estimate
 Estimate the delay of a fanout-of-1 inverter
A
2 Y
2
1
1
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 37
Inverter Delay Estimate
 Estimate the delay of a fanout-of-1 inverter
2C
R
A
2 Y
2
1
1
2C
2C
Y
R
C
C
C
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 38
Inverter Delay Estimate
 Estimate the delay of a fanout-of-1 inverter
2C
R
A
2 Y
2
1
1
2C
2C
2C
2C
Y
R
C
R
C
C
C
C
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 39
Inverter Delay Estimate
 Estimate the delay of a fanout-of-1 inverter
2C
R
A
2 Y
2
1
1
2C
2C
2C
2C
Y
R
C
R
C
C
C
C
d = 6RC
3: CMOS Transistor Theory
CMOS VLSI Design
Slide 40