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Lecture 2:
CMOS
Transistor
Theory
Original Lecture notes ©
2010 David Money Harris
Modified by Konstantinos
Tatas
Outline





Introduction
MOS Capacitor
nMOS I-V Characteristics
pMOS I-V Characteristics
Gate and Diffusion Capacitance
3: CMOS Transistor Theory
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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
3: CMOS Transistor Theory
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MOS Capacitor
 Gate and body form MOS
capacitor
V <0
 Operating modes
+
– Accumulation
– Depletion
(a)
– Inversion
0<V <V
g
g
polysilicon gate
silicon dioxide insulator
p-type body
t
+
-
depletion region
(b)
Vg > Vt
+
-
inversion region
depletion region
(c)
3: CMOS Transistor Theory
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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
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nMOS Cutoff
 No channel
 Ids ≈ 0
Vgs = 0
+
-
g
+
-
s
d
n+
n+
Vgd
p-type body
b
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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
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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
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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
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Channel Charge
 MOS structure looks like parallel plate capacitor
while operating in inversions
– Gate – oxide – channel
 Qchannel = CV
Cox = eox / tox
 C = Cg = eoxWL/tox = CoxWL
 V = Vgc – Vt = (Vgs – Vds/2) – Vt
gate
Vg
polysilicon
gate
W
tox
n+
L
n+
SiO2 gate oxide
(good insulator, eox = 3.9)
+
+
Cg Vgd drain
source Vgs
Vs
Vd
channel
+
n+
n+
Vds
p-type body
p-type body
3: CMOS Transistor Theory
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Carrier velocity
 Charge is carried by e Electrons are propelled by the lateral electric field
between source and drain
– E = Vds/L
 Carrier velocity v proportional to lateral E-field
– v = mE
m called mobility
 Time for carrier to cross channel:
– t=L/v
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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

W
 = mCox
L
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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
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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
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cutoff
linear
saturation
14
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
  mCox   350  

8
L
 100 10
 L
3: CMOS Transistor Theory
1
2
W


120
μA/V 2

L

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4
5
Vds
15
pMOS I-V
 All dopings and voltages are inverted for pMOS
– Source is the more positive terminal
 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
0
Vgs = -1
Vgs = -2
-0.2
Ids (mA)
Vgs = -3
-0.4
Vgs = -4
-0.6
-0.8
-5
Vgs = -5
-4
-3
-2
-1
0
Vds
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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
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Gate Capacitance
 Approximate channel as connected to source
 Cgs = eoxWL/tox = CoxWL = CpermicronW
 Cpermicron is typically about 2 fF/mm
polysilicon
gate
W
tox
n+
L
n+
SiO2 gate oxide
(good insulator, eox = 3.9e0)
p-type body
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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
2: CMOS Transistor Theory
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Example 1
 Consider an nMOS transistor in a 0.6 μm process
with W/L = 4/2λ. In this process, the gate oxide
thickness is 100 Å and the mobility of electrons is
350 cm^2/V · s. Give the Ids equation for the linear
and saturation regions
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Example 2
 A 90nm long transistor has a gate oxide thickness of
16 Å. What is its gate capacitance per micron of
width?
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