CMOS-dc

1
Chapter 2 MOS Transistor theory

2.1 Introduction

¤ An MOS transistor is a majority-carrier device, in which the
current in a conducting channel between the source and the
drain is modulated by a voltage applied to the gate.

¤ Symbols














¤ NMOS (n-type MOS transistor)
(1) Majority carrier = electrons

(2) A positive voltage applied on the gate with respect to the
substrate enhances the number of electrons in the channel and
hence increases the conductivity of the channel.

(3) If gate voltage is less than a threshold voltage Vt , the channel
is cut-off (very low current between source & drain).

¤ PMOS (p-type MOS transistor)
(1) Majority carrier = holes

(2) Applied voltage is negative with respect to substrate.
NMOS
PMOS
2
¤ Threshold voltage (Vt):
The voltage at which an MOS device begins to conduct ("turn
on")

¤ Relationship between Vgs (gate-to-source voltage) and the
source-to-drain current (Ids) , given a fixed drain-to-source
voltage (Vds).






















(1) Devices that are normally cut-off with zero gate bias are
classified as "enhancement-mode "devices.

(2) Devices that conduct with zero gate bias are called
"depletion-mode "devices.

(3) Enhancement-mode devices are more popular in practical use.


3
2.1.1 NMOS Enhancement Transistor












¤ Consist of
(1) Moderately doped p-type silicon substrate
(2) Two heavily doped n
+
regions, the source and drain, are
diffused.
(3) Channel is covered by a thin insulating layer of silicon dioxide
(SiO2) called " Gate Oxide "
(4) Over the oxide is a polycrystalline silicon (polysilicon) electrode,
referred to as the "Gate"

¤ Features
(1) Since the oxide layer is an insulator, the DC current from the
gate to channel is essentially zero.

(2) No physical distinction between the drain and source regions.

(3) Since SiO2 has low loss and high dielectric strength, the
application of high gate fields is feasible.

¤ In operation
(1) Set Vds > 0 in operation

(2) Vgs =0 ¬ no current flow between source and drain. They are
insulated by two reversed-biased PN junctions (see Fig 2.3).
4

(3) When Vg > 0 , the produced E field attracts electrons toward
the gate and repels holes.

(4) If Vg is sufficiently large, the region under the gate changes
from p-type to n-type(due to accumulation of attracted elections)
and provides a conducting path between source and
drain.÷¬The thin layer of p-type silicon is said to be
"inverted".

(5) Three modes (see Fig 2.4)
a. Accumulation mode (Vgs << Vt)
b. Depletion mode (Vgs =Vt)
c. Inversion mode (Vgs > Vt)
5
¤ Electrically
(1) An MOS device can be considered as a voltage-controlled
switch that conducts when Vgs >Vt (given Vds>0)

(2) An MOS device can be considered as a voltage-controlled
resistor (See Fig 2.5)

¤ Effective gate voltage (Vgs-Vt)

¤ At the source end , the full gate voltage is effective in the
inverting the channel.

¤ At the drain end , only the difference between the gate and
drain voltage is effective

6
¤ Pinch-off
(1) Vds > Vgs-Vt => Vgd < Vt => Vd > Vg –Vt (Vg is not big
enough)

(2) The channel no longer reaches the drain. (Fig 2.5 c)

(3) As electrons leave the drain depletion region and are
subsequently accelerated toward the drain.

(4) The voltage across the pinched-off region remains at (Vgs-Vt)
=>”saturated” state in which the channel current as controlled
by Vg , and is independent of Vd

¤ For fixed Vds and Vg , Ids is function of
(1) Distance between drain & source
(2) Channel width
(3) Vt
(4) Thickness of gate oxide
(5) The dielectric constant of gate oxide
(6) Carrier (hole or electron) mobility , £g .

¤ Conducting mode
(1) ”cut-off ” region : Ids ≈ 0 , Vgs < Vt
(2) ” Nonsaturated” region : weak inversion region, when Ids
depends on Vg & Vd
(3) ”Saturated“ region: channel is strongly inverted and Ids is
ideally independent of Vds (pinch-off region)
(4) ”Avalanche breakdown” (pinch-through) : very high Vd => gate
has no control over Ids

7
2.1.2 PMOS Enhancement Transistor

(1) Vg < 0

(2) Holes are major carrier

(3) Vd < 0 , which sweeps holes from the source through the
channel to the drain .


2.1.3 Threshold voltage

¤ A function of
(1) Gate conductor material
(2) Gate insulator material
(3) Gate insulator thickness
(4) Impurity at the silicon-insulator interface
(5) Voltage between the source and the substrate Vsb
(6) Temperature
a. -4 mV/’C – high substrate doping
b. -2 mV/’C – low substrate doping

8
2.2 MOS equations

2.2.1 Basic DC equations

¤ Three MOS operating regions
(1) Cutoff or subthreshold region
I
ds
=0, V
gs
≤V
t


(2) Nonsaturation, linear or triode region
( )






− − =
2
2
ds
ds t gs ds
V
V V V I β 0<Vgs<Vgs-Vt
| |
ds t gs
V V V − ≈ β When Vds << Vgs-Vt

(3) Saturation region
( )
2
2
t gs
ds
V V
I
−
= β , 0< Vgs-Vt<Vds


¤ Vd at which the device becomes saturated is called Vdsat
(drain saturation voltage)





9
¤ : MOS transistor gain factor
Function of (1) process parameter (2) device geometry
(1) £g = effective mobility of the carrier in the channel
(2) £` = permittivity of the gate oxide
(3) t
ox
= thickness of the gate oxide
Note:
ox
ox
C
t
=
ε
=>
|
.
|

\
|
=
L
W
C
ox
u β

¤ Example
Typical CMOS
¡· (~1£g ) process
(1) £g
n
=500 cm
2
/V-sec
(2) £` =3.9£`
0
=3.9*8.85*10
-14
F/cm (permittivity of SiO
2
)
(3) t
ox
=200
°
Α
2
/ 5 . 88 V
L
W
L
W
t
ox
n
Α =
|
.
|

\
|
= u
uε
β
¡·
2
2
9 . 31
sec
180
V
L
W
V
cm
p p
Α
= =>
−
=
u
β u
¡· 8 . 2 =
p
N
β
β
(2~3 depending on process)
10
2.2.2. Seven Second-order Effect

¤ SPICE : Simulation Program with Integrated Circuit Emphasis

¤ LEVEL: 1,2,3
(1) Basic DC Equations + Some second-order effects
(2) Based on device physics
(3) Add more parameters to match real circuits

e.g., Process gain factor
SPICE : Kp (10-100 £g A/V
2
with 10%-20% variation)

A. Channel-length modulation

¤ When an MOS device is in saturation.
¤ L
eff
= L - L
short


( ) ( ) Vt Vgs Vds
qN
L
A
si
short
− − =
ε
2
=>L¡õ =>£]¡ô => Ids¡ô
( ) ( )
ds t gs ds
V V V
L
W K
I λ + −
|
.
|

\
|
= 1
2
2

With
ox
t
K
uε
= : process gain factor
£f :channel length modulation factor (0.02V
-1
to 0.005 V
-1
)
(In SPICE level 1 : £f =LAMBDA)

B. Drain punchthrough (avalanche breakdown)

V
D
is very high , Ids is independent of Vgs
Good for I/O protection circuit.


11
C. Threshold voltage (Vt) – Body effect (Vsb)
¤
( )
ox
SB b A si
b fb
C
V qN
V Vt
+
+ + =
φ ε
φ
2 2
2
=> | |
b SB b t t
V V V φ φ γ 2 2
0
− + + =
(1) Vsb : Substrate bias
(2) Vt0 : Vt at Vsb=0
(3) £^ : a constant which describes the substrate bias effect
(range:0.4~1.2)
A si
ox
A si
ox
ox
N q
C
N q
t
ε ε
ε
γ 2
1
2 = =
(4) SPICE
¤ : GAMMA in SPICE model
¤ Vto : VT0
¤ N
A
: NSUB
¤
s
= 2£r
b
: PHI (the surface potential at the onset of strong
inversion)

Subthreshold region

¤ Cut-off = subthreshold region
¤ Ids≈0 (Subthreshold region)
¤ But the finite value of Ids may be used to construct very low
power circuits.
¤ In Level 1 SPICE , subthreshold current is set 0

Others:
- Mobility variation
- Fowler-Nordheim Tunneling
- Impact Ionization (Hot electrons effect)





12
2.2.3 MOS Models

¤ MOS model = Ideal Equations + Second-order Effects +
Additional Curve-fitting parameters

¤ Many semiconductor vendors expend a lot of effects to model
the devices they manufacture.(Standard : Level 3 SPICE)

¤ Main SPICE DC parameters in level 1,2,3 in 1£g n-well CMOS
process.

13
2.3 CMOS inverter DC characteristics



→ ← on turn

tp DD g gs
V V V V − < − =

in gs
V V =
tp DD g
V V V − < ⇒

out ds
V V =
tp DD in
V V V − < ⇒



(check Fig. 2.12)























14










Both transistors are “on”
α ⋅ =
2
fcv P
(Switching activity)

¤ Solve for
dsp dsn
I I − =

inp inn
V V =

(1) Region A.
tn in
V V ≤ ≤ 0
¡@ n-device is ‘ off ’, ) ( 0
dsp dsn
I I − = =
p-device is in ‘linear’ mode
¡@ 0 = = −
dsp DD out
V V V

DD out
V V = ⇒

(2) Region B.
2
DD
in tn
V
V V ≤ ≤
¡@ p-device : linear mode
n-device : saturation mode
n : ) ( ,
2
] [
2
n
n
ox
n
n
tn in
n dsn
L
W
t
V V
I
ε u
β β =
−
=
p :
DD in gs
V V V − =

DD out ds
V V V − =
15
¡ï ]
2
) (
) )( [(
2
DD out
DD out tp DD in p dsp
V V
V V V V V I
−
− − − − − = β

tp gs
V V −
ds
V
with ) (
p
p
ox
p
p
L
W
t
ε u
β =
solve for
dsn dsp
I I − =

2 2
) ( )
2
( 2 ) ( ) (
tn in
p
n
DD tp
DD
in tp in tp in out
V V V V
V
V V V V V V − − − − − − + − = ⇒
β
β


(3) Region C. PMOS, NMOS : saturation

2
) (
2
tp DD in
p
dsp
V V V I − − − =
β


2
) (
2
tn in
n
dsn
V V I − =
β

with
dsn dsp
I I − =


p
n
p
n
tn tp DD
in
V V V
V
β
β
β
β
+
+ +
= ⇒
1


⇒ by setting
p n
β β = and
tp tn
V V − =

¡@ we have : one value only


¡@ possible
out
V
N-MOS
ds tn gs
out tn in
V V V
V V V
< −
< −


2
DD
in
V
V =
16
P-MOS
ds tp gs
out DD tp in DD
V V V
V V V V V
> −
− > − − ) ( ) (


tp in out
V V V − < ⇒

⇒ ¡¸

Negative value
⇒
in
V is fixed at
2
DD
V
,
out
V varies
⇒ make the o/p transition very steep

(4) Region D.
tp DD in
DD
V V V
V
+ < <
2

P-MOS : saturation mode
N-MOS : linear mode


2
) (
2
1
tp DD in p dsp
V V V I − − − = β
]
2
) [(
2
out
out tn in n dsn
V
V V V I − − = β

solve
dsp dsn
I I − =

2 2
) ( ) ( ) (
tp DD in
n
p
tn in tn in out
V V V V V V V V − − − − − − = ⇒
β
β


(5) Region E.
tp DD in
V V V + ≥
→ p-device ‘ off ‘ ( n-device is in ‘ linear ’ mode )
→ 0 =
dsp
I 0 = ⇒
dsn
I 0 = ⇒
out
V
see Table 2.3 for summary

tp in out tn in
V V V V V − < < −
17
2.3.1 £] n¡þ£] p ratio ( watch Eq.(2.24) )





p
p
n
n
p
n
L
W
L
W
↔
β
β



¤ Note
5 . 1 −
∝T β (¡î T¡ô ,£g¡õ )

⇒



2.3.2 Noise Margin

¤ This parameter allows us to determine the allowable noise
voltage on the input of a gate so that the output will not be
affected.



min min IH OH H
V V NM − =

max max OL IL L
V V NM − =






¤ How to determine
L H
NM NM &
5 . 1 −
∝T I
ds
18

















3 . 2 =
IL
V
3 . 3 =
IH
V
OL
V are more difficult (will be discussed later)
OH
V

(left as your exercise)
19
2.4 Static Load MOS inverters

¤ Resistor-load inverter
Current-source-load inverter



2.4.1 Pseudo-NMOS inverter

¤ Fast (constant current)
¤ power-consuming P¡ô ⇒ I¡ô ⇒but speed¡ô

20
2.6 The Transmission Gate



(PMOS)

(NMOS)



¤ NMOS pass transistor
¡@
load
C is initially discharged

SS out
V V =
¡@ with S=0 ) (
SS
V
V V
gs
0 =
0 =
ds
I

out
V remains at
SS
V

t gs
V V V > = 5 , NMOS On ⇒ V V V
out in
0 = =
¡@ S=1 ) (
dd
V

DD gs
V V = (initially)

⇒ > =
t gs
V V V 5 charge
Þ
out in
V V > , current from
in
V to
out
V
Þ As the output voltage approaches
tn DD
V V − ,
the n-device begins to turn off



21

Þ S=0 (open circuit) ,
out
V remains at ) (
dd tn DD
V V V − ,
where ) (
dd tn
V V denotes the
t
V at
dd s
V V = ’(body effect)’


¡@ S=1
0 =
in
V
) (
dd tn DD out
V V V V − =


n-device begin to conduct , and
out
V fall to
ss
V

Transmission of Logic 1 is degraded, ) (
tn DD
V V −
Transmission of Logic 0 is not degraded, ) (
ss
V



¤ PMOS pass transistor

Þ S=1 ,(S=0) (open)

ss in
V V =

ss out
V V =



Þ S=0 (close)

DD in
V V = , current

out
V to
DD
V
charge (C_load)


22
Þ S=0 (close)

ss in
V V = ,

DD out
V V =

Þ Discharge C_load
until through p-device
until ) (
ss tp out
V V V = , at which point the transistor stops
conducting

⇒ p-MOS passes good ‘1’
p-MOS passes poor ‘0’

¤ Transmission gate can pass logic ‘1’ and ‘0’ without
degradation !
Þ overall behavior
(1) S=0 ) 1 ( = S :
N,P devices are ‘OFF’

SS in
V V = , Z V
out
= (high impedance)

DD in
V V = , Z V
out
=
(2) S=1 ) 0 ( = S :
N,P devices are ‘ON’

SS in
V V = ,
SS out
V V = ,
DD in
V V = ,
DD out
V V =



¤ Used in multiplexing element & latch element act as
voltage-controlled resistor connecting the input and output

¤ Example to analyze a CMOS circuit Way 1=MAN
Way 2=SPICE

23
(1) Capacitor loaded circuit






Cload at Vss

* Cload is large


Þ When S is ON NMOS , S = 0 1

PMOS , S = 1 0


Þ Results: Currents of the pass transistor are monitored

¡@ Vout¡ô (transmission gate) , 5 ) ( − = p V
gs
(constant current)
(PMOS)
It starts at ‘saturation’ ‘nonsaturation’
as
dsp tp gsp
V V V > −
¡@ Vout¡ô (transmission gate)
(NMOS)
always at ‘saturation’ , ¡î
gsn dsn
V V =

dsn tn gsn
V V V < − ⇒
Rise
After
tn DD out
V V V − → , NMOS is ‘off’



24
Þ Three regions of operation :


A

N saturation P saturation
tp out
V V <

B

N saturation P nonsaturation
tn DD out tp
V V V V − < <

C

N off P nonsaturation
out tn DD
V V V < −

a. Region A
p : constant current source
n : current varies inversely with Vout

b. Region B
both currents vary linearly (inverse) with Vout

c. Region C
p-current varies inverse linearly with Vout








Charge current amount








check :
SS DD out SS in
V V V V V → = = ,
25
(2) Lightly loaded circuit (Cload is small)

Þ Vout follows Vin very closely

Þ Fig 2.35(d) n-current for 1 . 0 − = −
in out
V V
p-current

Þ Three regions of operation :
a. n (linear) , p (off)
b. n (linear) , p (linear)
c. n (off) , p (linear)




¡ö can be monitored by using
SPICE





Combined