6.
012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 11-1
Lecture 11 - MOSFET (III)
MOSFET Equivalent Circuit Models
October 18, 2005
Contents:
1. Low-frequency small-signal equivalent circuit model
2. High-frequency small-signal equivalent circuit model
Reading assignment:
Howe and Sodini, Ch. 4, 4.5-4.6
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 11-2
Key questions
What is the topology of a small-signal equivalent circuit model of the MOSFET?
What are the key dependencies of the leading model
elements in saturation?
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 11-3
1. Low-frequency small-signal equivalent circuit model
Regimes of operation of MOSFET:
VDSsat=VGS-VT
ID
saturation
linear
ID
VDS
VGS
VGS
VBS
VGS=VT
0
0
cutoff
VDS
Cut-off:
ID = 0
Linear:
W
VDS
ID = nCox (VGS
VT )VDS
L
2
Saturation:
W
nCox (VGS VT )2 [1+(VDS VDSsat)]
ID = IDsat =
2L
Effect of back bias:
r
VT (VBS ) = VT o + ( 2p VBS 2p )
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 11-4
Small-signal device modeling
In many applications, interested in response of device to
a small-signal applied on top of bias:
ID+id
vgs +
-
VGS
+
v
- ds
+
v
- bs
VBS
VDS
Key points:
Small-signal is small
response of non-linear components becomes linear
Can separate response of MOSFET to bias and small
signal.
Since response is linear, superposition can be used
effects of different small signals are independent
from each other
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 11-5
MOSFET
small-signal
equivalent
circuit model
ID+id
+
v
- ds
+
v
- bs
VBS
vgs +
-
VGS
VDS
ID
id
VDS
VGS
VBS
vgs +
-
Mathematically:
iD (VGS + vgs, VDS + vds, VBS + vbs) '
ID
ID
ID
ID (VGS , VDS , VBS )+
| vgs +
| vds +
| vbs
VGS Q
VDS Q
VBS Q
where Q bias point (VGS , VDS , VBS )
Small-signal id:
id ' gm vgs + govds + gmb vbs
Define:
gm transconductance [S]
go output or drain conductance [S]
gmb backgate transconductance [S]
Then:
gm '
ID
|Q
VGS
go '
ID
|Q
VDS
gmb '
ID
|Q
VBS
+
v
- ds
+
v
- bs
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 11-6
2 Transconductance
In saturation regime:
W
nCox (VGS VT )2 [1 + (VDS VDSsat)]
ID =
2L
Then (neglecting channel length modulation):
ID
W
| ' nCox (VGS VT )
gm =
VGS Q
L
Rewrite in terms of ID :
v
u
u
u
u
t
gm = 2
W
nCox ID
L
gm
gm
saturation
saturation
cut-off
0
0
VT
VGS
ID
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 11-7
Transconductance of 3 m nMOSFET (VDS = 2 V ):
Equivalent circuit model representation of gm :
id
G
vgs
S
gmvgs
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 11-8
2 Output conductance
In saturation regime:
ID =
W
nCox (VGS VT )2 [1 + (VDS VDSsat)]
2L
Then:
go =
ID
W
ID
nCox (VGS VT )2 ' ID
|Q =
VDS
2L
L
Output resistance is inverse of output conductance:
ro =
go
1
L
go ID
go
saturation
saturation
cut-off
0
0
0
VT
VGS
ID
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 11-9
Output conductance of 3 m nMOSFET:
Equivalent circuit model representation of go :
id
G
vgs
S
ro
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 11-10
2 Backgate transconductance
In saturation regime (neglect channel-length modulation):
W
nCox (VGS VT )2
ID '
2L
Then:
gmb
ID
W
VT
=
| = nCox (VGS VT )(
| )
VBS Q
L
VBS Q
Since:
r
VT (VBS ) = VT o + ( 2p VBS 2p )
Then:
VT
r
| =
VBS Q 2 2p VBS
All together:
gmb =
gm
2 2p VBS
r
gmb inherits all dependencies of gm
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 11-11
Body of MOSFET is a true gate: output characteristics
for different values of VBS (VBS = 0 (3) V, VBS =
0.5 V , VGS = 2 V ):
Equivalent circuit model representation of gmb :
id
G
vgs
S
vbs
B
gmbvbs
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 11-12
Complete MOSFET small-signal equivalent circuit model
for low frequency:
id
G
vgs
S
vbs
B
gmvgs
gmbvbs
ro
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 11-13
2. High-frequency small-signal equivalent circuit model
Need to add capacitances. In saturation:
gate
Cfringe
source
Cgs,i
n+
n+
Cov
Cjsw
Cfringe
drain
Cov
n+
Csb,i
Cj
Cjsw
Cj
p
body
Cgs intrinsic gate capacitance
+ overlap capacitance, Cov (+fringe)
Cgd overlap capacitance, Cov
(+fringe)
Cgb (only parasitic capacitance)
Csb source junction depletion capacitance
+sidewall (+channel-substrate capacitance)
Cdb drain junction depletion capacitance
+sidewall
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 11-14
Complete MOSFET high-frequency small-signal equivalent circuit model:
id
Cgd
G
vgs
S
Cgs
gmbvbs
ro
vbs
B
gmvgs
Csb
Cdb
Plan for development of capacitance model:
Start with Cgs,i
compute gate charge QG = (QN + QB )
compute how QG changes with VGS
Add pn junction capacitances
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 11-15
Inversion layer charge in saturation
QN (VGS ) = W
L
0 Qn (y)dy
=W
VGS VT
0
Qn(Vc )
dy
dVc
dVc
But:
dVc
ID
=
dy
W nQn(Vc )
Then:
W 2Ln Z VGS VT 2
Qn(Vc )dVc
QN (VGS ) =
0
ID
Remember:
Qn(Vc ) = Cox (VGS Vc VT )
Then:
2 Z
W 2Ln Cox
VGS VT
2
QN (VGS ) =
(V
V
)
dVc
GS
c
T
0
ID
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 11-16
Do integral, substitute ID in saturation and get:
2
QN (VGS ) = W LCox (VGS VT )
3
Gate charge:
QG(VGS ) = QN (VGS ) QB,max
Intrinsic gate-to-source capacitance:
Cgs,i
dQG
2
=
= W LCox
dVGS 3
Must add overlap capacitance:
2
Cgs = W LCox + W Cov
3
Gate-to-drain capacitance - only overlap capacitance:
Cgd = W Cov
6.012 - Microelectronic Devices and Circuits - Fall 2005
body
Lecture 11-17
polysilicon gate
source
drain
gate
n+
p+
n+
n+
p
inversion layer
channel
gate oxide
gate length
p+
n+
n+
n+
gate width
n+
STI edge
Body-to-source capacitance = source junction capacitance:
v
u
u
u
u
t
diff u
Csb = Cj +Cjsw = W L
qsNa
+(2Ldiff +W )CJ SW
2(B VBS )
Body-to-drain capacitance = drain junction capacitance:
v
u
u
u
u
t
diff u
Cdb = Cj +Cjsw = W L
qs Na
+(2Ldiff +W )CJ SW
2(B VBD )
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 11-18
Key conclusions
High-frequency small-signal equivalent circuit model of
MOSFET:
id
Cgd
G
vgs
S
Cgs
gmbvbs
gmvgs
vbs
B
Csb
Cdb
In saturation:
v
u
u
u
u
t
W
gm
ID
L
go
ID
L
Cgs W LCox
ro
