Comparison of
MOST and Bipolar transistor
models
Willy Sansen
KULeuven, ESAT-MICAS
Leuven, Belgium
willy.sansen@esat.kuleuven.be
Willy Sansen
10-05 011
Table of contents
• Models of MOST transistors
• Models of Bipolar transistors
• Comparison of MOSTs and Bipolars
Ref.: W. Sansen : Analog Design Essentials, Springer 2006
Willy Sansen
10-05 012
From Bipolar to MOST transistors
100 GHz
10~40 GHz
GaAs
2~10 GHz
1~2 GHz
200 MHz
BIP
GaAs
10~40 GHz
BICMOS
1~2 GHz
BICMOS
CMOS
1994
CMOS
2000
Ref.Toshiba
Willy Sansen
10-05 013
The SIA roadmap
Year Lmin Bits/chip Trans/chip
µm Gb/chip millions/chip
Clock Wiring
MHz
1995 0.35
1998 0.25
2001 0.18
2004 0.13
2007 0.09
2010 0.065
2003
300
450
600
800
1000
1100
0.064
0.256
1
4
16
64
4
7
13
25
50
90
4-5
5
5-6
6
6-7
7-8
Semiconductor Industry Association
Willy Sansen
10-05 014
The law of Moore
10
L-Micron
1
.1
1980
Year
1985
1990
1995
2000
2005
Willy Sansen
10-05 015
ISSCC 2005 paper distribution
40
Analog/RF
35
30
Digital
25
20
15
10
5
0
350
250
180
130
90
65
nm Lmin
Willy Sansen
10-05 016
Price MPW silicon for different L (nm)
10000
Cost MPW
$/sq.mm
1000
1000
nm
100
100
Willy Sansen
10-05 017
MOST layout
B
S
p+
n+
p
G
D
S
n+
n+
G+
D+
n+
p
WM
LM
Willy Sansen
10-05 018
MOST layout : Cox and CD
G+
D+
S
tox
Cox
n+
CD
εsi
CD =
tsi
n+
Cox =
B
p
tsi
CD
Cox
εox
tox
=n-1
Willy Sansen
10-05 019
MOST layout : Cox and CD values
CD =
εsi
tsi
tsi =
2εsi(φ - VBD)
qNB
Example : L = 0.35 µm; W/L = 8
VBD = -3.3 V :
tox =
Lmin
50
εsi = 1 pF/cm
εox = 0.34 pF/cm
φ ≈ 0.6 V
q = 1.6 10-19 C
NB ≈ 4 1017 cm-3
tsi = 0.1 µm
CD ≈ 10 -7 F/cm2
tox = 7 nm
Cox ≈ 5 10
-7
F/cm2
CD
Cox
= n - 1 ≈ 0.2
Willy Sansen
10-05 0110
N-well CMOS technology
Gate oxyde
Polysilicon gate
Willy Sansen
10-05 0111
MOST IDS versus VGS and VDS
VDS = ct
IDS
IDS
linear
VGS
saturation
VGS
VGS
VGS
0
VT
VGS
0
VDS
Saturation because high VDS
Willy Sansen
10-05 0112
Table of contents
• Models of MOST transistors
• MOST as a resistor
• MOST as an amplifier in strong inversion
• Transition weak inversion-strong inversion
• Transition strong inversion-velocity saturation
• Capacitances and fT
• Models of Bipolar transistors
• Comparison of MOSTs & Bipolar transistors
Willy Sansen
10-05 0113
MOST IDS versus VDS
IDS
linear
saturation
VDS > VGS-VT
VGS-VT
n
Linear resistor
Ron =
1
β (VGS-VT)
W
β = KP L
0
VGS-VT
VDS
Willy Sansen
10-05 0114
MOST parameters β , KP , Cox , ...
KPn ≈ 300 µA/V2
W
β = KP L
Cox ≈ 5 10 -7 F/cm2
KP = µ Cox
Cox =
εox = 0.34 pF/cm
εox
εsi = 1 pF/cm
tox
tox = 7 nm
tox =
Lmin
50
Lmin = 0.35 µm
µ p ≈ 250 cm2/Vs
µ n ≈ 600 cm2/Vs
Willy Sansen
10-05 0115
Example : Analog switch on CL
VDD
vIN
vOUT
CL
We want to switch 0.6 V to a
load capacitance CL of 4 pF.
We want to do this fast,
with time constant 0.5 ns.
Supply voltage VDD = 2.5 V
VT = 0.5 V
Use standard 0.35 µm CMOS.
Choose
minimum channel length and
find an average VGS !
Willy Sansen
10-05 0116
Example : Analog switch on RL
VDD
vIN
vOUT
RL
vIN
Ron
vOUT
We want to switch 0.6 V to a
load resistor RL of 5 kΩ.
W/L = 8
Supply voltage VDD = 2.5 V
0.35 µm CMOS: VT = 0.5 V
vOUT ? Ron ?
Choose
minimum channel length !
RL
Willy Sansen
10-05 0117
Body effect - Parasitic JFET
VT = VT0 + γ [ |2ΦF| + VBS - |2ΦF| ]
n=
γ
|2ΦF| + VBS
= 1+
CD
Cox
|2ΦF| ≈ 0.6 V
n ≈ 1.2 … 1.5
γ ≈ 0.5 …0.8 V1/2
Reverse vBS increases |VT| and decreases |iDS | !!!
n = 1/κ subthreshold gate coupling coeff. Tsividis
Willy Sansen
10-05 0118
Ex. : Analog switch with nonzero VBS
VDD
vIN
vOUT
CL
VDD
vIN
Switch 0.6 V to a
load capacitance CL of 4 pF
or a load resistor RL of 5 kΩ.
W/L = 8 (Ron = 125 Ω @ VBS = 0)
Supply voltage VDD = 2.5 V
0.35 µm CMOS: VT = 0.5 V
vOUT ? for γ = 0.5 V-1
vOUT
RL
Start with VBS = 0.
Willy Sansen
10-05 0119
Table of contents
• Models of MOST transistors
• MOST as a resistor
• MOST as an amplifier in strong inversion
• Transition weak inversion-strong inversion
• Transition strong inversion-velocity saturation
• Capacitances and fT
• Models of Bipolar transistors
• Comparison of MOSTs & Bipolar transistors
Willy Sansen
10-05 0120
MOST IDS versus VGS
IDS
IDS ~ (VGS-VT)
vs
si
wi
log
IDS
VGS
IDS = K’n W (VGS-VT)2
L
K’ =
vs
KP
2n
n=
??
K’n ≈ 100 µA/V2
K’p ≈ 40 µA/V2
Slope q/nkT
VGS
VGS
IDS ~ exp nkT/q
Willy Sansen
10-05 0121
MOST small-signal model : gm & rDS
D
iDS
G
G
gmvGS
S=B
gm =
+
vGS
+
vGS
-
D
2K’
S
W
n L (VGS-VT) = 2
gm =
K’
n
diDS
rDS
S
dvGS
2 IDS
W
IDS =
L
VGS-VT
Willy Sansen
10-05 0122
The transconductance gm
Is gm ~
or
IDS
~ IDS
?
Willy Sansen
10-05 0123
MOST small-signal model : rDS
IDS
linear
rDS = ro =
saturation
λ =
VEL
IDS
1
VEL
VEn = 4 V/µmL
0
VGS-VT = VDSsat
VDS
W
’
IDS = K n
(VGS-VT) 2 (1 + λVDS)
L
L = 1 µm
IDS = 100 µA
ro = 40 kΩ
Willy Sansen
10-05 0124
MOST single-transistor gain Av
IB
vin
+
vout
Av = gmrDS =
2 VE L
VGS-VT
-
Av ≈ 100
VEL ≈ 10 V
and VGS-VT ≈ 0.2 V
If
Willy Sansen
10-05 0125
Design for high gain :
High gain
VGS-VT
Low (0.2 V)
L
High
High speed
VGS-VT sets the ratio gm/IDS !
Willy Sansen
10-05 0126
Example: single-transistor amplifier
We want to realize a three-stage amplifier
with a total gain of 10.000.
We use three single-transistor stages in series.
What minimum lengths do we have to use in
an advanced 65 nm CMOS technology
with VE = 4 V/µm ?
Choose
VGS-VT = 0.2 V !
Willy Sansen
10-05 0127
pMOST small-signal model
D
iDS
G
G
S=B
+
vGS
-
+
vGS
+
vGS
-
D
S=B
gmvGS
S
S
S
S
+
vGS
G
D
iDS
rDS
G
gmvGS
rDS
D
Willy Sansen
10-05 0128
MOST small-signal model: gm & gmb
G
iDS
+
vGS
-
+
+
vGS
-
-
vBS
S
D
rDS vBS
gmvGS
gm =
gmb
gm
=
CD
Cox
+
B
gmbvBS
diDS
dvGS
gmb =
diDS
dvBS
=n-1
Willy Sansen
10-05 0129
Table of contents
• Models of MOST transistors
• MOST as a resistor
• MOST as an amplifier in strong inversion
• Transition weak inversion-strong inversion
• Transition strong inversion-velocity saturation
• Capacitances and fT
• Models of Bipolar transistors
• Comparison of MOSTs & Bipolar transistors
Willy Sansen
10-05 0130
IDS & gm versus VGS : weak inversion
IDS
vs
wi : weak inversion
si
VGS
wi
VGS
gm
IDSwi = ID0
Subthreshold slope :
nkT/q ln(10)
vs
si
wi
W
exp nkT/q
L
VGS
gmwi =
IDSwi
nkT/q
Willy Sansen
10-05 0131
Transconductance gm versus VGS
gm
mS
gmsat
VT
6
vs
si
4
2
wi
0
0
0.5
0.2
VGS-VT
0.5
1
1.5
V
Willy Sansen
VGS
10-05 0132
Transition voltage VGSt between wi & si
VGS
IDSwi = ID0
gmwi =
gmwi
IDSwi
=
W
exp nkT/q
L
IDSwi
IDS = K’n W (VGS-VT) 2
L
gm =
nkT/q
1
gm
nkT/q
IDS
(VGSt-VT)t = 2n
=
2 IDS
VGS-VT
2
VGS-VT
kT
q
Willy Sansen
10-05 0133
Transition Voltage VGSt for different L
(VGSt-VT)t = 2n
kT
q
IDSt ≈
K’
n
kT 2
W
(2n
)
L
q
Is independent of channel length L
Is still true in … years !
(VGSt-VT)t = 2n
kT
q
≈ 70 mV
IDSt ≈ 2 µA for
W
L
= 10
for nMOST
Willy Sansen
10-05 0134
Transition wi - si
log IDS
wi
IDSt
~
si
~ (VGS-VT) 2
VGS
nkT/q
VT
VT + 70mV
VGS
Willy Sansen
10-05 0135
Ratio gm/IDS at the transition wi - si
gm
1
IDS
kT/q
20
4x
1
gm
nkT/q
IDS
=
2
VGS-VT
10
IDS
0
0.01
0.1
1
10
100
Willy Sansen
IDSt
10-05 0136
EKV model for smooth wi-si transition
IDS = K’
W
L
VGSTt2
[ ln (1 +
v=
Small v : ln (1 +
IDS = K’
W
L
Large v : ln (1 +
IDS = K’
W
L
ev
)≈
ev
)
]2
VGST
W
L
kT
q
VGSTt2
VGS-VT
exp (
)
n kT/q
IDSt
)≈v
v2
2n
≈ 70 mV
ev
VGSTt2
K’ =
VGSTt = (VGS-VT) t = 2n
VGSTt
VGSTt2 e2v = K’
ev
VGST = VGS-VT
KP
= K’
W
L
(VGS-VT) 2
Enz, AICSP ‘95,
83-114
Cunha, JSSC Oct.98
1510-1519
Willy Sansen
10-05 0137
Transition current IDSt between wi & si
IDSt = IDS = K’
V=1
i=1
W
L
IDSt = 2 µA for W/L = 10
VGSTt2
i=
IDS
IDSt
v = ln ( e
= [ ln (1 + ev ) ]2
i
inversion
coefficient
- 1)
VGS-VT = VGSTt ln ( e i - 1)
VGSTt = 2n
kT
q
≈ 70 mV
Willy Sansen
10-05 0138
Relation VGS-VT and inversion coefficient i
VGS-VT (mV)
800
700
weak inv.
600
moderate inv.
strong inv.
VGS-VT =
VGSTt ln ( e
500 mV
i
- 1)
500
400
300
200
100
0
VGSTt = 2n
200 mV
q
80 mV
0 mV
-100
-200
0.01
kT
0.5
0.1
1
2
8
10
40
100
i
i=
Willy Sansen
IDS
IDSt
10-05 0139
Transconductance gm between wi & si
i=
IDS
IDSt
gm ≈ ….
= [ ln (1 + ev ) ]2
gm nkT
1-eGM =
=
IDS q
i
i
Large i : GM =
1
i
Small i : GM = 1 -
i
2
Alternative approximation :
GM =
1
1+ 0.5 i + i
Large i : GM = 1
i
i
Small i : GM = 1 4
Willy Sansen
10-05 0140
GM versus inversion coefficient i
GM
gm nkT
GM =
IDS q
1.0
sqrt
0.9
0.8
0.7
GM =
exp
0.6
1-e-
0.5
i
i
0.4
1
0.3
1+ 0.5 i + i
0.2
0.1
0.0
0.01
8
0.1
1
10
100
i
i=
Willy Sansen
IDS
IDSt
10-05 0141
Table of contents
• Models of MOST transistors
• MOST as a resistor
• MOST as an amplifier in strong inversion
• Transition weak inversion-strong inversion
• Transition strong inversion-velocity saturation
• Capacitances and fT
• Models of Bipolar transistors
• Comparison of MOSTs & Bipolar transistors
Willy Sansen
10-05 0142
IDS & gm vs VGS : velocity saturation
IDS
vs
si
vs : velocity saturation
IDSvs = WCoxvsat (VGS-VT)
wi
VGS
gm
vs
gmsat = WCoxvsat
si
wi
vsat ≈ 107 cm/s
VGS
is absolute max. !
Willy Sansen
10-05 0143
The saturation region and velocity saturation
IDS
linear
saturation
(VGS-VT )vs
Saturation region
Square-law region
(VGS-VT )t
0
VGS-VT = VDSsat
VDS
Willy Sansen
10-05 0144
Transconductance gm versus VGS
gm
gmsat = WCoxvsat
mS
vsat = 107 cm/s
gmsat
VT
6
vs
si
4
2
wi
0
0
0.5
VGS-VT
0.5
0.2
1
1.5
V
Willy Sansen
VGS
10-05 0145
Velocity saturation : vsat & θ
[large VGS]
K’n W (VGS-VT) 2
L
IDS =
1 + θ (VGS-VT)
≈
θ
1 + (VGS-VT)
2
W
’
gmsat ≈ 2K n (VGS-VT) 2
L
[1 + θ (VGS-VT)] 2
µ 1
θL=
2n vsat
=
θ L
≈
(VGS-VT)
K’n W
θ
L
= WCoxvsat
1
Ec
K’n W
Ec is the vertical critical field !
θ L ≈ 0.2 µm/V : For L = 0.13 µm θ ≈ 1.6 V-1
Willy Sansen
10-05 0146
Velocity saturation : θ & RS & vsat
K’n W (VGS-VT) 2
L
IDS =
1 + θ (VGS-VT)
gmsat ≈
RS =
K’n W
θ
L
θ
K’n W/L
[large VGS]
gmRs =
gm
1 + gm RS
≈
1
RS
µ
1
1
RS ≈
≈
2n W K’nvsat
W Coxvsat
Willy Sansen
10-05 0147
Transition Voltage VGSTvs between si and vs
IDS =
K’n W (VGS-VT) 2
L
1 + θ (VGS-VT)
IDSsat = WCoxvsat (VGS-VT)
gmsat = WCoxvsat
vsat
1
(VGS-VT)vs =
≈ 2nL
µ
θ
K’n W
≈
θ L
Is proportional to
channel length L !!!
≈ 5 L ≈ 0.62 V if L = 0.13 µm
Willy Sansen
10-05 0148
Transition Current IDSvs between si and vs
IDSvs ≈ K’ WL (
IDSvs
W
2n vsat
µ
)2
≈ 10 A/cm
≈ 100 n εox W
µ
µCox
K’ =
2n
Cox =
W = 2.6 µm & L = 0.13 µm :
IDSvs ≈ 2.6 mA
vsat2
εox
L
tox =
50
tox
vsat = 107 cm/s
n = 1.4
µ= 500 cm2/Vs
Willy Sansen
10-05 0149
Transconductance gm between si and vs
gmsat = W Cox vsat
gmsat ≈ 17 10-5 W/L S/cm
W
gmK’ = 2K’
(VGS-VT)
L
gmK’ ≈ 1.2 10-9 VGST W/L2 S/cm
VGST
1
1
1
=
+
gm gmK’ gmsat
gm ≈
W
17 10-5
L 1 + 2.8 104 L / VGST
L
in cm
If VGST = 0.2 V, vsat takes over for L < 65 nm (If 0.5 V for L < 0.15 µm)
Willy Sansen
10-05 0150
Now in velocity saturation ?
VGS-VT ≈ 0.2 V
(0.5 V)
gm
W
gm 2K’
(VGS-VT)
=
W
L
mS/µm
10
vsat
gm 0.06 VGST
≈
W
L2 in µm
1
K’
0.2 V
0.1
10 nm
0.1 µm
0.5 V
L
1
gm
= Cox vsat
W
gm 0.17
≈
W
L
in µm
Willy Sansen
10-05 0151
Range of VGS-VT values for si vs time
10
VGS-VT (Volts)
v.sat
si
VGSTvs
VGSTvs/3
3VGSTwi
VGSTwi
1
clear si
.1
si
wi
Year
.01
1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008
Willy Sansen
10-05 0152
MOST operating region in si
VGS-VT ≈ 0.5 V
gm
VGS-VT ≈ 0.2 V
mS
gmsat
6
4
VT
vs
si
wi
2
0.2
0
0
0.5
1
0.5
VGS-VT
1.5
V
Willy Sansen
VGS
10-05 0153
gm vs VGS for different L (same tox)
Exercise :
gm
gm
L>>Lmin
Lmin ≈ 50 tox
L>>Lmin
VGS-VT
W = ct
Lmin ≈ 50 tox
W
= ct
L
VGS-VT
Willy Sansen
10-05 0154
gm vs VGS for different tox (≈ Lmin/50)
Exercise :
gm
gm
Lmin small
Lmin small
Lmin large
VGS-VT
W = ct
Lmin large
W
= ct
L
VGS-VT
Willy Sansen
10-05 0155
Table : MOST IDS , gm & gm/IDS
Summary :
Ref.: Laker, Sansen : Design of analog …, MacGrawHill 1994; Table 1-4
Willy Sansen
10-05 0156
Gate current
For 0.1 µm CMOS :
tox ≈ 2 nm
JG ≈ 4 10-2 A/cm2
For 10 x 0.5 µm
IG ≈ 2 nA
JG (A/cm2)
≈ 4.5 105 exp( L in nm
L
6.5
)
Ref. Koh, Tr ED 2001, 259Annema, JSSC Jan.05, 135.
Willy Sansen
10-05 0157
Table of contents
• Models of MOST transistors
• MOST as a resistor
• MOST as an amplifier in strong inversion
• Transition weak inversion-strong inversion
• Transition strong inversion-velocity saturation
• Capacitances and fT
• Models of Bipolar transistors
• Comparison of MOSTs & Bipolar transistors
Willy Sansen
10-05 0158
MOST capacitances
Willy Sansen
10-05 0159
MOST capacitances CGS & CGD
CGD
rG
G
CDB
D
+
CGS
-
vBS
vGS
gmvGS
gmbvBS
rDS
B
+
-
CSB
S
CGS
2
≈ 3 WLCox ≈ 2W fF/µm for Lmin
LminCox ≈ Lmin
εox
tox
≈ 50 εox ≈ 2 fF/µm
CGD = WCgdo
Willy Sansen
10-05 0160
MOST fT where iDS = iGS
iGS
G
D
iGS = vGS CGS s
+
CGS
-
iDS0
vGS
gmvGS
rDS
iDS = gm vGS
S
W
2
’
CGS = 3 WLCox gm = 2K L (VGS-VT)
fT =
gm
2π CGS
fmax ≈
3 µ
(VGS-VT)
=
2
2π 2n L
1
K’
µCox
=
2n
or ≈
vsat
2π L
fT / 8π rGCGD
Willy Sansen
10-05 0161
Design for high speed :
High gain
High speed
VGS-VT
Low (0.2 V)
High (0.5 V)
L
High
Low
VGS-VT sets the ratio gm/IDS !
Willy Sansen
10-05 0162
Maximum fT values versus channel length L
100
fm
fT
fTsat
f (GHz)
2πL2
fTsat =
10
VGS-VT = 0.2
1
fT =
µ
0.5
1V
fm =
(VGS-VT)
vsat
0.2 … 1 V
2πL
fT
1 + αBD
αBD ≈
.1
1
L (micron)
10
CBD
Cox
Processors
Willy Sansen
10-05 0163
fT model in si and velocity saturation
fT =
gm
CGS = kW
2π CGS
gm =
fT =
1
W
13.5
L 1 + 2.8 L / VGST
k = 2 fF/µm = 2 10 -11 F/cm
17 10-5
L 1 + 2.8 104 L / VGST
L in cm
GHz
L in µm
If VGST = 0.2 V, vsat takes over for L < 65 nm
for L < 0.15 µm
If VGST = 0.5 V
Willy Sansen
10-05 0164
fT model in si and weak inversion
fT =
gm
gm nkT
1-e=
GM =
q
IDS
i
2π CGS
gm =
gm =
fT
=
i (1 - e -
i)
fTH
≈ i for small i !
fTH =
=
IDS
1-e-
nkT/q
i
IDSt
nkT/q
i
but IDS = i IDSt
i (1 - e -
IDSt
2π CGS nkT/q
4 K’ nkT/q
2π Cox L2
i
=
i)
K’ VGSTt2 W/L
2π WL Cox nkT/q
= 2 µ kT/q
2π L2
Willy Sansen
10-05 0165
fT versus inversion coefficient i
fT
1
fTH
GM
fT
=
i (1 - e -
fTH
i)
GM =
0.5
1-e-
i
i
0
0.01
0.1
1
10
100
i=
Willy Sansen
IDS
IDSt
10-05 0166
Exercise: MOST fT or not fT ?
all L= Lmin
IDS
1 µ
K’IDS
fT =
=
(VGS-VT) =
2
π Cox WL3 πWLCox(VGS-VT)
2π L
fT
fT
IDS
VGST
IDS VGST=ct
W=ct > IDS
W=
> IDS =ct
VGST = VGS-VT
IDS =ct VGST
fT
W=ct VGST
W
VGST=ct
W
W
VGST
IDS
Willy Sansen
10-05 0167
MOST capacitances CSB & CDB
G
CGD
rG
CDB
D
+
CGS
S
CSB =
CDB =
-
vBS
vGS
gmvGS
CjSB0
1 + VSB/φjS
gmbvBS
rDS
B
+
-
CSB
φjS ≈ φjD ≈ 0.5 … 0.7 V
CjDB0
1 + VDB/φjD
Willy Sansen
10-05 0168
RF MOST model
CG /5
CGD
G
RG /3
CGS
D
+
-
vGS
rDS
gmvGS
S
CG = CGS + CGD
Ref. Tin, Tr. CAD, April 1998, 372
Ref. Sansen, etal, ACD, XDSL,
RFMOS models, Kluwer 1999
Willy Sansen
10-05 0169
Single-page MOST model
W (V -V ) 2
n
GS T
L
IDS =
K’
gm =
2K’
W
n L (VGS-VT) = 2
rDS = ro =
VEL
IDS
VGS-VT ≈ 0.2 V
K’
n
K’n ≈ 100 µA/V2
K’p ≈ 40 µA/V2
2 IDS
W
IDS =
L
VGS-VT
VEn ≈ 5 V/µmL VEp ≈ 8 V/µmL
vsat = 107 cm/s
vsat
3 µ
(VGS-VT) or now ≈
fT =
2
2π 2n L
2π L
1
Willy Sansen
10-05 0170
Growing number of parameters !
BSIM4 : http://www-device.eecs.berkeley.edu/bsim/bsim_ent.html
Model 11 : http://www.semiconductors.philips.com/Philips_Models/mos_models
EKV : http://legwww.epfl.ch/ekv/model.html
/model11/index.html
Willy Sansen
10-05 0171
Benchmark tests
1. Weak inversion transition for IDS and gm/IDS ratio
2. Velocity saturation transition for IDS and gm/IDS ratio
3. Output conductance around VDSsat
4. Continuity of currents and caps around zero VDS
5. Thermal and 1/f noise
6. High frequency input impedance (s11) and
transimpedance (s21)
Willy Sansen
10-05 0172
Table of contents
• Models of MOST transistors
• Models of Bipolar transistors
• Comparison of MOSTs & Bipolar transistors
Willy Sansen
10-05 0173
Bipolar transistors
WB
WB
Lateral PNP transistor
NPN transistor
Willy Sansen
10-05 0174
Bipolar transistor ICE versus VBE
B
+
vBE
-
iBE
C
iCE
iCE
0.7 V : not more
not less
E
0
VBE
ICE = IS exp
IS ≈ 10 -15 A
kT/q
kT/q = 26 mV at 300 K
vBE
0.5
1V
IBE =
ICE
β
is leakage current
β ≈ 10 … 1000
Willy Sansen
10-05 0175
Bipolar transistor small-signal model : gm & ro
C
iCE
B’
rB
B
B
+
vBE
-
rπ
+
vBE
-
E
C
ro
gmvBE
E
ICE
diCE
=
gm =
dvBE
kT/q
β
dvBE
dvBE
=
= β
rπ =
gm
diCE
diBE
E
gm
ICE
ro =
=
1
kT/q
VE
ICE
≈ 40 V-1
VEn ≈ 20 V
VEp ≈ 10 V
Willy Sansen
10-05 0176
Bipolar transistor capacitance Cπ
B’
rB
Cµ
B
C
+
rπ
Cπ
- vBE
CCS
gmvBE
ro
E
Cπ = CjBE + CD
CjBE =
CjBE0
1 + VBE/φjE
S
φjE ≈ 0.7 V
CD is the diffusion capacitance
Willy Sansen
10-05 0177
Diffusion capacitance CD
B’
rB
Cµ
B
C
+
rπ
Cπ
CCS
- vBE
E
gmvBE
ro
S
ICE
QB
diCE
CD =
= τF
= τFgm = τF
vBE
dvBE
kT/q
Base transit time τF =
≈ 10 … 200 ps
WB2
2Dn
or now ≈
WB
vsat
Willy Sansen
10-05 0178
Bipolar transistor capacitances Cµ & CCS
B’
rB
Cµ
B
C
+
rπ
Cπ
- vBE
E
Cµ = CjBC
CCS = CjCS
CjBC =
CjCS =
CCS
gmvBE
ro
CjBC0
S
1 + VBC/φjC
CjCS0
1 + VCS/φjS
φjC ≈ φjS ≈ 0.5 V
Willy Sansen
10-05 0179
Bipolar transistor fT
B’
rB
Cµ
B
C
+
rπ
Cπ
- vBE
gmvBE
CCS
ro
E=S
fT =
gm
2π Cπ
=
1
1
2π
τF + CjBE+Cµ
gm
For a current drive !
fmax ≈
or ≈
vsat
2π WB
fT / 8π rBCµ
Willy Sansen
10-05 0180
Bipolar transistor fT versus ICE
1
2πτF
fT
fT =
1
1
2π
τF + CjBE+Cµ
gm
ICE
1
2πfT
slope
τF
kT 1
1
= τF + (CjBE + Cµ)
q ICE
2πfT
1/ICE
slope
Willy Sansen
10-05 0181
Single-page Bipolar transistor model
VBE
ICE = IS exp
gm =
fT =
ICE
kT/q
1
2π
kT/q
ro =
IS ≈ 10 -15 A
VE
ICE
1
Cje+Cjc
τF +
gm
kT/q = 26 mV at 300 K
VEn ≈ 20 V VEp ≈ 10 V
or ≈
vsat
2π WB
Willy Sansen
10-05 0182
Table of contents
• Models of MOST transistors
• Models of Bipolar transistors
• Comparison of MOSTs and Bipolars
Willy Sansen
10-05 0183
Comparison MOST - Bipolar
β?
n=1+
CD
Cox
4… 6 x
Ref. Laker Sansen Table 2-8
Willy Sansen
10-05 0184
Comparison MOST - Bipolar : minimum VDS
IDS
VDSsat ≈ VGS-VT
VGS-VT ≈
0 VCEsat VDSsat
VDS
IDS
K’n W
L
VCEsat ≈ kT/q’s
Ref. Laker - Sansen Table 2-8
Willy Sansen
10-05 0185
Comparison MOST - Bipolar : gm/IDS ratio
gm
1
IDS
kT/q
4 X
V-1 20
1
nkT/q
10
IDS ICE
0
0.01
0.1
1
10
100
i
Willy Sansen
10-05 0186
Design plan for gm :
IDS = K’n W (VGS-VT) 2
L
gm =
2K’
W
n L (VGS-VT) = 2
K’
n
2 IDS
W
IDS =
L
VGS-VT
4 variables with 2 equations >> 2 free variables
Choose VGS-VT and L !
Willy Sansen
10-05 0187
Comparison MOST - Bipolar
dvi2
vsat ≈ 107 cm/s
Ref. Laker Sansen Table 2-8
Willy Sansen
10-05 0188
Table of contents
• Models of MOST transistors
• Models of Bipolar transistors
• Comparison of MOSTs and Bipolars
Ref.: W. Sansen : Analog Design Essentials, Springer 2006
Willy Sansen
10-05 0189
Reference books on Transistor models
T. Fjeldly, T. Ytterdal, M. Shur, “Introduction to Device Modeling and
Circuit Simulation”, Wiley 1998.
D. Foty, “MOSFET Modeling with SPICE, Prentice Hall
K. Laker, W.Sansen, "Design of Analog Integrated Circuits
andSystems", MacGrawHill. NY., Febr.1994.
A. Sedra, K.Smith, "Microelectronic Circuits", CBS College
Publishing, 2004.
Y. Taur, T. Ning, “Fundamentals of Modern VLSI Devices”
Cambridge Univ. Press, 1998.
Y. Tsividis, “Operation and modeling of the MOS transistor”,
McGraw-Hill, 2004.
A. Vladimirescu “The SPICE book”, Wiley, 1994
Willy Sansen
10-05 0190
References on Analog Design
P.Allen, D.Holberg, "CMOS Analog Circuit Design", Holt, Rinehart and Winston. 1987,
Oxford Press 2002
P.Gray, P.Hurst, S. Lewis, R.Meyer, "Analysis and Design of Analog Integrated
Circuits", Wiley, 1977/84/93/01
R.Gregorian, G.Temes, "Analog MOS Int. Circuits for Signal Processing", Wiley, 1986.
Huijsing, Van de Plassche, Sansen, "Analog Circuit Design", Kluwer Ac.Publ.
1993/4/5….
D.Johns, K.Martin, "Analog integrated circuit design", Wiley 1997.
K.Laker, W.Sansen, "Design of Analog Integrated Circuits and Systems",
McGraw Hill. NY., Febr.1994.
H.W.Ott, "Noise reduction techniques in Electronic Systems", Wiley, 1988.
B. Razavi, “Design of analog CMOS integrated circuits”, McGraw Hill. NY., 2000.
A.Sedra, K.Smith, "Microelectronic Circuits", CBS College Publishing, 1987.
Willy Sansen
10-05 0191