180
Compact Models for Integrated Circuit Design
V
V
d
dV
V
th
V V
th
V V
bs
th
bs
bm
bs
bm
Equation 5.5
Equation 5.7
E
(
)
=
(
)
=
=
q quation 5.5
Equation 5.7
(
)
=
(
)
=
=
V V
bs
th
V V
bs
bm
bs
bm
d
dV
V
Using the above conditions, we can show
γ
φ
φ
γ
φ
φ
φ
φ
1
2
1
2
s
b x
s
s
b m
s
bx
s
b m
s
bm
V
V
V
K
V
KV
−
−
(
) +
−
−
−
(
) =
−
−
(
) −
(5.8)
−
−
= −
−
−
γ
φ
φ
2
1
2
2
2
s
b m
s
bm
V
K
V
K
(5.9)
Solving Equations 5.8 and 5.9 simultaneously, we can show that
K
V
V
V
V
K
s
b x
s
s
b m
s
s
bm
s
b m
1
2
1
2
2
1
2
2
= −
−
(
)
−
−
(
) −
(
)
−
−
(
) +
=
−
γ
γ γ
φ
φ
φ
φ
φ
φ
γ
;
γ γ
φ
φ
φ
φ
φ
2
2
(
)
−
−
(
)
−
−
(
) +
s
b x
s
s
s
bm
s
b m
V
V
V
(5.10)
If K 1 and K 2 are not given, they can be computed from Equation 5.10 using the
channel doping concentration [27–29]. From Equation 5.6, we note that for a
conventional high–low channel doping profile, γ 1 > γ 2 ; then, from Equation
5.10, the value of K 2 > 0. And, therefore, the devices with conventional high–
low channel doping profile are sensitive to strong body bias. On the other
hand, in the devices with low–high channel doping profile, γ 1 < γ 2 ; therefore,
from Equation 5.10, K 2 < 0 and the devices are less sensitive to strong body
bias.
5.2.1.2 Threshold Voltage Modeling for Nonuniform
Lateral Channel Doping Profile
In advanced CMOS technologies, localized high doping concentration
regions of the same doping type as the channel are used near the source
and drain ends of the channel [3,4,23–26] to suppress SCEs [5,6]. This localized concentration of additional channel doping near the source and drain
ends of the channel is referred to as the halo or pocket doping as shown in
Figure 5.1a and is a critical technology parameter for optimizing the performance of MOSFET devices. Due to halo doping, the channel doping profile
becomes laterally nonuniform with higher concentration at the source and
drain ends and low concentration near the channel as shown in Figure 5.1b.
This nonuniform lateral channel doping profile can also be modeled by two
step functions as shown in Figure 5.4.
Compact Models for Integrated Circuit Design
V
V
d
dV
V
th
V V
th
V V
bs
th
bs
bm
bs
bm
Equation 5.5
Equation 5.7
E
(
)
=
(
)
=
=
q quation 5.5
Equation 5.7
(
)
=
(
)
=
=
V V
bs
th
V V
bs
bm
bs
bm
d
dV
V
Using the above conditions, we can show
γ
φ
φ
γ
φ
φ
φ
φ
1
2
1
2
s
b x
s
s
b m
s
bx
s
b m
s
bm
V
V
V
K
V
KV
−
−
(
) +
−
−
−
(
) =
−
−
(
) −
(5.8)
−
−
= −
−
−
γ
φ
φ
2
1
2
2
2
s
b m
s
bm
V
K
V
K
(5.9)
Solving Equations 5.8 and 5.9 simultaneously, we can show that
K
V
V
V
V
K
s
b x
s
s
b m
s
s
bm
s
b m
1
2
1
2
2
1
2
2
= −
−
(
)
−
−
(
) −
(
)
−
−
(
) +
=
−
γ
γ γ
φ
φ
φ
φ
φ
φ
γ
;
γ γ
φ
φ
φ
φ
φ
2
2
(
)
−
−
(
)
−
−
(
) +
s
b x
s
s
s
bm
s
b m
V
V
V
(5.10)
If K 1 and K 2 are not given, they can be computed from Equation 5.10 using the
channel doping concentration [27–29]. From Equation 5.6, we note that for a
conventional high–low channel doping profile, γ 1 > γ 2 ; then, from Equation
5.10, the value of K 2 > 0. And, therefore, the devices with conventional high–
low channel doping profile are sensitive to strong body bias. On the other
hand, in the devices with low–high channel doping profile, γ 1 < γ 2 ; therefore,
from Equation 5.10, K 2 < 0 and the devices are less sensitive to strong body
bias.
5.2.1.2 Threshold Voltage Modeling for Nonuniform
Lateral Channel Doping Profile
In advanced CMOS technologies, localized high doping concentration
regions of the same doping type as the channel are used near the source
and drain ends of the channel [3,4,23–26] to suppress SCEs [5,6]. This localized concentration of additional channel doping near the source and drain
ends of the channel is referred to as the halo or pocket doping as shown in
Figure 5.1a and is a critical technology parameter for optimizing the performance of MOSFET devices. Due to halo doping, the channel doping profile
becomes laterally nonuniform with higher concentration at the source and
drain ends and low concentration near the channel as shown in Figure 5.1b.
This nonuniform lateral channel doping profile can also be modeled by two
step functions as shown in Figure 5.4.