24.5 MOSFETs
717
measured field effect mobility is typically smaller than the effective mobility. The difference between
the effective and the field effect mobility is related to the gate voltage dependence of the effective
mobility; in the linear regime,
μ FE ≈ μ eff + (V G − V T )
∂μ eff
∂V G
V D =const.
.
(24.69)
The saturation current is approximately
I D,sat ∼ = μ n C i
m Z
L
(V G − V T )
2
,
(24.70)
where m depends on the doping concentration and is about 0.5 for low doping. The mobility extracted
from (24.70) is termed saturation mobility (μ sat ). Due to the neglect of the gate voltage dependence
in the definition for the saturation mobility, the experimental results usually yield μ sat < μ eff . For low
p-doping of the substrate, the threshold voltage in (24.70) for the saturation regime is also given by
(24.67). At higher doping, the threshold voltage becomes dependent on the gate voltage. C i denotes
the insulator capacitance
C i = i /d i .
(24.71)
The forward transconductance in the saturation regime is
g m,sat = μ n C i
2 m Z
L
(V G − V T ) .
(24.72)
For constant drift velocity (Fig. 24.23b for field-dependent mobility), the saturation current is given by
I D,sat = Z C i v s (V G − V T ) ,
(24.73)
and the forward transconductance in the saturation regime is
g m,sat = Z C i v s .
(24.74)
We note that the transistor properties depend on and can be separated into the geometry factor (Z /L)
and the material properties (μ C i = μ μ i /d i ).
The threshold voltage can be changed by the substrate bias V BS as (β = e/kT )
V T =
a
√
β
2 B + V BS −
2 B
,
(24.75)
with (L D being the Debye length (cf. 21.85b))
a = 2
s
i
d
L D
.
(24.76)
Experimental data are shown in Fig. 24.24. For a Si/SiO 2 gate diode, a = 1 for, e.g., d i = 10 nm and
N A = 10
16 cm
−3 . For gate voltages below V T , the current is given by the diffusion current, similar
to a npn transistor. This regime is important for low-voltage, low-power conditions. The related drain
current is termed the subthreshold current and is given by
717
measured field effect mobility is typically smaller than the effective mobility. The difference between
the effective and the field effect mobility is related to the gate voltage dependence of the effective
mobility; in the linear regime,
μ FE ≈ μ eff + (V G − V T )
∂μ eff
∂V G
V D =const.
.
(24.69)
The saturation current is approximately
I D,sat ∼ = μ n C i
m Z
L
(V G − V T )
2
,
(24.70)
where m depends on the doping concentration and is about 0.5 for low doping. The mobility extracted
from (24.70) is termed saturation mobility (μ sat ). Due to the neglect of the gate voltage dependence
in the definition for the saturation mobility, the experimental results usually yield μ sat < μ eff . For low
p-doping of the substrate, the threshold voltage in (24.70) for the saturation regime is also given by
(24.67). At higher doping, the threshold voltage becomes dependent on the gate voltage. C i denotes
the insulator capacitance
C i = i /d i .
(24.71)
The forward transconductance in the saturation regime is
g m,sat = μ n C i
2 m Z
L
(V G − V T ) .
(24.72)
For constant drift velocity (Fig. 24.23b for field-dependent mobility), the saturation current is given by
I D,sat = Z C i v s (V G − V T ) ,
(24.73)
and the forward transconductance in the saturation regime is
g m,sat = Z C i v s .
(24.74)
We note that the transistor properties depend on and can be separated into the geometry factor (Z /L)
and the material properties (μ C i = μ μ i /d i ).
The threshold voltage can be changed by the substrate bias V BS as (β = e/kT )
V T =
a
√
β
2 B + V BS −
2 B
,
(24.75)
with (L D being the Debye length (cf. 21.85b))
a = 2
s
i
d
L D
.
(24.76)
Experimental data are shown in Fig. 24.24. For a Si/SiO 2 gate diode, a = 1 for, e.g., d i = 10 nm and
N A = 10
16 cm
−3 . For gate voltages below V T , the current is given by the diffusion current, similar
to a npn transistor. This regime is important for low-voltage, low-power conditions. The related drain
current is termed the subthreshold current and is given by