708
24 Transistors
This equation can also be written, using (24.37) and
I P =
e
2
μ n N
2
D Z a
3
6 s L
,
(24.41)
as
I D = I P
3V D
V P
− 2
(V bi + V G + V D )
3/2
− (V bi + V G )
3/2
V
3/2
P
.
(24.42)
The saturation current is reached for y 2 = a or V bi + V G + V D = V P and is given by
I D,sat = I P
1 − 3
V bi + V G
V P
+ 2
V bi + V G
V P
3/2
.
(24.43)
The dependence of the saturation current on (V G + V bi )/V P is depicted in Fig. 24.15b. For the threshold
(gate) voltage of
V T = V P − V bi ,
(24.44)
the saturation current is zero since then V D = 0.
5 Around the threshold voltage, the drain saturation
current is given in lowest order of V G as
I D,sat ≈
3 I P
4
V G − V T
V P
2
.
(24.45)
Thus, in order to experimentally determine the threshold voltage,
√
I D is plotted versus the gate voltage
and extrapolated to I D = 0 (dash-dotted line in Fig. 24.15 and Fig. 24.16).
The source–drain voltage at the saturation point decreases with decreasing saturation current, shown
as dashed parabola-like line in Fig. 24.15a.
If the charge-carrier distribution differs from the homogeneous distribution assumed so far, a change
of transistor properties arises, as shown in Fig. 24.15b for a δ-like carrier distribution. The I –V characteristic is slightly less curved, but not linear. A linear characteristic is only achievable in the drift
velocity saturation regime (cf. Sect. 24.4.4).
For high source–drain voltage V D > V P − V bi − V G , the current remains essentially at its saturation
value. For very high source–drain voltage, breakdown in the gate–drain diode can occur, when the
maximum voltage, which is given by V G + V D at the end of the channel, is equal to the breakdown
voltage V B .
The forward transconductance g m and the drain transconductance g D are given by
g m =
∂ I D
∂V G
V D =const.
= g max
V bi + V G
V P
−
V bi + V G + V D
V P
(24.46)
g D =
∂ I D
∂V D
V G =const.
= g max
1 −
V bi + V G + V D
V P
,
(24.47)
where
g max =
3 I P
V P
=
e N D μ n Z a
L
.
(24.48)
5 The threshold voltage can also be obtained from the condition g D0 = 0 (cf. (24.49)).
24 Transistors
This equation can also be written, using (24.37) and
I P =
e
2
μ n N
2
D Z a
3
6 s L
,
(24.41)
as
I D = I P
3V D
V P
− 2
(V bi + V G + V D )
3/2
− (V bi + V G )
3/2
V
3/2
P
.
(24.42)
The saturation current is reached for y 2 = a or V bi + V G + V D = V P and is given by
I D,sat = I P
1 − 3
V bi + V G
V P
+ 2
V bi + V G
V P
3/2
.
(24.43)
The dependence of the saturation current on (V G + V bi )/V P is depicted in Fig. 24.15b. For the threshold
(gate) voltage of
V T = V P − V bi ,
(24.44)
the saturation current is zero since then V D = 0.
5 Around the threshold voltage, the drain saturation
current is given in lowest order of V G as
I D,sat ≈
3 I P
4
V G − V T
V P
2
.
(24.45)
Thus, in order to experimentally determine the threshold voltage,
√
I D is plotted versus the gate voltage
and extrapolated to I D = 0 (dash-dotted line in Fig. 24.15 and Fig. 24.16).
The source–drain voltage at the saturation point decreases with decreasing saturation current, shown
as dashed parabola-like line in Fig. 24.15a.
If the charge-carrier distribution differs from the homogeneous distribution assumed so far, a change
of transistor properties arises, as shown in Fig. 24.15b for a δ-like carrier distribution. The I –V characteristic is slightly less curved, but not linear. A linear characteristic is only achievable in the drift
velocity saturation regime (cf. Sect. 24.4.4).
For high source–drain voltage V D > V P − V bi − V G , the current remains essentially at its saturation
value. For very high source–drain voltage, breakdown in the gate–drain diode can occur, when the
maximum voltage, which is given by V G + V D at the end of the channel, is equal to the breakdown
voltage V B .
The forward transconductance g m and the drain transconductance g D are given by
g m =
∂ I D
∂V G
V D =const.
= g max
V bi + V G
V P
−
V bi + V G + V D
V P
(24.46)
g D =
∂ I D
∂V D
V G =const.
= g max
1 −
V bi + V G + V D
V P
,
(24.47)
where
g max =
3 I P
V P
=
e N D μ n Z a
L
.
(24.48)
5 The threshold voltage can also be obtained from the condition g D0 = 0 (cf. (24.49)).