716
24 Transistors
(a)
50
40
30
20
10
0
D
i
V (V)
D
0
5
10V
15
V V
G
T
9
8
7
6
5
4
3
1
saturation
region
(b)
3
2
1
0 0
5
1 0
I (mA)
D
V (mA)
D
V =5V
G
2V
3V
4V
1V
3V
5V
4V
µ=const.
µ( )
Fig. 24.23 a Idealized I –V characteristics for a MOSFET with constant mobility. The dashed line visualizes the drain
(saturation) voltage for which the current is equal to I D,sat . The solid lines are for various values of the gate voltage
V G − V T =1–10 V. Adapted from [574] b I –V characteristics taking into account the effect of field-dependent mobility
(solid lines) in comparison to the constant-mobility model (dashed lines) for various gate voltages as labeled. Adapted
from [2062]
dV (y) = I D d R =
I D dy
Z μ n |Q n (y)|
.
(24.64)
We note the drain current is independent of x. Using (24.61) and performing the integral of (24.64)
from V (y = 0) = 0 to V (y = L) = V D , we find
I D = μ n C i
Z
L
V G − 2 B −
V D
2
−
2
3
√
2e s N A
C i
(V D + 2 B )
3/2
− (2 B )
3/2
.
(24.65)
This characteristic is depicted in Fig. 24.23a. In the linear regime (small drain voltage, V D (V G −V T )),
the drain current is given by
I D ∼ = μ n C i
Z
L
(V G − V T ) V D .
(24.66)
The threshold voltage V T , i.e. the gate voltage for which the channel is opened and a current can flow,
is given for small drain voltage (linear regime) by
V T = 2 B +
√
4 e s N A B
C i
.
(24.67)
The transconductances in the linear regime are easily obtained as (cmp. (24.46), (24.47))
g m = μ n C i
Z
L
V D
(24.68a)
g D = μ n C i
Z
L
(V G − V T ) .
(24.68b)
The mobility extracted from evaluation of a characteristic using (24.68b) is termed effective mobility
(μ eff ). The mobility extracted from (24.68a) is termed field effect mobility (μ FE ). The experimentally
24 Transistors
(a)
50
40
30
20
10
0
D
i
V (V)
D
0
5
10V
15
V V
G
T
9
8
7
6
5
4
3
1
saturation
region
(b)
3
2
1
0 0
5
1 0
I (mA)
D
V (mA)
D
V =5V
G
2V
3V
4V
1V
3V
5V
4V
µ=const.
µ( )
Fig. 24.23 a Idealized I –V characteristics for a MOSFET with constant mobility. The dashed line visualizes the drain
(saturation) voltage for which the current is equal to I D,sat . The solid lines are for various values of the gate voltage
V G − V T =1–10 V. Adapted from [574] b I –V characteristics taking into account the effect of field-dependent mobility
(solid lines) in comparison to the constant-mobility model (dashed lines) for various gate voltages as labeled. Adapted
from [2062]
dV (y) = I D d R =
I D dy
Z μ n |Q n (y)|
.
(24.64)
We note the drain current is independent of x. Using (24.61) and performing the integral of (24.64)
from V (y = 0) = 0 to V (y = L) = V D , we find
I D = μ n C i
Z
L
V G − 2 B −
V D
2
−
2
3
√
2e s N A
C i
(V D + 2 B )
3/2
− (2 B )
3/2
.
(24.65)
This characteristic is depicted in Fig. 24.23a. In the linear regime (small drain voltage, V D (V G −V T )),
the drain current is given by
I D ∼ = μ n C i
Z
L
(V G − V T ) V D .
(24.66)
The threshold voltage V T , i.e. the gate voltage for which the channel is opened and a current can flow,
is given for small drain voltage (linear regime) by
V T = 2 B +
√
4 e s N A B
C i
.
(24.67)
The transconductances in the linear regime are easily obtained as (cmp. (24.46), (24.47))
g m = μ n C i
Z
L
V D
(24.68a)
g D = μ n C i
Z
L
(V G − V T ) .
(24.68b)
The mobility extracted from evaluation of a characteristic using (24.68b) is termed effective mobility
(μ eff ). The mobility extracted from (24.68a) is termed field effect mobility (μ FE ). The experimentally