712
24 Transistors
I D = v s Z
a
h
ρ(y) dy .
(24.54)
The forward conductance is given by
g m =
v s Z s
h(V G )
.
(24.55)
The transistor is more linear if the depletion-layer depth only weakly depends on the gate voltage.
This can be accomplished with a doping profile with increasing doping with depth. An increase with a
power law and a step-wise or exponential increase lead to a more linear I (V )-dependence. In the limit
of δ-like doping, a linear I D,sat vs. V G relation develops. Indeed, FETs with graded or stepped doping
profiles exhibit improved linearity and are used for analog circuits.
Nonequilibrium Velocity
Below the electric field for which the drift velocity in GaAs peaks, the carriers can be considered to be
in equilibrium. If the field is higher, velocity overshoot (Sect. 8.4.3 and Fig. 8.16) occurs. The carriers
have a higher velocity (and ballistic transport) before they relax to the lower equilibrium (or steadystate) velocity after intervalley scattering. This effect will shorten the transit time in short-channel
FETs.
24.4.5 High-Frequency Properties
Two factors limit the high-frequency performance of a FET: The transit time and the RC time constant.
The transit time t r is the time that the carrier needs to go from source to drain. For the case of constant
mobility (long channel) and constant drift velocity (short channel), the transit time is given by (24.56a
and b), respectively.
t r =
L
μ E
≈
L
2
μ V G
(24.56a)
t r =
L
v s
.
(24.56b)
For a 1-µm long gate in a GaAs FET, the transit time is of the order of 10 ps. This time is typically
small compared to the RC time constant due to the capacitance C GS and transconductance. The cutoff
frequency is given by
f T =
g m
2π C GS
.
(24.57)
24.5 MOSFETs
The MOSFET has four terminals. In Fig. 24.14b, two n-type regions (source and drain) are within a
p-type substrate. The n-type channel (length L) forms underneath a MIS diode. A forth electrode sets
the substrate bias. The source electrode is considered to be at zero potential. The important parameters
24 Transistors
I D = v s Z
a
h
ρ(y) dy .
(24.54)
The forward conductance is given by
g m =
v s Z s
h(V G )
.
(24.55)
The transistor is more linear if the depletion-layer depth only weakly depends on the gate voltage.
This can be accomplished with a doping profile with increasing doping with depth. An increase with a
power law and a step-wise or exponential increase lead to a more linear I (V )-dependence. In the limit
of δ-like doping, a linear I D,sat vs. V G relation develops. Indeed, FETs with graded or stepped doping
profiles exhibit improved linearity and are used for analog circuits.
Nonequilibrium Velocity
Below the electric field for which the drift velocity in GaAs peaks, the carriers can be considered to be
in equilibrium. If the field is higher, velocity overshoot (Sect. 8.4.3 and Fig. 8.16) occurs. The carriers
have a higher velocity (and ballistic transport) before they relax to the lower equilibrium (or steadystate) velocity after intervalley scattering. This effect will shorten the transit time in short-channel
FETs.
24.4.5 High-Frequency Properties
Two factors limit the high-frequency performance of a FET: The transit time and the RC time constant.
The transit time t r is the time that the carrier needs to go from source to drain. For the case of constant
mobility (long channel) and constant drift velocity (short channel), the transit time is given by (24.56a
and b), respectively.
t r =
L
μ E
≈
L
2
μ V G
(24.56a)
t r =
L
v s
.
(24.56b)
For a 1-µm long gate in a GaAs FET, the transit time is of the order of 10 ps. This time is typically
small compared to the RC time constant due to the capacitance C GS and transconductance. The cutoff
frequency is given by
f T =
g m
2π C GS
.
(24.57)
24.5 MOSFETs
The MOSFET has four terminals. In Fig. 24.14b, two n-type regions (source and drain) are within a
p-type substrate. The n-type channel (length L) forms underneath a MIS diode. A forth electrode sets
the substrate bias. The source electrode is considered to be at zero potential. The important parameters