8.11. DESIGN PROBLEMS 431
scatteringτscin such materials is∼1.0 ps. If the electron transit time is less than 1 ps, the
electron moves “ballistically,” i.e., without scattering. Consider a FET in which the
average electric field is 20 kV/cm. Electrons are injected at the source with thermal
velocities and move in the average electric field toward the drain. Estimate the gate length
at which the velocity overshoot effect will become important for Si, GaAs, and InAs.
Assume that the average scattering time is 1 ps for all three materials. Assume electron
effective masses of 0.26m 0 , 0. 067 m 0 ,and 0. 02 m 0 , respectively.
8.11 DESIGN PROBLEMS ...............................
Problem 8.1Consider ann-MESFET made from GaAs operating in an ON state. Sketch
schematically (i.e., only semi-quantitatively) the electric field in the channel below the
gate going from the source to the drain for the following cases:
(a) the device is in the linear regime, i.e., the drain bias is very small.
(b) the device is under a high drain bias (i.e.,VD∼VD(sat)).
Give reasons for your results.
Problem 8.2A field-effect transistor is to be made from the high-speed material
n-InGaAs. The doping is 1017 cm−^3. The bandgap of the material is 0.8 eV and the
maximum Schottky barrier height possible is 0.4 eV. In the device the maximum gate
leakage current density allowed is 10 −^2 Acm−^2. Discuss how you would design the FET
using the MESFET and JFET approach.
R∗ =4.7Acm−^2 K−^2
Dp =25cm^2 /s
Lp =1. 5 μm
ni =2× 1011 cm−^3
Discuss the limitations on the gate bias for the MESFET and the JFET.
Problem 8.3Ann-MESFET is made from GaAs doped at 1017 cm−^3. The gate widthZ
is 50.0μm and the gate length is 2.0μm and the channel thicknesshis 0.25μm.
To characterize the gate properties, the gate semiconductor current is measured and is
found to have the value (at 300 K)
IG=3. 12 × 10 −^14 [exp(eV /kBT)−1] A
whereVis the bias between the gate and the semiconductor. The mobility in the
semiconductor is measured to be 4000 cm^2 /V·s.
(a) Calculate the threshold voltageVTfor the device.
(b) Calculate the transconductance at saturation when the gate bias isVGS=− 2. 0 V.
Problem 8.4Consider a GaAs MESFET with a gold Schottky barrier of barrier height
0.8 V. Then-channel doping is 1017 cm−^3 and the channel thickness is 0.25μm. Calculate
the 300 K threshold voltage for the MESFET.
