428 CHAPTER 8. FIELD EFFECT TRANSISTORS
Problem 8.23Consider a 1.0μm channel lengthn-channel Si MESFET operating under
the condition that the average field in the channel is 15 kV/cm. Assume the electric field in
the channel is constant at this value. Calculate the electron transit time assuming a constant
mobility of 1000 cm^2 /V·s and using the velocity-field relations for Si given in the text.
Problem 8.24Consider twon-channel GaAs MESFETs operating at a source-drain bias
of 2.0 V. Assume that the electric field in the channel is constant and has a value ofVDS/L
whereL=1.0μm for one device and 5μm for the second. Calculate the transit time for
electrons in the two devices using two models for transit: (a) constant-mobility model with
μ= 6000 cm^2 /V·s; (b) correct velocity-field relations for the velocity. Use the curves given
in chapter B for the velocity field. Note that the discrepancy in the two models is larger for
the shorter channel device.
Problem 8.25Consider ann-channel GaAs MESFET with the following parameters:
Schottky barrier height, φb =0.8V
Channel doping, Nd =5× 1016 cm−^3
Channel depth, h =0. 5 μm
Channel mobility, μn = 5000 cm^2 /V·s
Channel length, L =1. 5 μm
Channel width, Z =20. 0 μm
Calculate the value ofVDS(sat)atVGS= 0. Also calculate the output resistance of the
channel atVDS=VDS(sat)+2.0V.
Problem 8.26Consider ann-channel GaAs with the same parameters as the device in
problem 8.25 except for the channel length. A maximum value ofVDSis 10.0 V for the
device, and it is required that the effective channel lengthL′atVGS= 0 and the maximum
drain voltage should be no less than 90% of the actual channel lengthL. What is the
smallest channel lengthLthat satisfies this requirement?
Problem 8.27Consider the nominal AlGaAs-GaAs (ΔEC=0. 25 eV) HEMT structure
shown in figure 8.50. The sheet charge in the channel is 1 × 1012 cm−^2.
(a) Calculate the sheet doping in the donor layer required to achieve that. Show clearly
the electric field distribution and the resultant band diagram of the structure.
(b) I wish to now have a flat quantum wll (as opposed to a triangular quantum well)
holding the same sheet charge density. First, clearly state the design methodology to
achieve this. Next, proceed with the quantitative analysis.
(c) Explain why I would want a flat quantum well. Are there any disadvantages?
(d) Calculate thegmvs.Vgscurve for the transistor assuming that
vs(GaAs)=1× 107 cms andvs(AlGaAs)=2× 107 cms. Use 3-d density of states
in the AlGaAs for your calculation.
