7.7. PROBLEMS 351
n
AlGaAs
GaAs
p n
Figure 7.25: Band diagram for device in problem 7.14.
Problem 7.14Consider a bipolar transistor where the wide bandgap collector is used,
such thatΔEc=0. 3 eV, as illustrated in figure 7.25. Calculate the additional delay
introduced by the barrier for a current density of 10 kA/cm^2. Assume thermionic emission
over the collector barrier. You may also assume that the notch is a quantum well of width
100 A with infinite barriers when calculating the Fermi level in the notch. ̊
Problem 7.15Tired of making planar HBT’s, I decide to make a cylindrical HBT as
shown in figure 7.26. (a) Derive an expression for the transit time delay in the collector of
this HBT.
(b) Calculate delays forRB=1μmandRC=3μm, and compare these delays with
values for planar HBT’s with the same base and collector thickness. Explain the
difference. Assume that the electron velocity is saturated in the collector.
(c) Calculate the minority charge distribution in the base of the cylindrical HBT and
compare it with the planar structure, assumingIeis the same in both cases. Assume no
recombination in the base. How is the delay affected relative to the planar HBT with the
same base width?
Problem 7.16Consider the HBT from prefxch07/6.36.
(a) Obtain an expression for the base transit time in this graded base. Compare it to an
HBT with an ungraded base, but with the same collector current.
(b) What is the base transit time when the current density is 10 kA·cm−^2. What will the
base transit time at this current level be if the base is not graded? Assume
μ= 1000cm^2 /(V·s),vsat=10^7 cm/s. You may assume that the electron velocity is
saturated for electric fields greater than 2 kV/cm.
Problem 7.17Consider two HBT structures, whose collector velocity profiles are shown
in figure 7.27. Derive expressions for the collector transit delays in these two structures in
terms of the saturated velocity vsand collector width, WC. Now, calculate the base transit
