10.7. PROBLEMS 509
10.7 PROBLEMS ....................................
Problem 10.1Consider a GaAs sample in which fields of 10 kV/cm and 100 kV/cm is
applied. Discuss the restrictions on scattering times under which Bloch oscillations can
occur. Also calculate the frequency of oscillations.
Problem 10.2Design a GaAs/AlAs superlattice structure in which Bloch oscillations
could occur when the scattering rate is 1013 s−^1 and the applied field is 100 kV/cm.
Discuss possible effects that could prevent the observation of the oscillations.
Problem 10.3Consider a Si crystal in which a field of 105 V/cm is applied. Calculate the
Bloch oscillation period if the field is applied along the i)[100]; ii)[110], and iii)[111]
directions. Discuss if these oscillations are feasible.
Problem 10.4In the resonant tunnel structure the transmission probability vs. energy plot
has resonances with a line widthΔEn. Show that ifEnis the energy of thenthresonance,
ΔEn∼
EnT 1 B
πn
whereT 1 Bis the transmission through a single barrier.
Problem 10.5Estimate the time an electron will take to tunnel through a resonant tunnel
double barrier structure. You can use the Heisenberg relationΔtΔE∼,whereΔEis
the energy line width of the transmission resonance.
Problem 10.6Consider a resonant tunneling structure with the following parameters:
Barrier height,V 0 =0.3eV
We l l s i z e,W =60A ̊
Barrier width,a =25A ̊
Effective mass,m∗ =0. 07 m 0
Calculate and plot the tunneling probability of electrons as a function of energy for
0 <E<V 0.
Problem 10.7Consider a 0. 1 μm AlGaAs/GaAs device in which a 2-dimensional gas is
formed with a density ofn 2 D=10^12 cm−^2. A split gate device is made from the
structure. Estimate the minimum gate voltage needed to switch a quantum interference
transistor. How does this compare to the voltage needed to switch regular FET?
Problem 10.8In normal transistors the ON and OFF states of the device are produced by
injecting and removing electrons in the device. Consider a Si device with an area of
