## Transcribed Text

For a certain device (that can be used as a detector of optical radiation) we fabricate a coupled
well structure, where electrons sitting inside GaAs layers see the interface with A1GaAs layer as
a potential barrier of height V = 60 eV. Assume that the width of the GaAs wells is d = 1 nm,
while the width of the barrier is W = 0.7 nm, the mass of electrons inside GaAs is MGAAS =
0.067m, MAIGAAS = 0.092m, where m is the mass of the free electron.
AlGaAs
GaAs
AlGaAs
V
GaAs
1. Compute energies of the first three energy levels for a single well with given parameters. Do
it, first assuming that the AlGaAs barrier has infinite height, then repeat these calculations for
the actual barrier height. Compare and comment on the results.
2.
Plot eigenfunctions for each of the three levels found in the case of the barrier of the finite
height.
3.
Still considering a single well, assume now that a constant electric field of strength Fgis
applied along the well. Using non-degenerate perturbation theory, find second order
corrections to energies and first order corrections to the wave functions assuming potential
barrier of the finite heightV. Plot the unperturbed and the perturbed wave functions on the
same plot. Comment on the results. (Take into account all discrete energy levels, but do not
4.
include into consideration states corresponding to continuous spectrum).
Now consider coupled wells and using the tight-binding approximation find the energy levels
resulting from splitting of (i) the ground states of the individual wells and (ii) of the first
excited states of the individual wells, In class we derived the tight binding approximation
using state only one state from each well as a basis. Repeat this derivation here first for the ground
excited wave functions, and then, separately, using wave functions and energies of the second
Compare the results. The splitting of which levels is larger?
states (in each case you are dealing with two by two tight-binding matrices).

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