Use a computer (Origin is best) to find and plot the bandstructure E(k) for
solutions (E < 10eV) to the Kronig-Penney model using the
following parameters: V=10eV, a=0.4nm, and b=0.1nm. Start
by creating a column of energies (say, 0 to 10eV in 0.01eV
increments), converting these energies to Joules, and using the energies to
compute k1, α, and the LHS of
the K-P eqn. Then solve for k = arccos(LHS)/d.
Finally, plot E vs k. I strongly advise doing all calculations in MKS units!
How many bound bands are there? How does the bandwidth
change with energy? Is the change consistent with finite
lattice results? Explain.
What is the energy (in eV) of the lowest allowed state?
What is the bandwidth of the lowest energy band? What is
the bandgap between the lowest two bands?
Use numerical differentiation to find the effective mass of the
lowest energy states.