Web Problems:

1. Use a computer (Origin is best) to find and plot the bandstructure E(k) for bound 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!

2. How many bound bands are there?  How does the bandwidth change with energy?  Is the change consistent with finite lattice results?  Explain.

3. 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?

4. Use numerical differentiation to find the effective mass of the lowest energy states.