Problem 1
Consider an organic semiconductor.

(a) Describe excitons, polarons, and bipolarons in organic semiconductors. How could they be measured experimentally?

(b) What experiments could you do to show that the charge carriers in an organic semicondutor are holes?

(c) Sketch the dielectric function of an organic semiconductor. How would you measure the dielectric function? What are the limiting values for the real and imaginary parts of the dielectric function at high and low frequency?

Problem 2
(a) Explain why the Fermi function is not valid for a system of interacting Fermions.

(b) How does Fermi liquid theory treat electrons as nearly non-interacting Fermions?

(c) Gold atoms on an fcc lattice with a 1 cm lattice constant act like an insulator. An electric field will polarize the atoms but no current flows. If the lattice constant were to be made continuously smaller, there would be an abrupt transition from an insulator to a metal as the lattice constant approached the lattice constant of the metal. How could you estimate the critical lattice constant?

Problem 3
You have been asked to characterize a ferroelectric material. What are the characteristics that people using this ferroelectric would want to know? Describe the experiments you would perform to measure these characteristics.

Problem 4
Bismuth is a semimetal with a very small Fermi surface.

(a) What does this tell you about the properties of Bi?

(b) How would you calculate the Fermi surface?

(c) How can you tell if the charge carriers are electrons or holes?

(d) How can you measure the Fermi surface experimentally?