(b) If plasmons are observed, is the real part of the dielectric function of the metal positive or negative at the frequency of the plasmons? Why?

(c) Could surface plasmons be measured with Raman spectroscopy? Would you be able to measure the plasmon dispersion relation?

(a) Sketch the specific heat of intrinsic Ge as a function of temperature. Explain why it has the shape you have drawn.

(b) Describe the electrical conductivity of intrinsic Ge. Is it a better conductor than silicon? Why?

(c) Germanium has the diamond crystal structure (fcc), has light holes and heavy holes and a conduction band minimum in the <111> direction. Sketch the band structure of germanium.

(d) Cyclotron resonance is sometimes used to measure the effective masses of electrons and holes. Explain how this works.

Problem 3

(a) An ellipsometery experiment is performed on some material used for optical lenses and the dielectric function is measured in the range 400 nm - 1000 nm. The imaginary part is nearly zero throughout this range as you would expect for a lens material. Can you say something about the imaginary part of the dielectric function at higher or lower frequencies or is that impossible from this measurement?

(b) You could change the index of refraction of a material by applying stress to it. Explain how you could start from the band structure and calculate the change in index of refraction with respect to stress.

Problem 4

(a) You are given three materials, one is a ferromagnet, one is a paramagnet, and one is an antiferromagnet. The transition temperatures for the magnetic phase transitions are at low temperatures and they are all paramagnets in the temperature range you can measure. How can you determine which material is which?

(b) Plot the order parameter of the antiferromagnet as a function of temperature. How could you measure the order parameter?

(c) What is the difference between a hard magnet and a soft magnet?