PHT.307 Advanced Solid State Physics
07.03.2018

Problem 1
ZnS goes through a structural phase transition from the zincblende structure to the wurzite structure at 1020°C.

(a) Plot the entropy of both phases as a function of temperature (the entropy is the derivative of the free energy).

(b) How could you predict the temperature of this phase transition starting with the Schrödinger equation? What would be a good way to observe the phase transition experimentally?

(c) ZnS is a wide band gap semiconductor in both phases. How could you estimate the concentration of electrons in the conduction band from the band structure?

(d) Would either phase exhibit piezoelectricity?

Problem 2
The differential equation that describes the motion of electrons in a diffusive metal is,

$$m\frac{d\vec{v}}{dt}+\frac{e\vec{v}}{\mu} = -e\vec{E}.$$

(a) Sketch the impulse response function that solves this equation.

(b) Explain how you can derive the electrical conductivity from this equation.

(c) We derived a frequency dependent conductivity using the dielectric function and a temperature dependent conductivity using the Boltzmann equation. How are these two quantities related? How are either of those solutions related to the differential equation above?

Problem 3
The piezoconductivity describes how stress induces changes in the electrical conductivity. This effect is used in accelerometers that are in most mobile phones.

(a) How can the stress lead to a change in the electrical conductivity? How could this be calculated? What kind of material would have a large piezoconductivity?

Problem 4
The pyroelectric coefficient describes how the polarization of a crystal changes as the temperature changes.

(a) Assume Landau's theory of a second order phase transition can be used to describe polarization of the crystal. Sketch the pyroelectric coefficient as a function of temperature. What is the order parameter in this case?

(b) If you measured the pyroelectric coefficient as a function of temperature and the electric susceptibilty as a function of temperature you would be able to predict the specific heat as a function of temperature in a certain temperature range. Explain how this is possible.