1. What is the Heisenberg model for magnetic interaction?
2. What are the characteristics of ferromagnetic, antiferromagnetic, and
ferrimagnetic ordering?
3. Explain the concept of spin-waves. What is meant by magnons? Derive
magnon
spectrum. What is the low-temperature dependence of the ferromagnetic
magnetization?
Carriers and charge transport in semiconductors.
A&M: Chapter 28, 29.
1. Calculate the carrier density in intrinsic semiconductors. Find position
of the chemical potential.
2. Discuss the effect of impurities on the carrier concentration. What is
the difference between donors and acceptors? What is the difference
between n-type and p-type semiconductors? How does the position of the
chemical potential change in the presence of impurities?
3. What is an impurity band? Explain an origin of the dielectric-metal
transitions. What is the Habbard gap?
4. Consider non-homogeneous distribution of impurities. What is the physics
of p-n interface? Calculate distribution of the electric potential across
p-n interface. What is the depletion layer?
5. Calculate current through p-n interface due to an applied voltage bias.