Hi. I am unsure about the last part of Q3 on the 2005 paper for 6 marks.
For the heat capacity of the electrons are you just meant to do the estimate where you say electrons within kbT of the fermi surface are raised by kbt? Or are you meant to do the proper integral as in 6.3d) of the revision set?
And for the lattice vibration heat capacity are you meant to do the Debye model method (without a cutoff as temperature is low)? Doesn't this require you to know the Riemann zeta type integral is just a number?
Confused as it is only for 6 marks and wondering if I am missing a easier method.
For Q4 it asks how the Fermi energy in a semi-conductor varies with temperature. Is he defining Fermi energy how we usually define chemical potential?