be considered as free electrons) in a metal with N = loz2 electrons/cm3 at
T=OK.
(UC, Berkeley)
Solution:
From the density of states
D(c)de = 4~(2rn)~/~&de/h~ ,
we get
h2 3N 2f3
2m (G)
Therefore, po = -
For N = loz2 electrons/cm3 = lo2' electrons/m3, it follows that
po = 2.7 x lo-'' J = 1.7 eV.
2095
D(E) is the density of states in a metal, and EF is the Fermi energy.
At the Fermi energy D(EF) # 0.
(a) Give an expression for the total number of electrons in the system
at temperature T = 0 in terms of EF and D(EF).
(b) Give an expression of the total number of electrons in the system
at T # 0 in terms of the chemical potential p and D(E).
(c) Calculate the temperature dependence of the chemical potential at
low temperatures, i.e., p >> kT.
(Chicago)