403(c) The electric current density j under the electric field E is
j = aE = -aV+(z).
The diffusion current density is J = -DVp. In equilibrium we have
j/e = -J/m i.e., aV$(x)/e = -DVp/m = -DVn.
The density of states at the Fermi surface is
The electric chemical potential fi
equilibrium. Thus
p + e+(x) does not depend on z in
Vfi = Vp+eV+(z) = 0,
i.e.,
Hence,2207
Consider a non-interacting Fernii gas of electrons. Assume the elec-
trons are nonrelativistic.
(a) Find the density of states N(E) as a function of energy (N(E) is- The particles are constrained to move only along a line of length
the number of states per unit energy interval) for the following cases:L.
2) The particles move only on a two dimensional area A.
3) The particles move in a three dimensional volume V.
(b) In a Fermi electron gas in a solid when T << TF (the gas tempera-
ture is much less than the Fermi temperature), scattering by phonons and