The Hall effect is discussed in Kittel Chs. 6.
a. Explain qualitatively why the Hall effect is sensitive to the sign
of the carriers, and why the Hall coefficient RH varies inversely with the
density of charge carriers.
b. Calculate the value of the Hall coefficient RH for Cu
metal treated as a free electron gas with the density of valence electrons
in Cu (1 valence electron/atom). Give your results in SI units.
Kittel, Problem 7-1, parts (a) and (b). Also answer part (c) but you
will not be penalized for a wrong answer. The idea is to think about whether
or a divalent element (2 electrons per atom) would be an insulator
or a metal (semimetal) in the simple cubic structure.
Kittel, Problem 7-2.
The law of mass action applied to a semiconductor
states that the product np is a constant
for a given crystal at a given temperature.
a. Give in a brief statement
the basic reasoning why the product should be constant.
b. The product np = 2.1 x 1019 cm-6 for Si at T=300K.
Find the density of electrons n for pure Si at 300K, and at 200 K.
c. Suppose a different crystal of Si is doped with 1018 donors/cm3
and each donor contributes one extra electron to the crystal.
(This is a reasonable range in devices.).What is the equilibrium concentration p
of holes in this crystal at T = 300K?
The lowest two bands in the 1-d nearly free electron problem
can be calculated by solving a 2 x 2 determinant as described in Kittel
Ch. 7 and in the lecture notes. Calculate the
expression for the effective masses for the two bands at the
at the zone boundary in terms of the free electron kinetic
energy at the zone boundary E0BZ and the gap
Egap at the zone boundary. (Note that one band curves
upward and the other band curves downward for k near the zone boundary.)
Evaulate the expressions for the case that E0BZ = 10 eV,
and for two values of the gap:
a. Egap = 1 eV;
b. Egap = 0.1 eV.
These are reasonable values for semiconductors.