Periodic representation of the energy bands.
Brillouin zones. Metals, semiconductors, insulators. Number of available
states (-how many electrons-) in the energy band. The energy gap
Boltzmann factor for a gap. Very small numbers,
but compare with Avogadros number. For large gaps, not
even the Avogadro can compensate. Nearly pure zero
in the conduction band - insulator.
Electrons and holes. Semiconductoe conductivity
i n c r e a s e s
with temperature. Demonstrations of energy gap:
electrical conductivity, photoconductivity, or
simply absorption of photons. Phonon assisted
Reminder: Fermi gas model - density of states.
Density of states for bands - analogy. See as well the
effective mass. Evaluation of the number of holes, i.e. number
of the electrons missing in the valence band. Position of the
Fermi distribution parameter mu
Holes. Evaluation of the
product of state density dependent on the
effective mass m*, volume V. And
the Fermi distribution function f, dependent on the
parameter mu. f replaced by approximate expression, close to the
Boltzmann factor due to the large value of the gap
as compared to the value of kT.
The valence band maximum EV.
Substitution variable x2.
Small drawing of the missing electrons.
Substitution and evaluation. Energy factor independent
of x2. Evaluation of the integral
Evaluation of the integrals. Below the famous error integral.
Above the symbolic serivation of our integral.
Density of holes derived. Density of electrons
to be derived next time.