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 between bands.


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 photoabsorption.


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.