  Effects of electron-phonon interactions on the band structure can be
experimentally investigated in detail by measuring the temperature dependence
of energy gaps or critical points (van Hove singularities) of the optical
excitation spectra. These studies have been complemented in recent years by
observing the dependence of such spectra on isotopic mass whenever different
stable isotopes of a given atom are available at affordable prices. In crystals
composed of different atoms, the effect of the vibration of each separate atom
can thus be investigated by isotopic substitution. Because of the zero-point
vibrations, such effects are present even at zero temperature (T = 0). In this
paper we discuss state-of-the-art calculations of the dielectric function
spectra and compare them with experimental results, with emphasis on the
differences introduced by the electron-phonon interaction. The temperature
dependence of various optical parameters will be described by means of one or
two (in a few cases three) Einstein oscillators, except at the lowest
temperatures where the T4 law (contrary to the Varshini T2 result) will be
shown to apply. Increasing an isotopic mass increases the energy gaps, except
in the case of monovalent Cu (e.g., CuCl) and possibly Ag (e.g., AgGaS2). It
will be shown that the gaps of tetrahedral materials containing an element of
the first row of the periodic table (C,N,O) are strongly affected by the
electron-phonon interaction. It will be conjectured that this effect is related
to the superconductivity recently observed in heavily boron-doped carbon.
