The growth of charge carriers in an avalanche in a uniform field E0 D V0/d is
described by the exponent e˛d. This is valid only as long as the electrical field
of the space charges of electrons and ions can be neglected compared to the
external field E0. In his studies of the effect of space charge of an avalanche
on its own growth, Raether observed that when the charge concentration was
higher than 106 but lower than 108 the growth of an avalanche was weakened.
When the ion concentration exceeded 108 the avalanche current was
followed by a steep rise in current and breakdown of the gap followed. Both
the underexponential growth at the lower concentration and rapid growth in the
presence of the high concentration have been attributed to the modification of
the originally uniform field E0 by the space charge field. Figure 5.15 shows
diagramatically the electric field around an avalanche as it progresses along