In semiconductors, nonlinear generation and recombination processes of free carriers and nonlinear charge transport can give rise to non-equilibrium phase transitions. At low temperatures, the basic nonlinearity is due to the autocatalytic generation of free carriers by impact ionization of shallow impurities. The electric field accelerates free electrons, causing an abrupt increase in free carrier density at a critical electric field. In static electric fields, this nonlinearity is known to yield complex filamentary current patterns bound to electric contacts.