Nonequilibrium Phase Transitions of Impact Ionization Breakdown in Extrinsic Semiconductors

A complex system may consist of many subsystems. The dimension of the equations used to model such a system may be enormously large. It is well kown that a nonequilibrium complex system may undergo a variety of bifurcations and exhibit diverse types of self-organization behavior. It was found, however, that in the vicinity of a bifurcation point the enormous number of subsystems is governed by a few coherent variables which force the subsystems to join a collective motion. Those coherent variables are often called order parameters. The dimension of the order parameters is much smaller than that of the initial complex system. The underlying slaving principle elucidates how, after the competition of various modes, a few coherent order parameters arise beyond the bifurcations to complex spaceand time-dependent configurations and how the many subsystems, or say variables, are controlled (or, enslaved) by them. Such ubiquitous processes of spontaneous self-organization can in general be formulated as nonequilibrium orderdisorder phase transitions [1]. In this presentation, we discuss the application of the universal approach outlined above to nonlinear transport phenomena in semiconductors providing a prototype situation with dynamical behavior ranging from orderly to chaotic [2]. In particular, recent experiments on impurity impact ionization avalanche breakdown in extrinsic germanium and gallium arsenide at