Bonilla, LL; Teitsworth, SW, *Theory of periodic and solitary space charge waves in extrinsic semiconductors*,
Physica D: Nonlinear Phenomena, vol. 50 no. 3
(1991),
pp. 545-559 .
**Abstract:**

*We present a theory of the existence and stability of traveling periodic and solitary space charge wave solutions to a standard rate equation model of electrical conduction in extrinsic semiconductors which includes effects of field-dependent impurity impact ionization. A nondimensional set of equations is presented in which the small parameter β = (dielectric relaxation time) / (characteristic impurity time) ≫ 1 plays a crucial role for our singular perturbation analysis. For a narrow range of wave velocities a phase plane analysis gives a set of limit cycle orbits corresponding to periodic traveling waves. while for a unique value of wave velocity we find a homoclinic orbit corresponding to a moving solitary space charge wave of the type experimentally observed in p-type germanium. A linear stability analysis reveals all waves to be unstable under current bias on the infinite one-dimensional line. Finally, we conjecture that solitary waves may be stable in samples of finite length under voltage bias. © 1991.*