Frequency locking and the loss of spatial coherence for driven space-charge domains in ultrapure Ge

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Abstract
Spatially resolved measurements of the dynamics of sinusoidally driven space-charge domains in ultrapure Ge are presented for frequency-locked and driven chaotic oscillations. At liquid-He temperatures, moving space-charge domains form due to impact ionization of shallow acceptors, resulting in a spontaneous periodic current oscillation for dc voltage bias. With a superimposed sinusoidal ac voltage bias, these oscillations exhibit frequency locking and a quasiperiodic transition to chaos similar to those studied previously in the time domain by Gwinn and Westervelt. Spatial measurements using an array of capacitive probes show that frequency locking and the transition to chaos initially occur via modulation of the amplitude and motion of a single domain; thus the dynamics can be described by a low-dimensional model. For larger ac drives in the chaotic region above the critical line, spatial coherence is lost as domains form and disappear in the interior of the sample, and the electric field profile becomes spatially complex.