Small-signal analysis of spontaneous current instabilities in extrinsic semiconductors with trapping: Application to ultrapurep-type germanium

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Abstract
An analysis of the spontaneous current instability in dc-voltage-biased extrinsic semiconductors is given. We use a standard rate-equation model of electrical conduction in long one-dimensional extrinsic semiconductors that includes effects of field-dependent impurity-impact ionization. The unique steady state is constructed and its current-voltage diagram characterized. It is shown that a negative differential resistance is necessary for linear instability of the steady state both above and below the field corresponding to impurity breakdown. We characterize the minimal sample length for oscillatory instability above the threshold field for impurity breakdown. The interval of voltages where the steady state is linearly unstable is then shown to belong to the relatively flat part of the steady current-voltage diagram. We comment on how our results may be related to recent observations on ultrapure p-type germanium.