We present a detailed study on the oscillatory behavior of p-type germanium at the onset of avalanche breakdown at low temperatures. Measuring the frequency and amplitude of these oscillations as a function of different control parameters, such as average current, perpendicular magnetic field, and outer circuit conditions, we can clearly distinguish two different types of oscillations. For one, we found an oscillatory mechanism that depends on the outer electrical circuit. It describes the behavior in detail and also clarifies the connection between the dynamical behavior and the actual appearance of the current-voltage characteristic. Whereas this first type is the result of a global mechanism involving sample voltage and sample resistance, the second type results from a local oscillatory mechanism. Therefore, the more complicated dynamical structure can be understood as a result of the coupling between different localized oscillatory modes.
I. INTRQDUCTIQNIt is a well-known fact that a variety of electrical systems displays spontaneous formation of spatial and temporal structures as a consequence of transport instabilities connected to a region of negative differential (ND) resistance in their current-voltage (I V) characteris-tics.Commonly, these instabilities can be classified as either ¹haped or S-shaped ND resistive systems, and it is well understood that a microscopic ND resistivity induces inhomogeneous spatial structures, such as high-field domains (in the case of X shape) or high-current filaments (for the 5 shape). ' As a consequence, the form of the I Vcharacteristic observed on the macroscopic level not only depends on the underlying microscopic N or S, but is also the result of the different spatial mechanisms; for example, the gradual growth or shrinking of structures or the switching between different conducting states. Beyond that, one of the main objectives of the present paper is to show that the actual appearance of the I-V characteristic in some regions is a consequence of an underlying dynamical structure. So far, one can conclude from the observation of the macroscopic ND resistance behavior the existence of a corresponding microscopic ND resistivity (yet not in the inverse direction ), but not in its details. In the following, we concentrate on the case of S-shaped ND resistance, but we emphasize that some general features of our results might also be applicable to ¹haped ND resistive systems.The behavior of an S-shaped electrical system can be understood as a nonequilibrium phase transition of a low conducting state to a high conducting state. ' The resulting formation of current filaments has been observed recently in many experimental systems, such as bulk semiconductors, semiconductor devices, and gaseous plasma discharges, but most of these systems also display the formation of spontaneous oscillations in the same parameter regime.The occurrence of spontaneous oscillations in electrical circuits containing an element displaying S-shaped (current controlled) ND resistance has been a we...
