Classification of spontaneous oscillations at the onset of avalanche breakdown inp-type germanium

Abstract

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...

Circuit-limited oscillations at the onset of impurity breakdown in ultrapure p-Ge with an S-shaped current-field characteristic

“…Thus, the dynamics of the system would be bulk-dominated [4]. This has been evidenced in typical experiments on p-Ge [6,7] and n-GaAs [6,[8][9][10] with doping concentrations $10 14 and $10 15 cm À3 , respectively. The observed pattern in this regime is the regular circuit-limited oscillation (CLO) except certain stochastic voltage spikes [11][12][13].…”

“…The observed pattern in this regime is the regular circuit-limited oscillation (CLO) except certain stochastic voltage spikes [11][12][13]. The CLO can be explained as a relaxation oscillation under the mechanism of switching between charging and discharging with the circuitry capacitance [7,14].…”

“…The observed pattern in this regime is the regular circuit-limited oscillation (CLO) except certain stochastic voltage spikes [11][12][13]. The CLO can be explained as a relaxation oscillation under the mechanism of switching between charging and discharging with the circuitry capacitance [7,14].So far, the SNDC has been well explained with the twolevel model, which is based on the mechanism of population inversion between the ground and a representative excited impurity level [2,15]. The bulk-dominated temporal behavior can be consistently modelled by the free carrier concentration, the bound carrier population at the ground level and the electric field.…”

First Evidence of Self-Organized Criticality in the Impact Ionization Breakdown of Semiconductors

“…In the following, we concentrate on the regime where the time periods between single spikes are long and show a broad distribution. Such a peak in the time trace of the current signal can be understood as a temporary breakdown of the resistance of the sample during the rise time of the spike (of less than 20 ps) [5]. Immediately after its occurrence, the breakdown is switched off again because, due to the increased current through the load resistor, the voltage drop across the sample is reduced.…”

“…An increase of the bias voltage leads to a larger time-averaged current, since the time intervals between the current spikes become shorter, ending up in a quasi-regular signal. For a detailed classification of the dynamical behavior of p-Ge, see [5]. In the following, we concentrate on the regime where the time periods between single spikes are long and show a broad distribution.…”