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

Abstract

We have investigated the dynamical behavior of p-Ge at the very onset of impact ionization breakdown. The statistical temporal distribution of the recurrent breakdown events exhibits a power law behavior supporting the model of selforganized criticality introduced by Bak, Tang, and Wiesenfeld.Key words: Semiconductor breakdown, Self-organized criticality.Recently, Bak, Tang, and Wiesenfeld (BTW) [1] introduced the concept of "self-organized criticality" for the modelling of spatially extended, dissipatively coupled systems. Self-organized criticality means that there exists a broad parameter interval where the system behaves critically in the sense that its dynamical nonequilibrium state can be characterized by a power law behavior.Semiconductor systems driven into parameter regimes where their current-voltage characteristic becomes highly nonlinear often show very complex spatio-temporal behavior [2][3][4]. The impact ionization breakdown of p-Ge which has been investigated in this paper belongs to this class of systems. It appears that for the first time our experimental results demonstrate the validity of the model developed by BTW.Slightly doped semiconductors cooled to low temperatures are almost ideal insulators because most of the extrinsic carriers are frozen out at the impurity atoms. But, if an applied electrical field exceeds a critical value, the few remaining carriers can gain enough energy to release bound carriers by impact ionization. This autocatalytic process ends up in an avalanche breakdown of the resistivity of the sample. pie and the load resistor R L (100 kQ) was biased with a constant voltage F0, while the current was measured via the voltage drop across R L . At low bias voltage, the current is typically less than 10 nA. If a certain voltage is reached, short current pulses occur with a statistical temporal distribution. The height of these pulses reaches some hundred nA. The pulse duration is about 100 ps. 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. 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.For investigating the dynamics at the onset of impact ionization breakdown, we took power spectra of the current signal. Two spectra are shown in Fig. 1 for the values of the bias voltage V 0 , 349 mV and 370 mV, both in the range where the current exhibits randomly distributed spikes separated by time delays between 0.2 and 10 ms. In the frequen...