Sequence of Different Types of Nonlinear Current Oscillation in n-GaAs

Self-generated chaotic current fluctuations in the post-breakdown regime of a n-GaAs layer at 4.2 K have been analyzed in detail. Without an external magnetic field only regular oscillations were observed. Increasing the magnetic field strength up to 100mT generates a sequence of quasiperiodic and frequency-locking current oscillations and finally a Ruelle-Takens-Newhouse scenario with chaos. This may be understood by assuming two coupled oscillatory processes caused by dielectric relaxation and energy relaxation in the distribution of free carriers. PACS: 05.40., 72.70., 72.20J High-purity semiconductors at low temperature show highly nonlinear current-voltage characteristics. For small electric fields almost all carriers are bound to shallow impurities yielding a low conductance of the sample. At a critical field of a few volts per cm the impact ionization rate of shallow impurities exceeds the capture rate for low carrier concentration resulting in a rapid increase of the current. The steady-state properties of the transition from the low-conducting state to the high-conducting state have been analyzed in terms of nonequilibrium phase transformations 1-14]. In the course of the transition, spontaneous oscillations and chaotic current fluctuations have been observed in several semiconductor materials 1,5-17]. Different types of, and routes to, chaos were recognized and discussed in terms of nonlinear dynamics [18-28]. Current fluctuations in semiconductors may occur spontaneously I-5-13] or be induced by an external periodic driving force 1-13-17]. In the present paper we report on a detailed study of self-generated current fluctuations in high purity n-GaAs epitaxial layers which occur within a limited bias voltage interval in the post-breakdown regime of the material. The observed phenomena depend critically on the strength of an external magnetic field. At zero field, B = 0, only regular oscillations were found. Increasing B up to not more than 100mT causes a sequence of quasiperiodic and frequency-locking current phenomena, finally undergoing a Ruelle-TakensNewhouse scenario to chaos. This behavior may be attributed to the coupling of two oscillatory processes, in the present case dielectric relaxation and an oscillation of the nonequilibrium electron distribution. The experimental results are in excellent agreement with the predictions of the circle-map theory. The coupling strength, frequencies and amplitudes of both selfsustained processes depend strongly on the magnetic field strength. 1. Experimental Setup The measurements were carried out on a n-GaAs epitaxial layer grown by liquid phase epitaxy on a Crcompensated substrate. Ohmic point contacts were formed 2 mm apart from each other on the 16 ~tm thick layer. The material characteristics of the sample are: carrier concentration n = 1.3 x 1014 cm3, electron mobility #=8.9 x 104cm2/Vs at 77K corresponding 9 to a donor concentration No = 5.7 x 1014 cm-3 and a compensation ratio of 77%. The sample was immersed in liquid helium and was shielded against ambient and thermal radiation. Using a superconducting solenoid a magnetic field B was applied perpendicular to the sample surface and the current through the layer. The bias voltage was applied with a load resistor of 200 kf~, and, as a probe of the current, the voltage across the sample was measured. 144 J. SpanNer et al. 2. Current-Voltage Characterist ics In order to localize regions in the current-voltage plane where fluctuations of a certain type occur, the currentvoltage characteristic for various magnetic field strengths were recorded. Current-voltage (I-V) characteristics are usually measured by averaging the fluctuations. This yields the well-known nonlinear I-V relations showing negative differential resistance, sharp kinks and hysteresis. These structures in the I-V characteristic depend on the amplitude of the fluctuations as well as on the shape of the oscillations as a function of time, which may be strongly affected by the external circuitry. To get rid of these artefacts we present a new method to visualize current-voltage characteristics with oscillatory regions. The sample was biased in series with a sufficiently large load resistor to have constant current conditions, and the voltage fluctuations across the sample were measured by applying broad-band electronics. In the currentvoltage plane the extrema of the voltage oscillations and the average voltage as a function of the current were recorded. The results are displayed in Fig. la where hatched regions show the extent of the fluctuation amplitudes. In these areas of the I-V plane virtually no definite relation between current and voltage exists. The oscillatory regimes of the I-V plane are different for increasing and decreasing current which is indicated by right and left inclined hatching in Fig. l a. The measurements show that in the area of the I-V plane where oscillations occur, two different regimes may be distinguished, that with large voltage amplitudes and that with small amplitudes. Increasing the magnetic field strength the large amplitude region shrinks on the current scale and new types of oscillation with small amplitudes appear for high currents. The large amplitudes decrease slightly and the small amplitudes increase drastically with rising magnetic field strength. For higher magnetic fields (not shown in Fig. 1) the large amplitude region totally vanishes. The results of the present investigation were obtained for currents at the top of and above the large voltage amplitude area inside the small amplitude region. Averaging the fluctuations yields typical currentvoltage characteristics with the well-known hysteresis effects as shown in Fig. lb. Comparison between the two kinds of recording proves that current-voltage hysteresis is not a steadystate property of the sample; rather, it is due simply to a change in the character of the fluctuations. 3. Spontaneous Osci l lat ions To analyze the spontaneous oscillations, time series of the voltage across the sample were digitally recorded with sampling intervals A t ranging from 50 to 5000 ns. The recorded signals were used to calculate power spectra, phase portraits, Poincar6 sections and the fractal dimension d of the fluctuations as functions of the voltage applied to the sample and the load resistor in series. Because of the strong fluctuations in the oscillatory regime, the bias voltage of the sample itself could not be taken as a control parameter. The power spectra were obtained by averaging 20 independent spectra of different time series consisting of 2048 sampling points. At B = 0, regular oscillations were found, which set in just above the breakdown voltage and remain