Oscillations and Chaotic Current Fluctuations in n-GaAs

Chaotic current fuctuations have been observed in the negative differential conductivity region of n-GaAs at 4.2 K under static external conditions. Power spectra, Poincar6 sections and the fractal dimension of the attractor were determined as functions of the applied voltage for various magnetic-field strengths B. For B = 0 only limit cycles were observed. For B > 0 our results indicate successive Hopf bifurcations and a Ruelle-Takens-Newhouse transition to chaos and point to a crucial role of the magnetic field. In high-purity semiconductors at low temperatures breakdown in the current-voltage characteristics occurs due t o impact ionization of shallow impurities yielding a rapid increase of the current at a critical voltage [l, 21. There is a nonequilibrium transition from a weakly conducting to a strongly conducting steady state, whose critical behaviour was investigated experimentally in n-GaAs by methods of far-infra-red photoconductivity E31 and described in terms of nonlinear carrier generation-recombination kinetics [4]. Associated with the impurity breakdown, spontaneous oscillations and chaotic current fluctuations have recently been discovered in several semiconductors [5-91. Upon varying the bias voltage across the samples the onset of chaotic behaviour was found either just below the threshold of the instability [ 5 , 6 ] or in the post-breakdown regime [71. It was shown that a periodic driving current in the presence of impact ionization can give rise to chaotic fluctuations[lO]. The physical mechanisms underlying spontaneous chaotic fluctuations in the absence of a periodic driving, however, are not well understood. In n-GaAs AOKI et al. [5] have obtained evidence that weak optical interband excitations are responsible for chaotic current fluctuations in the pre-breakdown regime. In view of the present uncertainty about physical origins, we have attempted to characterize the chaotic transition as far as possible from a detailed analysis of the time dependence of the chaotic signals using methods of nonlinear dynamics. We have investigated current fluctuations in high-purity n-GaAs epitaxial layers subject to a (*) Heisenberg fellow. 402 EUROPHYSICS LETTERS magnetic field a t liquid-helium temperature without any other external stimulations. The power spectra and the Poincare sections were derived as functions of the external voltage and the fractal dimension of the strange attractor was determined. Chaotic fluctuations were observed only for finite magnetic fields in the post-breakdown regime, whereas a t zero magnetic field solely relaxation oscillations were found. In contrast to the case studied by AOKI et al. in the pre-breakdown regime, our observation is independent of optical interband excitations. With increasing voltage the fractal dimension rises stepwise from 0 to 1.1 and to 2.0 indicating successive Hopf bifurcations. The formation of a torus and the existence of two incommensurate frequencies are also reflected in the Poincare surface of section and the power spectrum. At the transition to chaos the fractal dimension rises to 2.7. We thus conclude that the mechanism of the transition follows the Ruelle-Takens-Newhouse scenario. The measurements presented here were carried out on a high-purity n-GaAs epitaxial layer of 14.2 pm thickness grown by liquid-phase epitaxy on a Cr-compensated substrate. The carrier concentration and the electron mobility were n = 6.5. 1013 em-' and ,U = 1.4 lo5 vs. em-' at 77 K whii ?I corresponds to a donor concentration of N D = 2.7. 1014 emp3 at 70% compensation. Ohmic contacts were formed by alloying Au-Sn strips on the sample surface separated by 1.5 mm. The samples were immersed in liquid helium and shielded against visible and infra-red radiation. Using a superconducting solenoid a magnetic field B was applied perpendicular to the sample surface and parallel to the [loo] crystallographic direction. The sample was biased in series with a load resistor. Under these conditions the current-voltage characteristic showed a 5'-type behaviour a t B = 0 and in the whole range of the applied magnetic-field strength. The breakdown voltage of the sample increased from 0.5 V at B = 0 T to 0.9 V at B = 1 T. Time series of the voltage across the sample were digitally recorded with sampling intervals At ranging from 25 to 500 ns. We have analysed the recorded signals to determine power spectra, phase portraits, Poincare sections and the fractal dimension of the current fluctuations as functions of the voltage across the sample and a load resistor. The bias voltage of the sample itself could not be taken as a control parameter because of the strong fluctuations in the chaotic regime. The power spectra were obtained using the segment averaging method. For each spectrum 20 segments obtained from 10 independent time series were averaged. Without an external magnetic field regular oscillations are found, which set in just a t the breakdown voltage. Their frequency increases with rising voltage and decreases with increasing magnitude of the load resistor as is expected for RC-relaxation oscillations. These oscillations remain coherent up to voltages well above breakdown. No other spectral features could be observed. In the presence of an external magnetic field exceeding about O.lT, the spectral characteristics of the fluctuation change drastically. Again current oscillations occur a t breakdown. With increasing voltage, however, additional characteristic frequencies appear and finally the fluctuations become totally aperiodic. The experimental results for the power spectra are summarized in fig. 1 for B = 0.83 T. The fundamental frequency of the oscillation is fl = 91 kHz just above breakdown occurring a t 3 V for the applied load resistor. In contrast to the case of B = 0, fi slightly decreases upon raising the voltage. Above about 5 V a lower-lying oscillation of frequency fi = 5 kHz appears, which is also observed in side bands of thefl fundamental and its harmonics (fig. lb)). On further increase of the voltage an independent third oscillation of frequency f3 = 41 kHz occurs, which, within a very small voltage interval, merges with broad band noise of aperiodic chaotic fluctuations due to a drastic increase of the noise background. We have verified that the third frequency in fig. le) cannot be expressed as f3 = nfl + mfi for Inl, lml< 5. Above 6 V the noise background decreases again, the fl oscillation is still present, A. BRANDL et al.: OSCILLATIONS AND CHAOTIC CURRENT FLUCTUATIONS IN n-GaAs 403