The Nonlinear Dynamics Of Semiconductor Heterostructures Under External Fields

The carrier transport in semiconductors has a considerable attention with the development of semiconductor devices. Based on the real-space electron transfer model and the discrete drift model, we investigate theoretically the nonlinear dynamics of the semiconductor heterostructures under external fields. Main results are summarized as follows:(1) In the case for homogeneous GaAs/AlGaAs heterostructure, the static current-voltage characteristic curve exhibits an inverted S-shaped negative differential conductivity (NDC). Thus, the system shows complex dynamic behaviors under the magnetic field and the microwave irradiation. (i)As the dc bias is set within the NDC region, the current self-sustained oscillations can be found when a relatively small magnetic field is applied. Then, the hysteresis in the dynamic current-voltage curves can be found and two stable attractors coexist in the system. With further increasing the magnetic field, the stability of the system will be changed and the selfe-sustained oscillations disappear. However, the hysteresis phenomenon is more clearly and the width of the hysteresis is broader, (ii) Considering the action of the microwave irradiation and the magnetic fields, the system shows different oscillation modes like period,quasiperiodicity and frequency-locking due to the coupling between the internal and the external signal. The routes from period-doubling to chaos can be found with changes of the irradiation amplitude which is agreement with the experiment. Under a large magnetic field, the system will be transferred between two time-independent steady states; and the sustem longitudinal resistance shows an interesting oscillation with period tuned by the ratio of microwave radiation frequency. This provides a help to understand the "zero-resistance" experiment, (iii) The time-delayed feedback method is applied to control the chaotic dynamics in the system. The bifurcation about the dynamics with the control parameters is given. The results show that the system will be changed between different states with varying delayed time and feedback strength. As for the delayed time is equal to the period of the unstable period orbit embedded in the chaotic attractors, this orbit is stabilized and the feedback signal is close to zero.(2) In the case for inhomogeneous GaAs/AlGaAs heterostructure, the properties of the dynamics can be described by a set of partial differential equations. For pure dc bias at a fixed magnetic field, the self-sustained oscillations are observed due to the travelling high electric field domain in the system. Varying the magnetic field, the width of the domain and the oscillational amplitude will be changed. Driven by an periodic signal, the system shows similar results with the homogeneous GaAs/AlGaAs heterostructure except that the routes from intermittent to chaos.(3) In the case for weakly coupled GaAs/AlAs superlattices, the main electron vertical transport mechanism is sequential resonant tunneling. The drift velocity as a function of the applied electric field can result in the NDC and a monopole domain formed by charge accumulation layer appears in superlattices. Under the appropriate doping densities and applied dc voltages, the current oscillations occur due to the motion of the charge domain over a few periods of the SL. The magnetic field B seems to be favorite for the formation of the static electric field domains and to depress the current oscillation. Thus, the oscillation regime will be narrowed as the magnetic field strength increases. For different doping densities, the distribution of the electric field in superlattices is different. Driven by a periodic signal, the system shows interesting nonlinear behaviors like quasiperiodicity, frequency-locking, and period.