We present a general analysis of instabilities and oscillations of the sequential tunneling current in superlattices, based on the current-voltage characteristic of a single barrier. Our results depend only on the presence of a negative differential resistance region and are independent of the details of the model. We establish general conditions for the existence of a stable oscillatory region of current-voltage characteristic of the superlattice, and for instability leading to current self-oscillation. Our formalism permits a natural connection to standard results of chaos theory. ͓S0163-1829͑99͒50520-1͔Following the original suggestion of Esaki and co-workers, 1,2 there has been a great deal of experimental 3 and theoretical 4 work on resonant tunneling in double barrier quantum well structures and superlattices. Under the right conditions, such structures have current-voltage characteristics with regions of negative differential resistance ͑NDR͒, leading to a range of important possible applications. Many interesting phenomena related to the NDR have been found in superlattices ͑SL͒, ranging from current-voltage oscillations on the sequential resonance tunneling plateau, 5-10 current self-oscillations, 11-13 and chaos. 14 Self-oscillation has been observed in both doped and undoped SL systems.
10-12The oscillation can be induced by continuous illumination of a laser light 13 or by change of doping. 11 Recently, it has been shown that this self-oscillation can also be induced by applying an external magnetic field parallel to the SL layers.
15On the theoretical side, it is understood that the I-V oscillation is related to the formation of stationary electric-field domains 16 while the current self-oscillation is attributed to the motion of a domain boundary. 17 Different theoretical methods include the continuum model approach, 16 and the approach based on the rate equation for charge-carrier densities in quantum wells.17 By introducing a phenomenological carrier drift velocity curve, the second approach is capable of modeling both the formation of stationary electricfield domain and current self-oscillations. There are also microscopic Green's function calculations.18 While the microscopic approach would be accurate if all the microscopic parameters and mechanisms were known, it remains a challenge to deduce the rules of macroscopic behavior from the microscopic details. In this paper, we present a general analysis of instabilities and oscillations due to the existence of NDR in superlattices, under very general conditions. We make no assumption about the origin of the NDR, and we dispense with the concept of drift velocity, which is not well defined in a tunneling situation. We take the single well I-V characteristic, containing NDR regions, as given rather than starting from a first-principles microscopic model. This NDR may be due to any microscopic mechanism, such as offresonance tunneling, 19 or the Gunn effect. 20 Our goal is to study the consequences of this NDR in a superlattice. We will show that st...