Analytical model of the electrical instability mechanism in multibarrier heterostructures with tunnel-opaque barriers

Through mathematical modeling of the conductivity of multibarrier heterostructures, the steady-state current-voltage characteristics, the $S$-shaped behavior of which is indicative of electrical instability, are obtained. To study its dynamic parameters, an analytical model of instability is developed using known approximations of the physics of semiconductor devices. In the steady-state case, the model yields an $S$-shaped current-voltage characteristic close to numerical simulation results. This fact is considered as confirmation of the adequacy of the developed analytical model. In the small-signal case, the latter is generalized to the situation with harmonic electrical perturbation. The resulting formula for the frequency dependence of the small-signal impedance indicates the possibility of dynamic-resistance negativity up to terahertz frequencies. A clear physical interpretation of the instability in terms of positive feedback in the unit cell of the multibarrier heterostructures under study is proposed. The results of measurements of the quasi-stead-state current-voltage characteristics of fabricated test multibarrier GaAs/AlGaAs structures with a pronounced portion of negative differential resistance are also presented.