A possible minimum toy model with negative differential capacitance for self-sustained current oscillation

TL;DR

This paper introduces a minimal theoretical model for superlattices demonstrating that negative differential capacitance can induce self-sustained current oscillations, unifying phenomena of negative differential resistance and $I-V$ oscillations.

Contribution

The paper presents a simplified model incorporating negative differential capacitance, revealing conditions for stable steady states and oscillations in superlattice systems.

Findings

Positive differential capacitance yields stable steady states.

Negative differential capacitance leads to self-sustained oscillations.

The model unifies negative differential resistance and $I-V$ oscillation phenomena.

Abstract

We generalize a simple model for superlattices to include the effect of differential capacitance. It is shown that the model always has a stable steady-state solution (SSS) if all differential capacitances are positive. On the other hand, when negative differential capacitance is included, the model can have no stable SSS and be in a self-sustained current oscillation behavior. Therefore, we find a possible minimum toy model with both negative differential resistance and negative differential capacitance which can include the phenomena of both self-sustained current oscillation and $I-V$ oscillation of stable SSSs.