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