Enhanced negative capacitance in La-doped Pb(Zr$_{0.4}$Ti$_{0.6}$)O$_3$ ferroelectric capacitor from tuning of bias voltage pulse
We report a remarkable bias voltage dependent specific negative capacitance in multidomain La-doped Pb(Zr$_{0.4}$Ti$_{0.6}$)O$_3$ (PLZT) ferroelectric capacitors. The specific negative capacitance maximizes at a specific bias voltage because of emergence of maximum domain-wall density during ``switching" of the domains. Domain configuration changes from such an ``optimum" state if higher or lower bias voltage is applied at a much faster or slower rate. Phase-field simulation using time-dependent Ginzburg-Landau equation corroborates the experimental results and shows dependence of the domain-wall length during switching on the bias voltage amplitude and its maximization at a specific bias voltage amplitude. Interestingly, the radius of curvature of the resulting polarization ($P$) versus voltage ($V$) hysteresis loop at the coercive voltage ($V_C$), as well, turns out to be depending on the bias voltage. All these results indicate a close correlation among the bias voltage pulse profile (amplitude and time scale), domain-wall length during switching, shape of the resulting ferroelectric hysteresis loop, and the transient negative capacitance. It may have important ramifications both in the context of physics behind negative capacitance in a multidomain ferroelectric capacitor and devices being developed by exploiting its advantages.