Multiple factors of regulation for transient negative capacitance in PbZr_(1-x)Ti_(x)O₃ ferroelectric thin films

The negative capacitance (NC) of ferroelectric (FE) materials can effectively break the 'Boltzmann tyranny' and drive the continuation scaling of Moore's law. In this work, to find a novel way for amplifying the transient NC, a series network of external resistors and PbZr(1-x)Ti(x)O3 (PZT) FE capacitors was constructed. Uniform modeling and simulation were performed using Kirchhoff's current law, electrostatics equations, and Landau-Khalatnikov equations. The derived results revealed that the mismatch of switching rate between free charge and polarization during FE domain switching is responsible for the transient NC generation. Some interesting results were obtained for the regulation of the transient NC by various factors such as the strain between the FE film and substrate, the viscosity coefficient, the ratio of Ti components, the external resistance magnitude, and the operating temperature. This work provides considerable insight into the control of FE transient NC, and offers guidance for obtaining larger and longer transient NC in the widely used PZT thin films.