Macroscopic and microscopic picture of negative capacitance operation in ferroelectric capacitors.

The negative capacitance (NC) operation of ferroelectric materials has been originally proposed based on a homogeneous Landau theory, leading to a simple NC stabilization condition expressed in terms of macroscopic quantities. A multi-domain theory, however, has pointed out the importance of microscopic parameters, such as the domain wall energy coupling constant, and it helped explain the somewhat contradicting experiments for ferroelectric capacitors with or without a metal interlayer. In this work we use comprehensive numerical simulations and simplified equations to correlate the macroscopic features of the NC operation to the underlying microscopic picture. We show that, while the domain wall coupling constant plays a critical role in a quasi static operation, the transient NC operation is less sensitive to this parameter. In particular, ferroelectric capacitors with a very small coupling constant can still display a robust transient NC behavior, closely tracking the 'S'-shaped polarization versus field curve and with negligible hysteresis. Our results have been developed in the framework of a systematic comparison between simulations and experiments, and they provide both a better understanding of the NC operation and a sound basis for the design of future NC based devices.