Extraction of Polarization-Dependent Damping Constant for Dynamic Evaluation of Ferroelectric Films and Devices

Abstract

Damping constant ξ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FE</sub> is the key parameter that determines the maximum operating speed of the negative capacitance ferroelectric field-effect transistor (NC-FET). While most studies assume a constant ξ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FE</sub> of a specific ferroelectric material, in this letter, we propose a method to extract ξ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FE</sub> value which is dependent on its polarization. This method applies to both Miller model (positive capacitance) and Landau model (negative capacitance). It enables further analysis on dynamic characteristics of a ferroelectric film and therefore NC-FET. We apply this method to Pb(Zr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.4</sub> Ti <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.6</sub> )O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> (PZT) and P(VDF-TrFE) and find that ξ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FE</sub> reduces during polarization switching as compared with pre-switching. In addition, PZT exhibits a weaker damping effect than P(VDF-TrFE). Finally, the ξ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FE</sub> values of various ferroelectrics are compared. A wide range of ξ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FE</sub> values is observed, even for the same material. This indicates that ξ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FE</sub> is likely to vary with ferroelectric materials and their dimensions.