0741-3106 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LED.2018.2845946, IEEE Electron Device Letters Abstract - Damping constant FE 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 FE of a specific ferroelectric material, in this letter, we propose a method to extract FE 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(Zr0.4Ti0.6)O3 (PZT) and P(VDF-TrFE) and find that FE reduces during polarization switching as compared with pre-switching. In addition, PZT exhibits a weaker damping effect than P(VDF-TrFE). Finally, the FE values of various ferroelectrics are compared. A wide range of FE values is observed, even for the same material. This indicates that FE is likely to vary with ferroelectric materials and their dimensions. Index Terms - negative capacitance, field-effect transistor, ferroelectric, damping constant, Landau model, Miller model. I. INTRODUCTION HE superior sub-60 mV/decade subthreshold swing (SS) achieved by a negative capacitance ferroelectric field- effect-transistor (NC-FET) has attracted extensive investigation for its potential low-power circuit applications [1- 6]. Most of the previous experimental results confirmed its abrupt switching characteristics [2, 3] or NC effect [7-9] at low frequency below 1 MHz. However, due to the lack of corresponding results and the large ferroelectric switching time measured, it remains a question whether these features can still be achieved at high frequencies in the order of gigahertz. Based on the Landau-Khalatnikov (LK) equation, it has been clearly shown that damping constant FE is the dominant factor that determines the maximum operating frequency and minimum power consumption of an NC-FET [10, 11]. The circuit configuration consisting of a series connection between an external resistor and a ferroelectric film is adopted to estimate its value [12-15]. FE is roughly considered as a constant when fitting the transient response of the voltage drop across the ferroelectric using the LK equation. However, such a simple assumption cannot provide an insight into the physics of FE or guide further improvement in NC-FET performance at high frequencies. Therefore, it is important to establish a method that is able to provide an accurate extraction of FE from dynamic measurement results of ferroelectric films and NC-FETs. In this work, we propose a method to extract the polarization dependent FE based on dynamic measurement of the ferroelectric. This method is applied to Pb(Zr0.4Ti0.6)O3 (PZT 40/60) [16] and P(VDF-TrFE) [17]. The results confirm that FE is a function of polarization, not a constant as previously assumed. Finally, these results are compared with the previous ones reported for various ferroelectrics. II. METHOD There are two models to describe the static polarization density-electric field (P-EFE,S) characteristics of ferroelectric, namely Landau model [1] and Miller model [18]. Landau model is often used in NC-FET analysis and is able to explain the origin of NC [19]. The Landau parameter  is smaller than zero so that the P-EFE,S curve is S-shaped and the capacitance of the ferroelectric is negative at P of 0 C/cm 2 [Eq. (1)]. 3 5 , 2 4 6 FE S E P P P       . (1) On the other hand, the Miller model utilizes the tanh function to empirically resemble the hysteretic P-EFE,S relationship of a ferroelectric single film [Eq. (2)]. , tanh ( ) S FE S C P P wE E       , (2) where the coefficient w is 1 ln 2 S R C S R P P w E P P          . (3) Here, PS is the saturation polarization density, PR is the remnant polarization and EC is the static coercive field. Since tanh function is monotonically increasing, the capacitance of the ferroelectric is always positive. Although Landau and Miller models are used to describe negative and positive capacitance, respectively, they share a common feature: EFE,S is a function of P. For dynamic evaluation, the damping constant FE is often used to describe the time-dependent polarization switching. It is derived from the Lagrange equation of ferroelectric energy GFE, describing the relationship between the field (= -dGFE/dP) and the regression speed (= dP/dt, where t is time) of a given polarization fluctuation towards equilibrium [Eq. (4)] [20, 21]. FE can be represented as a polarization-dependent parameter. T Extraction of Polarization Dependent Damping Constant for Dynamic Evaluation of Ferroelectric Films and Devices Yang Li, Kaizhen Han, Yuye Kang, Eugene Yu Jin Kong, and Xiao Gong, Member, IEEE. The authors are with the Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, 117583 Singapore (e-mail: elegong@nus.edu.sg).