Ferroelectric System Dynamics and the Properties of Ferroelectric / Two-Dimensional Electron Gas Heterostructures: a Ginzburg–Landau Study
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Abstract
Understanding the electronic response of materials to applied electric fields is an outstanding goal in solid-state theory. One aspect of this goal is to accurately predict the electric polarization of certain materials and how that polarization changes the electronic structure of adjacent solids. This is motivated by applications that include next-generation field-effect transistors and other switching devices. Knowledge of the response of such devices to applied fields that extend into GHz frequencies is of particular interest so that systems can be designed to provide desired responses to such fields. By using a second-order time-dependent Ginzburg–Landau model, we simulate the dynamic polarization hysteresis behavior of a ferroelectric system subjected to a sinusoidal electric field. We examine polarization hysteresis loop structure as a function of both field amplitude and field frequency. The relationship between the latter and hysteresis loop area, i.e., hysteresis dispersion, is calculated. Previous work established that the model under consideration produces experimentally expected hysteresis dispersion in the low-frequency regime. We depart from this previous work and demonstrate that: (i) this model also produces experimentally expected hysteresis dispersion in the high-frequency regime; (ii) this dispersion implies, in agreement with experimental observations, that system relaxation is characterized by an effective characteristic time which is inversely proportional to field amplitude when the latter is sufficiently high; and (iii) the considered model predicts a symmetry-breaking transition that depends on both field frequency and field amplitude. The relationship between these field parameters and hysteresis loop structure is then further quantified by considering the Fourier transform spectra of the time series of polarization. These spectra are used to determine deforming factors that measure the frequency- and amplitude-dependent distortions of hysteresis loop structures from ellipticity. The results of this harmonic analysis agree with experimental observations, thus further validating the model. Having validated the considered model, we then employ a version of it in conjunction with: (i) a method for capturing variations in the polarization near surfaces of a ferroelectric that uses the so-called extrapolation length which was proposed by Kretschmer and Binder [Phys. Rev. B 20, 1065 (1979)]; and (ii) a treatment of graphene that was recently implemented by Kurchak et al. [Phys. Rev. Appl. 8, 024027 (2017)]. This provides a composite model that we use to predict the charge carrier densities induced in graphene layers coupled to an adjacent ferroelectric slab of LiNbO3. By comparing our results to those from density functional theory calculations that were performed by Baeumer et al. [Nat. Commun. 6, 6136 (2015)], we: (i) determine an estimate for the extrapolation length which can be used for future investigation of systems consisting of graphene deposited on LiNbO₃; and (ii) establish that the composite model may accurately predict graphene charge carrier density which results from an adjacent ferroelectric. A discussion pertaining to how our work contributes to the rational design of a system that provides passive tunable transmission of radio-frequency electromagnetic fields is provided. Moreover, we elaborate on how this work can be expanded in further pursuit of this functionality.
Table of Contents
Introduction -- Ferroelectrics, Related materials, and Landau Theory -- Graphene -- Applied Motivation -- Ferroelectric System Dynamics simulated by a second-order Landau Model -- Graphene charge carrier density induced from a ferroelectric -- Summary of results
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Ph.D. (Doctor of Philosophy)