Identifiability and Active Subspace Analysis for a Polydomain Ferroelectric Phase Field Model

2017 ◽  
Author(s):  
Lider S. Leon ◽  
Ralph C. Smith ◽  
William S. Oates ◽  
Paul Miles
Keyword(s):  
Domain Wall ◽  
Phase Field ◽  
Density Functional ◽  
Information Matrix ◽  
Synthetic Data ◽  
Phase Field Model ◽  
Ferroelectric Materials ◽  
Identifiability Analysis ◽  
Subspace Selection ◽  
Active Subspace

We consider subset selection and active subspace techniques for parameters in a continuum phase-field polydomain model for ferroelectric materials. This analysis is necessary to mathematically determine the parameter subset or subspace critically affecting the response, prior to model calibration using either experimental or synthetic data constructed using density functional theory (DFT) simulations. For the 180° domain wall model, we employ identifiability analysis using a Fisher information matrix methodology, and subspace selection to determine the active subspace. We demonstrate the implementation and interpretation of techniques that accommodate the model structure and discuss results in the context of identifiable parameter subsets and active subspaces quantifying the strongest influence on the model output. Our results indicate that the governing domain wall gradient energy exchange parameter is most identifiable.

scholarly journals Effects of Interface Trap on Transient Negative Capacitance Effect: Phase Field Model

Electronics ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 2141
Author(s):  
Taegeon Kim ◽  
Changhwan Shin
Keyword(s):  
Phase Field ◽  
Field Effect ◽  
Field Effect Transistor ◽  
Field Model ◽  
Phase Field Model ◽  
Ferroelectric Materials ◽  
Interface Trap ◽  
Negative Capacitance ◽  
Effect Transistor ◽  
The Impact

Ferroelectric materials have received significant attention as next-generation materials for gates in transistors because of their negative differential capacitance. Emerging transistors, such as the negative capacitance field effect transistor (NCFET) and ferroelectric field-effect transistor (FeFET), are based on the use of ferroelectric materials. In this work, using a multidomain 3D phase field model (based on the time-dependent Ginzburg–Landau equation), we investigate the impact of the interface-trapped charge (Qit) on the transient negative capacitance in a ferroelectric capacitor (i.e., metal/Zr-HfO2/heavily doped Si) in series with a resistor. The simulation results show that the interface trap reinforces the effect of transient negative capacitance.

Active subspace analysis and uncertainty quantification for a polydomain ferroelectric phase-field model

2019 ◽  
Vol 30 (14) ◽  
pp. 2027-2051
Author(s):  
Lider S Leon ◽  
Paul R Miles ◽  
Ralph C Smith ◽  
William S Oates
Keyword(s):  
Domain Wall ◽  
Uncertainty Quantification ◽  
Phase Field ◽  
Density Functional ◽  
Uncertainty Propagation ◽  
Subset Selection ◽  
Structure Evolution ◽  
Wall Structure ◽  
Credible Intervals ◽  
Parameter Subset Selection

We perform parameter subset selection and uncertainty analysis for phase-field models that are applied to the ferroelectric material lead titanate. A motivating objective is to determine which parameters are influential in the sense that their uncertainties directly affect the uncertainty in the model response, and fix noninfluential parameters at nominal values for subsequent uncertainty propagation. We employ Bayesian inference to quantify the uncertainties of gradient exchange parameters governing 180° and 90° tetragonal phase domain wall energies. The uncertainties of influential parameters determined by parameter subset selection are then propagated through the models to obtain credible intervals when estimating energy densities quantifying polarization and strain across domain walls. The results illustrate various properties of Landau and electromechanical coupling parameters and their influence on domain wall interactions. We employ energy statistics, which quantify distances between statistical observations, to compare credible intervals constructed using a complete set of parameters against an influential subset of parameters. These intervals are obtained from the uncertainty propagation of the model input parameters on the domain wall energy densities. The investigation provides critical insight into the development of parameter subset selection, uncertainty quantification, and propagation methodologies for material modeling domain wall structure evolution, informed by density functional theory simulations.

Phase-Field Simulation of Domain Structure Evolution in Ferroelectric Thin Films

2000 ◽  
Vol 652 ◽  
Author(s):  
Y. L. Li ◽  
S. Y. Hu ◽  
Z. K. Liu ◽  
L. Q. Chen
Keyword(s):  
Thin Films ◽  
Phase Transition ◽  
Domain Wall ◽  
Domain Structure ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Ferroelectric Thin Films ◽  
Structure Evolution ◽  
Field Simulation

ABSTRACTA phase-field model for predicting the domain structure evolution in constrained ferroelectric thin films is developed. It employs an analytical elastic solution derived for a constrained film with arbitrary eigenstrain distributions. In particular, the model is applied to the domain structure evolution during a cubic→tetragonal proper ferro- electric phase transition. The effect of substrate constraint on the volume fractions of domain variants, domain-wall orientations, and domain shapes is studied. It is shown that the predicted results agree very well with existing experimental observations in ferroelectric thin films.

Phase Field Simulation of Ferroelectric Single Crystals

Aerospace ◽  
2005 ◽  
Author(s):  
T. Liu ◽  
C. S. Lynch
Keyword(s):  
Phase Field ◽  
Wall Motion ◽  
Field Model ◽  
Landau Equation ◽  
Phase Field Model ◽  
Domain Wall Motion ◽  
Ferroelectric Materials ◽  
Time Dependent ◽  
Ginzburg Landau ◽  
Domain Structures

Ferroelectric materials exhibit spontaneous polarization and domain structures below the Curie temperature. In this study a cubic to tetragonal phase transformation and the evolution of domain structures in ferroelectric crystals are simulated by using the time-dependent Ginzburg-Landau equation. The effects of electric boundary conditions on the formation of domain patterns and field induced polarization switching are discussed. The phase field model is used to simulate the formation of domain structures, domain wall motion and the macroscopic response of ferroelectric materials under external fields.

A non-isothermal phase-field model for piezo–ferroelectric materials

2018 ◽  
Vol 31 (3) ◽  
pp. 741-750 ◽  
Author(s):  
A. Borrelli ◽  
D. Grandi ◽  
M. Fabrizio ◽  
M. C. Patria
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Ferroelectric Materials

Uncertainty Analysis of Ferroelectric Polydomain Structures

2017 ◽  
Author(s):  
Paul Miles ◽  
William Oates ◽  
Lider Leon ◽  
Ralph Smith
Keyword(s):  
Phase Field ◽  
Intelligent Systems ◽  
Density Functional ◽  
Large Scale ◽  
Ferroelectric Materials ◽  
Constitutive Behavior ◽  
Structure Evolution ◽  
Model Parameters ◽  
Structure Property ◽  
Exchange Parameters

Ferroelectric materials exhibit strong electromechanical behavior which has led to the production of a wide variety of adaptive structures and intelligent systems, ranging from structural health monitoring sensors, energy harvesting circuits, and flow control actuators. Given the large number of applications, accurate prediction of ferroelectric materials constitutive behavior is critical. This presents many challenges, including the need to predict behavior from electronic structures up to macroscropic continuum. Many of the structure-property relations in these materials can be accurately calculated using density functional theory (DFT). However, DFT is not necessarily conducive to the large scale computations required to solve these problems on a continuum scale. Introducing a phase field polarization order parameter is an alternative approach, which provides a means to simulate the length scale gap between nano- and microscale domain structure evolution. The introduction of the phase field approximation results in uncertainty. Bayesian statistical analysis is an ideal tool for quantifying the uncertainty associated with the continuum phase field model parameters. Analyses of monodomain structures allows for identification of Landau energy and electrostrictive stress parameters. Identifying the exchange parameters, which are proportional to the polarization gradients, requires consideration of polydomain structures. This is a nontrivial problem as domain wall structures are fully coupled between the Landau energy, electrostrictive, and exchange parameters. Accurately quantifying the uncertainty in the phase field parameters will provide insight into the nonlinear constitutive behavior.

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