Nucleation Limited Switching Model Research Articles

Investigation of ferro-resistive switching mechanisms in TiN/Hf0.5Zr0.5O2/WOx/W ferroelectric tunnel junctions with the interface layer effect

This study presents an in-depth analysis of ferro-resistive switching (FRS) behaviors in a TiN/Hf0.5Zr0.5O2(HZO)/WOx/W ferroelectric tunnel junction (FTJ) device, with a particular focus on the role of the tungsten oxide (WOx) interface layer (IL). Structural examinations confirm the presence of the WOx IL, which significantly influences the FRS properties of the device. Electrical measurements indicate the devices exhibit stable and reproducible FRS characteristics with an ON/OFF ratio of 9.7, predominantly attributed to the tunneling electro-resistance (TER) effect driven by the ferroelectric polarization. Comprehensive numerical simulations, incorporating the nucleation-limited switching model and Simmons tunneling mechanism, provide detailed insights into how the WOx IL and the trapped charges at the HZO/WOx interface affect polarization switching mechanisms and the electronic potential barrier profile. These findings underscore the importance of interface effects in HfO2-based FTJs and advance the understanding of the TER mechanism in multilayer ferroelectric systems.

On the Existence of Negative Capacitance: Examining Ferroelectric-Dielectric Stack Experiments Using the NLS and LK Models

The Landau–Khalatnikov (LK) model of ferroelectric switching includes an inherent region of negative capacitance (NC) in its lossless charge versus voltage description and allows the possibility of stabilization of the ferroelectric in this region to achieve quasi-static NC (QSNC). On the other hand, the nucleation-limited switching (NLS) model, which is another model used to describe ferroelectric switching, precludes QSNC and offers an alternative explanation for the appearance of an NC region in recent voltage-pulse experiments performed on ferroelectric-dielectric (FE-DE) stacks. As such, we investigate such experiments that probe the existence of an NC region using both the LK and NLS models. While the LK model can reproduce all experimental results seen in prior literature, we find that the NLS model is incapable of properly reproducing results under a multitude of investigation metrics. Hence, we conclude that the use of the NLS model to exclude the existence of QSNC is problematic.

Nucleation-Limited Switching Dynamics Model for Efficient Ferroelectrics Circuit Simulation

The nucleation-limited switching (NLS) model has been shown in the literature to explain successfully the dynamics of polarization switching of polycrystalline ferroelectric films (FE) in various experiments. However, because of its mathematical complexity, the NLS model has yet to be implemented correctly and efficiently in the simulation of actual, experimental circuits with complex driving waveforms. Here, we reformulate NLS as a generalized polarization rate equation that captures correctly the incubation time of nucleation and the intra- and inter-grain switching statistics of kinetics without any restrictions on waveform and switching time scales. This formulation forms the basis for efficient numerical finite-difference computation, which is verified in realistic circuit simulations of a number of experiments.

Ferroelectric properties of ZrO2 films deposited on ITO-coated glass

In this work, the ferroelectric characteristics of ZrO2 thin films grown on ITO-coated glass have been investigated. The ferroelectric nature of the ZrO2 films has been studied by polarization-electric field (P-E) hysteresis loops and found to be optimum for the films processed by rapid thermal annealing at 600 °C. The increase in the annealing temperature improves the ferroelectric properties through the increase of the in-plane strain that causes the formation of the ferroelectric orthorhombic phase. The formation of the orthorhombic phase was confirmed through high-resolution transmission electron microscopy. The effect of the electric field on the polarization switching kinetics of ZrO2 films has been investigated revealing that the switching kinetics follows the nucleation limited switching (NLS) model. The activation fields estimated from the peak values of the polarization currents (im) and the time (tm) at which im occurs are in good agreement with the values obtained from the switching characteristic time of the NLS model. This work paves the way towards the integration of (pseudo)-binary oxide thin films on cheap substrates like glass for the next-generation of non-volatile memories.

Effect of annealing temperature on switching properties in Si-doped HfO2 films

The discovery of hafnium oxide-based ferroelectrics has resulted in the pursuit of ferroelectric field-effect transistors with higher scalability, lower power consumption, and enhanced switching speed. An in-depth understanding of ferroelectric polarization switching kinetics is essential for both scientific and technological purposes. Polarization switching is analyzed based on the nucleation-limited switching model with a Lorentzian distribution of logarithmic switching times. The activation field governing the switching kinetics is explained by a dependence on the density of oxygen vacancies, which are caused by various annealing temperatures. This indicates that oxygen vacancies can be a dominant factor in the polarization switching of Si-doped HfO2 films.

Comparative studies on ferroelectric switching kinetics of sputtered Hf0.5Zr0.5O2 thin films with variations in film thickness and crystallinity

Ferroelectric Hf0.5Zr0.5O2 (HZO) thin film capacitors with Pt/HZO/TiN structures were characterized to investigate the effects of oxygen partial pressure (PO2) and film thickness on the ferroelectric properties and switching dynamics of sputter-deposited HZO thin films. The PO2 during deposition and the film thickness varied from 0% to 1.5% and from 20 to 30 nm, respectively. The ferroelectric remnant polarization (2Pr) was 24.8 μC/cm2 for the 20-nm-thick HZO thin film deposited at a PO2 of 0% and decreased with increasing PO2 and film thickness due to variation in the amount of ferroelectric orthorhombic phase. The 2Pr of the 30-nm-thick HZO film deposited at a PO2 of 1% was 9.60 μC/cm2. The switching times and related parameters of the HZO films were estimated and analyzed by Kolmogorov–Avrami–Ishibashi and nucleation-limited switching (NLS) models. The NLS model provided better fitting results over the full range of polarization switching. The switching times could be modulated with variations in PO2 and film thickness from 0.46 to 1.58 μs. The activation field for polarization reversal increased with increasing PO2, and the degree of PO2 dependence was higher for a thinner film.

Ultrafast measurements of polarization switching dynamics on ferroelectric and anti-ferroelectric hafnium zirconium oxide.

The ultrafast measurements of polarization switching dynamics on ferroelectric (FE) and antiferroelectric (AFE) hafnium zirconium oxide (HZO) are studied. The transient current during the polarization switching process is probed directly on the nanosecond scale. The switching time is determined to be as fast as 10 ns to reach fully switched polarization with characteristic switching times of 5.4 ns for FE HZO and 4.5 ns for AFE HZO by the nucleation limited switching model. The limitation by the parasitic effect on capacitor charging is found to be critical in the correct and accurate measurements of intrinsic polarization switching speed of HZO.

Monte Carlo Simulation of Switching Dynamics in Polycrystalline Ferroelectric Capacitors

Ferroelectric (FE) materials are being studied for a variety of applications in memory, logic, and neuromorphic computing, for which predictive models of FE polarization are essential. In this paper, we present a Monte Carlo simulation framework capable of predicting the dynamic, history-dependent response of an FE under arbitrary input waveforms. The simulation is developed by generalizing the physics-based nucleation-limited switching model for polarization reversal in a polycrystalline FE. Measured polarization reversal data from fabricated FE Hf0.5Zr0.5O2 capacitors are used to extract the statistical distribution of FE grains. After parameter extraction, the model is able to predict the dynamics of the FE capacitor without further calibration. Finally, the model is applied to characterize the dynamic response of FE–dielectric bilayer structures and quantify the reduction in memory window due to device variability.

Ferroelectric Polarization-Switching Dynamics and Wake-Up Effect in Si-Doped HfO2.

The ferroelectricity in ultrathin HfO2 offers a viable alternative to ferroelectric memory. A reliable switching behavior is required for commercial applications; however, many intriguing features of this material have not been resolved. Herein, we report an increase in the remnant polarization after electric field cycling, known as the "wake-up" effect, in terms of the change in the polarization-switching dynamics of a Si-doped HfO2 thin film. Compared with a pristine specimen, the Si-doped HfO2 thin film exhibited a partial increase in polarization after a finite number of ferroelectric switching behaviors. The polarization-switching behavior was analyzed using the nucleation-limited switching model characterized by a Lorentzian distribution of logarithmic domain-switching times. The polarization switching was simulated using the Monte Carlo method with respect to the effect of defects. Comparing the experimental results with the simulations revealed that the wake-up effect in the HfO2 thin film is accompanied by the suppression of disorder.

Switching Dynamics of Ferroelectric Zr-Doped HfO2

Ferroelectric Zr-doped HfO2 (HZO) is a promising candidate for steep slope transistors and memory technology. For these applications, it is essential to understand and optimize the switching dynamics of the ferroelectric film. In this letter, we characterize the polarization reversal of an 8 nm-thick HZO film deposited by the atomic layer deposition with voltage pulses varying in amplitude (0.8–2 V) and duration (200 ns–7.6 ms). We show that the measurements are well described by a nucleation limited switching model, which enables extraction of the minimum switching time and the probability distribution of local electric field variations in the polycrystalline film. The close model fit spanning 5 orders of magnitude in pulse duration indicates the applicability of this model to HZO. This characterization framework can be used to quantify, compare, and optimize the switching dynamics of ferroelectric HZO.

Ferroelectric switching dynamics in 0.5Ba(Zr0.2Ti0.8)O3-0.5(Ba0.7Ca0.3)TiO3 thin films

In this work, the ferroelectric characteristics of 0.5Ba(Zr0.2Ti0.8)O3-0.5(Ba0.7Ca0.3)TiO3 (BCZT) thin films grown on 0.7 wt. % Nb-doped (001)-SrTiO3 (Nb:STO) single-crystal have been investigated. High-resolution transmission electron microscopy and electron energy loss spectroscopy revealed a very sharp Nb:STO/BCZT interface, while selected area electron diffraction revealed the epitaxial growth of the BCZT layer on the Nb:STO substrate. The ferroelectric nature of the BCZT films have been investigated by piezoresponse force microscopy and hysteresis loops. The effect of electric field on polarization switching kinetics has been investigated and has been analyzed by the nucleation limited switching model with a Lorentzian distribution function. The local field variation was found to decrease with the increase in the electric field, and thus, the switching process becomes faster. The peak value of the polarization current and the logarithmic characteristic switching time exhibited an exponential dependence on the inverse of electric field. This model gave an excellent agreement with the experimental polarization reversal transients throughout the whole time range.

Polarization switching in the PbMg1/3Nb2/3O3 relaxor ferroelectric: An atomistic effective Hamiltonian study

An atomistic effective Hamiltonian technique is employed to investigate the polarization switching mechanism of the (metastable but long-living) ferroelectric state of ${\mathrm{PbMg}}_{1/3}{\mathrm{Nb}}_{2/3}{\mathrm{O}}_{3}$ relaxor ferroelectric, resulting from the application of a dc electric field along the $[\overline{1}\overline{1}\overline{1}]$ direction---that is, opposite to the initial polarization. It is predicted that such switching is of inhomogeneous type. It involves the creation of intermediate short-range ordered, relaxor-like phases in between long-range ordered states inside which an infinite cluster exists and has dipoles near either the initial polarization direction (for shorter times) or the field's direction (for longer times). In contrast, dipoles belonging to finite clusters or being isolated can deviate away from [111] and $[\overline{1}\overline{1}\overline{1}]$, and, in fact, rotate in average from [111] to $[\overline{1}\overline{1}\overline{1}]$ when time increases. Such rotations govern the reversal of the polarization from [111] to $[\overline{1}\overline{1}\overline{1}]$ occurring within the intermediate relaxor-like states' region, while always resulting in the overall cancellation of any Cartesian component of the polarization that is perpendicular to [111]. These rotations occurring at the atomic scale also naturally imply that some fundamental assumptions of the original nucleation-limited-switching (NLS) model are not valid, despite the fact that we numerically further find that the whole temporal behavior of the macroscopic polarization can be well fitted by the general formula associated with NLS. In other words, we have stumbled into a novel switching or at least a switching that should be denoted as a generalized NLS model. Finally, three different electric-field regimes are predicted, with each of them having its own dependency of the switching time on the magnitude of the applied electric field and only one of them obeying the Merz's law. The existence of these three regimes is explained in terms of specific microscopic features.

Nucleation limited switching (NLS) model for HfO2-based metal-ferroelectric-metal (MFM) capacitors: Switching kinetics and retention characteristics

HfO2-based ferroelectrics (FE-HfO2) have shown promise as an emerging 1-T (single-transistor) non-volatile memory candidate because of its attractive features, such as CMOS compatibility, scalability, fast switching speed, low power, and long retention. The nucleation limited switching (NLS) model, which attributes the polarization switching mainly to the waiting time of nucleation of reversed domains, has been well developed to interpret experimental results for both ferroelectric switching and retention of metal-ferroelectric-metal (MFM) devices based on conventional perovskite ferroelectric materials [such as Pb(Zr, Ti)O3]. However, the applicability of this model to HfO2-based MFM capacitors is not well understood, although some recent experimental evidence has suggested so. In this study, we thoroughly investigated the switching kinetics and the retention characteristics of FE-HfO2 in the context of the NLS model. We show that (1) the NLS model agrees well with the experimental results of switching kinetics over 5 orders of pulse widths, and the extracted modeling parameters are also consistent with those predicted by the density-functional-theory analysis, indicating that the nucleation of reversed domain indeed dominates the switching speed and (2) the NLS model also agrees well with the experimental retention characteristics of HfO2-based MFM devices both at room temperature and at 85 °C.

Nanoscopic studies of domain structure dynamics in ferroelectric La:HfO2 capacitors

Visualization of domain structure evolution under an electrical bias has been carried out in ferroelectric La:HfO2 capacitors by a combination of Piezoresponse Force Microscopy (PFM) and pulse switching techniques to study the nanoscopic mechanism of polarization reversal and the wake-up process. It has been directly shown that the main mechanism behind the transformation of the polarization hysteretic behavior and an increase in the remanent polarization value upon the alternating current cycling is electrically induced domain de-pinning. PFM imaging and local spectroscopy revealed asymmetric switching in the La:HfO2 capacitors due to a significant imprint likely caused by the different boundary conditions at the top and bottom interfaces. Domain switching kinetics can be well-described by the nucleation limited switching model characterized by a broad distribution of the local switching times. It has been found that the domain velocity varies significantly throughout the switching process indicating strong interaction with structural defects.

Real-time observation of local strain effects on nonvolatile ferroelectric memory storage mechanisms.

We use in situ transmission electron microscopy to directly observe, at high temporal and spatial resolution, the interaction of ferroelectric domains and dislocation networks within BiFeO3 thin films. The experimental observations are compared with a phase field model constructed to simulate the dynamics of domains in the presence of dislocations and their resulting strain fields. We demonstrate that a global network of misfit dislocations at the film-substrate interface can act as nucleation sites and slow down domain propagation in the vicinity of the dislocations. Networks of individual threading dislocations emanating from the film-electrode interface play a more dramatic role in pinning domain motion. These dislocations may be responsible for the domain behavior in ferroelectric thin-film devices deviating from conventional Kolmogorov-Avrami-Ishibashi dynamics toward a Nucleation Limited Switching model.

Ferroelectric switching behavior of pulsed laser deposited Ba0.8Sr0.2TiO3 thin films

The effect of pulse amplitude on the ferroelectric and switching properties of pulsed laser deposited Ba0.8Sr0.2TiO3 thin films has been studied. The structural and morphological analysis revealed that the films had a well crystallized perovskite phase and grain size of about 30–40nm. A well saturated P–E hysteresis loop was observed with a remnant polarization (Pr)≈4.8μC/cm2 and a coercive field≈100kV/cm at a frequency of 1kHz. The Pr has been found to be decreased only 4.3% after passing 8.0×108 cycles. The analysis of switching response with nucleation limited switching model reveals that characteristic switching time (t0) variance is due to the random distribution of the local electric fields. The peak value of polarization current and t0 exhibits exponential dependence on reciprocal of pulse amplitude.

Analysis of ferroelectric polarization switching in (NH4)0.39K0.61NO3 films using nucleation limited switching model

The polarization switching transients of spray deposited ferroelectric (NH4)0.39K0.61NO3 (NKN) films has been analyzed with nucleation limited switching (NLS) model by considering domain growth limited process. The experimentally measured microscopic polarization switching curves fitted well with NLS model and the characteristic switching times obeyed the Lorentzian distribution function. The local field variation was found to be minimum at pulse amplitude 15 V, which makes the polarization reversal more probable. The value of spontaneous polarization, Ps and coercive field, Ec was found to be 6.58 μC/cm2 and 4.10 kV/cm, respectively. The value of Ps from the switching and P-E loop is in good agreement with each other. The field emission scanning electron microscopy and atomic force microscopy images of the NKN film reveal the formation of nanoparticles of NKN.

Polarization switching properties of spray deposited CsNO3: PVA composite films

The ferroelectric and switching properties of spray deposited cesium nitrate: poly (vinyl alcohol) composite films at different substrate temperatures (Ts) have been studied. The optimum value of remanent polarization was obtained in the film deposited at Ts=200°C, which may be due to larger structural distortion (c/a ratio) and less porosity as revealed by x-ray diffraction and field emission scanning electron microscope (FESEM) analysis. The switching current transients have been analyzed by nucleation limited switching model (NLS) with the Lorentzian distribution function. This model gives excellent agreement with the experimental polarization current throughout the whole time range. The switching parameters were determined in the composite films deposited at different Ts and found to be optimum at Ts=200°C. The effect of pulse amplitude on the domain switching properties has also been studied and analyzed. The peak value of polarization current exhibits an exponential dependence on the external applied field.

Polarization reversal behavior of spray deposited sodium nitrite:poly(vinyl alcohol) composite films

The time dependence of polarization reversal current of spray deposited sodium nitrite:poly(vinyl alcohol) composite films has been investigated. The switching current transients have been analyzed by considering domain growth limited process with the Lorentzian distribution function of characteristic domain growth times based on nucleation limited switching model. This model gives excellent agreement with the experimental polarization reversal transients throughout the whole time range. The switching parameters were determined in the composite films deposited at different substrate temperatures (Ts). The minimum value of the activation field at Ts=200 °C makes the polarization reversal more probable. The peak value of polarization current exhibits exponential dependence on the external applied field.

Microscopic aspects of the region-by-region polarization reversal kinetics of polycrystalline ferroelectric Pb(Zr,Ti)O3 films

The region-by-region polarization switching in ferroelectric Pb(Zr,Ti)O3 thin films sandwiched between Pt electrodes has been directly observed using piezoelectric scanning probe microscopy. A resolution improved by one order-of-magnitude compared to the standard piezoelectric response imaging technique for ferroelectric capacitors was achieved by reducing the top electrode thickness to 10–15nm through polishing. It was demonstrated that the individually switched regions correspond to single grains or clusters of grains where the grain boundaries act as frontiers limiting the propagation of the switched state. The study of the propagation of the reversed polarization state as a function of voltage applied shows a rather discontinuous growth of the switched areas, the movement of the domain walls being triggered abruptly by different threshold voltages. This result agrees with the earlier proposed nucleation-limited switching model. The observation of the frozen regions that do not switch even at higher voltages provides significant insight into the “bits-failure” problem in submicron ferroelectric capacitors used for nonvolatile memory applications.