Ferroelectric Capacitor Model Research Articles

SPICE compatible semi-empirical compact model for ferroelectric hysteresis

This paper reports a semi-empirical, SPICE compatible and computationally efficient compact model for ferroelectric capacitors (Fe-CAP) description. This compact model is inspired by the Jiles–Atherton model of ferromagnets, which features significantly smaller computational effort than other state-of-the-art models. It successfully computes the evolution of the memory window and hysteresis of ferroelectric capacitors for any arbitrary signal. We have successfully calibrated this model with the experimentally characterized polarization switching dynamics of fabricated 10 nm silicon-doped hafnium oxide based Fe-CAP.

Dielectric, ferroelectric, impedance and photocatalytic water splitting study of Y3+ modified SrBi2Ta2O9 ferroelectrics

Sr1-xY2x/3Bi2Ta2O9 bismuth-layered compounds with composition x = 0, 0.05, 0.075 and 0.1 are synthesized by the modified conventional solid-state route. The smaller ionic radii of Y3+ in SrBi2Ta2O9 decreases the lattice parameters and increases the orthorhombic distortion (b/a) confirms the lattice mismatch in the perovskite structures by X-ray diffraction. Micro - Raman spectroscopy is used to identify the various modes of metal-oxide bonds in the system. A decrease in Raman intensity and increase in full width at half-maximum of the Ta–O stretching mode at 800 cm−1 may be due to a decrease in orthorhombic distortion of the unit cells. Temperature dependence dielectric study shows the ferroelectric to paraelectric transition above 270 °C and donor substitution reduces the dielectric loss. Using a ferroelectric capacitor model, the expression for switching dipoles polarization (P) dependence of the electric field (E) is used to fit the P-E loop and gives best fit with the experimental data. The equivalent electrical circuit is modeled to identify the different components by complex impedance spectroscopy and KWW function is used to confirm the respective components by modulus spectroscopy. The water splitting photocatalysis of Sr1-xY2x/3Bi2Ta2O9 ferroelectrics for H2/O2 evolution from water in the presence of sacrificial reagents are also tested. The highest rate of H2/O2 evolution achieved for these modified ferroelectric materials under UV-light irradiation (350WHg lamp) is about 1.7 folds higher than that of pure SrBi2Ta2O9. Improved photoactivity is restructured in terms of effective charge severance of photogenerated e−/h+ pairs owing to the favourable ferroelectric polarization.

Ferroelectric properties and ac conductivity studies of yttrium modified Pb(Fe0.5Nb0.5)O3 ceramics

Using a high-temperature standard solid-state reaction (i.e., mixed oxide) method several yttrium modified ferroelectric ceramics of type Pb1−xYx(Fe0.5Nb0.5)1−x/4O3 (PYFN)with different concentration (x = 0.00, 0.02, 0.04, 0.06, 0.08) were prepared. Preliminary X-ray structural analysis reveals that all the samples were crystallized in monoclinic crystal system. The crystal structure is almost invariant with small Y-concentration. Microstructure of the samples exhibits grain growth on increasing Y content. Curie temperature of Y-substituted samples decreases slightly as compared to that of PFN (Pb(Fe1/2Nb1/2)O3). However, Y substitution results in a notable enlargement of remnant polarization (2Pr). The 2Pr of PYFN (x = 0.02) reaches to a large value (23 μC/cm2) which is nearly 5 times greater than that of x = 0.00 (4.6 μC/cm2). A phenomenological model (i.e., ferroelectric capacitor model) used to simulate hysteresis loops was found to be suitable to explain experimental results. Jonscher's single power law (σac(ω) = σ(0) + Aωn) was well fitted to the frequency dependence of conductivity for all the samples.

Structural, ferroelectric and impedance spectroscopy properties of Y3+ modified Pb(Fe0.5Nb0.5)O3 ceramics

Some ceramic samples of Pb1−xYx(Fe0.5Nb0.5)1−x/4O3 (PYFN) (0.00≤x≤0.08) were synthesized by a mixed oxide route. X-ray diffraction patterns of all the above samples confirm the formation of single phase material crystallizing in monoclinic structure. Dielectric properties (εr and tanδ) were analyzed in a wide temperature (30–350°C) and frequency range (100Hz–1MHz). Ferroelectric properties of these compounds were confirmed from polarization (P–E hysteresis loop) measurements at room temperature. All the room temperature hysteresis loops of PYFN ceramics were well simulated using the ferroelectric capacitor model. Yttrium substitution resulted in notable enlargement of room temperature remnant polarization (2Pr). The 2Pr of PYFN (x=0.02) reaches to a large value (23μC/cm2), which is nearly 5 times greater than that of PFN ceramic (4.6μC/cm2). All the compounds exhibits negative temperature coefficient of resistivity (NTCR) type behavior as that of semiconductors. Dc conductivity (estimated via bulk resistivity) variation with temperature of all the samples follows Arrhenius type of electrical conductivity.

Key Technologies for FeRAM Backend Module

AbstractFerroelectric random access memory (FeRAM) is believed to be the most promising candidate for the next generation non-volatile memory due to its fast access time and low power consumption. Fabrication technologies of FeRAM can be divided into two parts: CMOS technologies for circuits which are standard and can be shared with traditional IC process line, and process relating to ferroelectric which is separated with CMOS process and defined as backend module. This paper described technologies for integrating ferroelectric capacitors into standard CMOS, mainly about modeling of ferroelectric capacitors and backend fabrication technologies. Hysteresis loop of the ferroelectric capacitor is the basis for FeRAM to store data. Models to describe this characteristic are the key for the design of FeRAM. A transient behavioral ferroelectric capacitor model based on C-V relation for circuit simulation is developed. The arc tangent function is used to describe the hysteresis loop. “Negative capacitance” phenomenon at reversing points of applied voltage is analyzed and introduced to the model to describe transient behaviors of the capacitor. Compact equivalent circuits are introduced to integrate this model into HSPICE for circuit simulation. Ferroelectric materials fabrication, electrodes integration and etching are the main technologies of FeRAM fabrication process. An metal organic chemical vapor deposition (MOCVD) process is developed to fabricate high quality Pb(Zr1-xTix)O3 (PZT) films. Pt is known to cause the fatigue problems when used as electrodes with PZT. Ir is used as electrodes to improve the fatigue property of PZT based capacitors, and mechanism of the fatigue is analyzed. Hard mask is used to reduce the size of the capacitors and damage caused in etching process. In our process, Al2O3 is developed as hard mask, which simplifies the FeRAM backend integration process.

A COMPACT FERROELECTRIC CAPACITOR MACRO MODEL FOR FRAM CIRCUIT SIMULATION

ABSTRACT A piecewise-linear based behavioral model for ferroelectric capacitors is presented. The model simply consists of two linear capacitors, two diodes and two dc voltage sources. By adjusting empirical parameters to fit the measured hysteresis loops, the model repeats the ferroelectric DC characteristics in accord with the measurements. In addition, the model predicts quite well the transient characteristics of a ferroelectric memory. It is shown, from the standpoint of practical application, that the proposed model is very suitable for use in simulations of the ferroelectric memory circuits.

Dielectric permittivity–voltage hysteresis behavior in deformed helix ferroelectric liquid crystal

Dielectric permittivity–voltage ( ε′– V) hysteresis behavior of a deformed helix ferroelectric liquid crystal (DHFLC) material viz. MIP0806 has been explained on the basis of electronic equivalent circuit and the Preisach model for ferroelectric capacitors over the broad frequency and temperature ranges. Observed inversion of the ε′– V hysteresis curves above, 230 kHz, is attributed to the high frequency sign change of dielectric biaxiality. The molecular rotation around short axis is accounted for the re-entrant inversion of ε′– V hysteresis behavior at about 6 MHz. For the present DHFLC system, temperature and frequency dependent coercive field has also been observed and analyzed.

Synthesis, Structure, and Properties of Bi3.25Pr0.75Ti2.97V0.03O12 Ferroelectric Ceramics

Praseodymium and vanadium cosubstituted Bi4Ti3O12 was synthesized using a modified citrate-gel method. The crystallization was promoted by the oxidation of residual carbon produced by decomposition of −CHx groups resulting in a crystallization temperature as low as 450 °C. The as-synthesized powder consisted of uniform spherical particles with a mean size of 57 nm and a standard deviation of 14 nm. The ceramic prepared from the as-synthesized powder at 900 °C consisted mainly of randomly arranged platelets with a thickness of 200 nm. The Rietveld refinement in the orthorhombic space group Aba2 for the as-prepared Pr3+ and V5+ cosubstituted Bi4Ti3O12 resulted in a convergent refinement (Rwp = 5.01%). The remanent polarization (2Pr) and coercive field (2Ec) values measured at room temperature with a maximum electric field of ±300 kV/cm were 35 μC/cm2 and 148 kV/cm, respectively. The ceramic has a very low ohmic conductivity, and the leakage current density is below 1 μA/cm2 up to 200 kV/cm. No profound fatigue was observed after switching over 108 cycles. The evolution of 2Ec, 2Pr, Pmax (maximum polarization), and Pmax/Pr with Emax (maximum electric field) is discussed using an ideal and a four components ferroelectric capacitor model. The observed linear relationship between Pmax/Pr and Emax provides the possibility to calculate the field independent dielectric constant (282) and nonremanent polarization (2.7 μC/cm2 at Emax = 300 kV/cm) for the ceramic studied.

A Ferroelectric Capacitor Mathematical Model for Spice Simulation

A behavioral ferroelectric capacitor model based on Q-V expression with model parameters extracted from experimental hysteresis loops is proposed. A compact equivalent circuit of this model is described for spice simulation of nonvolatile memories. Excellent agreement was achieved between our measurements and simulation results. The runtime for simulation of a hysteresis loop with 10,000 points is 1.55 seconds, which is similar to 1.15 seconds for a normal capacitor.

Modeling ferroelectric capacitors for memory applications

The ferroelectric capacitor model is the foundation for accurate simulation of ferroelectric hysteresis loops and minor loops, transitions between the loops under arbitrary voltage patterns, transient responses of ferroelectric capacitors to short voltage pulses with widths in the nano-second range, and temperature behaviors of ferroelectric capacitors. The simulation speed is the same as that for a typical nonlinear capacitor. To the circuit designers, a ferroelectric capacitor is represented as a two-port device like a capacitor. The parameters are extracted easily and reliably by curve fitting the measured hysteresis loops. The model is applicable to fast circuit simulations for large ferroelectric memory designs.

A Novel Simulation Program with Integrated Circuit Emphasis (SPICE) Model of Ferroelectric Capacitors Using Schmitt Trigger Circuit

We have proposed a novel parallel-element simulation program with integrated circuit emphasis (SPICE) model for ferroelectric capacitors, in which Schmitt trigger circuits are used for representing dipoles in the ferroelectric films. It is found that the model expresses the hysteretic characteristics of polarization accurately, even when voltages are applied asymmetrically to the capacitors. We have also proposed a method to introduce the polarization reversal time in the proposed model and demonstrated the circuit response for high-speed pulses in which the polarization reversal time cannot be neglected.

Advanced simulation tool for FeRAM design

A ferroelectric capacitor model was derived, and a ferroelectric device library was implemented into SPICE (both PSPICE and HSPICE) simulation tool. With this SPICE model, 1T-1C/2T-2C, or any other ferroelectric circuit, such as FeFET, chain cell, link cell can be simulated accurately and in real-time. Simulations of hysteresis loops, TVS, switching characteristics are shown in this paper.

An improved behavioral model of ferroelectric capacitors

An improved behavioral model for ferroelectric capacitors is proposed successfully. This model gives accurate simulation results for FeRAM writing and reading process, which helps to the optimization of FeRAM circuit design. The model can also be adapted to express the P-V characteristic of a FE capacitor imposed by nonsymmetrical voltage.

Implementation of a ferroelectric capacitor model using the preisach hysteresis theory

The design of the new ferroelectric memories requires a ferroelectric capacitor model that should be easy to incorporate in a circuit simulator and easy to calibrate based on the experimental measurements. Such a model can be developed by applying the Preisach theory of hysteresis to ferroelectric materials. This theory assumes a distribution of the ferroelectric coercitive voltages. This paper presents the Preisach model and its implementation for the ferroelectric materials based on the experimental determination of the bidimensional Preisach distribution. The relaxation current of the ferroelectric capacitor is also incorporated in the model. Relaxation plays an important roll in the frequency response of these materials. The whole model was implemented into the Spectre® circuit simulator. The simulations of the hysteresis loops show a good agreement with the experiment even for partial hysteresis loops. The memory cell simulations show that the model can be successfully used for the real memory design.

Theoretical investigation of the influence of space charges on ferroelectric properties of PbZrTiO3 thin film capacitor

During ion etching (IE) processes used for making a Pt electrode in the fabrication of ferroelectric capacitors, the film is exposed to radiation and energetic ion bombardment. The influence of such processes on polarization-electric field characteristics of lead zirconate titanate thin film capacitor has been reported by E. G. Lee [Appl. Phys. Lett. 69, 1223 (1996)]. A large field shift and a constriction in the hysteresis loop are experimentally observed. For these authors, this behavior is probably due to the existence of space charges trapped near electrodes. For a better understanding of these phenomena, we have developed a model of ferroelectric capacitor based on the phenomenological Landau–Devonshire theory. A two-dimensional lattice of dipoles is assumed to describe the film. By solving Poisson’s equation, the electric-field distribution inside the film is calculated, which allows us to locally determine the evolution of the polarization by minimizing free energy. IE effects and probably the existence of space charges in the film are introduced by means of a doping layer in the film near the electrode. The influence of important parameters such as doping level, and thickness of the doped layer on the hysteresis loop are investigated. Main experimental thin film electric behaviors are well reproduced and explained considering dipoles switched inside the lattice. Results are interpreted by splitting the hysteresis loop deformation into two effects with different origins: a constriction effect related to the number of impurities inside the film and a shift effect related to the asymmetrical impurities distribution.

A semi-empirical cad model of ferroelectric capacitor for circuit simulation

A semi-empirical CAD model of ferroelectric capacitor for circuit simulation as well as for device characterization is proposed. The model can successfully describe the followings with only 5 parameters(Vc, Vo, Ps, Co, τ which have definite meanings. These are 1) hysteresis of charge vs. voltage (Q-V) relationship and capacitance vs. voltage (C-V) relationship, including partial polarization switching by minor voltage sweep. 2) characteristic time dependent polarization reversal (switching) current.

Effect of the sensing capacitance in a ‘sawyer-tower’ set-up on hysteresis loops

Abstract It is well known that, for a given ferroelectric capacitor, the tilting of the hysteresis loops and the amount of remanent polarization measured in a ‘Sawyer Tower’ set-up are dependent on the sense capacitance (or load). However, it is less intuitive that a small sense capacitance will cause horizontal loop shifts and that these shifts depend on the state of the ferroelectric capacitor before the measurement. Since typical ferroelectric non-volatile memories operate with small sense-to-bit capacitance ratios, it is important to have models that can predict such effects. Complicated experimentation is necessary to implement the load and initial state effects properly in a load-line model. In contrast, the numerical ferroelectric capacitor model does not require any special experimentation to predict such effects. Experimental results from SrBi2Ta2O9 are compared with both models.

Effect of post-metallization annealing on the ferroelectric properties of sol-gel derived PZT thin films

A series of monolithic Pt-PZT-Pt capacitors was prepared based on sol-gel derived PZT 53/47 films fired to 700 C. After deposition of top Pt electrodes, the capacitors were subjected to post-metallization annealing (PMA) temperatures of 100 C to 700 C. Dielectric and ferroelectric (FE) characterizations were performed. Increasing the PMA temperature produced lower values of spontaneous and remanent polarizations, dielectric constant and leakage currents. The observations are correlated with a proposed FE capacitor model.