Modeling of dynamic response of ferroelectric capacitors

Abstract

A simulation model of ferroelectric capacitors which describes both hysteresis loops under arbitrary voltage profile and time dependence of polarization change is developed based on the parallel-element model. In the model, a ferroelectric capacitor is assumed to consist of parallel capacitor elements with different coercive voltage and switching polarization. A new method of pulse measurement is designed to obtain the switching behavior of individual element. The measurement on a sol-gel SrBi₂Ta₂O₉ capacitor revealed that the switching time depended on the difference between the applied voltage and the coercive voltage of the capacitor element. The switching behavior is reproduced by inserting a nonlinear resistor in series with each capacitor in the model. All the parameters used in the model are determined from the measured data and no arbitrary fitting parameters are used.     

Process dependent electrical characteristics and equivalent circuit model of sol-gel based PZT capacitors

Abstract

Studies of electrical properties and an equivalent circuit model is developed for ferroelectric PZT(Ti = 60%) thin film capacitors made by sol-gel spin coating with Pt electrodes. The equivalent circuit consists of two major parts: serial space charge capacitors demonstrating surface effects and parallel elements modeling the inner polycrystalline ferroelectric regions. This model is based on device physics which can demonstrate both the measured capacitance voltage characteristics and hysteresis curves. From the model fit to the data, an estimate of the space charge concentration at the surface and inner grain boundary region of 57times;10²⁰ cm^?3 and 1×10¹⁸ cm^?3 respectively is made. Further electrical characterizations such as pulse switching and polarization degradation (fatigue) have also been studied. Using the equivalent circuit, other characteristics such as the switching time can be studied showing its dependence on applied voltage and capacitor area. The applied voltage dependence of fatigue is shown via an empirical equation where the degradation rate is electric field activated.     

Pulse width dependent polarizations of ferroelectric (Pb,La)(Zr,Ti)O3 thin film capacitors

Abstract

We report the measurements of pulse polarizations of (Pb, La)(Zr, Ti)O₃ ferroelectric capacitors as a function of pulse width. Pulse polarizations were measured from the switching current responses in the pulse width range from 1 μs to 1 s. The relation between pulse polarizations(switched(P?) and non-switched polarization(P?)) and hysteresis loop parameters was studied. In the case of all write/read pulse widths are same, P? increased but P? decreased with increasing pulse width. These results are explained by poling effects and confirmed by measuring pulse width dependencies with different patterns of pulse trains.     

Models for the frequency dependence of coercive field and the size dependence of remanent polarization in ferroelectric thin films

Abstract

We have confirmed the theory of Ishibashi and Orihara for the frequency dependence of coercive fields in ferroelectric thin films.SrBi₂NbTaO₉, SrBi₂Ta₂O₉, and PbZr_1-x Ti _x O₃ (PZT) data from DeVilbis et al. reveal a power-law dependence of form E_c (f) = Bf^d/α , where d is the dimensionality of domains (ca. unity in uniaxial ferroelectrics such as SBT and SBNT) and α is approximately 6, in agreement with theoretical predictions. Models are also presented for the polarization and fatigue data from NEC of micron-sized thin-film strontium bismuth tantalate capacitors, emphasizing behaviour at unsaturated voltages.     

Graphic Solution and Analysis of Voltage Distribution Between Ferroelectric Capacitor/Capacitors and Bitline Capacitance

Voltage distribution between ferroelectric capacitor/capacitors and normal capacitor in ferroelectric devices is difficult to calculate or simulate due to the complicated electrical properties of the ferroelectric capacitor. This paper presents a mathematical method combined with graphic solution to analyze the voltage distribution. Analysis of voltage distribution of different structures (1FC/1NC, 2FC, 2FC/1NC) or operation patterns is summarized. The dependence of the medial value and difference of bitline voltages between “0” and “1” state after the driving pulse of plateline on the value of C_b/C_fm has been analyzed.     

High-Voltage Pulse Generation in Nonlinear Transmission Line with Ceramic Capacitors

Usual axial cables and aerial lines are distributed constant linear transmission lines which can transmit a pulse without changing its initial shape. On the other hand, a nonlinear transmission line consisting of nonlinear capacitors can sharpen the front of a propagating pulse. In this study, a transmission line with commercially available ferroelectric BaTiO₃ ceramic capacitors is constructed to obtain high-voltage pulses with short rise-time. Strong dependence of their capacitance on the applied voltage has been found. The rise-time of the input pulse with 300 V in amplitude was shortened from 60 ns after propagating through the line.     

Surfaces structure of bulk and thin film ferroelectrics

Abstract

Based on the experimental results of thickness dependences of breakdown voltage and dielectric permittivity for BaTiO₃ family ceramics, (Pb, La)TiO₃ thin films and commercial multilayer capacitors, surface layer structures are discussed. Surface layers inside ferroelectric materials are consisting of non-ferroelectric Kanzig layer with low dielectric permittivity and with higher concentrations of impurities due to the inter diffusion between substrates and bulk, internal stresses induced by lattice mismatch, cubic-tetragonal phase transition, electric field induced anisotropies and internal bias field (space charge field). The Voltage - Current characteristics (V-I curve), D-E loops of ferroelectric materials show asymmetric behaviors. Saturation phenomena of V-I curves are observed only ferroelectric temperature region. The breakdown voltage almost depends on the non-ferroelectric Kanzig layer and the dielectric permittivity depends on the volume fraction of non-ferroelectric parts. Log-log plots of dielectric permittivity and breakdown voltage suggest that the thickness of non-ferroelectric Känzig layer should be at least more than 10～20 nm and in the grain boundary thickness of bulk ferroelectric materials should be more, especially in the liquid phase sintering, the thickness of grain boundary is a order of 0.1～0.2 μm.     

Imprint testing of ferroelectric capacitors used for non-volatile memories

Abstract

A set of criteria is presented, based on the polarization versus electric field hysteresis characteristics, which can be used to reveal a tendency towards imprint failure in ferroelectric capacitors. A series of pulsed voltage waveforms, generated by the RT66A ferroelectric tester, are utilized to validate our established criteria for the tendency towards imprinting. The tests have been performed on hetero-structure Pb(Zr_xTi_1?x)O₃(PZT)-based capacitors produced by a pulsed laser ablation depositon technique (PLAD). The loss of retained charge in the ferroelectric capacitors is considered in light of the imprint test methodology. Rates of retention loss and imprint are extracted from the experimental data and treated as separate processes that lead to device failure. The rate of approach towards imprint failure is found to be influenced by the magnitude of the read pulse.     

GHZ polarization dynamics in ferroelectric thin films

Abstract

We present results from experiments which measure the local dielectric response of ferroelectric thin films driven by microwave-frequency electric fields. The repetition rate of a mode-locked Ti:Sapphire laser is used to generate a microwave drive signal that is phase-locked to an optical probe pulse and applied to the ferroelectric thin film. The induced polarization change in the ferroelectric film is measured stroboscopically via the electro-optic effect. Polarization images are acquired by scanning the laser beam across the sample in a confocal geometry. Time resolution is achieved by changing the delay between the electrical pump and the optical probe. Initial results show large local phase shifts in the ferroelectric response of closely separated regions of a Ba_0.5Sr_0.5TiO₃ thin film. This new experimental technique may help to understand the physical mechanisms of dielectric loss in these materials.     

Fast decay component of the remanent polarization in thin-film PZT capacitors

Abstract

The remanent polarization (2P_r) of thin-film PZT capacitors was examined using a voltage pulse method. The amount of polarization remaining after a “write” pulse was found to be a function of both the time between the write and read pulses and the duration of the write pulse. The 2P_r was found to decrease significantly from 3 μs to 100 ms after the initial write. In some cases the remanent polarization decayed by almost 70 percent in this time regime. The fast decay component of 2P_r was also observed to be dependent on the duration of the write pulse (the write, pulse width). The longer the write pulse was applied the smaller the fast decay component became, leaving more measurable charge retained after 100 ms.     

Measurement and simulation of partial switching in ferroelectric PZT thin-films

Abstract

In digital memory applications, metal ferroelectric metal (MFM) capacitors are typically fully switched from one polarization state to the other, with the difference in displacement current allowing determination of the cell state. However, by applying a pulse of insufficient amplitude and/or duration to fully switch the ferroelectric, such a device may be partially polarized. Here, the measurement of partial switching in sol-gel derived PZT MFM capacitors due to applied voltage pulses is reported. SPICE, a commonly used circuit simulation program, has been modified to incorporate a ferroelectric capacitor device model. The MFM device model added to SPICE is reviewed, and the simulation of partial switching is demonstrated. Simulation results modeling the PE hysteresis loops and switching transients due to applied voltage steps closely match those measured in the laboratory. We conclude with the modeling of incomplete switching due to applied pulses of insufficient amplitude to cause polarization saturation, which is attributed to the polycrystalline nature of the thin-films.     

Data disturb characteristics of 1T2C ferroelectric memory array

Abstract

The data disturb characteristics of a newly proposed 1T2C-type ferroelectric memory with an array structure were investigated, in which one ferroelectric capacitor C_fa was used for storing data and the other capacitor C_fb was used for reading out the data. It was found that the data disturb problem in write operation was much improved by using a lower write voltage and a compensation pulse. It was also demonstrated that the use of a thicker film in C_fa was a very effective approach for realizing reliable disturb-free read-out operation.     

Modification of PZT nucleation and growth using oxide layer in multi-layered electrodes

Abstract

The ferroelectric properties of PZT on RuO₂ electrodes were compared to those on RuO₂/Pt electrodes. The better hysteretic properties were obtained from Pt/RuO₂/PZT/RuO₂/Pt ferroelectric capacitors. The enhancement of ferroelectric properties is likely attributed to the modification in the microstructure of PZT film. The interfacial modification would be affected by the factors such as surface roughness, stress, and porosity of RuO₂ film. As the result of the interfacial modification, better quality PZT films are produced, thereby resulting in better ferroelectric properties. We made an effort to understand the relationship between the grain size and the coercive voltage in terms of the domain formation and the domain pinning in connection with defects like grain boundaries.     

Low temperature preparation of ferroelectric SrBi2Ta2O9 thin films by a modified RF magnetron sputtering technique

Abstract

Bi–layered ferroelectric SrBi₂Ta₂O₉ (SBT) films were successfully prepared on Pt/Ti/SiO₂/Si substrates at 650°C by a modified rf magnetron sputtering technique. The SBT films annealed for 1 h in O₂ (760 torr) and again for 30 min in O₂ (5 torr) at 650°C show a average grain size of about 49 nm. The SBT films annealed at 65 0°C have a remanent polarization (P_r) of 6.0 μC/cm² and coercive field (E_c) of 36 kV/cm at an excitation voltage of 5 V. The films showed fatigue–free characteristics up to 4.0 × 10¹⁰ switching cycles under 5 V bipolar pulse. The retention characteristics of SBT films looked very promosing up to 1.0 × 10⁵ s.     

Origin of giant dielectric response in ferroelectric thin film multilayers

Abstract

A thermodynamic theory of dielectric response in ferroelectric thin film multilayers is developed. The solution of Lame equation for static dielectric susceptibility has shown that susceptibility diverges at the transition temperature of the thickness induced ferroelectric phase. This divergence is shown to be the origin of the giant dielectric response observed in some multilayers. The theory gives an excellent fit to the temperature dependence of the giant susceptibility observed recently in multilayers of PbTiO₃-Pb_1-xLa_xTiO₃ (x = 0.28).     

Surface potential of ferroelectric domain investigated by kelvin force microscopy

We have investigated the surface potential of poled area by varying the poled size and the sign of applied voltage on 100 nm thick Pb(Zr_0.25Ti_0.75)O₃ films grown by chemical solution deposition using Kelvin force microscopy (KFM). In the negative poled area, as the poled size increases from 300 to 4800 nm, the domain size and the KFM contrast increased in a linear way. However, in the positive poled area, the KFM contrast increased at first and then didn’t increase because of Coulomb repulsion. In two opposite poled areas, the values of the KFM contrast differed because of the internal field near the ferroelectric/electrode interface. These results imply that the surface overcharge of poled area in ferroelectric materials should be increased and the ferroelectric/electrode interface should be improved for the ultra high-density memory device.     

Ferroelectric field effect in (La,Sr)CoO3/Pb(Zr,Ti)O3/(La,Sr)CoO3 heterostructures

Abstract

Epitaxial LaCoO₃/Pb(Zr,Ti)O₃/(La,Sr)CoO₃ (LSCO) heterostructures have been grown on LaAlO₃ by pulsed laser deposition for investigating ferroelectric field effect. In the heterostructure, semiconducting LaCoO₃ was used as a conducting channel layer, instead Si. The resistivity of the LaCoO₃ (LCO) channel layer was found to be dependent on an oxygen ambient, primarily the ambient oxygen pressure during deposition. The resistivity of the LCO layer varied in the range of 0.1 – 100 Ω cm. Ferroelectric field effect induced in LaCoO₃ layer was observed by measuring the resistance modulation of the LCO layer with respect to the polarized state of the PZT layer. The resistance modulation of 9% was obtained in the 680 Å thick LCO layer. Further the resistance modulation was improved up to 45% after applying dc bias. It is suggested that the LCO/PZT/LSCO heterostructure can be used as a ferroelectric field effect transistor.     

Deposition of large-area graded (Pb1−xLax)TiO3 thin films by pulsed laser depesition

Abstract

Thin films of the composition (Pb_1?xLa_x)TiO₃, PLT, with x=0.05, 0.10 and 0.15 were sequentially pulsed laser deposited on Pt(Si) substrates at 200°C, followed by post-annealing at 550–600°C in furnace to result in a film with graded composition. The ferroelectric properties of the graded materials are markedly different from those of the uniform thin PLT films. For down graded materials, which contain PLT5 composition (x=0.05) at the top and PLT 15 composition (x=0.15) at the bottom of the films, the hysteresis loops are slim and the width of the P-E curves increases with voltage cycling, attaining an equilibrium polarization states similar to the P-E properties of PLT 15 thin films. By contrast, the ferroelectric hysteresis properties reaches the same value as those of PLT5 thin films when the composition is up-graded.     

The role of buffer layer in strontium bismuth tantalate based ferroelectric gate mos structures for non-volatile non destructive read out memory applications

Abstract

Metal Ferroelectric Insulator Semiconductor (MFIS) structure has been fabricated with strontium bismuth tantalate (SBT) as the ferroelectric thin film and zirconium oxide (ZrO₂) as the insulating buffer layer. SBT film was deposited by spin-on metal organic deposition (MOD) technique. ZrO₂ film was deposited by electron beam evaporation. The capacitance versus voltage characteristics(C-V) of the MFIS structure shows hysteresis and the direction of hysteresis corresponds to ferroelectric polarization. The C-V characteristics of MFIS structure shows memory window of 1.8 volts for a write/erase voltage of 9V at a sweep rate of 1 sec/1.8V. In order to understand the role of coercive voltage on the memory window in MFIS structures, C-V characteristics metal-ferroelectric-metal (MFM) structures with various SBT film thickness’ were also studied.     

Reflection and refraction of light at the boundaries between ferroelectric and antiferroelectric phases in chiral smectic liquid crystals

Abstract

Light deflection phenomena in antiferroelectric chiral smectic liquid crystals were investigated. Characteristic deflected lights were observed at electric field induced phase transitions between antiferroelectric (AF) state to ferroelectric (F) one. On the basis of a numerical analysis of Huygens construction at the phase boundaries between coexisting AF and F states, it is concluded that the light deflection is not due to diffraction but due to refraction and reflection at the phase boundaries. The characteristic dependence of the deflection angle on the angle of incidence was proposed as a possible evidence of coexistence of phases or domains in materials.