Paul D. Beale

FATIGUE AND SWITCHING IN FERROELECTRIC MEMORIES : THEORY AND EXPERIMENT

A theoretical model of fatigue in ferroelectric thin‐film memories based upon impact ionization (e.g., Ti+4 to Ti+3 conversion in PbZr1−xTixO3), resulting in dendritic growth of oxygen‐deficient filaments, is presented. The predictions of spontaneous polarization versus switching cycles Ps(N) are compared with both Monte Carlo simulations for a two‐dimensional Ising model and with experimental data on small‐grain (40 nm) sol‐gel PZT films. Excellent agreement between theory and experiment is obtained. In addition to modeling the Ps(N) curves, the theory developed explains the observed linear proportionality between switching time ts(N) and polarization Ps(N) during fatigue; other models of aging do not account for this. Earlier theories of switching are also extended to include finite grain sizes, surface nucleation, triangular drive pulses, and dipolar forces. Good agreement with sol‐gel PZT switching data is obtained.

Properties of ceramic KNO3 thin-film memories☆

Abstract We have measured electrical and spectroscopic properties of thin films (d = 75–500 nm) of ferroelectric ceramic potassium nitrate and developed a mean field theory which explicitly incorporates film thickness effects. Variations of Tc(d) are observed as are changes in the shape of Ps(T) with thickness. Comparisons with earlier work on TGS are made.

Transforming Upper‐Division Quantum Mechanics: Learning Goals and Assessment

In order to help students overcome documented difficulties learning quantum mechanics (QM) concepts, we have transformed our upper‐division QM I course using principles of learning theory and active engagement. Key components of this process include establishing learning goals and developing a valid, reliable conceptual assessment tool to measure the extent to which students achieve these learning goals. The course learning goals were developed with broad faculty input, and serve as the basis for the design of the course assessment tool. The development of the assessment tool has included significant faculty input and feedback, twenty‐one student interviews, a review of PER literature, and administration of the survey to two semesters of QM I students as well as to a cohort of graduate students. Here, we discuss this ongoing development process and present initial findings from our QM class for the past two semesters.

Two-dimensional hard dumbbells. I. Fluctuating cell model

We apply the fluctuating cell model to the calculation of free energies and pressures of high density phases of two-dimensional hard dumbbells using the Metropolis algorithm to generate configurations in the NVT ensemble. The natural logarithm of the average free volume is found to yield a better approximation of the free energy of the system than the value obtained from simple cell theory for all reduced bond lengths except very near the previously calculated hard disk limit. The proposed approximation for the free energy, when used in combination with a semianalytic algorithm to calculate free volumes, is found to be of comparable efficiency to the lattice-coupling method of Frenkel and Ladd. Unlike the simple cell model, the fluctuating cell model is applicable to molecules that freeze into plastic crystals as well as orientationally ordered crystals. We also calculate the distribution of free volumes in the solid phase. The nature of the distribution of free volumes changes abruptly near the hard-disk...

SOLID-LIQUID EQUILIBRIUM OF DIPOLAR HETERONUCLEAR HARD DUMBBELLS IN A GENERALIZED VAN DER WAALS THEORY : APPLICATION TO METHYL CHLORIDE

The solid-liquid equilibrium of hard dumbbells with embedded point dipoles is calculated using a generalized van der Waals theory to account for long range attractive forces. Molecular parameters are chosen to model a methyl chloride molecule. The solid free energy is calculated using the cell theory of Lennard-Jones and Devonshire with the dipolar contribution estimated by static lattice sums. Thermodynamic perturbation theory is used to add dipolar effects to a hard dumbbell fluid equation of state. The resulting phase equilibria show that the dipole does have a significant effect in determining the stable solid structure on freezing. In particular, the dipole moment stabilizes a non-close-packed orthorhombic structure, similar to the known solid structure of methyl chloride. An increase in the ratio of triple point temperature to critical point temperature is also observed as the dipole moment is increased, as is a decrease in the density change on freezing. At high pressure and temperature a solid-sol...

Microscopic modeling of thin-film ferroelectrics: Fatigue

Abstract Ferroelectric thin-films are observed to fatigue (reduce their switched charge) as the number of switching cycles increases. A number of qualitative observations have been made. Initially there is a rapid fatigue then the switched charge roughly levels off for a large number of cycles (it decreases only logorithmically with the number of polarization reversals). During this period the time required to switch the sample decreases as the fatigue increases. The switched charge falls off precipitously as the device fails. After failure the conductivity across the sample is large and dendritic growth has been observed in failed samples. A high temperature annealing procedure in which the sample is kept within the ferroelectric phase can restore the samples to near-new condition. A model involving the diffusion and trapping of charged defects is postulated and examined. This model qualitatively explains these phenomena in terms of the dendritic growth of conducting defects near the surfaces of the samp...

Creation of nanometer-scale patterns with selected metal films

We demonstrate the utilization of various transition metals in a biologically derived, nanometer-scale patterning process. This process created large arrays of nanometer-scale dots (nanodot arrays) with several of these metals. The correlation between nanodot array formation and the interaction energies between metal atoms, other metals atoms, and the surface of the sample was explored. The behavior of the metal films was then investigated with the aid of a Monte Carlo solid-on-solid simulation.

Capacitance and dielectric breakdown of metal loaded dielectrics

The authors review and extend analytic, numerical and experimental work on the capacitance, C(f), and dielectric breakdown field, Eb(f), of a simple insulator containing volume fraction, f, of randomly located metal inclusions. In the case of spherical inclusions, they find Eb(f)=Eb(0)/(1+kc(ln V/ mod ln f mod )alpha ). V is the sample volume divided by the average volume of an inclusion, kc is a constant and 1/2< alpha <1 for large ln V/ mod ln f mod . In the dilute inclusion limit, the statistics of the dielectric breakdown field are shown to be of a modified Gumbel form. The scaling theory of capacitance in composites with percolation microstructures is outlined, and the authors discuss extensions to include hard core repulsion between inclusions. They have fabricated many samples of paraffin wax (a simple insulator) containing various concentrations of stainless-steel spheres (size range 10-65 mu m). The capacitance and dielectric breakdown field of these samples is presented and the results are compared with theory.

Controlled morphology of biologically derived metal nanopatterns

We report the ability to control the morphology of nanometer thick Ti oxide films that were created via a parallel nanofabrication process using a two-dimensional protein crystal as a template. Atomic force microscopy was used to examine the evolution of these structures from a periodic array of nanometer-scale dots (nanodots) to a screen containing a periodic array of nanometer-scale holes (nanoscreen) as the film thickness was increased. A Monte Carlo solid-on-solid simulation was then developed to explain the thickness dependence of the morphology as the metal film self-organizes into these nanopatterns.

Raman spectroscopic study of high-Tc superconductors YBa2Cu3-xSnxO7-y

Abstract Raman spectra of YBa 2 Cu 3-x Sn x O 7-y have been obtained for x from 0 to 3. The critical dopant concentration x c for Sn, at which superconductivity disappears, is found to be approximately 1.0. This is in agreement with a metal-insulator transition model in which x c = 1.27. Above x = 1.0, the system is semiconducting up to x = 3.0 (pure Sn), at which it is an insulator. The 506 cm −1 Cu-0 vibration is present for all superconducting samples (x ≤ 1.0) but broadens anomalously as x→1 and is absent for all semiconducting samples.