Room-temperature current-voltage dependence of ultrafine-grained ferroelectric Pb(Zr, Ti)O3 thin films has been investigated. Both strong varistor type behavior and space charge limited conduction (SCLC) were observed. Differences in the current-voltage characteristics are attributed to differences in the nature of the grain boundaries resulting from variations in processing conditions. The strong varistor type behavior is believed to be due to the presence of highly resistive grain boundaries and thus may be termed grain boundary limited conduction (GBLC). A double-depletion-layer barrier model is used to describe the origin of high resistivity of the grain boundaries. It is suggested that the barrier height varies significantly with the applied field due to the nonlinear ferroelectric polarization, and that the barrier is overcome by tunneling at sufficiently high fields. In some other cases, the resistivity of the grain boundaries is comparable to that of the grains, and therefore the intrinsically heterogeneous films degenerate into quasi-homogeneous media, to which the SCLC theory is applicable. As such, a unified grain boundary modeling reconciles different types of conduction mechanisms in the ultrafine-grained ferroelectric thin films. This grain boundary modeling also well accounts for some other dc-related phenomena observed, including abnormal current-voltage dependencies, remanent polarization effect, electrode interface effect, and unusual charging and discharging transients. In addition, many other electrical properties of the ferroelectric films may be better understood by taking the effect of grain boundaries into account.

Recurrence gives powerful tools to investigate the statistical properties of dynamical systems. We present in this paper some applications of the statistics of first return times to characterize the mixed behavior of dynamical systems in which chaotic and regular motion coexist. Our analysis is local: we take a neighborhood A of a point x and consider the conditional distribution of the points leaving A and for which the first return to A, suitably normalized, is bigger than t. When the measure of A shrinks to zero the distribution converges to the exponential e(-t) for almost any point x, if the system is mixing and the set A is a ball or a cylinder. We consider instead a system, a skew integrable map of the cylinder, which is not ergodic and has zero entropy. This map describes a shear flow and has a local mixing property. We rigorously prove that the statistics of first return is of polynomial type around the fixed points and we generalize around other points with numerical computations. The result could be extended to quasi-integrable area preserving maps such as the standard map for small coupling. We then analyze the distribution of return times in a region which is composed by two invariants subdomains: one with a mixing dynamics and the other with an integrable dynamics given by our shear flow. We show that the statistics of first return in this mixed region is asymptotically given by the exponential law, but this limit is attained by an intermediate regime where exponential and polynomial laws are linearly superposed and weighted by some factors which are proportional to the relative sizes of the chaotic and regular regions. The result on the statistics of first return times for mixed regions in the phase space can provide a basis to analyze such a property for area preserving maps in mixed regions even when a rigorous result is not available. To this end we present numerical investigations on the standard map which confirm the results of the model.

A multi-ion-beam reactive sputter (MIBERS) deposition technique was devised to grow ferroelectric lead zirconate titanate (PZT) thin films of different compositions (Zr/Ti ratios of 50/50 and 56/44) from individual metal targets of Pb, Zr, and Ti. This technique offers a highly controllable deposition process allowing excellent uniformity in composition and thickness over a large area (7.5 cm diameter) on a reproducible basis. The PZT films were deposited on a variety of unheated substrates and annealed by two different techniques, rapid thermal annealing and conventional furnace annealing. Both techniques induced a perovskite phase with good morphology. The effect of the excess Pb content was observed in terms of the crystallization and morphology. It was seen that the presence of excess Pb tends to enhance perovskite phase formation but degrades the morphology. The effect of the substrates was observed in terms of crystallization and orientation. A low-energy oxygen ion beam was employed to modify the film growth. Secondary-ion bombardment seems to be a promising approach to optimize the film quality as it showed a variety of effects such as enhancing crystallization, inducing preferred orientation, and improving the film morphology. The present MIBERS-grown PZT films showed fairly high dielectric constants, about 850 for PZT (50/50) and about 1150 for PZT (56/44), and low dielectric losses. Ferroelectricity of these films was established with the values of the remnant polarization and the coercive field for PZT (50/50) of 23 μC/cm2 and 80 kV/cm and for PZT (56/44) of 20 μC/cm2 and 60 kV/cm, respectively. The low-energy oxygen ion-beam bombardment during the growth of PZT (50/50) films caused an increase in the dielectric constant to about 1000, reduction in the dissipation factor to 0.02, increase in the remnant polarization to about 26 μC/cm2, and decrease in the coercive field to about 60 kV/cm. The C-V characteristics of PZT (50/50) films in a metal-ferroelectric-metal configuration also indicated a clear dielectric polarization hysteresis.

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