Critical currents in inhomogeneous triangular Josephson arrays: a model for polycrystalline superconductors

Characterization of Textured Aluminum Lines and Modelling of Stress Voiding

It is well known from studies of individual interfaces that grain boundaries exhibit a spectrum of properties because their structure is misorientation dependent. Usually this variability is neglected and properties are modeled using a mean field approach. The limitations inherent in this approach can be overcome, in principle, using a combination of experimental techniques, theory and modeling. The bamboo structure of an interconnect is a particularly simple polycrystalline structure that can now be readily characterized experimentally and modeled in the computer. The grain misorientations in a [111] textured aluminum line have been measured using the new automated technique of orientational imaging microscopy. By relating boundary angle to diffusivity the expected stress voiding failure processes can be predicted through the link between misorientation angle, grain boundary excess free energy and diffusivity. Consequently it can be shown that the high energy boundaries are the favored failure sites thermodynamically and kinetically.

Toward Realizing the Structure-Property Link in Polycrystalline Thin Films

Many materials for engineering applications are used in polycrystalline form and contain grain boundaries with a range of structures and properties. However, most research on grain boundaries to date has focussed exclusively on symmetric coincidence site lattice interfaces. To go beyond descriptions for these simple interfaces and thence to an aggregate of grains and grain boundaries in a polycrystal will require a new approach. Here we discuss two models for properties of polycrystalline materials, including their advantages and drawbacks, and indicate the microstructural variables available to optimize properties.

A New Approach to Grain Boundary Engineering for Photovoltaic Polysilicon by Unidirectional and Rotational Solidification

A new approach to grain boundary engineering for photovoltaic polysilicon has been attempted using a new processing method of unidirectional and rotational solidification from the melt, in order to control the grain boundary microstructure and to produce desirable bulk electrical properties. The effect of grain boundary microstructure on bulk electrical properties of polysilicon can be more precisely evaluated by introducing a new parameter “directional grain boundary density (DGBD)” in connection with basic knowledge of structure-dependent grain boundary electrical properties, the grain boundary character distribution (GBCD) and grain boundary geometrical configuration which can be experimentally determined by Orientation Imaging Microscopy (OIM). We report the usefulness of this approach to development of high performance polysilicon.

Statistical physics of grain-boundary engineering

Percolation theory is now standard in the analysis of polycrystalline materials where the grain boundaries can be divided into two distinct classes, namely "good" boundaries that have favorable properties and "bad" boundaries that seriously degrade the material performance. Grain-boundary engineering (GBE) strives to improve material behavior by engineering the volume fraction c and arrangement of good grain boundaries. Two key percolative processes in GBE materials are the onset of percolation of a strongly connected aggregate of grains, and the onset of a connected path of weak grain boundaries. Using realistic polycrystalline microstructures, we find that in two dimensions the threshold for strong aggregate percolation c(SAP) and the threshold for weak boundary percolation c(WBP) are equivalent and have the value c(SAP) = c(WBP) =0.38 (1) , which is slightly higher than the threshold found for regular hexagonal grain structures, c(RH) =2 sin (pi/18) =0.347... . In three dimensions strong aggregate percolation and weak boundary percolation occur at different locations and we find c(SAP) =0.12 (3) and c(WBP) =0.77 (3) . The critical current in high T(c) materials and the cohesive energy in structural systems are related to the critical manifold problem in statistical physics. We develop a theory of critical manifolds in GBE materials, which has three distinct regimes: (i) low concentrations, where random manifold theory applies, (ii) critical concentrations where percolative scaling theory applies, and (iii) high concentrations, c> c(SAP) , where the theory of periodic elastic media applies. Regime (iii) is perhaps most important practically and is characterized by a critical length L(c) , which is the size of cleavage regions on the critical manifold. In the limit of high contrast epsilon-->0 , we find that in two dimensions L(c) proportional, gc/ (1-c) , while in three dimensions L(c) proportional, g exp [ b(0) c/ (1-c) ] / [c (1-c) ](1/2) , where g is the average grain size, epsilon is the ratio of the bonding energy of the weak boundaries to that of the strong boundaries, and b(0) is a constant which is of order 1. Many of the properties of GBE materials can be related to L(c) , which diverges algebraically on approach to c=1 in two dimensions, but diverges exponentially in that limit in three dimensions. We emphasize that GBE percolation processes and critical manifold behavior are very different in two dimensions as compared to three dimensions. For this reason, the use of two dimensional models to understand the behavior of bulk GBE materials can be misleading.