Microstructural Size and Alignment Effects on the Dielectric Response of Inhomogeneous Media
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KIM F. FERRIS, GREGORY J. EXARHOS, AND STEVEN M. RISSER*, Pacific Northwest National Laboratory, Materials and Chemical Sciences Center, Richland, WA 99352, * Texas A&M University-Commerce, Department of Physics, Commerce, TX 75429
ABSTRACT The dielectric response of inhomogeneous media presents a complex boundary problem dependent upon dielectric susceptibility and volume fraction of its components, as well as the physical size of the heterogeneities. In this paper, we have used the LOCALF method to examine the size dependent problem for cubic and columnar defects for ZrO 2 dielectric films of varying microstructure size and volume fraction. Both the alignments of low dielectric components with respect to the applied field and their size can effectively modulate the composite response. Comparison of these results with the conventional effective medium approximation methods reinforces the need to include microstructural detail in the modeling approach. INTRODUCTION The microstructure of dielectric films is an inherent characteristic of the fabrication process, and imposes distinctive behavior on the electric field distributions. The interaction of the voids, defects and the multiple components that define the microstructure of the dielectric film also imposes complex boundary conditions, which prevent analytical solutions for the electric fields in inhomogeneous media. However, accurate predictions of dielectric behavior are critical to the deposition and diagnostic processes for fabricating optical and electronic components. Even in ideal situations, both voided volumes and structural defects are introduced in the fabrication process, and have been suggested to play important roles in determining their optical and electronic properties. Film characterization methods and modeling efforts often share a common picture. The film is depicted as a randomly oriented collection of isotropic media with a specific void fraction. A variety of spectroscopic and ellipsometric probes are available to characterize the optical properties of the material, requiring a fundamental knowledge of the general light scattering properties of the media. However, microstructural level information is often lost with the basic premise that defects are sufficiently scarce such that they do not interact with each other, so that the interaction of a defect with its surroundings can be replaced by an effective medium. The ideal solution would be to solve Maxwell's equations for the electric field at arbitrary location within the inhomogeneous media - a difficult task given the complex microstructure in dielectric materials. To approach this problem, we developed a numerical solution method for a general non-magnetic medium based upon the selfconsistent determination of both the total electric field and polarization within a lattice of
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Mat. Res. Soc. Symp. Proc. Vol. 492 © 1998 Materials Research Society
cubic dielectric elements in the long wavelength limit [1,2]. In this paper, we have used the self-consistent lattice element model to e
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