TY - JOUR
T1 - Spectral representation of the electrical properties of layered materials
AU - Day, A. R.
AU - McGurn, A. R.
AU - Bergman, D. J.
AU - Thorpe, M. F.
N1 - Funding Information:
ARD, ARM, and DJB acknowledge the hospitality of the Center for Fundamental Materials Research at Michigan State University, where some of this work was performed. Partial support for the research of ARD and MFT was provided by the NSF under grants DMR97-04099 and DMR00-X8361. Partial support for the research of DJB was provided by grants from the US–Israel Binational Science Foundation and the Israel Science Foundation.
PY - 2003/10
Y1 - 2003/10
N2 - We present a spectral representation for the effective conductivity of two homogeneous layers joined at a rough interface. This spectral representation is closely related to the Bergman-Milton spectral representation for bulk composites, and is easily extended to multilayered materials. By comparing the layered system to a reference layered system that has a flat interface, we form a surface spectral density that captures all the effects of surface structure on the effective conductivity of the layered sample, and is independent of the conductivities of the two layers. Because of the anisotropy of the layered system there are two surface spectral densities, one for the case where the applied field is parallel to the interface, and one for the case where the applied field is perpendicular to the interface. We discuss the relationship between these two spectral representations and present sum rules that are directly related to the degree of surface roughness. We present numerical calculations of the surface spectral density for Gaussian random surfaces which have been extensively used to study light scattering from rough surfaces.
AB - We present a spectral representation for the effective conductivity of two homogeneous layers joined at a rough interface. This spectral representation is closely related to the Bergman-Milton spectral representation for bulk composites, and is easily extended to multilayered materials. By comparing the layered system to a reference layered system that has a flat interface, we form a surface spectral density that captures all the effects of surface structure on the effective conductivity of the layered sample, and is independent of the conductivities of the two layers. Because of the anisotropy of the layered system there are two surface spectral densities, one for the case where the applied field is parallel to the interface, and one for the case where the applied field is perpendicular to the interface. We discuss the relationship between these two spectral representations and present sum rules that are directly related to the degree of surface roughness. We present numerical calculations of the surface spectral density for Gaussian random surfaces which have been extensively used to study light scattering from rough surfaces.
KW - Composites
KW - Dielectric properties
KW - Rough surfaces
KW - Spectral representation
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U2 - 10.1016/S0921-4526(03)00453-8
DO - 10.1016/S0921-4526(03)00453-8
M3 - Conference article
AN - SCOPUS:0242409510
SN - 0921-4526
VL - 338
SP - 24
EP - 30
JO - Physica B: Condensed Matter
JF - Physica B: Condensed Matter
IS - 1-4
T2 - Proceedings of the Sixth International Conference on Electrica (ETOPIM 6)
Y2 - 15 July 2002 through 19 July 2002
ER -