Isotropic Substrate Research Articles

Analysis of printed-circuit antennas with chiral substrates with the method of lines

In this paper, a new method is presented in order to illustrate how the method of lines can be generalized for the analysis of stratified guided wave structures filled with isotropic chiral dielectric substrates. The new proposed method derives the dyadic Green's function for stratified isotropic chiral dielectric layers from the wave equation in the spectral domain. The result leads to a clear equivalent circuit representation of the whole structure, which can be used to readily handle the hyperbolic nature of the Maxwell equations. The application demonstrates the validity of the method to the well-known example of a single microstrip patch antenna on a single grounded isotropic dielectric layer. The technique is subsequently applied to more complicated structures with multiple isotropic chiral layers and electric sources and/or metallizations in arbitrary interfaces.

Scattering From a Frequency Selective Surface Supported By a Bianisotropic Substrate - Abstract

In this paper a method for the analysis of a frequency selective surface (FSS) supported by a bianisotropic substrate is presented. The frequency selective structure is a thin metallic pattern - the actual FSS - on a plane supporting substrate. Integral representations of the fields in combination with the method of moments carried out in the spatial Fourier domain are shown to be a fruitful way of analyzing the problem with a complex substrate. This approach results in a very general formulation in which the supporting substrate can have arbitrary bianisotropic properties. The bianisotropic slab can be homogeneous, stratified, or it can have continuously varying material parameter as a function of depth. The analysis presented in this paper is illustrated in a series of numerical examples. Results for isotropic, anisotropic and bianisotropic substrates are given.

Thin-Film-Edge-Induced Stresses in Substrates

ABSTRACTWe have obtained an analytic solution of linear elasticity for the stress distribution under a thin film edge in isotropic substrates of finite thickness and of infinite extent in the other two directions. The following boundary conditions are considered. At the film/substrate interface and the free surfaces at the top and bottom of the substrate, the normal stress component vanishes. Far from the film edge on the side without the film, all stress components are zero. Far from the film edge under the film, the stress distribution is in accordance with that given by the bimetallic strip theory. Two examples of comparison between theory and experiments were given to demonstrate the validity of this solution. The infrared photoelastic stress fringe pattern obtained by a dark-field plane polariscope in a Si substrate under an oxide film edge was successfully reproduced. The calculated and experimental results of Raman-shift of Si under patterned CoSi2 line structures also showed good agreement with each other.

Qualitative study of beta silicon carbide residual stress by Raman spectroscopy

Silicon carbide was grown by chemical vapor deposition on isotropic pyrolytic graphite substrates using methyltrichlorosilane as the source gas and hydrogen as the carrier gas. Raman microscopy was used to qualitatively determine the residual stress existing in chemical vapor deposition (CVD) beta silicon carbide. The results showed that the residual stress of CVD beta silicon carbide not only depends on the deposition temperature but also on the other reaction parameters, such as precursor concentration and carrier gas flow rate. Raman microscopy study results were tried to compare with those of the wafer central deflection method which was reported previously, and explained using scanning electron microscopy (SEM) photographs and transmission electron microscopy (TEM) observations. The residual stress of CVD beta silicon carbide is always compressive and can be relaxed by recovery and recrystallization processes because intrinsic stress is the predominant stress in the films.

Strength of Memory-Induced Anchoring of 5CB on Bare Untreated ITO

We realize uniform planar alignment of 5CB on isotropic untreated ITO substrate. The counterplate orientation is “imprinted” on ITO and memorized by adsorption of an oriented nematic layer. We measure the azimuthal and the zenithal anchoring energies. We show that the memory induced anchoring strength is similar to the one usually found for substrates with high anisotropy. Studying rubbed ITO substrate, we show that in this case also the azimuthal anchoring is mainly due to memory effect.

Thermal Deformation of Initially Curved Substrates Coated by Thin Inhomogeneous Layers

Thermal curvature changes and membrane strains are analyzed for elastic shallow shell substrates which are coated by thin, generally inelastic, inhomogeneous and anisotropic layers. The analysis is restricted to linear kinematics. It is shown that the deformation is governed by the corresponding solution for a flat substrate and a correction due to the initial curvature. The correction is determined from a shallow shell problem for the bare substrate with a loading expressed by the coefficients of thermal curvature for the substrate/layer system. For constant initial curvatures, certain analytic solutions are presented. For situations when the initial deflection of the substrate is much larger than the substrate thickness, a boundary layer solution is derived. In the particular case of a circular isotropic substrate with a spherical initial curvature and a coating of arbitrary anisotropy, the solution is presented in closed form. For nonflat substrates, measured curvatures can generally not be used to extract layer stresses without a proper compensation for the initial curvature. In the paper, it is explicitly presented how to accurately compensate for a spherical initial curvature. The results are particularly discussed in relation to curvature measurements on Silicon substrates.

Effect of substrate dielectric anisotropy on the frequency behavior of microstrip circuits

In this paper, we carry out a full-wave analysis of shielded two-port microstrip circuits, in which the metallizations are embedded in a multilayered substrate that may contain isotropic dielectrics and/or anisotropic dielectrics. The Galerkin's method in the spectral domain is applied for determining the current density on the metallizations of the circuits when their feeding lines are excited by means of delta-gap generators, and the matrix pencil technique is subsequently used for deembedding the scattering parameters from the computed current densities. Results are presented for the scattering parameters of some microstrip discontinuities and filters printed on both isotropic dielectric substrates and anisotropic dielectric substrates. These results show that when substrate dielectric anisotropy is ignored, errors arise when computing the scattering parameters of microstrip discontinuities and when predicting the operating frequency band of microstrip filters.

Nonlinear surface waves in isotropic elastic substrates with thin films

Surface waves in isotropic elastic solids are nondispersive. Considered here is the effect of dispersion, due to a thin solid film on the surface of an isotropic substrate, on nonlinear propagation. The analysis is performed with the theoretical model developed by Zabolotskaya [J. Acoust. Soc. Am. 91, 2569 (1992)] augmented to include dispersion. The dispersion relation is obtained from linear theory but is otherwise exact. Approximations leading to a relation of the Korteweg–de Vries or Benjamin–Ono type, sometimes proposed for the study of dispersive nonlinear surface waves, are not employed. Both loading and stiffening films are considered. Loading films decrease the surface wave speed. Stiffening films increase the surface wave speed until it equals the shear wave speed in the substrate, where cutoff of the surface wave mode occurs. Computations were performed with elastic moduli for a fused quartz substrate, which exhibits negative nonlinearity in the sense that rarefaction rather than compression shocks form in the horizontal particle velocity waveform. Gold (loading) and alumina (stiffening) films are considered. Weak, moderate, and strong dispersion (corresponding to increasing film thickness) relative to nonlinearity are examined. Stationary wave solutions are obtained for the alumina film. [Work supported by ONR.]

Microstructural study of residual stress in chemically vapor deposited β-SiC

Silicon carbide was chemically vapor deposited (CVD) on isotropic pyrolytic graphite substrates by using methyltrichlorosilane as the source gas and hydrogen as the carrier gas. Transmission electron microscopy was used to observe microstructural defects in CVD β-SiC caused by residual stresses. Microstructures resulting from recovery and annealing effects during the deposition processes were also observed and are discussed. The magnitude of residual stress between deposition temperatures of 1400 and 1600°C decreased from about 2000 to about 250 MPa, estimated by the wafer central deflection method.

Bending of crystalline plates under the influence of surface stress — a finite element analysis

Changes in the surface stress Δ τ (s) at the solid–vacuum and the solid–liquid interface are typically measured via the bending of a (thin) crystalline plate. The bending is converted into Δ τ (s) with the help of elasticity theory. Although the conversion is trivial for the unconstrained bending of an elastic isotropic substrate, it becomes less straightforward for single crystals. In this paper we firstly consider the analytical solution for the free two-dimensional bending of a cubic substrate under the influence of a homogeneous, but anisotropic surface stress. Secondly, the bending is calculated numerically for the experimentally mostly realized case of a sample with (100) or (111) surfaces clamped along one edge. In principle, separate numerical calculations are required for each individual material and surface orientation. It is shown that a parameterized form of the analytical solution for the unconstrained bending can still be used in most cases. The appropriate parameters are calculated for various Poisson ratios and crystal anisotropies.

Effect of the Dielectric Anisotropy on the Propagation Properties of Microstrip Tapers with Height Variations

This paper deals with the design and application of nonuniform microstrip transmission lines on anisotropic substrates. A rigorous analysis is based on the use of Hertz vector potentials, moment method and transmission line theory to determine the dispersion characteristics of single and coupled tapered microstrip lines for accurate performance prediction. Results are presented for the main parameters providing the necessary information to design several devices on tapered microstrip, with variation on the strip width and dielectric height, for (M)MIC and antennas applications. A good agreement was observed with the results available in the literature for tapered lines on isotropic substrates.

Resonant frequency and bandwidth of a superstrate-loaded rectangular patch on a uniaxial anisotropic substrate

In this paper, the effects of both uniaxial anisotropy in the substrate and isotropic superstrate loading on the resonant frequency and bandwidth of a rectangular microstrip patch in a substrate–superstrate configuration are investigated. The problem is rigorously formulated using an integral equation, the kernel of which is the full-wave spectral domain dyadic Green's function for multilayer dielectric substrates. The proposed method for determining the Green's function leads to a concise form of this, diagonalized in the (TM,TE) representation. Using Galerkin's moment method to solve the integral equation, the complex resonance frequencies for the TM01 mode are studied with sinusoidal basis functions. The improper double integrals of the moment method matrix are efficiently calculated by means of a proper choice of the path of integration in the complex wavenumber plane, the upper bound of truncation, and the method of quadrature. For an isotropic substrate, it is demonstrated that the bandwidth decreases with increasing ratio of superstrate-to-substrate thickness for high permittivity and low thickness of superstrate. Also, we show that the resonant frequency and bandwidth are highly dependent on the permittivity variations along the optical axis. Simple approximate formula for the resonant frequency is derived. Other theoretical results obtained show that the resonant frequency decreases monotonically with increasing superstrate thickness, the decrease being greater for high permittivity loading and negative uniaxial anisotropy of the substrate. Thin superstrate with high permittivity together with negative uniaxial anisotropy of the substrate are shown to be the favourable conditions for severe degradation of the half-power bandwidth of the antenna. Copyright © 2000 John Wiley & Sons, Ltd.

The Near- and Far-Zone Fields of Periodic Spherical Arrays of Dipole Antennas on Spherical Chiral Substrates

This paper presents an analytic formulation of the near- and far-field distributions due to periodic spherical arrays of dipole antennas on two spherical biisotropic substrates, i.e., on the chiral sphere and on a perfectly conducting sphere coated with one-layer chiral medium, respectively. For an arbitrary orientation of the dipole antenna array, the dyadic Green's functions in the form of an eigenfunction expansion in terms of the normalized spherical vector wave functions are directly employed. Thereby, exact representations of the radiated fields in both near and far zones are obtained in closed form. They are all in a superposition of right- and left-handed circularly polarized waves, and are also applicable for the cases of spherical arrays of dipole antennas on spherical isotropic substrates. Furthermore, the constitutive parameter effects of the chiral medium on the three-dimensional patterns of the far-zone field and its polarized feature are demonstrated numerically.

The Near- and Far-Zone Fields of Periodic Spherical Arrays of Dipole Antennas On Spherical Chiral Substrates - Abstract

This paper presents an analytic formulation of the near- and far-field distributions due to periodic spherical arrays of dipole antennas on two spherical biisotropic substrates, i.e., on the chiral sphere and on a perfectly conducting sphere coated with one-layer chiral medium, respectively. For an arbitrary orientation of the dipole antenna array, the dyadic Green's functions in the form of an eigenfunction expansion in terms of the normalized spherical vector wave functions are directly employed. Thereby, exact representations of the radiated fields in both near and far zones are obtained in closed form. They are all in a superposition of right- and left-handed circularly polarized waves, and are also applicable for the cases of spherical arrays of dipole antennas on spherical isotropic substrates. Furthermore, the constitutive parameter effects of the chiral medium on the three-dimensional patterns of the far-zone field and its polarized feature are demonstrated numerically.

“Fuse Safety Device” on an Atomic Scale

We study a nonlinear response of the underdamped generalized Frenkel-Kontorova model (a system of interacting atoms placed into an external periodic potential) on the dc driving force. Both studied variants of the model, one with a transverse degree of freedom, and another with two-dimensional isotropic substrate potential, exhibit an interesting ``fuse''-like behavior: at small forces the system is in the regime of running kinks with a nonzero conductivity, while at higher forces the system is trapped in an immobile state. This behavior is explained in terms of a dynamical transition between two states of kinks.

Shadow-angle method for anisotropic and weakly absorbing films

A method for determining the optical properties of a film on an isotropic substrate is proposed. The method is based on the existence of two specific incidence angles in the angular interference pattern of the p-polarized light where oscillations of the reflection coefficient cease. The first of these angles, theta(B1), is the well-known Abelès angle, i.e., the ambient-film Brewster angle, and the second angle theta(B2) is the film-substrate Brewster angle. In the conventional planar geometry and in a vacuum ambient there is a rigorous constraint epsilon(1) + epsilon > epsilon(1)epsilon on the film and the substrate dielectric permittivities epsilon(1) and epsilon, respectively, for the existence of the second angle theta(B2.) The limitation may be removed in an experiment by use of a cylindrical lens as an ambient with epsilon(0) > 1, so that both angles become observable. This, contrary to general belief, allows one to adopt the conventional Abelès method not only for films with epsilon(1) close to the substrate's value epsilon but also for any value of epsilon(1). The method, when applied to a wedge-shaped film or to any film of unknown variable thickness, permits one to determine (i) the refractive index of a film on an unknown substrate, (ii) the vertical and the horizontal optical anisotropies of a film on an isotropic substrate, (iii) the weak absorption of a moderately thick film on a transparent or an absorbing isotropic substrate.

Improved model for the magnetostrictive deflection of a clamped film–substrate system

The effect of clamping at one end on the deflection produced by magnetostrictive strain of a magnetic film deposited on an isotropic elastic substrate was predicted. The proposed model takes advantage of previous literature results obtained for a free state or for the case of a clamped bimorph without transverse curvature. The minimization of energy gives a displacement at the free end of the sample which is different from that obtained in the not clamped sample by an amount which depends on the Poisson's ratio of the substrate. This improvement in the analytical evaluation of the deflection produces an accurate calculation (in the most generally used experimental conditions) which supports the preceding results obtained by finite element modeling.

Thermoelastic analysis of periodic thin lines deposited on a substrate

Thermoelastic stresses and curvatures arising from patterned thin lines on initially flat isotropic substrates are analyzed. A connection is made between substrates with patterned lines and laminated anisotropic composites containing transverse matrix cracks. Using this analogy along with anisotropic plate theories, approximate analytical expressions are derived for volume-averaged stresses as well as curvatures along and normal to the lines, for any thickness, width and spacing of the lines. The predictions of the analysis are shown to compare favorably with finite element simulations of stresses and curvatures for Si substrates with Al, Cu or SiO 2 lines. The predictions also match prior experimental measurements of curvatures along and normal to patterned SiO 2 lines on Si wafers, and further capture the general experimental trends reported previously for curvature evolutions in Si wafers with Al lines. The model presented here thus provides a very convenient and simple analytical tool for extracting stresses in thin lines on substrates from a knowledge of experimentally determined film stress, thereby circumventing the need for detailed computations for a wide range of unpassivated line geometries of interest in microelectronic applications.

Formation Mechanism of SiC Gradient in Carbon Materials

High-density isotropic graphite substrates with and without a notch produced at the surface were contactedwith metallic silicon and heated at 1350 and 1450°C. The contribution of open pores in the substrates for the formationof SiC-gradient was discussed. At 1350°C, no SiC-gradient was observed at the surface of the substrate without thenotch, but the gradient in the substrate was formed at 1450°C. On the substrates with notch, fibers were formed on thenotch wall of the substrate heated at 1350°C. By heating at 1450°C, however, SiC was detected at the portion beyondthe nose of notch. In present study, it was expected that small amount of 02 are enclosed in the open pores and in thenotch. Based on the expected reactions among silicon, carbon and oxygen, the formation of SiC-gradient in thesubstrate at 1450°C was found to be possibly formed due to the reaction between carbon on the wall of pores and SiOgas through the open pores from the surface of the substrate.

Ellipsometric study of refractive index anisotropy in porous silicon

Porous Si layers of different thicknesses were prepared by anodising p +-type Si substrates with a resistivity of 0.01 Ω cm. The porosity of the samples ranged from 23% to 62%. The refractive index values for the ordinary and extraordinary rays were determined by multiple angle of incidence ellipsometry, from which an optical anisotropy parameter varying from 13% to 20% was obtained. The porous Si layers were modelled as uniaxially anisotropic films on an isotropic substrate, with an optical axis perpendicular to the sample surface. The morphological anisotropy which is typical for the p +-type porous Si with a predominating cylindrical geometry is responsible for these optical properties. All the porous Si layers studied were found to be optically negative.