Isotropic Substrate Research Articles

Ring-resonator method - effective procedure for investigation of microstrip line

In addition to the traditional application of the ring-resonator method for determination of the microstrip line effective permittivity, measurements of the insertion losses and equivalent substrate permittivity are proposed. The obtained data for a number of isotropic and anisotropic substrate materials are in good agreement with the results predicted theoretically.

Mesopatterning of Thin Liquid Films by Templating on Chemically Patterned Complex Substrates

Surface directed instability and dewetting in thin films and resulting morphologies are studied using 3D nonlinear simulations based on the equations of motion, both for the isotropic and anisotropic 2D substrate patterns. Three different substrate (wettability) patterns are considered: (a) arrays of more (or completely) wettable rectangular blocks on a less wettable substrate, (b) arrays of less wettable blocks on a more (or completely) wettable substrate, and (c) a checkerboard pattern of alternating more and less wettable blocks. An ideal replication of the surface energy pattern produces an ordered 2D array of liquid columns (in case 1), or a matrix of holes on a flat liquid sheet (in case 2), or a checkerboard pattern of alternating liquid columns and holes/depressions (in case 3). The effects of pattern periodicity, domain widths, anisotropy, and wettability on the morphological phase transitions are presented. Regardless of the precise geometry of the substrate pattern, templating is found to be b...

An improved reflectometric method to measure the azimuthal anchoring energy of nematic liquid crystals.

Some years ago we developed an automatized reflectometric method to measure the surface azimuthal anchoring energy of nematic liquid crystals on an optically isotropic substrate. This method provides a high accuracy and sensitivity but requires the use of wedge glass plates and a sufficiently high anisotropy of the intensity reflectivity coefficients. This latter condition restricts greatly the number of possible substrates that can be investigated with this technique. Here we develop a new reflectometric method which offers comparable or better accuracy and sensitivity but does not require wedge plates and high anisotropy of the reflectivity coefficients. The method is fully automated and provides a direct measurement of the azimuthal director angle. The experimental procedure exploits the dependence of the reflectivity tensor on the surface director orientation. The measurement of the azimuthal angle does not require any knowledge of the optical parameters of the nematic material and of the optically isotropic substrate, and provides an absolute accuracy better than 0.2( degrees ) in the whole range 0-360( degrees ) and a sensitivity better than 0.1( degrees ). This reflectometric method can be also used with weakly anisotropic substrates as well as thin rubbed polymeric layers. In this latter case, the effective uncertainty in the measurement of the director azimuthal angle depends on the substrate anisotropy. A simple and direct experimental procedure to estimate this uncertainty is proposed.

A COUPLED-MODE THEORY-BASED ANALYSIS OF COUPLED MICROSTRIP LINES ON A FERRITE SUBSTRATE - ABSTRACT

Presented herein is a coupled-mode formulation for coupled microstrip lines on a magnetized ferrite substrate. The formulation discussed here is an extension of the coupled-mode theory for microstrip lines on an isotropic substrate. Since the magnetized ferrite exhibits a biaxial anisotropy in its permeability, the guided-wave fields in the magnetized ferrite are not subject to the conventional reciprocity relation for fields in an isotropic medium. Thus, a generalized reciprocity relation is first derived from two sets of guided-wave fields, which propagate in ferrite magnetized transversely along the strip surface. The reciprocity relation is then used to derive coupled-mode equations for coupled microstrip lines on a ferrite substrate. As a basic numerical example, the new formulation is applied to two coupled microstrip lines on a ferrite substrate.

Radiation efficiency and surface waves for patch antennas on inhomogeneous substrates

Surface wave characteristics, as well as radiation efficiency of a patch antenna, with a given current distribution, located on top of an inhomogeneous, isotropic substrate are calculated. The substrate is infinite in the lateral directions and inhomogeneous with respect to the height coordinate. The surface waves in the substrate are analysed using the propagator technique and residue calculus. The propagators and the residues are found by solving two sets of systems of ordinary differential equations (ODEs). Several dispersion curves of the surface waves for inhomogeneous substrates are calculated. The radiation efficiency is compared with the corresponding quantities of a printed antenna on a homogeneous substrate.

Delamination of thin film strips

Delamination of residually stressed thin film strips is analyzed to expose the dependence on strip width and film/substrate elastic mismatch. Isotropic films and substrates are assumed. The residual stress in the film is tensile and assumed to originate from mismatch due to thermal expansion or epitaxial deposition. Full and partial delamination modes are explored. In full delamination, the interface crack extends across the entire width of the strip and releases all the elastic energy stored in the strip as the crack propagates along the interface. The energy release rate available to propagate the interface crack is a strong function of the strip width and the elastic modulus of the film relative to that of the substrate. The energy release rate associated with full delamination is determined as a function of the interface crack length from initiation to steady-state, revealing a progression of behavior depending in an essential way on the three dimensionality of the strip. The dependence of the energy release rate on the remaining ligament as the interface crack converges with the strip end has also been calculated, and the results provide an effective means for inferring interface toughness from crack arrest position. A partial delamination propagates along the strip leaving a narrow width of strip attached to the substrate. In this case, the entire elastic energy stored in the strip is not released because the strain component parallel to the strip is not relaxed. A special application is also considered, in which a residually stressed metal superlayer is deposited onto a polymer strip. The energy release rate for an interface crack propagating along the interface between the polymer and the substrate is determined in closed form.

Thermomechanical deformation of a bimaterial plate––as applied to laminate IC assemblies

This paper examines thermomechanical warpage in a bimaterial plate. It considers the suitability of axisymmetric and generalized plane strain finite element analyses, and it compares these to the 3-D analysis of a bimaterial plate in which properties of one of the materials vary in orthogonal directions within the plane of the plate. These findings are compared to results from mechanical measurement of a BGA substrate. The influence of orthotropic versus isotropic substrate properties is investigated with regard to warpage. The root cause of previously unexplained saddle-shaped warpage is identified as the asymmetry of the copper traces, and design rules regarding substrate layout are recommended.

In-situmeasurement of magnetostrictive coefficient and elastic properties for thin films during growth

A method to determine simultaneously the magnetostrictive coefficient and the elastic properties (Young’s modulus and Poisson ratio) of a thin film during the growth was developed based on minimization of the total elastic energy of a cantilever film-substrate system. Compared to other published measurement methods, an inaccuracy in the magnetostrictive coefficient, caused by assuming the elastic properties of the film as those of the bulk material, could be avoided. Only one elastic isotropic substrate is employed in the present method. The experimental data of an Fe-based amorphous thin film was analyzed using the model. The calculated dependence of the magnetostrictive coefficient on the external magnetic field was compared with the experiment, and the discrepancy between both results is explained. Furthermore, the elastic properties of the film were also obtained.

Spatiotemporal mapping of surface acoustic waves in isotropic and anisotropic materials

We demonstrate a new method for a real-time imaging of surface acoustic waves at frequencies up to 1 GHz with picosecond temporal and micron spatial resolutions using an ultrafast optical pump and probe technique combined with a common path interferometer. Using samples with isotropic or anisotropic substrates coated with metallic thin films, we observe the propagation of Rayleigh-like modes and surface-skimming bulk modes as well as resolving surface phonon focusing effects. In addition we image surface acoustic wave propagation in a laterally inhomogeneous sample.

Evolution of leaky modes on printed-circuit lines

The frequency evolution of dominant (quasi-TEM) and higher order modes on an open printed-circuit structure such as a microstrip is examined. Three different mode types are considered, including bound modes (BMs), leaky modes that leak into the surface wave of the background structure, and leaky modes that also leak into space. One of the fundamental goals is to establish the conditions under which one type of mode can transition into another type as the frequency changes. One important conclusion is that the dominant BM can never transition into a leaky mode for a microstrip structure with an isotropic substrate, but such a transition is possible for an anisotropic substrate, observed originally by Tsuji et al. and Shigesawa et al. However, higher order BMs can directly transition into leaky modes, as shown by Oliner and Michalski and Zheng. On other structures such as coplanar strips, where the bound dominant mode exhibits odd symmetry, a transition from a bound dominant mode to a leaky mode is possible, as shown by Shigesawa et al. and Tsjui et al. In addition to examining the mathematical transitions that are possible, the physical continuation of modes is also investigated, by examining the frequency evolution of the currents excited by a practical source. It is concluded that there may be physical continuity between modes, even if there is no mathematical continuity.

Scattering from a Frequency Selective Surface Supported by a Bianisotropic Substrate

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. (Less)

U‐patch antenna loaded by complex substrates for multifrequency operation

AbstractIn this paper, the analysis of patch antennas with U‐shaped metalization loaded by bianisotropic media is developed. A theoretical study is performed to obtain transmission‐line equations for bianisotropic materials, and then a method‐of‐lines (MoL) procedure is applied to obtain the radiative characteristics. Presented results assure, for particular patch dimensions and feed application geometry, a multifrequency operation in the microwave range, even for isotropic substrates. The application of bianisotropic materials gives better performances for bandwidth and input impedance at the central frequency, but degrades other frequency operation performances. © 2002 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 3–5, 2002.

Novel Polarized-Light Emitting Polymer Systems: II. Use of Form Birefringent Polarization-Selective Mirrors

In reflectivity measurements on submicron-embossed polystyrene films, we found that form-birefringent polymer gratings can be described by generalized Fresnel equations for a biaxially anisotropic film in an optically isotropic medium. Thus, polarized-light emitting illumination systems may be envisioned that basically consist of an optically isotropic substrate, into which light is coupled from an external light source, and a second layer, which comprises a form-birefringent, submicron relief structure on the bottom surface that acts as polarization-selective mirror and a light out-coupling structure on the top surface. Such a design should simplify device manufacturing considerably as the main parts of the systems could be produced by injection molding using inexpensive bulk polymers.

Analytic solution of stress distribution under a thin film edge in substrates

We have obtained an analytic solution for the stress distribution under a thin film edge in isotropic substrates of finite thickness and of infinite extent in the other two directions. Far from the film edge on the side without the film, all stress components are zero and far from the film edge under the film, the stress distribution is in accordance with that given by the bimetallic strip theory. To demonstrate the validity of this solution, the experimental infrared photoelastic stress fringe pattern obtained by a dark-field plane polariscope in a Si substrate under an oxide film edge was successfully reproduced using this solution.

Generally polarized acoustic waves trapped by high aspect ratio electrode gratings at the surface of a piezoelectric material

It has been shown theoretically and demonstrated experimentally that shear horizontal (SH) surface waves can exist when the surface of an isotropic substrate is perturbed by a strong corrugation, for instance consisting of deep grooves etched in the substrate, whereas these waves cannot exist without this perturbation. It is shown in this article that a periodic array of metallic electrodes (wires) exhibiting large aspect ratios deposited over a piezoelectric substrate give rise to surface acoustic waves with general polarization. The admittance of an interdigitated transducer, which is a basic tool for predicting the waves parameters, is calculated by a combination of finite element analysis and a boundary integral method. This approach has been extended to obtain the polarization of the acoustic waves. For different piezoelectric substrates, we predict various surface acoustic modes and their polarization. Along with mostly SH modes, we also find modes mostly polarized in the sagittal plane. We discuss the frequency behavior of the surface modes as a function of the electrode height compared to the period.

Simultaneous measurements of the magnetostrictive coefficient, Young’s modulus, and Poisson ratio of thin films

A method, which determines simultaneously the magnetostrictive coefficient, Young’s modulus, and Poisson ratio of a thin film utilizing the minimization of the total elastic energy of a cantilever film–substrate system, is suggested. An inaccuracy for the magnetostrictive coefficient, caused by assuming the elastic properties of the film as those of the corresponding bulk material, could be avoided and only a single elastic isotropic substrate is employed in the present method. The experimental data of an Fe-based amorphous thin film were analyzed by using the model. The calculated dependence of the magnetostrictive coefficient on the external magnetic field was compared with the experiment, and the discrepancy between both results were explained. The elastic properties of the film were also obtained.

Optical Studies of Chiral Mesophases in Sandwich Cells with Planar Degenerated Anchoring

We use a surface treatment allowing to obtain planar anchoring, azimuthally degenerated, by deposition of a silane coupling agent (GLYMO) on an isotropic substrate (bare glass plate). This technique of “passivation'' prevents the liquid crystal adsorption on the substrate and avoids memory effects. We present a method of measure of the spontaneous geometric parameters for chiral mesophases by simple optical observations, using a cell with variable thickness and azimuthally degenerated planar anchoring on one of the plates. The cholesteric and the TGB phases were studied for two: 12F2BTFO1M7(TGBc) and 10F2BTFO1M7 (TGBA). The cell allows to observe the slabs, even for the TGBA phase, and to measure independently their thickness and twist. Our results are in agreement with previous X-ray measurements.

Thermal and mechanical stresses in transversely isotropic coatings

Three-dimensional sliding contact and thermal contact stress analysis of transversely isotropic coatings on isotropic or transversely isotropic substrate is presented. Fourier transforms are used to obtain solutions for temperature rise and stresses. The solutions are illustrated with temperature rise and stresses in a single layered half-space induced by moving Hertz pressure. The effects of coating thickness, friction coefficient and Peclet number (dimensionless heat source velocity) on temperature rise and stresses in coated bodies are discussed. It is found that the effect of the isotropy parameter of coating (ratio of lateral thermal conductivity to normal thermal conductivity) on dimensionless surface temperature rise is not significant at higher Peclet numbers. It is also found that frictional heating can lower the maximum surface tensile stress. In low friction contacts, the thermal effects on Von Mises stress in the coating and the substrate are not particularly significant.

Infrared Photoelastic Study of Thin-Film-Edge-Induced Stresses in Silicon Substrates

ABSTRACTThe stress distribution in silicon substrates under a silicon dioxide thin film edge, long oxide thin film stripes and long oxide window structures have been studied using the infrared photoelastic (IRPE) method. The experimental IRPE stress fringe patterns were compared with the simulated patterns based on an analytic solution we obtained recently for the stress distribution under a thin film edge in isotropic substrates. Dependence of the stress distribution in these structures on the geometrical parameters such as the stripe width, window width, and substrate thickness were also studied. The implication of a slight discrepancy between the experimental and simulated IRPE patterns on the singular behavior of stress field in the substrate at the film edge and the concentrated force assumption are discussed.

Broad-Band U-Slot Patch Antennas Loaded By Chiral Material

The analysis of wide band microstrip/slot antennas residing in cavities with arbitrary patch shapes and in presence of both isotropic and chiral materials is proposed in this paper. The theoretical approach is based on the variational formulation and the numerical solution is carried out by applying a combined Finite Element-Boundary Integral (FE-BI) Method. Such an approach already known in the literature only for isotropic and anisotropic media is extended also to the case of biisotropic dielectrics, including chiral materials. A numerical code based on the new theory here presented has been developed and it is employed in order to investigate the main features of chiral materials as substrates for cavity backed microstrip antennas. This numerical code allows to study also antennas loaded by isotropic substrates as particular cases when imposing the chiral admittance to vanish. To test this capability the design of an U-slot microstrip antenna printed on a conventional isotropic dielectric for wide band applications is proposed. Finally, it is shown how the employment of chiral substrates instead of isotropic ones reduces the antenna size for a fixed working frequency and improves the impedance bandwidth, without decreasing too much the other radiating properties.