Anisotropy driven interrupted coarsening of the Asaro-Tiller-Grinfeld instability

We investigate the effects of surface energy anisotropy on the coarsening dynamics of the Asaro-Tiller-Grinfeld instability at stake in thin semiconductor films. We consider a continuum model which accounts for wetting interactions between the film and its substrate, elasticity driven mass currents and surface energy anisotropy. We derive an explicit non-linear, non-local evolution equation for the film height that we solve numerically. Anisotropy, which dictates the island shapes, impacts the growth kinetics by weakening the possible elastic relaxation, which can lead during annealing to an interruption of Ostwald ripening. The resulting stationary state is characterized by square-based pyramids separated by a wetting layer. It is found that the instability onset is delayed when the film thickness decreases above the critical thickness for the instability to occur. We characterize the influence of the growing flux used for the film deposition on the stationary state reached during subsequent annealing, and find that the density of the resulting self-organized islands increases with the flux.     

Optical effect of the substrate on the anomalous absorption of aggregated silver films

The optical effect of the substrate on the anomalous absorption of aggregated silver films is taken into account in terms of the dipole interaction between an island particle and its mirror image in the substrate. The previously reported relation 2F|+F⊥<1, which holds for the observed values of the apparent depolarizing factors of island particles for an electric field parallel to (F|) and perpendicular to (F|) the substrate surface, is explained by the effect. The parameters characterizing the film structure are optically evaluated by stretching the substrate, and are compared with those evaluated from electron micrographs.     

Edge delamination in an orthotropic bimaterial consisting of a thin film and a substrate

This paper investigates edge delamination in an orthotropic layered structure composed of a thin film and a substrate under a temperature change. An edge interface crack is analyzed for two configurations in which it emerges from an interior or corner edge of the film. Special attention is paid to the effects of orthotropic material constants on delamination cracking. The necessary material parameters involved in the energy release rate and mode mixity for the interface crack are found based on a modified Stroh formalism. The explicit dependence of the energy release rate and mode mixity on one orthotropic parameter for the film is discovered using an orthotropy rescaling technique. The effects of other material parameters on the energy release rate and mode mixity are examined numerically, and the growth and arrest of edge interface cracks are discussed based on an energy criterion.     

An explicit elastic solution for a brittle film with periodic cracks

A two-dimensional explicit elastic solution is derived for a brittle film bonded to a ductile substrate through either a frictional interface or a fully bonded interface, in which periodically distributed discontinuities are formed within the film due to the applied tensile stress in the substrate and consideration of a “weak form stress boundary condition” at the crack surface. This solution is applied to calculate the energy release rate of three-dimensional channeling cracks. Fracture toughness and nominal tensile strength of the film are obtained through the relation between crack spacing and tensile strain in the substrate. Comparisons of this solution with finite element simulations show that the proposed model provides an accurate solution for the film/substrate system with a frictional interface; whereas for a fully bonded interface it produces a good prediction only when the substrate is not overly compliant or when the crack spacing is large compared with the thickness of the film. If the section is idealized as infinitely long, this solution in terms of the energy release rate recovers Beuth’s exact solution for a fully cracked film bonded to a semi-infinite substrate. Interfacial shear stress and the edge effect on the energy release rate of an asymmetric crack are analyzed. Fracture toughness and crack spacing are calculated and are in good agreement with available experiments.     

Interfacial crack propagation in a thin viscoelastic film bonded to an elastic substrate

Edge decohesion along the interface of a thin viscoelastic film bonded to an elastic substrate under tensile residual stresses is considered. The tensile residual stress in the film is replaced by a combination of edge loads, and an explicit relation of strain energy with respect to time is obtained through simple beam analysis. The strain energy function is discretized into time steps which are assumed to be very small so that the dissipation effects over the time steps can be neglected. The energy release rate is then calculated using a Griffith type energy balance. An analytical model is developed to predict the crack growth and its velocity. Extent of crack growth along the interface is prediced based on a fracture criteria. The analytical predictions are compared with results from a viscoelastic finite element analysis.     

Absolute thermoelectric power and temperature coefficient of resistance of thin continuous metal films

General expressions are derived in terms of a function F(K), which is equal to the ratio of film to bulk conductivity, for the following: the ratio of film to bulk resistivity, the absolute thermoelectric power of the film material and the ratio of film to bulk temperature coefficient of resistance. The exact and approximate forms of the function F(K) for various theories of the scattering mechanism at the film surfaces are reported. Also plots of the derived expressions using some of these forms are given.     

Influence of substrate absorption on the optical and geometrical characterization of thin dielectric films

The role played by a glass substrate on the accurate determination of the optical constants and the thickness of a thin dielectric film deposited on it, when well-known envelope methods are used, is discussed. Analytical expressions for the two envelopes of the optical transmission spectra corresponding to film. with both uniform and nonuniform thicknesses are derived, assuming the substrate to be a weakly absorbing layer. It is shown that accurate determination of the refractive index and the film thickness is notably improved when the absorption of the substrate is considered. The analytical expressions for the upper and lower envelope, are used to characterize optically and geometrically both uniform and nonuniform amorphous chalcogenide films. The results obtained are compared with those derived by use of expressions for the envelopes that neglect the substrate absorption. The comparison shows that overestimated refractive indexes and underestimated thicknesses are obtained when the conventional approach, in which the substrate absorption is neglected, is used.     

Noise Loading Analysis of a Memoryless Nonlinearity Characterized by a Taylor Series of Finite Order

Noise loading analysis of a mhemoryless nonlinearity characterized by a Taylor series of finite order is presented in terms of the autocorrelation function of the input signal. For narrow-band application, an explicit expression for the noise power ratio at the output of the nonlinearity is given up to seventh-order characteristic. The corresponding 3-tone intermodulation distortion of type ?1 + ?2 - ?3 is also given for comparison.     

Angular correlation function of speckle patterns scattered from a one-dimensional rough dielectric film on a glass substrate

We present the experimental results of the angular correlation function of far-field speckle patterns scattered by a one-dimensionally random rough surface of a thin dielectric film on a glass substrate when a polarized beam of light is incident upon the rough surface from vacuum. This surface, which separates the vacuum and the dielectric, is rough enough that only diffused speckles are observed. The experiment for the correlation measurement was set up to make use of a CCD camera to obtain the image of the speckle pattern in the specular direction for each given angle of incidence; the cross-correlation function is then calculated from the digitized images. It is found that the intensity correlation functions exhibit two distinct maxima: one arises from the autocorrelation and the other from the reciprocity condition. It is also found that different scattering processes give rise to quite different correlation functions: multiple-scattering processes produce narrow peaks with secondary maxima and single-scattering processes produce relatively broad peaks.     

Photon correlation spectroscopy on flowing polydisperse fluid-particle systems: theory

We develop an analytical expression for the homodyne autocorrelation function of laser light scattered by a laminar flow of a polydisperse particle-fluid system. In contrast to the already existing literature on the development of autocorrelation functions, we explicitly begin with the effects of the finite linewidth of the light source, the spatial and temporal intensity averaging that is due to the detection process, the Brownian particle movement on the amplitudes of the scattered light waves as well as on the degree of resolution that we introduce in this paper, and a general system velocity v = (v(x), v(y), v(z)). One main result is a new physical interpretation of the well-known, generally empirically introduced coherence factor. Quantities that are comparable to the well-known degree of coherence, coherence area, and number of coherence areas have also been obtained. Finally the investigations are simplified to an autocorrelation function that can be used for the analysis of fluid-particle systems in the low Knudsen number regime. It is shown that in this case particle size or size distribution, system velocity, and particle concentration can be obtained simultaneously. The developed autocorrelation function is related to frequently analyzed special cases and compared with expressions from the literature.     

A new method for the structural analysis of thin island films

Analytical formulas for a systemic analysis of the structural coarsening of an island film on a solid substrate are obtained based on a comparison of the characteristics of theoretical and experimental distributions of the island size. This approach established a correlation between the features of transformation of the experimental distributions (histograms) and the features of processes in the island film material.     

Influence of substrate properties on the growth of titanium films: part III

The growth of thin Ti-oxide films (12 nm) on alumina substrate films formed by reactive evaporation of Ti in an oxygen atmosphere was studied by in situ internal stress measurements under ultra high vacuum conditions and transmission electron microscopy. Oxygen pressure and substrate temperatures were the varied parameters of the reactive evaporation. These Ti-oxide-films with different oxygen content (O₂/Ti-films) were then used as substrate films for the deposition of a clean titanium film. The growth stress of the titanium film on the as-deposited O₂/Ti-substrate films is comparable with that previously found for H₂O/Ti-substrates and indicates island growth and the formation of polycrystalline titanium films. Annealing (400°C, 20 min) of the as-deposited – amorphous – O₂/Ti-films gives rise to the formation of crystalline TiO₂. The amount of TiO₂ formed during annealing is strongly dependent on the oxygen content of the O₂/Ti-film. The oxygen content, in return, is dependent on oxygen partial pressure and substrate temperature during O₂/Ti-film deposition. The corresponding changes in the substrate film properties (oxygen content, crystallinity, etc.) are reflected in significant changes in the growth stress of the titanium film. The stress vs. thickness curve of these titanium films appears to indicate a superposition of the growth stress of two different growth modes, i.e. growth of a polycrystalline film with island growth on the as-deposited, amorphous oxide substrate and epitaxial growth of a quasi single crystalline film on the crystalline TiO₂-substrate.     

General expression for the temperature coefficient of resistivity of polycrystalline semi-metal films

After calculating the different contributions to the resistivity of a thin film, a general expression for the temperature coefficient of resistivity in a polycrystalline semi-metal film is derived by taking into consideration the influence of internal size effects on the film resistivity in terms of the Mayadas-Shatzkes function, thermal strains and the difference in the thermal expansion coefficients between the film and its substrate. A comparison with experimental data, in the temperature range 77 to 500 K, over grain size range 30 to 200 nm, for antimony films, 200 nm thick, is made. Good agreement has been found between experiments and the theoretical equations we proposed.     

A higher-order triangular plate bending element revisited

A new formulation of an eighteen-degrees-of-freedom higher-order triangular plate bending element using triangular area co-ordinates is presented. The displacement function w is taken as the complete fifth-order polynomial in area co-ordinates. The normal slope along an edge of the triangle is constrained to vary cubically. The twenty-one constants are expressed explicity in terms of eighteen degrees of freedom. The element stiffness matrix is expressed as a product of component matrices for which explicit expressions are developed and presented. No numerical inversion or integration is necessary. The formulation is expected to be useful specially for microcomputers.     

Hillock and island formation during annealing of gold films

Kinetics of the hillock and island formation during annealing of thin gold film has been studied. The reorganisation of gold film has been distinguished in five stages in progression from the original film to the final island structure. The area occupied by the holes remained virtually constant until the removal of the metal from the substrate started. No increase in the number of holes was detected in the induction period. Hole densities decrease with increasing film thickness. Agglomerates were frequently found at the side of an enlarging hole. The hole growth rate increased steadily with temperature. The growth rate of holes eventually leads to a network structure. The catchment area increased with increasing initial film thickness.     

Controlled layer-by-layer formation of ultrathin TiO2 on silver island films via a surface sol-gel method for surface-enhanced Raman scattering measurement

A surface sol-gel process has been demonstrated to be an effective method for the surface modification of silver island films as unique SERS substrates for monitoring molecular adsorption on a dielectric titania surface. This layer-by-layer approach allows control of the thickness of the dielectric surface with a monolayer precision on silver surfaces. The enhancement of Raman scattering from adsorbed Rhodamine 6G molecules is inversely proportional to the thickness of the titania film, which is consistent with the decay of electromagnetic enhancement. Despite a reduction in the sensitivity of the film, a substantial improvement in the film was achieved as a result of the enhanced stability of this substrate compared to the silver island film without a TiO(2) coating.     

On the purely analytic computation of laminar boundary layer flow over a rotating cone

The fundamental purpose of the present research is to obtain analytical expressions for the solution of the steady laminar flow of an incompressible viscous Newtonian fluid over a rotating cone. Using a proper similarity transformation akin to the classical one of Von Karman the nonlinear equations of motion are reduced to a boundary value problem whose solution is then derived in terms of a series of exponentially-decaying functions for the full range of cone half-angle ? characterizing the conical flow structure. The exact numerical method is found to improve as the cone half-angle is decreased. The effects of the cone half-angle on the physically significant relevant parameters, such as the wall shears, the torque and the vertical suction are clarified. Purely explicit analytical expressions for the solution of governing equations to support the numerically evaluated solutions are also obtained via the homotopy analysis method.     

Phase shifts in frustrated total internal reflection and optical tunneling by an embedded low-index thin film

Simple and explicit expressions for the phase shifts that p- and s-polarized light experience in frustrated total internal reflection (FTIR) and optical tunneling by an embedded low-index thin film are obtained. The differential phase shifts in reflection and transmission deltar, deltat are found to be identical, and the associated ellipsometric parameters psir, psit are governed by a simple relation, independent of film thickness. When the Fresnel interface reflection phase shifts for the p and s polarizations or their average are quarter-wave, the corresponding overall reflection phase shifts introduced by the embedded layer are also quarter-wave for all values of film thickness. In the limit of zero film thickness (i.e., for an ultrathin embedded layer), the reflection phase shifts are also quarter-wave independent of polarization (p or s) or angle of incidence (except at grazing incidence). Finally, variable-angle FTIR ellipsometry is shown to be a sensitive technique for measuring the thickness of thin uniform air gaps between transparent bulk media.     

Aspheric wave-front recording optics for holographic gratings

The geometric theory of aspheric wave-front recording optics is extended to include the fourth-order groove parameters that correspond to the fourth-order holographic terms in the light-path function. We derived explicit expressions of the groove parameters by analytically following an exact ray-tracing procedure for a double-element optical system that consists of a point source, an ellipsoidal mirror, and an ellipsoidal grating blank. Design examples of holographic gratings for an in-plane Eagle-type vacuum-UV monochromator are given to demonstrate the capability of the present theory in the design of aspheric wave-front recording optics.