Analytical relations for thin-film total internal reflection phase retarders

Single-layer coatings on total internal reflection boundaries that produce any specific phase retardation are analyzed. One- and two-reflection phase-retarding systems are considered. Simple quadratic equations are obtained for an unknown layer phase thickness at a given angle of incidence and phase retardation. Equations for specific multilayer coatings that are equivalent to single-layer designs are also deduced. Diagrams of solution zones for refractive indices are given comparatively for one- and two-reflection systems.     

Unified analysis and mathematical representation of film-thickness behavior of film-substrate systems

The ellipsometric function p of a film-substrate system is studied as the film thickness d is kept constant and the angle of incidence phi is changed. The generated constant-thickness contours (CTCs) are characterized by an introduced mathematical behavior indicator that represents a group of CTCs. The behavior of each group is developed and studied in the four planes phi-d, X, Z, and p, where X is the film-thickness exponential function and Z is a previously introduced intermediate plane. In the phi-d plane the film-thickness domain is identified and divided into a sequence of disconnected thickness subdomains (DTSs), depending on only N0 and N1, and their number depending on the range in which N0/N1 lies. The behavior of the CTCs in the successive planes X, Z, and p is then studied in each DTS, and the CTC's space is divided into disconnected subfamilies according to the behavior indicator. Equivalence classes that reduce the infinite number of subfamilies into a finite number are then introduced. The transformation from each plane to the next is studied with the origin of the Z plane mapped onto the point at infinity of the p plane, forming a singularity. A multiple-film-thickness inequality is derived to determine the unique solution of the film thickness. The type of reflection being internal or external at both ambient-film and film-substrate interfaces affects the analysis and is also considered. To conclude we introduce the design of polarization-preserving devices and a novel oscillating single-element ellipsometer to fully characterize zero film-substrate systems as examples of applying the knowledge developed here.     

Closed-form inversion of the reflection ellipsometric function of a film-substrate system: absorbing-substrate optical constant

A closed-form inversion expression for obtaining the optical constant (complex refractive index) of the substrate of an absorbing-film-absorbing-substrate system from one reflection ellipsometry measurement is derived. If, in addition, the film thickness is to be determined, a second measurement at another angle of incidence may or may not be used. The derived formula does not introduce errors itself, and tolerates errors in input variables very well. Random and systematic errors in the measured ellipsometric parameters do not affect the value obtained for the optical constant of the substrate: it is always the true value to two decimal places. Two examples in ellipsometry and in the design of reflection-type optical devices, one each, are presented and discussed. In addition, experimental results for a commercially available wafer are also presented. Two other closed-form inversion expressions for obtaining the optical constant of the substrate from two and three measurements are also presented and briefly discussed.     

Indentation and imprint mapping for the identification of interface properties in film-substrate systems

Indentation tests are frequently employed at present for the identification of material parameters at different scales. An innovative inverse analysis technique, recently proposed by the Authors, combines the traditional indentation test with the mapping of the residual deformations (imprint), thus providing experimental data apt to be used to identify material parameters in film-substrate systems. In this paper, such methodology is enhanced to permit the identification of the fracture properties of the interface between a coating and its substrate once the bulk material parameters are known. In order to make the inverse problem well posed, a further set of experimental data, namely the horizontal displacement field measured on the film external surface, is considered as available experimental information. The sought material parameters are recovered through recursive calculations of the mechanical response of the film-substrate system, performed by a finite strain numerical simulation. The coating and a significant portion of the underlying bulk material are incorporated in the finite element models built up to this purpose, while delamination is accounted for through cohesive elements. The inverse analysis procedure rests on a batch, deterministic approach and conventional optimization algorithms are employed for the minimization of a suitably defined discrepancy norm. Extensive numerical computations have been performed in order to test the performance of the proposed methodology in terms of result accuracy and computational effort.     

A review of theoretical analysis techniques for cracking and corrosive degradation of film-substrate systems

This paper contains a review of the most vital concepts regarding the analysis and design of film systems. Various techniques have been presented to analyse and predict the failure of films for all common types of failure: fracture, delamination, general yield, cathodic blistering, erosive and corrosive wear in both organic and inorganic films. Interfacial fracture or delamination is the loss of bonding strength of film from substrate, and is normally analysed based on the fracture mechanics concepts of bi-material systems. Therefore, keeping the focus of this review on bonding strength, the emphasis will be on the interfacial cracking of films and the corresponding stresses responsible for driving the delamination process. The bi-material characteristics of film systems make the nature of interfacial cracks as mixed mode, with cracks exhibiting various complex patterns such as telephone cord blisters. Such interfacial fracture phenomenon has been widely studied by using fracture mechanics based applicable analysis to model and predict the fracture strength of interface in film systems. The incorporation of interfacial fracture mechanics concepts with the thermodynamics/diffusion concepts further leads to the development of corrosive degradation theories of film systems such as cathodic blistering. This review presents suggestions for improvements in existing analysis techniques to overcome some of limitations in film failure modelling. This comprehensive review will help researchers, scientists, and academics to understand, develop and improve the existing models and methods of film-substrate systems.     

Embedded centrosymmetric multilayer stacks as complete-transmission quarter-wave and half-wave retarders under conditions of frustrated total internal reflection

A centrosymmetric multilayer stack of two transparent materials, which is embedded in a high-index prism, can function as a complete-transmission quarter-wave or half-wave retarder (QWR or HWR) under conditions of frustrated total internal reflection. The multilayer consists of a high-index center layer sandwiched between two identical low-index films with high-index-low-index bilayers repeated on both sides of the central trilayer, maintaining the symmetry of the entire stack and constituting a QWR (Delta(t)=90 degrees or 270 degrees ) or HWR (Delta(t)=180 degrees ) in transmission. A QWR design at wavelength lambda=1.55 microm is presented that employs an 11-layer stack of Si and SiO(2) thin films, which is embedded in a GaP cube prism. The intensity transmittances for the p and s polarizations remain >99% and Delta(t) deviates from 90 degrees by <+/-3 degrees over a 100 nm spectral bandwidth (1.5< or =lambda< or =1.6 microm), and by < or =+/-7 degrees over an internal field view of +/-1 degrees (incidence angle 44 degrees < or = phi(0)< or =46 degrees inside the prism). An HWR design at lambda=1.55 microm employs seven layers of Si and SiO(2) thin films embedded in a Si cube, has an average transmittance >93%, and Delta(t) that differs from 180 degrees by <+/-0.3 degrees over a 100 nm bandwidth (1.5< or =lambda< or =1.6 microm) and by <+/-17 degrees over an internal field view of +/-1 degree . The sensitivity of these devices to film-thickness errors is also considered.     

Infrared quarter-wave reflection retarders designed with high-spatial-frequency dielectric surface-relief gratings on a gold substrate at oblique incidence

One- and two-dimensional high-spatial-frequency dielectric surface-relief gratings on a Au substrate are used to design a high-reflectance quarter-wave retarder at 70° angle of incidence and 10.6-μm light wavelength. The equivalent homogeneous anisotropic layer model is used. It is shown that equal and high reflectances (>98.5%) for the p and the spolarizations and quarter-wave retardation can be achieved with two-dimensional ZnS surface-relief gratings. Sensitivities to changes of incidence angle, light wavelength, grating filling factor, and grating layer thickness are considered.     

Straightness measurements by use of a reflection confocal optical system

Straightness measurement is a very important technique in the field of mechanical engineering. A particular application for straightness measurement is high-accuracy machining on a diamond-turning lathe. We propose a novel, to our knowledge, optical method for measuring the straightness of motion, and its mathematical analysis is outlined. The technique is based on measurement of the lateral displacement of point images by use of reflection confocal optical systems. The advantages of this method are that (i) the lateral displacements in the direction of the two axes perpendicular to the optical axis can be measured, (ii) the rotation angles around all three axes can be measured, and (iii) reflection optical systems are more compact in length than are transmission optical systems.     

The surface effect on the strain energy release rate of buckling delamination in thin film-substrate systems

Gurtin-Murdoch continuum surface elasticity model is employed to study the buckling delamination of ultra thin film-substrate system. The effects of surface deformation and residual stress on the large deflection of ultra thin film are considered in analysis. A concept of effective bending rigidity (EBR) for ultra thin plate is proposed on the basis of Gurtin-Murdoch continuum theory and the principle of minimum potential energy. The governing equations with EBR are formally consistent with the classical plate theory, including both small deflection and large deflection. A surface effect factor is introduced to decide whether there is need to consider the surface effect or not. Combining the buckling theory and interface fracture mechanics, we obtain analytical solutions of the critical buckling load and the energy release rate of the interface crack in the film-substrate system. It is seen that the surface deformation and residual stress have significant effects on the buckling delamination of ultra thin film-substrate system.     

Highly efficient broadband conversion of light polarization by composite retarders

Driving on an analogy with the technique of composite pulses in quantum physics, we propose highly efficient broadband polarization converters composed of sequences of ordinary retarders rotated at specific angles with respect to their fast-polarization axes.     

Beam shaping with diffuse light by use of a single reflection

A technique for diffuse beam shaping is presented. The beam shaping is achieved by a single reflection on an element, which consists of many displaced parallel planar reflecting facets. The reflecting facets approximate a designed curved surface. We demonstrate the validity of the method for the conversion of a diffuse Gaussian beam into a uniform one in one of the spatial dimensions.     

Theory of oblique-incidence phase retarders

Phenomenological and mathematical analyses of oblique incidence in total-internal-reflection phase retarders and the procedure for constructing extremely achromatic quarter-wave retarders are presented. It is shown that the retardance can assume the same value twice at two definite spectral lines. As an example, a quarter-wave phase retarder is described that introduces a retardance of exactly 90 degrees at two He-Ne laser lines of 632.8 and 1150 nm with a maximum deviation of 0.007 degrees for other wavelengths between these two lines. This application is advantageous in conjunction with two-line and multiline lasers where the radiation is usually pumped in a state of circular polarization.     

Quasi-stationary thermal regime in a film-substrate system during periodic-pulsed heating by laser radiation

The effect of thermal conductivity of the film-substrate contact boundary on the establishment of the quasi-stationary thermal regime during periodic-pulsed heating is studied.Moscow Institute of Electronics and Mathematics. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 4, pp. 401–407, April, 1993.     

Fail-safe design of integral metallic aircraft structures reinforced by bonded crack retarders

This paper presents an investigation on the effectiveness of crack growth retarders bonded to integral metallic structures. The study was performed by both numerical modelling and experimental tests. It focuses on aluminium alloy panels reinforced by bonded straps made of carbon-epoxy, glass-epoxy composite materials or a titanium alloy. The goal was to develop a fail-safe design for integrally stiffened skin-stringer panels applicable to aircraft wing structures. The modelling strategy and finite element models are presented and discussed. The requirements that the models should meet are also discussed. The study has focused on establishing the extent of crack retarder benefits, in terms of fatigue crack growth life improvement, by numerical simulation and experimental tests of various crack retarders. The results of predicted fatigue crack growth retardation have been validated by tests of laboratory samples. This study concludes that by bonding discrete straps to an integral structure, the fatigue crack growth life can be significantly improved.     

Thermal boundary resistance of a granular film-substrate interface

The results of measurements of the thermal boundary resistance (R _FS) of the interface between a one-layer granular film on a substrate are presented, which reveal the relationship between the R _FS value and the grain size in the film material. For a 10-nm-thick nanocrystalline (Fe_0.5Co_0.5)_0.4Cu_0.6 film deposited on a silicon substrate with a 50-nm-thick SiO₂ oxide layer (interlayer), R _FS is increased by almost two orders of magnitude compared to the minimum reported value (10^?7 (m² K)/W). The thermal boundary resistance of a La_0.65Ca_0.35MnO₃ film with a microcrystalline structure, which was deposited over a YBa₂Cu₃O_7?δ interlayer on a SrTiO₃ substrate, is R _FS = 10^?6 (m² K)/W.     

Extremely-high-intensity photoluminescence from CuBr films fabricated by film-substrate chemical reaction of CuCl films on KBr-crystal substrate

High quality CuBr film is fabricated by film-substrate chemical reaction of CuCl on KBr, where CuCl is vacuum-deposited film of the order of ∼ 100 nm thickness and KBr is fleshly-cleaved single crystal. The resulting CuBr films show ∼ 10³ times higher efficiency of free-exciton photoluminescence (PL) than conventional CuBr films. The efficiency exceeds that of conventional CuCl films even by a factor of ∼ 10², despite the general recognition that the free-exciton PL from CuBr is much weaker than that from CuCl. The present result encourages us to challenge to rethink the exciton PL in CuBr as well as in CuCl, because the compounds are the model materials for basic and application studies of linear/nonlinear exciton-related PL properties of solids.     

Overview and applicability of residual stress estimation of film-substrate structure

Residual stresses arising from thermal mismatch in layered structures rank among the major causes of mechanical failures in light-emitting diodes, integrated circuits, electronic packages, and micro-electro-mechanical systems. Applying analytical solutions to predict or calculate residual stresses’ magnitude and distribution in multilayer film-substrate system has been widely adopted by many researchers. These researches are based on multilayer theories of film-substrate systems, such as Suhir's formula, Stoney's equation, and extend Stoney's equations. To discuss and distinguish the characteristics of these approaches, finite element analysis numerical solutions and multilayer theory analytical solutions are compared and analyzed. This encompasses the theories’ application spectrum as well as their prediction capability. In addition, this work not only discusses the theories’ property and workability but also demonstrate the feasibility of the finite element method (FEM) and bilayer theories in experiment. The experimental result demonstrates that FEM is a reliable approach in predicting the mechanical behavior of multilayer structures. Hence, when calculating or predicting thin film stress using the aforementioned theories, the methodology proposed in this research can be employed to effectively validate the feasibility of these theories.