Effective absorption coefficient and effective thickness in attenuated total reflection spectroscopy.

Since the introduction of attenuated total reflection (ATR) spectroscopy for the characterization of materials, attempts have been made to relate the measured reflectivity (R) to the absorption coefficient (α) of the absorbing material of interest. The common approach is limited to the low absorption case under the assumption R∼exp(-αde), where de is an effective thickness, which is evaluated for the lossless case. In this Letter, a more detailed derivation leads to R=exp(-ßdp/2), enabling the definition of an ATR-effective absorption coefficient ß and the penetration depth dp of the electric field in the absorbing material. It is found that ß∼4πε2/λ, where ε2 is the imaginary part of the complex dielectric function of the absorbing material, and λ is the wavelength. An alternative formulation is R=exp(-αdef), where def is a generalized effective thickness for arbitrary strength of absorption which reduces to de in the low absorption limit. The experimental data for water, the biopolymer chitosan, and soda-lime glass prove the reliability of the ATR-effective absorption coefficient in the infrared range.

Graded pitch profile for the helicoidal broadband reflector and left-handed circularly polarizing cuticle of the scarab beetle Chrysina chrysargyrea.

The cuticle of the beetle Chrysina chrysargyrea reflects left-handed polarized light in the broad spectral range from 340 to 1000 nm. Interference oscillations in the experimental Mueller-matrix spectroscopic ellipsometry data reveal that transparent materials comprise the cuticle. A spectral analysis of the interference oscillations makes evident that the pitch profile across the cuticle is graded. The graded pitch and effective refractive indices are determined through non-linear regression analysis of the experimental Mueller matrix by using a cuticle model based on twisted biaxial dielectric slices. Non-uniformity in cuticle thickness as well as in pitch profile near the cuticle surface account for depolarizance of the Mueller matrix. Transmission electron microscopy supports the reliability of the results.

Structural circular birefringence and dichroism quantified by differential decomposition of spectroscopic transmission Mueller matrices from Cetonia aurata.

Transmission Mueller-matrix spectroscopic ellipsometry is applied to the cuticle of the beetle Cetonia aurata in the spectral range 300-1000 nm. The cuticle is optically reciprocal and exhibits circular Bragg filter features for green light. By using differential decomposition of the Mueller matrix, the circular and linear birefringence as well as dichroism of the beetle cuticle are quantified. A maximum value of structural optical activity of 560°/mm is found.

Sum decomposition of Mueller-matrix images and spectra of beetle cuticles.

Spectral Mueller matrices measured at multiple angles of incidence as well as Mueller matrix images are recorded on the exoskeletons (cuticles) of the scarab beetles Cetonia aurata and Chrysina argenteola. Cetonia aurata is green whereas Chrysina argenteola is gold-colored. When illuminated with natural (unpolarized) light, both species reflect left-handed and near-circularly polarized light originating from helicoidal structures in their cuticles. These structures are referred to as circular Bragg reflectors. For both species the Mueller matrices are found to be nondiagonal depolarizers. The matrices are Cloude decomposed to a sum of non-depolarizing matrices and it is found that the cuticle optical response, in a first approximation can be described as a sum of Mueller matrices from an ideal mirror and an ideal circular polarizer with relative weights determined by the eigenvalues of the covariance matrices of the measured Mueller matrices. The spectral and image decompositions are consistent with each other. A regression-based decomposition of the spectral and image Mueller matrices is also presented whereby the basic optical components are assumed to be a mirror and a circular polarizer as suggested by the Cloude decomposition. The advantage with a regression decomposition compared to a Cloude decomposition is its better stability as the matrices in the decomposition are determined a priori. The origin of the depolarizing features are discussed but from present data it is not possible to conclude whether the two major components, the mirror and the circular polarizer are laterally separated in domains in the cuticle or if the depolarization originates from the intrinsic properties of the helicoidal structure.

On liquid crystal diffractive optical elements utilizing inhomogeneous alignment.

Formation of a desired liquid crystal (LC) director distribution by the use of inhomogeneous anchoring and pre-tilt angle for electrically controlled diffractive optical elements (DOE) is studied. Such LC DOE can have high periodicity and diffraction efficiency. At the same time they are free of constructive regularities, e.g. a periodic arrangement of the electrodes or thickness deviations, which have undesired impact on diffractive characteristics of LC DOE of other types. We focus on evaluation of potential functional abilities of LC DOE with inhomogeneous alignment. The reasons causing restriction of the LC DOE diffraction efficiency and periodicity are considered. Approaches for improvement of characteristics of the LC DOE are discussed.

Fano interference in supported gold nanosandwiches with weakly coupled nanodisks.

We studied the far-field optical response of supported gold-silica-gold nanosandwiches using spectroscopic ellipsometry, reflectance and transmittance measurements. Although transmittance data clearly shows that the gold nanodisks in the sandwich structure interact very weakly, oblique reflectance spectra of s- and p-polarized light show clearly asymmetric line-shapes of the Fano type. However, all experimental results are very well described by modeling the gold nanodisks as oblate spheroids and by employing a 2 × 2 scattering matrix formulation of the Fresnel coefficients provided by an island film theory. In particular, the Fano asymmetry can be explained in terms of interference between the scattered waves from the decoupled nanodisks in the spectral range limited by their respective plasmon resonances. We also show that the reflectance and ellipsometry spectra can be described by a three-layer system with uniaxial effective dielectric functions.

Optical response of supported gold nanodisks.

It is shown that the ellipsometric spectra of short range ordered planar arrays of gold nanodisks supported on glass substrates can be described by modeling the nanostructured arrays as uniaxial homogeneous layers with dielectric functions of the Lorentz type. However, appreciable deviations from experimental data are observed in calculated spectra of irradiance measurements. A qualitative and quantitative description of all measured spectra is obtained with a uniaxial effective medium dielectric function in which the nanodisks are modeled as oblate spheroids. Dynamic depolarization factors in the long-wavelength approximation and interaction with the substrate are considered. Similar results are obtained calculating the optical spectra using the island-film theory. Nevertheless, a small in-plane anisotropy and quadrupolar coupling effects reveal a very complex optical response of the nanostructured arrays.

Protein adsorption on thin films of carbon and carbon nitride monitored with in situ ellipsometry.

Thin films of amorphous carbon and amorphous, graphitic and fullerene-like carbon nitride were deposited by reactive magnetron sputtering and optically characterized with spectroscopic ellipsometry. Complementary studies using scanning electron microscopy and atomic force microscopy were performed. The films were exposed to human serum albumin (HSA) and the adsorption was monitored in situ using dynamic ellipsometry. From the ellipsometric data the adsorbed amount of proteins was quantified in terms of surface mass density using de Feijter's model. The results indicate larger adsorption of proteins onto the amorphous films compared to the films with a more textured structure. Complementary studies with 125I-labeled HSA showed an apparent protein adsorption up to six times larger compared to the ellipsometry measurement. In addition, the four types of films were incubated in blood plasma followed by exposure to anti-fibrinogen, anti-HMWK or anti-C3c, revealing the materials' response to complement and contact activation. The amorphous and graphitic carbon nitride exhibit rather high immune activity compared to a titanium reference, whereas the amorphous carbon and the fullerene-like CNx show less immune complement deposition. Compared to the reference, all films exhibit indications of a stronger ability to initiate the intrinsic pathway of coagulation. Finally, the surfaces' bone-bonding ability was investigated by examination of their ability to form calcium phosphate crystals in a simulated body fluid, with a-CNx depositing most calcium phosphate after 21 days of incubation.

Optical properties of carbon nanofiber photonic crystals.

Carbon nanofibers (CNFs) are used as components of planar photonic crystals. Square and rectangular lattices and random patterns of vertically aligned CNFs were fabricated and their properties studied using ellipsometry. We show that detailed information such as symmetry directions and the band structure of these novel materials can be extracted from considerations of the polarization state in the specular beam. The refractive index of the individual nanofibers was found to be n(CNF) = 4.1.

Formation and cross-linking of fibrinogen layers monitored with in situ spectroscopic ellipsometry.

Thick matrices of fibrinogen with incorporation of a matrix metalloproteinase inhibitor were covalently bonded on functionalized silicon surfaces using an ethyl-3-dimethyl-aminopropyl-carbodiimide and N-hydroxy-succinimide affinity ligand coupling chemistry. The growth of the structure was followed in situ using dynamic ellipsometry and characterized at steady-state with spectroscopic ellipsometry. The growth was compared with earlier work on ex situ growth of fibrinogen layers studied by single wavelength ellipsometry. It is found that in situ growth and ex situ growth yield different structural properties of the formed protein matrix. Fibrinogen matrices with thicknesses up to 58 nm and surface mass densities of 1.6 microg/cm2 have been produced.

Computer screen photoassisted off-null ellipsometry.

The ellipsometric measurement of thickness is demonstrated using a computer screen as a light source and a webcam as a detector, adding imaging off-null ellipsometry to the range of available computer screen photoassisted techniques. The results show good qualitative agreement with a simplified theoretical model and a thickness resolution in the nanometer range is achieved. The presented model can be used to optimize the setup for sensitivity. Since the computer screen serves as a homogeneous large area illumination source, which can be tuned to different intensities for different parts of the sample, a large sensitivity range can be obtained without sacrificing thickness resolution.

Penetration and loading of human serum albumin in porous silicon layers with different pore sizes and thicknesses.

Human serum albumin was adsorbed into porous silicon layers with thickness up to 3 microm and with different mean pore radius in the range 4.5-10 nm. The adsorbed amount of protein was quantified by I(125) radioactive labeling techniques and ellipsometry. The results show that albumin penetrated into the pores when the mean pore radius was larger than 5.5 nm, but could not totally occupy the available surface area when the layer thickness was larger than 1 microm. Loading of albumin both into porous layers and onto plane silicon as a function of albumin concentration was also investigated. These measurements show that loading of protein increased with protein concentration at least up to 10 mg/ml for porous silicon and up to 1 mg/ml for plane silicon. The maximum deposition into the type of porous layers used here was 28 microg/cm(2), compared to 0.36 microg/cm(2) for plane silicon.

Monitoring specific interaction of low molecular weight biomolecules on oxidized porous silicon using ellipsometry.

Porous silicon dioxide surfaces have been used for monitoring the specific affinity binding of low molecular weight molecules to streptavidin. Streptavidin was immobilized to the porous silicon dioxide surface by spontaneous adsorption at pH 7.4. Binding of biotin and an oligopeptide synthesized by means of combinatorial chemistry were monitored with an in situ null ellipsometer. Measurements were also done with hydroxy-azobenzene-2-carboxylic acid and DL-6-8-thioctic acid amide. The performance of porous silicon dioxide as a potential surface in biosensor applications was compared with a planar silicon dioxide surface. Porous silicon dioxide showed a 10-fold amplification of the response compared to planar silicon dioxide. It was possible to monitor the binding of biotin and the oligopeptide in the concentration range 2-40 microM. A response time as low as 30 s was obtained for the oligopeptide at 40 microM.

Porosity Depth Profiling of Thin Porous Silicon Layers by use of Variable-Angle Spectroscopic Ellipsometry: A Porosity Graded-Layer Model.

Variable-angle spectroscopic ellipsometry was used to determine nondestructively the porosity depth profile and thickness of thin porous silicon layers produced by anodization of p(+)-doped silicon wafers. A porosity graded-layer model is presented and used in the analysis of the material. In the porosity graded-layer model an inhomogeneous layer is built up by several thin sublayers with the porosity changing slightly from one sublayer to the next. Results from the ellipsometry analysis and from transmission electron microscopy reveal inhomogeneous layers whose porosity and thereby optical properties change with their depth in the layers.

Determination of refractive index and thickness of thick transparent films by variable-angle spectroscopic ellipsometry: application to benzocyclobutene films.

An analysis procedure for evaluating the refractive index and the thickness of 5-10-µm-thick transparent films has been developed based on variable-angle spectroscopic ellipsometry. As an example of application, results from an analysis of benzocyclobutene films are presented. The sensitivities in ψ and Δ with respect to the refractive index and the thickness of the films are also discussed.

A biosensor concept based on imaging ellipsometry for visualization of biomolecular interactions.

A new type of optical biosensor system is proposed and its application to detection of antigen-antibody complexes on a silicon substrate is demonstrated. The biosensor system is utilizing specificities of biomolecular interactions in combination with protein patterned surfaces. Visualization of the thickness distributions of thin layers (protein patterns) on a surface is achieved by using imaging ellipsometry. This technique uses a CCD camera whereby an ellipsometric analysis of a large surface can be made. The biosensor system has the advantages of high spatial resolution, fast data acquisition, and simplicity in use.

Optical constants and Drude analysis of sputtered zirconium nitride films.

Opaque and semitransparent dc magnetron-sputtered ZrN films on glass and silicon have been optically characterized with spectral reflectance measurements and ellipsometry. High rate sputtered ZrN has good optical selectivity, i.e., higher than 90% infrared reflectance and a pronounced reflectance step in the visible to a reflectance minimum of less than 10% at 350 nm. The results are comparable with those obtained for single crystalline samples and those prepared by chemical vapor deposition. The complex optical constant (N = n v ik) for opaque films has been determined in the 0.23-25-µm wavelength range with Kramers-Kronig integration of bulk reflectance combined with oblique incidence reflectance for p-polarized light. A variable angle of incidence spectroscopic ellipsometer has been used for determination of the optical constants in the 0.28-1.0-µm wavelength region. The results of the two methods show excellent agreement. The results indicate that ZrN is free electronlike and the Drude model can be applied. The best opaque films had Drude plasma energies (hω(p) between 6.6 and 7.5 eV and relaxation energies (h/τ) between 0.29 and 0.36 eV. Ellipsometer data for the semitransparent films show that the refractive index (n) in the visible increases with decreasing film thickness whereas the extinction coefficient (k) is essentially unchanged. The optical properties are improved by deposition upon a heated substrate.

Quasi three-dimensional, n-bit optical memory based on the ellipsometric principle: model calculations.

Model calculations on the ellipsometric memory are presented. The ellipsometric memory is an n-bit optical memory whose information is extracted by use of the ellipsometric principle. The memory cells of the device consist of thin-film multilayer structures, and the information of each memory cell is contained in the optical properties of the thin films. Several thin-film multilayer structures were examined in order to find out how different choices of layer materials and other system parameters such as layer thicknesses and wavelength affect resolutions and limitations of the ellipsometric memory. Such calculations are also useful for optimizing the readout resolution. It was found that it is possible to use memory cells having up to at least eight layers, which would permit 8-bit words to be stored at each location. It was also found that, in principle, several types of materials can be used as layer materials, and various aspects of different choices of materials are discussed.

Line-shape analysis of ellipsometric spectra on thin organic films.

A methodology for the line-shape analysis of ellipsometric spectra on thin (<200-A) organic films is presented. Four different line shapes are employed: Gaussian, Lorentzian, phase-relaxed Lorentzian, and a critical-point line shape. An analysis of analytic data addresses the problem of the modeling of unsymmetric absorption bands. The method is exemplified by an analysis of thin films of phthalocyanine and poly(3-hexylthiophene), and we show that the number and type of resonances in an absorption band can be obtained. The possibility of resolving the cause of a shift in the peak position of an absorption band is also demonstrated. In the case being studied the shift is due to the redistribution of the oscillator strengths between the individual resonances in the band and not to shifts in the energies of the resonances.