Correlation of sidelobe suppression between rugate filters and multilayer mirrors.

We present the study of the correlation between refractive index profiles and the optical response of rugate filters and multilayer mirrors. The conventionally used method in multilayer mirrors for ripple suppression in the passband will be compared with a similar simple method to remove the rugate filter sidelobes without apodization. The resulting layers are compared in performance with a typical quintic matching layer. An example based on silicon oxynitride alloys with refractive indices ranging between 1.47 and 1.83 was designed and deposited.

Metrology of replicated diffractive optics with Mueller polarimetry in conical diffraction.

The feasibility of metrological characterization of the one-dimensional (1D) holographic gratings, used in the nanoimprint molding tool fabrication step, by spectroscopic Mueller polarimetry in conical diffraction is investigated. The studied samples correspond to two different steps of the replicated diffraction grating fabrication process. We characterized master gratings that consist of patterned resist layer on chromium-covered glass substrate and complementary (replica) gratings made of nickel. The profiles of the gratings obtained by fitting the experimental spectra of Mueller matrix coefficients taken at different azimuthal angles were confirmed by atomic force microscopy (AFM) measurements. The calculated profiles of corresponding master and replica gratings are found to be complementary. We conclude that the Mueller polarimetry, as a fast and non-contact optical characterization technique, can provide the basis for the metrology of the molding tool fabrication step in the nanoimprint technique.

Application of Mueller polarimetry in conical diffraction for critical dimension measurements in microelectronics.

Fast and efficient metrology tools are required in microelectronics for control of ever-decreasing feature sizes. Optical techniques such as spectroscopic ellipsometry (SE) and normal incidence reflectometry are widely used for this task. In this work we investigate the potential of spectral Mueller polarimetry in conical diffraction for the characterization of 1D gratings, with particular emphasis on small critical dimensions (CDs). Mueller matrix spectra were taken in the visible (450-700 nm) wavelength range on a photoresist grating on a Si substrate with 70/240 nm CD/period nominal values, set at nine different azimuthal angles. These spectra were fitted with a rigorous coupled-wave analysis (RCWA) algorithm by using different models for the grating profile (rectangular and trapezoidal, with or without rounded corners). A detailed study of the stability and consistency of the optimal CD values, together with the variation of the merit function (the mean square deviation D2) around these values, clearly showed that for a given wavelength range, this technique can decouple some critical parameters (e.g., top and bottom CDs, left and right sidewall projections) much more efficiently than the usual SE.

Effective medium approximation of anisotropic lamellar nanogratings based on Fourier factorization.

Anisotropic lamellar sub-wavelength gratings (nanogratings) are described by Effective Medium Approximation (EMA). Analytical formulas for effective medium optical parameters of nanogratings from arbitrary anisotropic materials are derived using approximation of zero-order diffraction mode. The method is based on Rigorous Coupled Wave Analysis (RCWA) combined with proper Fourier factorization method. Good agreement between EMA and the rigorous model is observed, where slight differences are explained by the influence of evanescent higher Fourier harmonics in the nanograting.

Mueller polarimetric imaging system with liquid crystals.

We present a new polarimetric imaging system based on liquid-crystal modulators, a spectrally filtered white-light source, and a CCD camera. The whole Mueller matrix image of the sample is measured in approximately 5 s in the transmission mode. The instrument design, together with an original and easy-to-operate calibration procedure, provides high accuracy over a wide spectral range (500-700 nm). This accuracy has been assessed by measurement of a linear polarizer at different orientations and a thick wedged quartz plate as an example of a partially depolarized retarder. Polarimetric images of a stained hepatic biopsy with significant fibrosis have been taken at several wavelengths. The optical properties of Picrosirius Red stained collagen (diattenuation, retardance, and polarizance) have been measured independently from each other between 500 and 700 nm.

Characterization of bidimensional gratings by spectroscopic ellipsometry and angle-resolved Mueller polarimetry.

We studied two bidimensional square gratings of square holes formed in photoresist layers deposited on silicon wafers, both by classical spectroscopic ellipsometry (1.5-4.5-eV spectral range) at a constant incidence angle (70.7 degrees) and by angle-resolved Mueller polarimetry at a constant wavelength (532 nm). The grating period was 1 microm in both directions, and the nominal hole sizes were 250 and 500 nm, respectively. The ellipsometric spectra were fitted by rigorous coupled-wave analysis simulations with two adjustable parameters, the resist layer thickness and the hole size. These parameters were found to be in good agreement with independent scanning electron microscopy measurements. The experimental angle-resolved Mueller spectra were remarkably well reproduced by the simulations, showing that angle-resolved Mueller polarimetry has a great potential for grating metrology applications.

Optimized Mueller polarimeter with liquid crystals.

We demonstrate a Mueller polarimeter in which the polarization-state generator and analyzer are both composed of a linear polarizer and two liquid-crystal variable retarders. The polarimeter is designed to optimize the accuracy of the final results by minimization of the condition numbers of the modulation and analysis matrices. The polarimeter calibration, a difficult task by conventional procedures, is achieved easily by use of the eigenvalue method of Compain et al. [Appl. Opt. 38, 3490 (1999)]. The overall polarimeter performance is tested with a linear polarizer at various angles and a compensator at various retardations.

Application of Fourier transform infrared ellipsometry to assess the concentration of biological molecules.

Spectroscopic ellipsometry is a noninvasive optical characterization technique mainly used in the semiconductor field to characterize bare substrates and thin films. In particular, it allows the gathering of information concerning the physical structure of the sample, such as roughness and film thickness, as well as its optical response. In the mid-infrared (IR) range each molecule exhibits a characteristic absorption fingerprint, which makes this technique chemically selective. Phase-modulated IR ellipsometry does not require a baseline correction procedure or suppression of atmospheric CO2 and water-vapor absorption bands, thus greatly reducing the subjectivity in data analysis. We have found that ellipsometric measurements of thin films, such as the solid residuals left on a plane surface after evaporation of a liquid drop containing a given compound in solution, are particularly favorable for dosing purposes because the intensity of IR absorptions shows a linear behavior along a wide range of solution concentrations of the given compound. Our aim is to illustrate with a concrete example and to justify theoretically the linearity experimentally found between radiation absorption and molecule concentration. For the example, we prepared aqueous solutions of glycogen, a molecule of huge biological importance currently tested in biochemical analyses, at concentrations ranging from 1 mg/l to 1 g/l which correspond to those found in physiological conditions. The results of this example are promising for the application of ellipsometry for dosing purposes in biochemistry and biomedicine.

Full-field optical coherence tomography with thermal light.

A simple optical coherence tomography system has been developed based on a white-light Linnik interferometric microscope with its reference mirror mounted on a piezoelectric translator. The geometrical extension of the optics allows efficient illumination of this device with a low-power (3-W) light bulb, yielding full-field interferometric images at 50 Hz with a fast CCD camera. Owing to the very broad spectral width of the light source and of the camera response, we achieved axial resolutions equal to 1.1 microm in free space and 0.7 microm through a standard microscope cover plate. Tomographic images of an epithelial cell smear and of an hematological sample are shown.

Direct numerical inversion method for kinetic ellipsometric data. I. Presentation of the method and numerical evaluation.

A direct numerical inversion method for the determination of the refractive index and the thickness of the outermost layer of a thin transparent film on top of a multilayer has been developed. This method is based on a second-order Taylor decomposition of the coefficients of the Abelès matrices of the newly grown layer. The variations of the real-time spectroscopic ellipsometry data are expressed as polynomial fuctions depending on the dielectric constant and the thickness of the newly grown layer. The method is fast, capable of single-wavelength and multiwavelength inversion of continuous as well as discontinuous-index profiles, and can be adapted to many different polarimetric instruments.

Direct numerical inversion method for kinetic ellipsometric data. II. Implementation and experimental verification.

A direct numerical inversion method is applied to the monitoring of thin-film growth. Several improvements of the method, including a correction for weakly absorbing materials, are presented. The method has been successfully applied to the inversion of the growth of constant-refractive-index layers andused for the process calibration of plasma-enhanced chemical vapor deposition of silicon oxynitrides. The validity of this calibration has been successfully tested on a linear index gradient and quintic matching layer between a polycarbonate substrate and a scratch-resistant coating.

Muller matrix measurements of small spherical particles deposited on a c-Si wafer.

Müller matrix ellipsometry measurements are performed on accurately sized polystyrene latex and silicon oxide spherical particles deposited on a crystalline silicon surface. The mean particle diameter ranges from 0.2 to 1.5 microm. An argon laser beam (wavelength, 515 nm) impinges on the sample at a fixed near-grazing-incidence angle. The Müller matrix of the diffuse light scattered by the particles is measured in the plane of incidence as a function of the scattering angle. Results are presented and compared with Bobbert and Vlieger's theory. In particular the validity range of Videen's model is estimated.