Calibration of polarization-state generators (PSG's), polarimeters, and Mueller-matrix ellipsometers (MME's) is an important factor in the practical use of these instruments. A new general procedure, the eigenvalue calibration method (ECM), is presented. It can calibrate any complete MME consisting of a PSG and a polarimeter that generate and measure, respectively, all the states of polarization of light. In the ECM, the PSG and the polarimeter are described by two 4 x 4 matrices W and A, and their 32 coefficients are determined from three or four measurements performed on reference samples. Those references are smooth isotropic samples and perfect linear polarizers. Their optical characteristics are unambiguously determined during the calibration from the eigenvalues of the measured matrices. The ECM does not require accurate alignment of the various optical elements and does not involve any first-order approximation. The ECM also displays an efficient error control capability that can be used to improve the MME behavior. The ECM is illustrated by an experimental calibration, at two wavelengths (458 and 633 nm), of a MME consisting of a coupled phase modulator associated with a prism division-of-amplitude polarimeter.
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.
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.
We report the results of an in situ spectroscopic ellipsometry study concerning the substrate dependence of the evolution of microcrystalline silicon films deposited by alternating amorphous silicon deposition and hydrogen plasma treatment. The evolution of the composition of the films during growth, up to thicknesses of ∼100 nm, indicates that besides etching, the diffusion of atomic hydrogen efficiently promotes the growth (and/or nucleation) of buried crystallites. Moreover, the evolution of the films strongly depends on the nature of the substrate. This substrate selectivity is discussed in terms of initial growth processes. The effect of the hydrogen plasma well below the film surface, which produces the thickness-dependent film composition, along with the substrate selectivity, may be of prime importance in technological applications of microcrystalline silicon.
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.
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