Salvador Bosch

Vectorial structure of nonparaxial electromagnetic beams

A representation of the general solution of the Maxwell equations is proposed in terms of the plane-wave spectrum of the electromagnetic field. In this representation the electric field solution is written as a sum of two terms that are orthogonal to each other at the far field: One is transverse to the propagation axis, and the magnetic field associated with the other is also transverse. The concept of the so-called closest field to a given beam is introduced and applied to the well-known linearly polarized Gaussian beam.

Ultraviolet optical and microstructural properties of MgF2 and LaF3 coatings deposited by ion-beam sputtering and boat and electron-beam evaporation

Single layers of MgF2 and LaF3 were deposited upon superpolished fused-silica and CaF2 substrates by ion-beam sputtering (IBS) as well as by boat and electron beam (e-beam) evaporation and were characterized by a variety of complementary analytical techniques. Besides undergoing photometric and ellipsometric inspection, the samples were investigated at 193 and 633 nm by an optical scatter measurement facility. The structural properties were assessed with atomic-force microscopy, x-ray diffraction, TEM techniques that involved conventional thinning methods for the layers. For measurement of mechanical stress in the coatings, special silicon substrates were coated and analyzed. The dispersion behavior of both deposition materials, which was determined on the basis of various independent photometric measurements and data reduction techniques, is in good agreement with that published in the literature and with the bulk properties of the materials. The refractive indices of the MgF2 coatings ranged from 1.415 to 1.440 for the wavelength of the ArF excimer laser (193 nm) and from 1.435 to 1.465 for the wavelength of the F2 excimer laser (157 nm). For single layers of LaF3 the refractive indices extended from 1.67 to 1.70 at 193 nm to approximately 1.80 at 157 nm. The IBS process achieves the best homogeneity and the lowest surface roughness values (close to 1 nm(rms)) of the processes compared in the joint experiment. In contrast to MgF2 boat and e-beam evaporated coatings, which exhibit tensile mechanical stress ranging from 300 to 400 MPa, IBS coatings exhibit high compressive stress of as much as 910 MPa. A similar tendency was found for coating stress in LaF3 single layers. Experimental results are discussed with respect to the microstructural and compositional properties as well as to the surface topography of the coatings.

Diffraction theory of Fresnel lenses encoded in low-resolution devices

A mathematical model that describes the behavior of low-resolution Fresnel lenses encoded in any low-resolution device (e.g., a spatial light modulator) is developed. The effects of low-resolution codification, such the appearance of new secondary lenses, are studied for a general case. General expressions for the phase of these lenses are developed, showing that each lens behaves as if it were encoded through all pixels of the low-resolution device. Simple expressions for the light distribution in the focal plane and its dependence on the encoded focal length are developed and commented on in detail. For a given codification device an optimum focal length is found for best lens performance. An optimization method for codification of a single lens with a short focal length is proposed.

A general-purpose software for optical characterization of thin films: specific features for microelectronic applications

Abstract We present a detailed description of the features and capabilities of a new software for the optical characterization of thin films from spectrophotometric and/or ellipsometric measurements. The program allows the analysis of a wide range of multi-layered structures, either with respect to the composition, microstructure or thickness of any of the layers. Several spectra corresponding to different measurement techniques of a single sample may be fitted simultaneously. A short description of the dispersion models actually implemented to represent the materials is given. Several examples of use are discussed. These have been selected to illustrate important aspects that may be relevant to microelectronic applications.

Plasmonic layers based on Au-nanoparticle-doped TiO2 for optoelectronics: structural and optical properties

The anti-reflective effect of dielectric coatings used in silicon solar cells has traditionally been the subject of intensive studies and practical applications. In recent years the interest has permanently grown in plasmonic layers based on metal nanoparticles, which are shown to increase light trapping in the underlying silicon. In the present work we have combined these two concepts by means of in situ synthesis of Au nanoparticles in a dielectric matrix (TiO2), which is commonly used as an anti-reflective coating in silicon solar cells, and added the third element: a 10-20% porosity in the matrix. The porosity is formed by means of a controllable wet etching by low concentration HF. As a consequence, the experimentally measured reflectance of silicon coated by such a plasmonic layer decreases to practically zero in a broad wavelength region around the localized surface plasmon resonance. Furthermore, we demonstrate that extinction and reflectance spectra of silicon coated by the plasmonic films can be successfully accounted for by means of Fresnel formulae, in which a double refractive index of the metal-dielectric material is used. This double refractive index cannot be explained by effective medium theory (Maxwell-Garnett, for example) and appears when the contribution of Au nanoparticles located at the TiO2/Si interface is high enough to result in formation of interface surface plasmon modes.

Ellipsometric methods for absorbing layers: a modified downhill simplex algorithm

A modified downhill simplex algorithm for single wavelength ellipsometry is presented. The algorithm finds the best-fitting solution (n, k, d) for a sample consisting of a single absorbing layer when ellipsometric data corresponding to different incidence angles (at least two) are available. The method is easy to be implemented numerically and gives i) very good convergence properties and ii) simple adaptability to different practical situations, such as those in which there are more than two angles of incidence or those in which several independent measurements have been made of the same incident angle.

Spectroscopic ellipsometric characterization of transparent thin film amorphous electronic materials : Integrated analysis

Abstract Silicon dioxide and silicon oxynitride thin films deposited on crystalline silicon substrates were characterized by phase modulated spectroscopic ellipsometry in the UV-visible range. The thickness and the refractive index of the films were calculated by assuming an ambient/film/substrate system with three different approaches: modeling the dielectric function with Cauchys dispersion formula, using the Bruggeman effective medium approximation and using a direct inversion algorithm method. The comparison of the results obtained by these approaches along with the subsequent qualitative study of possible weak absorption and depth inhomogeneities in the samples allows us to evaluate the accuracy of the experimental data as well as the reliability of the model and results.

Diffraction efficiency of low-resolution Fresnel encoded lenses.

A mathematical model to describe the behavior of low-resolution Fresnel lenses encoded in any low-resolution device (e.g., a spatial light modulator) is developed. From this model the diffraction efficiency is calculated in terms of all the parameters that characterize these lenses.

Spatial width and power-content ratio of hard-edge diffracted beams.

On the basis of the intensity-moment formalism, certain analytical relationships are obtained for both the angular domain and the size of a transverse region of the beam that ensure a power content of at least 75% of the total power. As an illustrative application, the analytical results are compared with the exact values (numerically computed) of the amplitude of a lowest-order Gaussian beam diffracted by slits.

Numerical algorithm for spectroscopic ellipsometry of thick transparent films

We present a numerical method for spectroscopic ellipsometry of thick transparent films. When an analytical expression for the dispersion of the refractive index (which contains several unknown coefficients) is assumed, the procedure is based on fitting the coefficients at a fixed thickness. Then the thickness is varied within a range (according to its approximate value). The final result given by our method is as follows: The sample thickness is considered to be the one that gives the best fitting. The refractive index is defined by the coefficients obtained for this thickness.