J.L. de la Peña

Sizing particles on substrates. A general method for oblique incidence

We have developed an experimental light-scattering method to size metallic spherical and cylindrical particles on flat substrates using obliquely incident light. We modify an earlier model to include effects such as the shadowing of the incident and scattered beams. We provide empirical expressions for sizing spheres and cylinders on substrates based on the positions of their minima. The results have been experimentally verified for both types of particle. The extension of the method to oblique incidence angles allows an alternative dynamic procedure.

Scattering from particles on surfaces:?visibility factor and polydispersity

We have developed an experimental method based on the visibility factor of light-scattering minima to obtain size-polydispersity information from contaminants upon a flat substrate. We verify the method by using double-interaction-model calculations and use this technique to examine experimentally the radial variation of a micrometer-sized fiber and the size polydispersity of spherical particles upon a substrate.

Profile of a fiber from backscattering measurements.

The angular positions of the light-scattering minima obtained from structures placed on flat substrates are closely related to the geometry of the scattering object. We show how the profile of a fiber can be determined, and possible irregularities located, by measurement of the backscattering patterns. An approximate double-interaction model is used to fit the results.

Light scattering computational methods for particles on substrates

Abstract Four theoretical and computational methods to describe the scattering from simple particles on substrates are presented and discussed. These methods are based on the extinction theorem, image theory, the double-interaction model, and geometrical optics (ray-tracing). We compare the four methods with measurements of scattered light from gold metallic cylinders resting on a gold metallic substrate. In particular, we analyze the co-polarized (s and p polarization) full-scan and back-scattering intensities in the far field within the plane of incidence. Advantages and disadvantages of each method as a computational and reliable tool are discussed.

Detection and recognition of local defects in 1D structures

The use of a scattering model, based on the double interaction model, to explore microdefects in 1D microstructures on flat surfaces is proposed. Due to their high sensitivity, backscattering experiments have been performed for the case of a cylindrical fiber resting on a flat substrate. They show that some local defects may be identified by comparing the predictions of the model with the experimental results. The possibilities of this procedure for quality control in semiconductor industry are envisaged.

Light Scattering by Regular Particles on Flat Substrates

Light scattering intensity patterns produced by particles on substrates depend strongly on the size and shape of the particles. For some regular particle shapes, like spheres and cylinders, minima exist in the intensities and a relationship exists between their angular positions and the particle size. This dependence may be established using a simple double-interaction model which considers only the following: a) the scattering solution for the isolated particle; b) the coherent addition of four contributions of the scattering amplitudes to account for the field reflections off the substrate; and c) some geometrical factors which include the path differences, the Fresnel reflection coefficients, and the geometrical shadowing. This model has been used to size particles when illuminated at both normal and oblique incidence. For a collection of polydisperse particles on a substrate, scattering patterns can also produce very useful information; for instance, the visibility of the minima is directly related to the variance in size for low polydispersity samples. For large values of polydispersity (more than 30%), the width of the enhanced-backscattering peak can provide useful information.

Application of a double-interaction model to the backscattering from particulate surfaces

A modified double-interaction model is applied to the study of backscattering from metallic particles on conducting substrates. Polarization parallel or perpendicular to the plane of incidence is considered. The agreement with the experiment is successfully checked for metallic spheres of two different diameters and for a metallic cylinder on a flat conducting substrate. Using the model this enables a systematic study of some features of the backscattering patterns and, in particular, the angular positions of the minima, strongly dependent on the size. Some applications of this dependence are proposed, in particular, the possibility of distinguishing the size of the particle on the substrate and the distance from its center to the substrate.

Enhanced backscatter from monodisperse contaminants on a substrate

Abstract Enhanced backscatter has been used to characterize rough, irregular substrates and polydispersions of contaminants on a substrate. For monodisperse contaminants, the enhanced-backscatter peak can be obscured by the structure of the total intensity signal. Averaging backscatter intensities from a substrate contaminated by monodisperse contaminants when the system is illuminated by plane waves of different incident angles removes the structure of the individual intensity signals, isolating the backscatter peak. The resulting peak contains information which can be used to characterize the contaminants. We demonstrate this technique by modeling the size and shape of this peak for monodisperse spherical contaminants on a substrate and comparing these results with experimental measurements.

Intensity and Polarization Fluctuation Statistics of Light Scattered by Systems of Particles

The analysis of intensity and polarization fluctuations of light scattered by systems with particles is of interest in the resolution of the so-called inverse problem. In this chapter we study the possibility of obtaining information, by means of light scattering techniques, about the geometrical and optical properties of systems composed of two Rayleigh particles, either in volume or located on a substrate. Intensity fluctuations are studied using the normalized second order moment. Polarization fluctuations are studied using the probability of getting null values when measuring the cross-polarized component P(I cross =0). It is observed that the behavior of these parameters depends on both the polarizability of the particles and the distance between them. Some experimental results are shown with measurements of the parameter P(I cross =0) for the case of metallic particles on a flat conducting substrate.

Visibility factor for low-particle-size polydispersity

We have developed an experimental light-scattering method to obtain information about particles with low polydispersities in size on flat substrates. It is based on the analysis of the visibility factor of the lobes in the light scattering patterns obtained from flat metallic substrates seeded with the particles. The visibility factor of a pattern is obtained for different minima. The solution of the scattering problem may be provided by a theoretical model, and analytical expressions for the visibility are derived. This relation between visibility and polydispersity is experimentally tested, and it is shown how the origin of the loss of visibility may be exploited to characterize the polydispersity.