Parametric uncertainty in nanoscale optical dimensional measurements.

Image modeling establishes the relation between an object and its image when an optical microscope is used to measure the dimensions of an object of size comparable to the illumination wavelength. It accounts for the influence of all of the parameters that can affect the image and relates the apparent feature width (FW) in the image to the true FW of the object. The values of these parameters, however, have uncertainties, and these uncertainties propagate through the model and lead to parametric uncertainty in the FW measurement, a key component of the combined measurement uncertainty. The combined uncertainty is required in order to decide if the result is adequate for its intended purpose and to ascertain if it is consistent with other results. The parametric uncertainty for optical photomask measurements derived using an edge intensity threshold approach has been described previously; this paper describes an image library approach to this issue and shows results for optical photomask metrology over a FW range of 10 nm to 8 µm using light of wavelength 365 nm. The principles will be described; a one-dimensional image library will be used; the method of comparing images, along with a simple interpolation method, will be explained; and results will be presented. This method is easily extended to any kind of imaging microscope and to more dimensions in parameter space. It is more general than the edge threshold method and leads to markedly different uncertainties for features smaller than the wavelength.

Images of strips on and trenches in substrates.

The computation of images of lines or strips on a substrate and trenches in a substrate or a layer above a substrate, all made of dielectric or conducting materials, is presented. The method is based on integral equations, of the single-integral-equation kind, equivalent to Maxwell's equations and on Fourier optics. Examples of computed images illustrating some of the features found in the images are provided. Approximations involved in the model of the actual scatterer and microscope as well as in the theoretical and numerical representations are discussed.

Scatterfield microscopy for extending the limits of image-based optical metrology.

We have developed a set of techniques, referred to as scatterfield microscopy, in which the illumination is engineered in combination with appropriately designed metrology targets to extend the limits of image-based optical metrology. Previously we reported results from samples with sub-50-nm-sized features having pitches larger than the conventional Rayleigh resolution criterion, which resulted in images having edge contrast and elements of conventional imaging. In this paper we extend these methods to targets composed of features much denser than the conventional Rayleigh resolution criterion. For these applications, a new approach is presented that uses a combination of zero-order optical response and edge-based imaging. The approach is, however, more general and a more comprehensive set of analyses using theoretical methods is presented. This analysis gives a direct measure of the ultimate size and density of features that can be measured with these optical techniques. We present both experimental results and optical simulations using different electromagnetic scattering packages to evaluate the ultimate sensitivity and extensibility of these techniques.

Ray model of light scattering by flake pigments or rough surfaces with smooth transparent coatings.

We derive expressions for the intensity and polarization of light singly scattered by flake pigments or a rough surface beneath a smooth transparent coating using the ray or facet model. The distribution of local surface normals is used to calculate the bidirectional reflectance distribution function (BRDF). We discuss the different distribution functions that can be used to characterize the distribution of local surface normals. The light-scattering model is validated by measurements of the BRDF and polarization by a metallic flake pigmented coating. The results enable the extraction of a slope distribution function from the data, which is shown to be consistent over a variety of scattering geometries. These models are appropriate to estimate or predict the appearance of flake pigment automotive paints.

X-Ray Lithography Mask Metrology: Use of Transmitted Electrons in an SEM for Linewidth Measurement.

X-ray masks present a measurement object that is different from most other objects used in semiconductor processing because the support membrane is, by design, x-ray transparent. This characteristic can be used as an advantage in electron beam-based x-ray mask metrology since, depending upon the incident electron beam energies, substrate composition and substrate thickness, the membrane can also be essentially electron transparent. The areas of the mask where the absorber structures are located are essentially x-ray opaque, as well as electron opaque. This paper shows that excellent contrast and signal-to-noise levels can be obtained using the transmitted-electron signal for mask metrology rather than the more commonly collected secondary electron signal. Monte Carlo modeling of the transmitted electron signal was used to support this work in order to determine the optimum detector position and characteristics, as well as in determining the location of the edge in the image profile. The comparison between the data from the theoretically-modeled electron beam interaction and actual experimental data were shown to agree extremely well, particularly with regard to the wall slope characteristics of the structure. Therefore, the theory can be used to identify the location of the edge of the absorber line for linewidth measurement. This work provides one approach to improved x-ray mask linewidth metrology and a more precise edge location algorithm for measurement of feature sizes on x-ray masks in commercial instrumentation. This work also represents an initial step toward the first SEM-based accurate linewidth measurement standard from NIST, as well as providing a viable metrology for linewidth measurement instruments of x-ray masks for the lithography community.

Certification of SRM1960: Nominal 10 µm Diameter Polystyrene Spheres ("Space Beads").

Experimental, theoretical, and calculational details are presented for the three independent micrometrology techniques used to certify the mean diameter of Standard Reference Materisd 1960, nominal 10 µm diameter polystyrene spheres ("space beads"). The mean diameters determined by the three techniques agreed remarkably well, with all measurements within 0.1% of each other, an unprecedented achievement in the dimensional metrology of microspheres. Center distance finding (CDF), a method based on optical microscopy, gave a value of 9.89 ± 0.04 µm, which was chosen to be the certified mean diameter. The supporting measurements were done using metrology electron microscopy (MEM) and resonance light scattering (RLS). The MEM technique, based on scanning electron microscopy, yielded 9.89±0.06 µm for the mean diameter of the microspheres in vacuum, while the RLS value was 9.90 ±0.03 µm for the microspheres in liquid suspension. The main peak of the diameter distribution for SRM 1960 is nearly Gaussian with a certified standard deviation of 0.09 µm, as determined by CDF. Off the main peak, there are about 1% oversized particles and a negligible amount of undersized particles. The report gives a detailed description of the apparatus, the experimental methods, the data-reduction techniques, and an error analysis for each of the micro-metrology techniques. A distinctive characteristic of this SRM is that it was manufactured in microgravity aboard the NASA space shuttle Challenger and is the first commercial product to be made in space.

Development of a One-Micrometer-Diameter Particle Size Standard Reference Material.

The average diameter of the first micrometer particle size standard (Standard Reference Material 1690), an aqueous suspension of monosized polystyrene spheres with a nominal 1 µm diameter, was accurately determined by three independent techniques. In one technique the intensity of light scattered by a diluted suspension of polystyrene spheres was measured as a function of scattering angle, using a He-Ne laser polarized in the vertical direction. The second technique consisted of measuring as a function of angle the intensity of light scattered from individual polystyrene spheres suspended in air, using a He-Cd laser with light polarized parallel and perpendicular to the scattering plane. The measurement of row length by optical microscopy for polystyrene spheres arranged in close-packed, two-dimensional hexagonal arrays was the basis of the third technique. The measurement errors for each technique were quantitatively assessed. For the light scattering experiments, this required simulation with numerical experiments. The average diameter determined by each technique agreed within 0.5% with the most accurate value being 0.895±0.007 µm based on light scattering by an aqueous suspension. Transmission electron microscopy, flow through electrical sensing zone counter measurements, and optical microscopy were also used to obtain more detailed information on the size distribution including the standard deviation (0.0095 µm), fraction of off-size particles, and the fraction of agglomerated doublets (1.5%).

Size and Refractive Index Determination of Single Polystyrene Spheres.

The intensity of the light scattered from individual dielectric spheres was measured as a function of the scattering angle, for light polarized parallel and perpendicular to the scattering plane. These sets of data were used to determine the radius and refractive index of the spheres by fitting the data to the scattering function obtained from Mie theory. The light was produced by a He-Cd laser (λ=441.6 nm). Measurements were performed on particles of six discrete sizes with radii in the range 117-1175 nm. Several different measures of the quality of fit were examined, and the least-squares fit, unweighted or weighted with a factor sin2(θ/2), was found to be the best. The values obtained for the index of refraction were found to be within 1% of the published bulk value 1.615. The measured radii differed by several percent from those specified by the manufacturer. Several sources of error were analyzed, and their effects were simulated in numerical experiments. The largest source of error in the instrument was a discrepancy between the actual scattering angle and the reading provided by the instrument. Less significant was the noise introduced by the motion of the particle within the laser beam. A calibration eliminated most of the error in the scattering angle. The precision and accuracy of this technique are estimated to be 0.2% and 0.9%, respectively, of the particle size for particles of a nominal radius of 457 nm.