Egon Marx

Regimes of surface roughness measurable with light scattering.

In this paper we summarize a number of previous experiments on the measurement of the roughness of metallic surfaces by light scattering. We identify several regimes that permit measurement of different surface parameters and functions, and we establish approximate limits for each regime. Using a straightforward criterion, we calculate that the smooth-surface regime, in which the angular distribution of scattered light is closely related to the power spectral density of the roughness, ranges over 0 < σ/λ ≲ 0.05, where σ is the rms roughness and λ is the opitcal wavelength. Above that the surfaceautocorrelation function may be calculated from a Fourier transform of the angular distribution over 0 < σ/λ ≲ 0.14. Then comes the specular regime where the specular beam can still be identified andmeasured over 0 < σ/λ ≲ 0.3. For all these regimes and for rougher surfaces too, the rms width of thescatter distribution is proportional to the rms slope of the surface.

Direct and inverse problems for light scattered by rough surfaces

Calculations are performed to relate the stylus profile of a one-dimensionally rough surface to the angular distribution of the light scattered by such a surface. In the direct problem, the angular distribution of the scattered light calculated from the profile is shown to agree with the measured one. In the inverse problem, the rms roughness and the autocorrelation function are found by a least-squares fit to the measured angular distribution. For the smoother surfaces, the rms roughness is mostly determined by the ratio between the power of the specular beam and the total power of the scattered light; the computed values are proportional to those calculated directly from the stylus profiles. The values of the parameters obtained by the least-squares fit are affected by a variety of errors and agree only partially with those obtained from the stylus profile.

Optical Reflectance of Metallic Coatings: Effect of Aluminum Flake Orientation

A set of aluminum-flake pigmented coatings having different flake orientations was prepared using various spraying conditions. The flake surface topography and the orientations of individual flakes were determined from images obtained by laser scanning confocal microscopy. Reflectance measurements were carried out to quantify the optical properties of the coatings. Both a Gaussian distribution (used to represent the measured flake orientation distribution) and a topographic map (including local surface roughness and orientation) of the flakes were then used as input to a ray scattering model to calculate the optical reflectance of each coatings Flake orientation distributions and examples of measured optical reflectance as a function of scattering angle are shown, and the latter are compared to calculated reflectance values.

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.

Fundamental limits of optical critical dimension metrology: a simulation study

This paper is a comprehensive summary and analysis of a SEMATECH funded project to study the limits of optical critical dimension scatterometry (OCD). The project was focused on two primary elements: 1) the comparison, stability, and validity of industry models and 2) a comprehensive analysis of process stacks to evaluate the ultimate sensitivity and limits of OCD. Modeling methods are a requirement for the interpretation and quantitative analysis of scatterometry data. The four models evaluated show good agreement over a range of targets and geometries for zero order specular reflection as well as higher order diffraction. A number of process stacks and geometries representing semiconductor manufacturing nodes from the 45 nm node to the 18 nm node were simulated using several measurement modalities including angle-resolved scatterometry and spectrally-resolved scatterometry, measuring various combinations of intensity and polarization. It is apparent in the results that large differences are observed between those methods that rely upon unpolarized and single polarization measurements. Using the three parameter fits and assuming that the sensitivity of scatterometry must meet the criterion that the 3σ uncertainty in the bottom dimension must be less than 2% of the linewidth, specular scatterometry solutions exist for all but the isolated lines at 18 nm node. Scatterometry does not have sufficient sensitivity for isolated and semi-isolated lines at the 18 nm node unless the measurement uses wavelengths as short as 200 nm or 150 nm and scans over large angle ranges.

Single integral equation for wave scattering

When a wave interacts with an obstacle, the scattered and transmitted fields can be found by solving a system of integral equations for two unknown fields defined on the surface of the body. By choosing a more appropriate unknown function, the system of equations is reduced to a single singular integral equation of the first kind. This reduction is done here for transient and monochromatic waves, for a scalar field that obeys the wave equation, and for electromagnetic fields that obey Maxwell’s equations.

Power spectral densities: A multiple technique study of different Si wafer surfaces

Power spectral densities (PSDs) were used to characterize a set of surfaces over a wide range of lateral as well as perpendicular dimensions. Twelve 200-mm-diameter Si wafers were prepared and the surface finishes ranged from as-ground wafers to epitaxial wafers. The wafer surfaces were then measured with different methods: atomic force microscopy, angle-resolved light scatter, interferometric microscopy, optical profiling, stylus profiling, and capacitance-based wafer thickness gaging. The data were used to compute one-dimensional PSDs and the curves were plotted as functions of spatial frequencies, comparing results for different samples or for different instruments. The useful frequency range for each method is indicated and differences in the calculated PSD values in the overlapping region of two or more methods are discussed. The method used to convert two-dimensional PSDs to one-dimensional ones is presented.

Light scattering from glossy coatings on paper.

The application of angle-resolved light scattering (ARLS) to the measurement of the surface roughness of glossy coatings on paper was investigated. To this end, ARLS patterns were measured for laser light scattered from several glossy paper samples, and these patterns were compared with those calculated using a theoretical model based on plane-wave scattering from an isotropic rough surface. Mechanical stylus profilometry data for the rms roughnesses and the autocorrelation functions of the coatings were used as input to calculate the patterns. For all the paper samples measured, as well as for all the incidence angles used, there was good agreement between the experimental and the calculated patterns when all the rms roughnesses measured by profilometry were reduced by 30%. The indication from these experiments is that ARLS may be used to determine the roughness parameters of the coatings. As a check on these results, measurements were also performed with a commercial optical surface probe; these data agreed well with both the ARLS and the stylus profilometry results.

Measurements and predictions of light scattering by clear coatings

Comparisons are made between calculated and measured angle-resolved light-scattering distributions from clear dielectric isotropic epoxy coatings over a range of rms roughness conditions, resulting in strongly specular scattering to diffuse scattering characteristics. Calculated distributions are derived from topography measurements performed with interferometric microscopes. Two methods of calculation are used. One determines the intensity of scattered light waves with a phase integral in the Kirchhoff approximation. The other is based on the reflection of light rays by locally flat surfaces. The angle-resolved scattering distributions for the coatings are measured with the spectral trifunction automated reference reflectometer (STARR) developed by the National Institute of Standards and Technology. Comparisons between measured and calculated results are shown for three surfaces with rms roughness values of approximately 3, 150, and 800 nm for an angle of incidence of 20 degrees .

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.