An optimization method for the sensitivity of diffraction efficiency measurements is presented. I define the sensitivity as the estimation precision of the grating parameters. The optimization method called sensitivity analysis for fitting scans all the possible measurement configurations and selects the configuration that yields the best sensitivity. The scan is made over the domain of the experimental parameters of the arrangement, such as the azimuth angle of the grating and the orientation angles of the analyzer and the polarizer. These parameters can be freely varied, and among the multitude of possible combinations there is one configuration that provides optimum sensitivity. Comparison with experimental results reveals a qualitative agreement between theory and practice.
We describe a fast computational algorithm able to evaluate the Rayleigh-Sommerfeld diffraction formula, based on a special formulation of the convolution theorem and the fast Fourier transform. What is new in our approach compared to other algorithms is the use of a more general type of convolution with a scale parameter, which allows for independent sampling intervals in the input and output computation windows. Comparison between the calculations made using our algorithm and direct numeric integration show a very good agreement, while the computation speed is increased by orders of magnitude.
Phase-modulation scatterometry is a metrology technique for determining, by means of a phase modulator as a key device, the parameters of gratings. The main source of error to be dealt with are the fluctuations of the phase-modulation amplitude. The grating zeroth-order reflectance modulated by the phase modulator is converted into a signal by the photodetector. The measurables are the direct term and the first two harmonics of the signal. For experimental data fitting, we used the ratio of the harmonics over the direct term because it significantly improves the accuracy. A sensitivity analysis was performed for two samples, one real and one theoretical, to find the measurement configuration that insures optimum determination precision for the grating parameters. For the real sample, comparison of the theoretical predictions for sensitivity with the actual values showed a good agreement. For both samples the sensitivity analysis indicated subnanometric precision for the critical dimension (grating linewidth).
Thin film Si structures between 10 and 200nm in thickness and configured into two terminal metal-semiconductor-metal structures have been characterized for optical and electrical properties. Dark currents, spectral response, dc quantum efficiency, and ultrafast time response up to 400nm femtosecond laser illuminations at low fields have been studied. Dark currents and dc photocurrent measurements showed an increase in the film conductivity between 75 and 35nm, suggesting an increase in the carrier effective velocities due to confinement. An increase in the carrier effective velocity below 75nm was also confirmed through the transient response analysis. The measured spectral responses are in good agreement with Fresnel’s theoretical model for thin film coupling. The electron-limited transient signal has a full width at half maximum (FWHM) approximately 40ps for the 10nm Si film as compared to 490ps for a 200nm structure. For a hole-limited transit time signal the FWHM was about 82ps for the 10nm film as compared to 2.5ns for the 200nm film reduction in FWHM for both electrons and holes for the 10nm film, signifying that carriers travel much faster as the film thickness is reduced.
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