Accurate metrology of nanostructures gains more and more importance and for efficiency reasons optical methods play a significant role here. Unfortunately, conventional optical microscopy is subject to the well-known resolution limit. The necessity to resolve objects smaller than this limit led to the development of superresolution methods which however are barely used in metrology for practical reasons. Non-imaging indirect optical methods like scatterometry and ellipsometry however are not limited by diffraction and are able to determine the critical dimensions of nanostructures. We investigate the application of different approaches for specifically manipulated near-fields in Mueller matrix ellipsometry to achieve an enhanced sensitivity for polarization based sub-wavelength topological information. To this end, we present first numerical simulations of these approaches. To examine the relationship between structural properties and Mueller matrix elements we designed individual structures based on geometrical shapes of varying parameters as well as small arrays. They are realized by lithography as holes in PMMA resist. First, we characterize SEM images of the structures to validate the fabrication process. Numerical simulations of the Mueller matrices of the structures by finite element method are discussed. Results indicate that conventional Mueller matrix ellipsometry alone is unsuitable but the extension to imaging Mueller matrix microscopy is promising for the characterization of sub-wavelength features.
Collinear photothermal deflection spectroscopy (PDS) is a widely used method for the spatially resolved determination of the optical attenuation coefficient. In this work we rigorously model the signal contributions in PDS on semiconductors below the band gap energy. The dependencies of the PDS signal on selected experimental parameters (pump beam intensity, crossing angle, chopper frequency and distance from the pump beam focus) are computed and compared with previous calculation results that are based on simplified assumptions. We find that for high pump beam intensities and sample materials with high two photon absorption coefficients beside the mirage effect nonlinear absorption mechanisms have a strong impact on the signal. Furthermore, we show that angular deflection effects can significantly enhance the PDS signal. For example, the conical refractive index field due to the pump beam divergence leads to an angular deflection at readout points outside the pump beam focus. Considering these additional signal contributions is crucial to determine proper absorption properties.
The optical performance of wire grid polarizers crucially depends on the fabrication accuracy. Reducing the application wavelengths to the ultraviolet spectral range sets the challenge that structural deviations in the range of typically a few nanometers become comparable to the feature sizes of the structure. In this contribution we present a concept to determine structural parameters and structural deviations of DUV wire grid polarizers fabricated with self-aligned double patterning. To this end, we evaluate the properties (i.e the spectral positions, the angular dependence of the spectral positions and widths) of asymmetry induced resonances in the transmittance spectra which occur at wavelengths larger than 380 nm. We derive requirements for measurement setup for nanoscale determination of the structural properties. Our results indicate that the investigation of the angular dependent transmittance at only two different wavelengths and one polarization state is sufficient to determine structural deviations with uncertainties of ±1:7nm for the effective shift of the ridge and ±0:34° for the effective tilt. Thus, the proposed method allows us to retrieve deep subwavelength structural information at the nanoscale with easily accessible transmittance measurements in the visible spectral range.
Controlling the polarization of light is crucial in numerous applications such as spectroscopy, ellipsometry, photo
lithography or industrial vision. Polarization control can be realized by wire grid polarizers (WGPs), which are large
aspect ratio, zero order gratings. These elements provide an anisotropic transmittance depending on the polarization
direction of the incident light. WGPs’ high attractiveness originates from their large free aperture, while simultaneously
being extremely thin. Furthermore, these elements can be easily integrated into other nano-optical devices. Recently,
such elements were successfully developed for applications down to the deep ultra violet spectral range. However, at
shorter wavelengths the influence of roughness of the structures poses a severe limitation on the feasible optical
performance. To tackle this problem, we numerically simulated the impact of line edge roughness on the polarization
properties of WPGs. Therefore, we generated edge position data of rough grating lines by means of the Thorsos method
and calculated the resulting optical response by finite difference time domain method. With this procedure the influence
of standard deviation, correlation length, Hurst exponents and wavelength was investigated. We find that for standard
deviations of 2.5 nm and 5.0 nm the polarization contrast is reduced by a factor of 3 and 7, respectively. The polarization
contrast shows a minimum for intermediate correlation lengths, while virtually no impact of the Hurst exponent is
observed. This is explained by several mechanisms occurring for different ratios between the spatial frequency of the
roughness and the frequency of incident light. Our theoretical findings correlate well with experimental results we
retrieved with measured roughness parameters of fabricated elements.
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