While conventional ellipsometry is only applicable to homogeneous sample areas large enough to cover the illumination spot, imaging ellipsometry, combining ellipsometry and microscopy, offers a solution to this. It enables the local examination of polarization properties, yet it is not widely used in metrology, mostly due to a lack of proper evaluation methods.
We discuss approaches for an advanced evaluation of imaging Mueller matrix ellipsometry for nanometrological applications. This encompasses ways to evaluate Mueller matrix images without 3D simulations, using techniques inspired by machine learning, as well as the algorithmic treatment of thermal instabilities. Also, we discuss the applicability of plasmonic lenses (PL) for the advancement of ellipsometric methods. We developed a new design for PLs to enable higher fabrication rates for possible applications. Simulations showed that PLs significantly enhance the sensitivity of ellipsometric measurements to subwavelength structures.
This project 20FUN02 “POLight” has received funding from the EMPIR programme co-financed by the Participating States and from the European Union’s Horizon 2020 research and innovation programme.
Nanowire structures can be used for energy harvesting from renewable sources. These pillar structures with lateral dimensions in the nanometre range offer several advantages due to their small physical size and their large surface-to-volume ratio. The required nanodimensional characterization can be achieved efficiently by optical methods such as Mueller matrix ellipsometry. Here the measured Mueller matrices need to be analysed with numerical simulations to reconstruct the structural parameters of interest. We present the measurement method and measurement results on silicon nanowire test structures as well as the simulations on exemplary structures and a discussion of the results.
Plasmonic lenses are metastructures that use the excitation of surface plasmon polaritons in metallic nanoslits to focus light to particularly small focal spots at arbitrary distances. This facilitates possibilities for improving nano-optical methods, for example in ellipsometry. We developed two- and three-dimensional plasmonic lenses with a new inverted design that complies the fabrication process. However, plasmonic lenses show chromatic aberrations. In this contribution, we explore different approaches and limitations to expand the inverted plasmonic lens design to achromatic applications. We use numerical simulations based on the Finite Element Method to investigate in different lens geometries.
Spectroscopic polarization measurement and control using channeled spectrum has several unique features and
is useful for various spectroscopic instruments. It utilizes the strong dispersion characteristics in polarization
retardation of high-order retarders so that the polarization modulation can be made without using mechanical
or active elements for polarization modulation. In this presentation, we describe its principle, basic features, and
several applications including a spectroscopic ellipsometer and ultrafast rotations of beam profile and polarization.
Using conventional Mueller matrix ellipsometry, the geometries of periodic nanostructures can be easily determined if the measurement fields are not smaller than the illumination spot size. Measurements on individual nanostructures smaller than this can be accounted for by imaging ellipsometry, which allows measuring all 16 Mueller matrix elements for each pixel in the camera of the imaging system. These so-called Mueller matrix images contain additional information about the spatial distribution of the sample’s polarizing properties that are useful in the characterization of individual nanostructures. We built an imaging Mueller matrix ellipsometry system for measurements in the visible regime. Our system allows for the analysis arm, which holds the CCD camera and the polarization state analyser, to be rotated freely around the sample. By this, measurements in reflection and in transmission can be performed at arbitrary angles of incidence between 37.5° and 90°. Additionally, we implemented a reflection mode for 0° angle of incidence. Using this setup, our goal is to characterize the shape of individual nanostructures much smaller than the illumination spot using the additional information from the Mueller matrix images. Thus, we designed and fabricated a sample containing various individual nanostructures with different geometrical features. The structures are of square or circular shape, ranging in size from 5 µm to 50 nm. Additionally, the square structures feature corner rounding with different radii for a transition between circle and square. With these structures, we systematically measure the influence of the shape on the Mueller matrix elements. We also investigate in using Mueller matrix images for the characterization of subwavelength sized features significantly smaller than the resolution limit of our microscope system at about 800 nm. First results show clear distinctions between opposing edges of the nanostructures in off-diagonal Mueller matrix images.
To precisely characterize nanostructures while keeping the advantages of optical measurements, modern methods are still being refined. Plasmonic lenses, which are designable with less computational effort than dielectric metalenses, are promising. Simulations showed that sub-wavelength sized focal spots in arbitrary distances are achievable. We describe our simulations of the lens-sample interaction with plasmonic lenses with working distances up to 1 mm combined with single and periodic nanostructures using finite element method. Scanning the focal spot over the sample, we examine transmission and reflection in the far field, the field-structure interaction in the near field, and the applicability in Mueller ellipsometry.
With the persistent progress in nanotechnology the importance to accurately characterize nanoscale structures steadily increases. Optical measurement techniques have proven to be well suited for this purpose. We investigate different approaches to gain more information about nanoscale features by combining polarimetric setups with specially designed nanostructures. Our experimental setup combines a dual-rotating compensator Mueller matrix ellipsometer with an optical microscope. One arm of the ellipsometer is rigid and consists of a light source, polarization state generator, and optics to focus the light onto a sample. Samples under investigation are mounted on top of a combination of rotation and translation stages to precisely adjust them into the microscope’s focus. The other arm forms the microscope part with a long working distance objective, a polarization state analyser and a CCD camera. A large aperture rotation stage allows to rotate this arm around the sample stage. Thus, measurements in reflection and transmission under different angles of incidence can be performed. The setup measures Mueller matrices for each pixel in the obtained image. Therefore, it allows to examine the polarizing properties of the sample spatially and helps to gain further topological information. This information can be additionally enhanced by supporting nanostructures placed close to the sample to extract information from the near field. Therefore, we designed plasmonic lenses for different measurement configurations. The investigations are complemented by numerical finite element simulations. These are performed to validate the design of the nanostructures and to compare them with measured values. Up to now, we characterized the experimental setup and designed and validated the supporting nanostructures and reference structures. Future steps include extending the setup with a monochromator to ensure flexible illumination, measurement of the reference structures, and the combination of setup and plasmonic lenses to further enhance the sensitivity to subwavelength sized features.
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.
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