Coherent Fourier Scatterometry for sensitive detection of subwavelength structures and particles

The phenomenon of scattering is ubiquitous. The human eye sees it as a ``blue" sky in a summer morning or a diffuse glow during the night, the color of a laser or fog in the air. Alternatively, scattering recorded with a state-of-the-art instrument manifests itself in collisions between atoms, electrons, and photons, such as processes in nuclear reactors or inside an accelerator, and high-energy electrons precipitation in the atmosphere. Scientists across the world are interested in studying the scattering effects that take part in the interaction between the light and matter in order to determine the physical properties of materials. The dimensions of an arbitrary structure and its quality is adequately studied with optical metrology, which is the science of measurements with light. Staring from the height and width determination of a distant object by triangulation over many decades, optical metrology has developed to the vibrant area of technological advancements.
Numerous optical techniques and instruments, such as microscopes, wavefront sensors, optical comparators, and interferometers are available now where subnanometer precision is achieved. By studying the properties of the electromagnetic field that is generated from the interaction between the probe and the unknown target, it is nowadays possible to retrieve intricate parameters of the object such as its shape and roughness. Commonly, the measurement in the far-field regime is adopted since it is noninvasive. In the far-field, for successful information retrieval of features smaller than the Rayleigh limit, the inverse problem of scatterometry (optical metrology with scattered light) requires a priori information. In many cases, we assume that the target under the study is guaranteed to exist, and it is partially known. For example, one can deposit particles of certified material on top of a surface, measure the intensity of the scattered field, and by combining this information with electromagnetic models, one can deduce parameters such as size and position of the scatterer. However, when the target becomes extremely small, as for example, a fraction of the wavelength, the question arises: given the measuring instrument, would we still detect this target? The answer is yes, if the sensitivity of the instrument is high enough. Many areas of optics and physics rely on the detection and localization of tiny objects on top of a surface. The main examples include contamination and nanofabricated features and defects in the semiconductor industry, the studies of viruses and bacteria for biological and medical sciences, air and water pollution with toxic particles in environmental science.
In this thesis, we will concentrate on the application of scatterometry for isolated nanoparticle detection aimed at quality control in the semiconductor industry.