The characterization of nanostructured surfaces with sensitivity in the sub-nm range is of high importance for the development of current and next-generation integrated electronic circuits. Modern transistor architectures for, e.g., FinFETs are realized by lithographic fabrication of complex, well-ordered nanostructures. Recently, a novel characterization technique based on X-ray fluorescence measurements in grazing incidence geometry was proposed for such applications. This technique uses the X-ray standing wave field, arising from an interference between incident and the reflected radiation, as a nanoscale sensor for the dimensional and compositional parameters of the nanostructure. The element sensitivity of the X-ray fluorescence technique allows for a reconstruction of the spatial element distribution using a finite element method. Due to a high computational time, intelligent optimization methods employing machine learning algorithms are essential for timely provision of results. Here, a sampling of the probability distributions by Bayesian optimization is not only fast, but it also provides an initial estimate of the parameter uncertainties and sensitivities. The high sensitivity of the method requires a precise knowledge of the material parameters in the modeling of the dimensional shape provided that some physical properties of the material are known or determined beforehand. The unknown optical constants were extracted from an unstructured but otherwise identical layer system by means of soft X-ray reflectometry. The spatial distribution profiles of the different elements contained in the grating structure were compared to scanning electron and atomic force microscopy and the influence of carbon surface contamination on the modeling results were discussed. This novel approach enables the element sensitive and destruction-free characterization of nanostructures made of silicon nitride and silicon oxide with sub-nm resolution.

The increasing importance of well-controlled ordered nanostructures on surfaces represents a challenge for existing metrology techniques. To develop such nanostructures and monitor complex processing constraints fabrication, both a dimensional reconstruction of nanostructures and a characterization (ideally a quantitative characterization) of their composition is required. In this work, we present a soft x-ray fluorescence-based methodology that allows both of these requirements to be addressed at the same time. By applying the grazing-incidence x-ray fluorescence technique and thus utilizing the x-ray standing wave field effect, nanostructures can be investigated with a high sensitivity with respect to their dimensional and compositional characteristics. By varying the incident angles of the exciting radiation, element-sensitive fluorescence radiation is emitted from different regions inside the nanoobjects. By applying an adequate modeling scheme, these datasets can be used to determine the nanostructure characteristics. We demonstrate these capabilities by performing an element-sensitive reconstruction of a lamellar grating made of Si 3 N 4 , where GIXRF data for the O-Kα and N-Kα fluorescence emission allows a thin oxide layer to be reconstructed on the surface of the grating structure. In addition, we employ the technique also to three dimensional nanostructures and derive both dimensional and compositional parameters in a quantitative manner.

Parameter reconstructions are indispensable in metrology. Here, the objective is to explain K experimental measurements by fitting to them a parameterized model of the measurement process. The model parameters are regularly determined by least-square methods, that is, by minimizing the sum of the squared residuals between the K model predictions and the K experimental observations, 𝝌 2 . The model functions often involve computationally demanding numerical simulations. Bayesian optimization methods are specifically suited for minimizing expensive model functions. However, in contrast to least-square methods such as the Levenberg-Marquardt algorithm, they only take the value of 𝝌 2 into account, and neglect the K individual model outputs. A Bayesian target-vector optimization scheme with improved performance over previous developments, that considers all K contributions of the model function and that is specifically suited for parameter reconstruction problems which are often based on hundreds of observations is presented. Its performance is compared to established methods for an optical metrology reconstruction problem and two synthetic least-squares problems. The proposed method outperforms established optimization methods. It also enables to determine accurate uncertainty estimates with very few observations of the actual model function by using Markov chain Monte Carlo sampling on a trained surrogate model.

The spatial and compositional complexity of 3D structures employed in today's nanotechnologies has developed to a level at which the requirements for process development and control can no longer fully be met by existing metrology techniques. For instance, buried parts in stratified nanostructures, which are often crucial for device functionality, can only be probed in a destructive manner in few locations as many existing nondestructive techniques only probe the objects surfaces. Here, it is demonstrated that grazing exit X‐ray fluorescence can simultaneously characterize an ensemble of regularly ordered nanostructures simultaneously with respect to their dimensional properties and their elemental composition. This technique is nondestructive and compatible to typically sized test fields, allowing the same array of structures to be studied by other techniques. For crucial parameters, the technique provides sub‐nm discrimination capabilities and it does not require access‐limited large‐scale research facilities as it is compatible to laboratory‐scale instrumentation.

For the reliable fabrication of the current and next generation of nanostructures it is essential to be able to determine their material composition and dimensional parameters. Using the grazing incidence X-ray fluoresence technique, which is taking advantage of the X-ray standing wave field effect, nanostructures can be investigated with a high sensitivity with respect to the structural and elemental composition. This is demonstrated using lamellar gratings made of Si 3 N 4 . Rigorous field simulations obtained from a Maxwell solver based on the finite element method allow to determine the spatial distribution of elemental species and the geometrical shape with sub-nm resolution. The increasing complexity of nanostructures and demanded sensitivity for small changes quickly turn the curse of dimensionality for numerical simulation into a problem which can no longer be solved rationally even with massive parallelisation. New optimization schemes, e.g. machine learning, are required to satisfy the metrological requirements. We present reconstruction results obtained with a Bayesian optimization approach to reduce the computational effort.