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To support the ongoing size reduction in integrated circuits, the need for accurate depth measurements of on-chip structures becomes increasingly important. Unfortunately, present metrology tools do not offer a practical solution. In the semiconductor industry, critical dimension scanning electron microscopes (CD-SEMs) are predominantly used for 2D imaging at a local scale. The main objective of this work is to investigate whether sufficient 3D information is present in a single SEM image for accurate surface reconstruction of the device topology. In this work, we present a method that is able to produce depth maps from synthetic and experimental SEM images. We demonstrate that the proposed neural network architecture, together with a tailored training procedure, leads to accurate depth predictions. The training procedure includes a weakly supervised domain adaptation step, which is further referred to as pixel-wise fine-tuning. This step employs scatterometry data to address the ground-truth scarcity problem. We have tested this method first on a synthetic contact hole dataset, where a mean relative error smaller than 6.2% is achieved at realistic noise levels. Additionally, it is shown that this method is well suited for other important semiconductor metrics, such as top critical dimension (CD), bottom CD and sidewall angle. To the extent of our knowledge, we are the first to achieve accurate depth estimation results on real experimental data, by combining data from SEM and scatterometry measurements. An experiment on a dense line space dataset yields a mean relative error smaller than 1%.

The motivation of the investigation is critical pressure loss in cryogenic flexible hoses used for LNG transport in offshore installations. Our main goal is to estimate the friction factor for the turbulent flow in this type of pipes. For this purpose, two-equation turbulence models (k–ε and k–ω) are used in the computations. First, fully developed turbulent flow in a conventional pipe is considered. Simulations are performed to validate the chosen models, boundary conditions and computational grids. Then a new boundary condition is implemented based on the “combined” law of the wall. It enables us to model the effects of roughness (and maintain the right flow behavior for moderate Reynolds numbers). The implemented boundary condition is validated by comparison with experimental data. Next, turbulent flow in periodically corrugated (flexible) pipes is considered. New flow phenomena (such as flow separation) caused by the corrugation are pointed out and the essence of periodically fully developed flow is explained. The friction factor for different values of relative roughness of the fabric is estimated by performing a set of simulations. Finally, the main conclusion is presented: the friction factor in a flexible corrugated pipe is mostly determined by the shape and size of the steel spiral, and not by the type of the fabric which is wrapped around the spiral.