A multiple mapping conditioning model for differential diffusion

This work introduces modeling of differential diffusion within the multiple mapping conditioning (MMC) turbulent mixing and combustion framework. The effect of differential diffusion on scalar variance decay is analyzed and, following a number of publications, is found to scale as Re. The ability to model the differential decay rates is the most important aim of practical differential diffusion models, and here this is achieved in MMC by introducing what is called the side-stepping method. The approach is practical and, as it does not involve an increase in the number of MMC reference variables, economical. In addition we also investigate the modeling of a more refined and difficult to reproduce differential diffusion effect - the loss of correlation between the different scalars. For this we develop an alternative MMC model with two reference variables but which also makes use of the side-stepping method. The new models are successfully validated against DNS results available in literature for homogenous, isotropic two scalar mixing

influence of block copolymer feature size on reactive ion etching pattern transfer into silicon

A successful realisation of sub-20 nm features on silicon (Si) is becoming the focus of many technological studies, strongly influencing the future performance of modern integrated circuits. Although reactive ion etching (RIE), at both micrometric and nanometric scale has already been the target of many studies, a better understanding of the different mechanisms involved at sub-20 nm size etching is still required. In this work, we investigated the influence of the feature size on the etch rate of Si, performed by a cryogenic RIE process through cylinder-forming polystyrene-block-polymethylmethacrylate (PS-b-PMMA) diblock copolymer (DBC) masks with diameter ranging between 19–13 nm. A sensible decrease of the etch depth and etch rate was observed in the mask with the smallest feature size. For all the DBCs under investigation, we determined the process window useful for the correct transfer of the nanometric cylindrical pattern into a Si substrate. A structural and physicochemical investigation of the resulting nanostructured Si is reported in order to delineate the influence of various RIE pattern effects. Feature-size-dependent etch, or RIE-lag, is proved to significantly affect the obtained results