Statistical analysis and simulation techniques in wall-bounded turbulence

The present work is devoted to the assessment of the energy fluxes physics in the space of scales and physical space of wall-turbulent flows. The generalized Kolmogorov equation will be applied to DNS data of a turbulent channel flow in order to describe the energy fluxes paths from production to dissipation in the augmented space of wall-turbulent flows. This multidimensional description will be shown to be crucial to understand the formation and sustainment of the turbulent fluctuations fed by the energy fluxes coming from the near-wall production region. An unexpected behavior of the energy fluxes comes out from this analysis consisting of spiral-like paths in the combined physical/scale space where the controversial reverse energy cascade plays a central role. The observed behavior conflicts with the classical notion of the Richardson/Kolmogorov energy cascade and may have strong repercussions on both theoretical and modeling approaches to wall-turbulence. To this aim a new relation stating the leading physical processes governing the energy transfer in wall-turbulence is suggested and shown able to capture most of the rich dynamics of the shear dominated region of the flow. Two dynamical processes are identified as driving mechanisms for the fluxes, one in the near wall region and a second one further away from the wall. The former, stronger one is related to the dynamics involved in the near-wall turbulence regeneration cycle. The second suggests an outer self-sustaining mechanism which is asymptotically expected to take place in the log-layer and could explain the debated mixed inner/outer scaling of the near-wall statistics. The same approach is applied for the first time to a filtered velocity field. A generalized Kolmogorov equation specialized for filtered velocity field is derived and discussed. The results will show what effects the subgrid scales have on the resolved motion in both physical and scale space, singling out the prominent role of the filter length compared to the cross-over scale between production dominated scales and inertial range, lc, and the reverse energy cascade region lb. The systematic characterization of the resolved and subgrid physics as function of the filter scale and of the wall-distance will be shown instrumental for a correct use of LES models in the simulation of wall turbulent flows. Taking inspiration from the new relation for the energy transfer in wall turbulence, a new class of LES models will be also proposed. Finally, the generalized Kolmogorov equation specialized for filtered velocity fields will be shown to be an helpful statistical tool for the assessment of LES models and for the development of new ones. As example, some classical purely dissipative eddy viscosity models are analyzed via an a priori procedure.

TCAD approaches to multidimensional simulation of advanced semiconductor devices

Technology scaling increasingly emphasizes complexity and non-ideality of the electrical behavior of semiconductor devices and boosts interest on alternatives to the conventional planar MOSFET architecture. TCAD simulation tools are fundamental to the analysis and development of new technology generations. However, the increasing device complexity is reflected in an augmented dimensionality of the problems to be solved. The trade-off between accuracy and computational cost of the simulation is especially influenced by domain discretization: mesh generation is therefore one of the most critical steps and automatic approaches are sought. Moreover, the problem size is further increased by process variations, calling for a statistical representation of the single device through an ensemble of microscopically different instances. The aim of this thesis is to present multi-disciplinary approaches to handle this increasing problem dimensionality in a numerical simulation perspective. The topic of mesh generation is tackled by presenting a new Wavelet-based Adaptive Method (WAM) for the automatic refinement of 2D and 3D domain discretizations. Multiresolution techniques and efficient signal processing algorithms are exploited to increase grid resolution in the domain regions where relevant physical phenomena take place. Moreover, the grid is dynamically adapted to follow solution changes produced by bias variations and quality criteria are imposed on the produced meshes. The further dimensionality increase due to variability in extremely scaled devices is considered with reference to two increasingly critical phenomena, namely line-edge roughness (LER) and random dopant fluctuations (RD). The impact of such phenomena on FinFET devices, which represent a promising alternative to planar CMOS technology, is estimated through 2D and 3D TCAD simulations and statistical tools, taking into account matching performance of single devices as well as basic circuit blocks such as SRAMs. Several process options are compared, including resist- and spacer-defined fin patterning as well as different doping profile definitions. Combining statistical simulations with experimental data, potentialities and shortcomings of the FinFET architecture are analyzed and useful design guidelines are provided, which boost feasibility of this technology for mainstream applications in sub-45 nm generation integrated circuits.