Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach

We apply adjoint-based sensitivity analysis to a time-delayed thermo-acoustic system: a Rijke tube containing a hot wire. We calculate how the growth rate and frequency of small oscillations about a base state are affected either by a generic passive control element in the system (the structural sensitivity analysis) or by a generic change to its base state (the base-state sensitivity analysis). We illustrate the structural sensitivity by calculating the effect of a second hot wire with a small heat-release parameter. In a single calculation, this shows how the second hot wire changes the growth rate and frequency of the small oscillations, as a function of its position in the tube. We then examine the components of the structural sensitivity in order to determine the passive control mechanism that has the strongest influence on the growth rate. We find that a force applied to the acoustic momentum equation in the opposite direction to the instantaneous velocity is the most stabilizing feedback mechanism. We also find that its effect is maximized when it is placed at the downstream end of the tube. This feedback mechanism could be supplied, for example, by an adiabatic mesh. We illustrate the base-state sensitivity by calculating the effects of small variations in the damping factor, the heat-release time-delay coefficient, the heat-release parameter, and the hot-wire location. The successful application of sensitivity analysis to thermo-acoustics opens up new possibilities for the passive control of thermo-acoustic oscillations by providing gradient information that can be combined with constrained optimization algorithms in order to reduce linear growth rates. © Cambridge University Press 2013.

Atom probe tomography for advanced metallization

In microelectronics, the increase in complexity and the reduction of devices dimensions make essential the development of new characterization tools and methodologies. Indeed advanced characterization methods with very high spatial resolution are needed to analyze the redistribution at the nanoscale in devices and interconnections. The atom probe tomography has become an essential analysis to study materials at the nanometer scale. This instrument is the only analytical microscope capable to produce 3D maps of the distribution of the chemical species with an atomic resolution inside a material. This technique has benefit from several instrumental improvements during last years. In particular, the use of laser for the analysis of semiconductors and insulating materials offers new perspectives for characterization. The capability of APT to map out elements at the atomic scale with high sensitivity in devices meets the characterization requirements of semiconductor devices such as the determination of elemental distributions for each device region. In this paper, several examples will show how APT can be used to characterize and understand materials and process for advanced metallization. The possibilities and performances of APT (chemical analysis of all the elements, atomic resolution, planes determination, crystallographic information...) will be described as well as some of its limitations (sample preparation, complex evaporation, detection limit, ...). The examples illustrate different aspect of metallization: dopant profiling and clustering, metallic impurities segregation on dislocation, silicide formation and alloying, high K/metal gate optimization, SiGe quantum dots, as well as analysis of transistors and nanowires. © 2013 Elsevier B.V. All rights reserved.