Stephan C. Kramer

Analysis of local strain in aluminium interconnects by energy filtered CBED

Energy filtered convergent beam electron diffraction (CBED) was used to investigate localised strain in aluminium interconnects. The quantitative analysis of the experimental patterns is based on a multi-step evaluation procedure which is the main subject of the present paper. The improvements which were made to the analysis method aim at increasing both the automation and the accuracy. The detection of the higher order Laue zone (HOLZ) line positions is performed by means of the Hough transform. The required sub-pixel resolution can be achieved routinely and the achievable accuracy is only limited by the line width and the amount of noise in the patterns. The determination of the strain state is performed via a refinement algorithm which is based on varying the strain state in the sample coordinate system and simulating the patterns for the individual grains until a best fit with the experiment is obtained. For the simulation we have developed a new correction scheme in which the dynamical effects are treated separately for each individual HOLZ line. The results show that the main source of the observed strains is the difference in thermal expansion coefficients. The strain is substantially reduced underneath a hillock in the interconnect. Asymmetries in the strain distribution around the hillock show that the unidirectional diffusion during electromigration tests causes peak strains in areas next to the hillock which may be possible failure sites.

Interaction of subducted slabs with the mantle transition‐zone: A regime diagram from 2‐D thermo‐mechanical models with a mobile trench and an overriding plate

Transition zone slab deformation influences Earths thermal, chemical and tectonic evolution. However, the mechanisms responsible for the wide-range of imaged slab morphologies remain debated. Here, we use 2-D thermo-mechanical models with a mobile trench, an overriding plate, a temperature- and stress-dependent rheology, and a 10, 30 or 100-fold increase in lower mantle viscosity, to investigate the effect of initial subducting- and overriding-plate ages on slab transition-zone interaction. Four subduction styles emerge: (i) a “vertical folding” mode, with a quasi-stationary trench, near-vertical subduction and buckling/folding at depth (VF); (ii) slabs that induce mild trench retreat, which are flattened/“horizontally deflected” and stagnate at the upper-lower mantle interface (HD); (iii) inclined slabs, which result from rapid sinking and strong trench retreat (ISR); (iv) a two-stage mode, displaying backward-bent and subsequently inclined slabs, with late trench retreat (BIR). Transitions from regime (i) to (iii) occur with increasing subducting-plate age (i.e. buoyancy and strength). Regime (iv) develops for old (strong) subducting and overriding plates. We find that the interplay between trench motion and slab deformation at depth dictate the subduction style, both being controlled by slab strength, which is consistent with predictions from previous compositional subduction models. However, due to feedbacks between deformation, sinking rate, temperature and slab strength, the subducting-plate buoyancy, overriding-plate strength and upper-lower mantle viscosity jump are also important controls in thermo-mechanical subduction. For intermediate upper-lower mantle viscosity jumps (×30), our regimes reproduce the diverse range of seismically imaged slab morphologies.

Fluidity: A fully unstructured anisotropic adaptive mesh computational modeling framework for geodynamics

We present a new computational modeling framework, Fluidity, for application to a range of two- and three-dimensional geodynamic problems, with the focus here on mantle convection. The approach centers upon a finite element discretization on unstructured simplex meshes, which represent complex geometries in a straightforward manner. Throughout a simulation, the mesh is dynamically adapted to optimize the representation of evolving solution structures. The adaptive algorithm makes use of anisotropic measures of solution complexity, to vary resolution and allow long, thin elements to align with features such as boundary layers. The modeling framework presented differs from the majority of current mantle convection codes, which are typically based upon fixed structured grids. This necessitates a thorough and detailed validation, which is a focus of this paper. Benchmark comparisons are undertaken with a range of two- and three-dimensional, isoviscous and variable viscosity cases. In addition, model predictions are compared to experimental results. Such comparisons highlight not only the robustness and accuracy of Fluidity but also the advantages of anisotropic adaptive unstructured meshes, significantly reducing computational requirements when compared to a fixed mesh simulation.

Gold and thiol surface functionalized integrated optical Mach–Zehnder interferometer for sensing purposes

Abstract We demonstrate an integrated optical Mach–Zehnder interferometer for sensing purposes with a surface functionalized by thiols via an additional gold layer. Therefore, the oxidic silicon oxynitride waveguide surface was first covered by a thiol terminated silane self-assembled monolayer. An ultrathin gold layer was then deposited onto the “active” sulfur surface by OMCVD. This gold layer was finally functionalized by a biotinylated thiol in order to specifically bind streptavidin and a biotinylated antibody. Unspecific binding of streptavidin was tested also.

Plasmon energy mapping in energy-filtering transmission electron microscopy

In this paper, we demonstrate the two-dimensional mapping of plasmon energies by energy-filtering transmission electron microscopy. The maps are obtained from a series of energy-filtered images in the plasmon energy region. Examples are shown for a nano-crystalline Si-B-C-N ceramic. This material contains SiC and Si(3)N(4) grains as well as intergranular regions composed of hexagonal BN (h-BN) and turbostratic carbon (t-C). The different phases can be clearly identified by their specific plasmon energies. An energy resolution of < or =0.1eV is achieved. In addition, the plasmon map of an amorphous carbon film is used to visualize the non-isochromaticity of the Corrected Omega filter (90 degrees filter) of the SESAM2. A procedure is proposed for the correction of the non-isochromaticity.

A community benchmark for viscoplastic thermal convection in a 2‐D square box

Numerical simulations of thermal convection in the Earth’s mantle often employ a pseudoplastic rheology in order to mimic the plate-like behavior of the lithosphere. Yet the benchmark tests available in the literature are largely based on simple linear rheologies in which the viscosity is either assumed to be constant or weakly dependent on temperature. Here we present a suite of simple tests based on nonlinear rheologies featuring temperature, pressure, and strain rate-dependent viscosity. Eleven different codes based on the finite volume, finite element, or spectral methods have been used to run five benchmark cases leading to stagnant lid, mobile lid, and periodic convection in a 2-D square box. For two of these cases, we also show resolution tests from all contributing codes. In addition, we present a bifurcation analysis, describing the transition from a mobile lid regime to a periodic regime, and from a periodic regime to a stagnant lid regime, as a function of the yield stress. At a resolution of around 100 cells or elements in both vertical and horizontal directions, all codes reproduce the required diagnostic quantities with a discrepancy of at most

Solving the Poisson equation on small aspect ratio domains using unstructured meshes

3% in the presence of both linear and nonlinear rheologies. Furthermore, they consistently predict the critical value of the yield stress at which the transition between different regimes occurs. As the most recent mantle convection codes can handle a number of different geometries within a single solution framework, this benchmark will also prove useful when validating viscoplastic thermal convection simula- tions in such geometries.

Local Strains Measured in Al Lines During Thermal Cycling and Electromigration Using Convergent-beam Electron Diffraction

Abstract We discuss the ill-conditioning of the matrix for the discretised Poisson equation in the small aspect ratio limit, and motivate this problem in the context of nonhydrostatic ocean modelling. Efficient iterative solvers for the Poisson equation in small aspect ratio domains are crucial for the successful development of nonhydrostatic ocean models on unstructured meshes. We introduce a new multigrid preconditioner for the Poisson problem which can be used with finite element discretisations on general unstructured meshes; this preconditioner is motivated by the fact that the Poisson problem has a condition number which is independent of aspect ratio when Dirichlet boundary conditions are imposed on the top surface of the domain. This leads to the first level in an algebraic multigrid solver (which can be extended by further conventional algebraic multigrid stages), and an additive smoother. We illustrate the method with numerical tests on unstructured meshes, which show that the preconditioner makes a dramatic improvement on a more standard multigrid preconditioning approach, and also show that the additive smoother produces better results than standard SOR smoothing. This new solver method makes it feasible to run nonhydrostatic unstructured mesh ocean models in small aspect ratio domains.

Design optimisation and resource assessment for tidal-stream renewable energy farms using a new continuous turbine approach

In situ local measurement of sub-threshold strains generated during the electromigration of a 0.3-μm-wide Al interconnect was performed for the first time using convergent-beam electron diffraction (CBED) in a transmission electron microscope (TEM). Thermal strains were also analyzed and provided verification for the electromigration analysis. Spatially averaged strains resulting from thermal cycling and electromigration quantitatively agree with models and data from previous studies. However, the local strains exhibited variations as large as 2 × 10 −3 . After eliminating other possible mechanisms, the strain inhomogeneity is attributed to local plasticity through source-limited dislocation activity.

The Mantle Wedge's Transient 3-D Flow Regime and Thermal Structure

This paper presents a new approach for optimising the design of tidal stream turbine farms. In this approach, the turbine farm is represented by a turbine density function that specifies the number of turbines per unit area and an associated continuous locally-enhanced bottom friction field. The farm design question is formulated as a mathematical optimisation problem constrained by the shallow water equations and solved with efficient, gradient-based optimisation methods. The resulting method is accurate, computationally efficient, allows complex installation constraints, and supports different goal quantities such as to maximise power or profit. The outputs of the optimisation are the optimal number of turbines, their location within the farm, the overall farm profit, the farms power extraction, and the installation cost. We demonstrate the capabilities of the method on a validated numerical model of the Pentland Firth, Scotland. We optimise the design of four tidal farms simultaneously, as well as individually, and study how farms in close proximity may impact upon one another.