Dirk Vandepitte

Recent advances in non-probabilistic approaches for non-deterministic dynamic finite element analysis

SummaryThere is a growing awareness of the impact of non-deterministic model properties on the numerical simulation of physical phenomena. These non-deterministic aspects are of great importance when there is a large amount of information to be retrieved from the numerical analysis, as for instance in a numerical reliability study or reliability based optimisation during a design process. Therefore, the non-deterministic properties form a primordial part of a trustworthy virtual prototyping environment. The implementation of such a virtual prototyping environment requires the inclusion of non-deterministic properties in the numerical finite element framework. This articel gives an overview of the emerging non-probabilistic approaches for non-deterministic numerical analysis, and compares them to the classical probabilistic methodology. Their applicability in the context in engineering design is discussed. The typical implementation strategies applied in literature are reviewed. A new concept is introduced for the calculation of envelope frequency response functions. This method is explained in detail and illustrated on a numerical example.

Influence of annealing conditions on the mechanical and microstructural behavior of electroplated Cu-TSV

In this paper, the effect of annealing condition on the microstructural and mechanical behavior of copper through-silicon via (Cu-TSV) is studied. The hardness of Cu-TSV scaled with the Hall–Petch relation, with the average hardness values of 1.9 GPa, 2.2 GPa and 2.3–2.8 GPa, respectively for the annealed, room temperature (RT) aged and the as-deposited samples. The increase in hardness toward the top of the as-deposited sample is related to the decrease in grain size. The annealed and the as-deposited samples showed a constant elastic modulus (E-modulus) value across the length of Cu-TSV of 140 GPa and 125 GPa respectively, while the RT aged sample showed a degradation in E-modulus from the bottom of the TSV (140 GPa) to the top (110 GPa). These differences in E-modulus values and trends under the different test conditions were found to be unrelated with the crystallographic texture of the samples, but could be related to the presence of residual stresses. No correlation is found between the hardness and E-modulus data. This is attributed to the coupling and competitive effects of grain size and residual stresses, with the grain size effect having a dominant influence on hardness, while the presence of residual stresses dominated the E-modulus result.

Extraction of the Appropriate Material Property for Realistic Modeling of Through-Silicon-Vias using μ-Raman Spectroscopy

Experimental μ-Raman spectroscopy (μRS) results are used to determine the appropriate plastic yield criterion for an accurate finite element modeling of stress in and near copper filled through-silicon-vias (TSV). It is found that the strain-hardening yield criterion gives the most accurate correlation between the ¿RS results and the finite element modeling. The verified yield criterion is used to simulate the effective keep-away-zone of transistors from the TSV. It is shown that transistor proximity is influenced by the via diameter.

Fuzzy Finite Element Method for Frequency Response Function Analysis of Uncertain Structures

A concept is presented for incorporating fuzzy uncertainties in dynamic e nite element analyses of uncertain structures. The objective is twofold. The e rst goal is to clarify and extend the classical fuzzy e nite element (FFE) method as it was introduced for static analyses. The shortcomings of the classical approach are described, and an extension to a generalized approach is proposed. This generalized approach is proven to be a more realistic and therefore more reliable concept for taking uncertainty into account. The second goal is to illustrate the applicability of the method for dynamic analyses. The classical and the generalized approach are compared using an eigenvalue analysis of a simple numerical example. The FFE method is also applied to the calculation of the total envelope frequency response function (FRF) using the modal superposition principle. This method requires safe approximations of the individual mode envelope frequency response functions. For this purpose a number of safe approximate optimization strategies are introduced. The numerical example shows that useful results are obtained using this FFE approach for FRF calculations.

Analysis of the Induced Stresses in Silicon During Thermcompression Cu-Cu Bonding of Cu-Through-Vias in 3D-SIC Architecture

A new approach to 3D stacking of chips is being developed at IMEC and is called 3D-stacked IC (3D-SIC). In this approach, interconnection between strata is achieved by thermo-compression bonding of Cu-vias to a Cu-landing pad. In this paper we use finite element methods to study the influence of the resultant induced stresses in silicon as a result of CTE mismatch between silicon and copper and that also caused by the applied thermo-compression bonding force. Bonding temperature is found to be the main cause of induced stresses during thermo-compression bonding. The induced stresses decreased with a decrease in the silicon thickness. The keep-away-zone of the transistors from the influence of stresses from the Cu-vias is found to be dependent on the diameter of the Cu-via and the doping concentration of the transistors.

A hybrid bioregulatory model of angiogenesis during bone fracture healing

Bone fracture healing is a complex process in which angiogenesis or the development of a blood vessel network plays a crucial role. In this paper, a mathematical model is presented that simulates the biological aspects of fracture healing including the formation of individual blood vessels. The model consists of partial differential equations, several of which describe the evolution in density of the most important cell types, growth factors, tissues and nutrients. The other equations determine the growth of blood vessels as a result of the movement of leading endothelial (tip) cells. Branching and anastomoses are accounted for in the model. The model is applied to a normal fracture healing case and subjected to a sensitivity analysis. The spatiotemporal evolution of soft tissues and bone, as well as the development of a blood vessel network are corroborated by comparison with experimental data. Moreover, this study shows that the proposed mathematical framework can be a useful tool in the research of impaired healing and the design of treatment strategies.

Thermomechanical models for leadless solder interconnections in flip chip assemblies

Analytical thermomechanical models have been developed in order to calculate the thermally induced stresses in leadless solder interconnection systems. Two different analytical models are highlighted: the peripheral and area array thermomechanical model which describe the thermally induced stresses for two components connected to each other with a peripheral, respectively, area array of joints. The analytical models are based on structural mechanics and have the ability to characterize the nature and estimate the magnitude of the joint stresses. Using these models, structural design optimization of interconnection systems can be performed very quickly in order to reduce time consuming experiments and finite element simulations. It is found that the largest stresses in the solder joints of flip chip assemblies are at the top and bottom surface of the connection and that they are especially caused by bending moments subjected to the joints. Comparisons with finite element simulations have proved a good accuracy of the thermomechanical models.

Optimization of filament-wound parts based on non-geodesic winding

Abstract When designing filament-wound parts, use of an integrated strategy is recommended to take advantage of the benefits of composites despite limitations of the filament winding process. This paper describes a computer-integrated methodology for the design of filament-wound parts which includes: (1) initial part design using a computer-aided design system; (2) preliminary finite element analysis to determine ideal fibre orientations; (3) fibre path generation, including non-geodesics, to obtain feasible fibre paths; (4) choice of final lay-up sequence; and (5) composite finite element analysis to adapt the final lay-up until strength and stiffness requirements are met. The proposed methodology, embodied in the computer code CAWAR, is illustrated by application to a conical filament-wound part.

Elimination of the axial deformation problem of Cu-TSV in 3D integration

The out‐of‐plane expansion of Copper Through‐Silicon‐Via (Cu‐TSV) is a concern in 3D stacking of chips, since it pushes against the BEOL, thus posing a possible reliability risk. In this study we demonstrate a solution for the Cu‐TSV out‐of‐plane expansion problem resulting in a non‐deformed BEOL. This is achieved through gaining a good understanding of the thermo‐mechanical behavior of Cu by experiments and adopting this learning in our process flow.

Solder parameter sensitivity for CSP life-time prediction using simulation-based optimization method

Finite element modeling (FEM) is widely used for estimating the solder joint reliability of electronic packages. However, the solder properties are strongly process and geometry dependent. Even for the same type of solder, measurements conducted by different people at different locations show different results, due to differences in application conditions, benching etc. Those differences may lead to differences in constitutive equations and/or the parameter values. Therefore the effect of the solder parameter variation and parameter sensitivity should be taken into account before a reliable solder fatigue prediction can be made. In this research, a simulation based optimization method is used to investigate the sensitivity of the chosen solder parameters for the solder fatigue prediction using an inelastic strain criterion.