van der O Olaf Sluis

Overall behaviour of heterogeneous elastoviscoplastic materials: effect of microstructural modelling

Homogenisation methods provide an efficient way to model the mechanical behaviour of heterogeneous materials. In this paper, a homogenisation procedure is adopted that allows to determine apparent properties for Perzynas elastoviscoplastic constitutive law for arbitrary microstructures. Numerical simulations on a representative volume element (RVE) are performed, from which the volume averaged state variables are acquired, necessary to establish the constitutive equations for the equivalent homogeneous medium. The applicability of mixed and periodic boundary conditions has been assessed. In addition, the difference between uniform and irregular distributions of the microstructural constituents is discussed. To substantiate our findings, a comparison is made between the global response of a heterogeneous and the corresponding homogenised structure.

Cohesive zone modeling for structural integrity analysis of IC interconnects

Due to the miniaturization of integrated circuits, their thermo-mechanical reliability tends to become a truly critical design criterion. Especially the introduction of copper and low-k dielectric materials cause some reliability problems. Numerical simulation tools can assist developers to meet this challenge. This paper considers the first bond integrity during wire bond qualification testing. During testing, metal peel off may occur. This mechanical failure mode is caused by delamination of several layers of the interconnect structure. An interfacial damage model is employed for simulating delamination. However, the fact that the considered interfaces are brittle triggers some reported numerical difficulties. This paper illustrates the potential of the interface damage mechanics approach for simulating metal peel off and it highlights the computational aspects to be developed to render a practically applicable approach.

Stretching-induced interconnect delamination in stretchable electronic circuits

Stretchable electronics offer increased design freedom of electronic products. Typically, small rigid semiconductor islands are interconnected with thin metal conductor lines on top of, or encapsulated in, a highly compliant substrate, such as a rubber material. A key requirement is large stretchability, i.e. the ability to withstand large deformations during usage without any loss of functionality. Stretching-induced delamination is one of the major failure modes that determines the amount of stretchability that can be achieved for a given interconnect design. During peel testing, performed to characterize the interface behaviour, the rubber is severely lifted at the delamination front while at the same time fibrillation of the rubber at the peel front is observed by ESEM analyses. The interface properties are established by combining the results of numerical simulations and peeling experiments at two distinct scales: the global force–displacement curves and local rubber lift geometries. The thus quantified parameters are used to predict the delamination behaviour of zigzag- and horseshoe-patterned interconnect structures. The accuracy of these finite element simulations is assessed by a comparison of the calculated evolution of the shape of the interconnect structures and the fibrillation areas during stretching with experimental results obtained by detailed in situ analyses.

Homogenisation of structured elastoviscoplastic solids at finite strains

Abstract Studying the relation between microstructural phenomena and the macroscopic behaviour will provide a way to design the microstructure of a material such that specific requirements on the resulting macroscopic mechanical behaviour can be fulfilled. One way to obtain a quantitative relation between the separate scales is to use homogenisation methods. A numerical homogenisation method has been developed to model the mechanical behaviour of heterogeneous elastoviscoplastic solids at finite strains. The thus obtained constitutive equation enables the modelling of complex macrostructures, while taking into account the influence of the microstructure. The method has been validated by comparing results of homogenised simulations with reference solutions. For this purpose, a specimen with a periodic microstructure and an irregular microstructure has been considered.The continuous matrix material is assumed to be polycarbonate, whereas the heterogeneities are taken to be rubber particles and voids.

Effective properties of a viscoplastic constitutive model obtained by homogenisation

Abstract Heterogeneous materials are used more and more frequent due to their enhanced mechanical properties. If the relation between the microscopic deformation and the macroscopic mechanical behaviour can be obtained, it can be used to design new materials with desired properties such as high strength, high stiffness or high toughness. A method for obtaining this relation is called homogenisation, by which the heterogeneous material is replaced by an equivalent homogeneous continuum. In this paper, a homogenisation method is proposed which offers the possibility to determine effective material properties for the homogeneous equivalent continuum, modelled by Perzynas viscoplastic constitutive law. To this end, finite element calculations are performed on a representative volume element, the geometry of which is defined by the microstructure of the considered material. The mechanical behaviour of this RVE will also be described by a viscoplastic model, clearly with a given parameter set. The proposed homogenisation strategy provides a way to acquire the constitutive parameters for the equivalent medium. To validate the results of the homogenisation, finite element calculations of the deformation behaviour of a perforated plate that is subjected to different loading histories are performed. The global mechanical behaviour of the homogenised simulations and direct calculations, where the heterogeneous structure is completely discretised, will be compared.

Characterization of semiconductor interfaces using a modified mixed mode bending apparatus

This research deals with the experimental assessment of the strength of bi-material interfaces as a function of mode mixity, focusing on two dimensional problems. A modified mixed mode bending apparatus is designed and tested, which can be used to measure small forces involved in the delamination of semiconductor packaging materials. Using this setup, it is possible to measure interface strength over nearly the full range of mode mixities using a single specimen design. A finite element model is used to determine interface strength and mode mixity. As an example, the combined numerical-experimental procedure is applied to the interface between copper lead frame (LF) and epoxy molding compound (MCE). A remarkable result is that a double cantilever beam (DCB) test of this interface does not yield the lowest possible interface strength, meaning that it can not be used as a worst case test.

Efficient damage sensitivity analysis of advanced Cu/low-k bond pad structures by means of the area release energy criterion

For integrated circuit (IC) wafer back-end development, state-of-the-art CMOS-technologies have to be developed and robust bond pad structures have to be designed in order to guarantee both functionality and reliability during waferfab processes, packaging, qualification tests, and, of course, usage. It is now well established that for future CMOS-technologies (CMOS065 and beyond), low-k dielectric materials will be integrated in the back-end structures. However, bad thermal and mechanical integrity as well as weak interfacial adhesion result in major thermo-mechanical reliability issues. Especially the forces resulting from packaging related processes such as dicing, wire bonding, bumping and molding are critical and can easily induce cracking, delamination and chipping of the IC back-end structure when no appropriate precautions are taken. This paper presents an efficient method to describe the damage sensitivity of three-dimensional multi-layered structures. The index that characterizes this failure sensitivity is an energy measure called the Area Release Energy, which predicts the amount of energy that is released upon crack initiation at an arbitrary position along an interface. The benefits of the method are: (1) the criterion can be used as damage sensitivity indicator for complex three-dimensional structures; (2) the criterion is energy-based, thus more accurate than stress-based criteria; (3) unlike recent fracture mechanics approaches, no initial defect size and location has to be assumed a priori. A mesh objectivity condition is formulated resulting from numerical experiments. The method is applied to advanced IC back-end structures, revealing not only the most critical back-end design but also the critical interfaces in the bond pad structures at which delamination might occur. In order to bridge the length scale difference between the wafer level and the back-end structures, a multi-scale method has been implemented in the finite element code MSC.Marc. In this way, effects of e.g., packaging and wire bond loading at the global level can be studied while taking into account the possibility of occurring failure phenomena at the local, back-end level. The validity and applicability of the method will be demonstrated by considering several Cu/low-k back-end structures. The obtained results are in good agreement with experimental observations.

Interfacial Adhesion Method for Semiconductor Applications Covering the Full Mode Mixity

Currently, prediction of interface strength is typically done using the critical energy release rate. Interface strength, however, is heavily dependent on mode mixity. Accurately predicting delamination therefore requires a material model that includes the mode dependency of interface strength. A novel test setup is designed which allows mixed mode delamination testing. The setup is a stabilized version of the mixed mode bending test previously described by Reeder and Crews (1990, 1991). It allows for the measurement of stable crack growth over the full range of mode mixities, using a single specimen design. The crack length, necessary for calculation of the energy release rate, is obtained from an analytical model. Crack length and displacement data are used in a finite element model containing a crack tip to calculate the mode mixity

FE calculations on a three stage metal forming process of Sandvik Nanoflex

Sandvik NanoflexTM combines good corrosion resistance with high strength. This steel has good deformability in austenitic conditions. It belongs to the group of metastable austenites, which means that during deformation a strain-induced transformation into martensite takes place. After deformation, transformation continues as a result of internal stresses. Both transformations are stress-state and temperature dependent. A constitutive model for this steel has been formulated, based on the macroscopic material behaviour measured by inductive measurements. Both the stress-assisted and the strain-induced transformation into martensite have been incorporated in this model. Path-dependent work hardening has also been taken into account. This article describes how the model is implemented in an internal Philips FE code called CRYSTAL, which is a dedicated robust and accurate finite element solver. The implementation is based on lookup tables in combination with feed-forward neural networks. The radial return method is used to determine the material state during and after plastic flow, however, it has been extended to cope with the stiff character of the partial differential equation that describes the transformation behaviour.

Mixed mode bending test for interfacial adhesion in semiconductor applications

Currently, prediction of interface strength is typically done using the critical energy release rate. Interface strength, however, is heavily dependent on mode mixity. Accurately predicting delamination therefore requires a material model that includes the mode dependency of interface strength. A novel test setup is designed which allows mixed mode delamination testing. The setup is a stabilized version of the mixed mode bending test previously described by Reeder and Crews (1990; 1991). It allows for the measurement of stable crack growth over the full range of mode mixities, using a single specimen design. The crack length, necessary for calculation of the energy release rate, is obtained from an analytical model. Crack length and displacement data are used in a finite element model containing a crack tip to calculate the mode mixity