Optimization and finite element analysis for reliable electronic packaging

This paper demonstrates a modeling and design approach that couples computational mechanics techniques with numerical optimisation and statistical models for virtual prototyping and testing in different application areas concerning reliability of eletronic packages. The integrated software modules provide a design engineer in the electronic manufacturing sector with fast design and process solutions by optimizing key parameters and taking into account complexity of certain operational conditions. The integrated modeling framework is obtained by coupling the multi-phsyics finite element framework - PHYSICA - with the numerical optimisation tool - VisualDOC into a fully automated design tool for solutions of electronic packaging problems. Response Surface Modeling Methodolgy and Design of Experiments statistical tools plus numerical optimisaiton techniques are demonstrated as a part of the modeling framework. Two different problems are discussed and solved using the integrated numerical FEM-Optimisation tool. First, an example of thermal management of an electronic package on a board is illustrated. Location of the device is optimized to ensure reduced junction temperature and stress in the die subject to certain cooling air profile and other heat dissipating active components. In the second example thermo-mechanical simulations of solder creep deformations are presented to predict flip-chip reliability and subsequently used to optimise the life-time of solder interconnects under thermal cycling.

Effects of thermal cycling profiles on the performance of chip-on-flex assembly using anisotropic conductive films

Anisotropic conductive films (ACFs) are widely used in the electronic packaging industries because of their fine pitch potential and the assembly process is simpler compared to the soldering process. However, there are still unsolved issues in the volume productions using ACFs. The main reason is that the effects of many factors on the interconnects are not well understood. This work focuses on the performance of ACF-bonded chip-on-flex assemblies subjected to a range of thermal cycling test conditions. Both experimental and three-dimensional finite element computer modelling methods are used. It has been revealed that greater temperature ranges and longer dwell-times give rise to higher stresses in the ACF interconnects. Higher stresses are concentrated along the edges of the chip-ACF interfaces. In the experiments, the results show that higher temperature ranges and prolonged dwell times increase contact resistance values. Close examination of the microstructures along the bond-line through the scanning electron microscope (SEM) indicates that cyclic thermal loads disjoint the conductive particles from the bump of the chip and/or pad of the substrate and this is thought to be related to the increase of the contact resistance value and the failure of the ACF joints.

Review of methods to predict solder joint reliability under thermo-mechanical cycling

Solder joints are often the cause of failure in electronic devices, failing due to cyclic creep induced ductile fatigue. This paper will review the modelling methods available to predict the lifetime of SnPb and SnAgCu solder joints under thermo-mechanical cycling conditions such as power cycling, accelerated thermal cycling and isothermal testing, the methods do not apply to other damage mechanisms such as vibration or drop-testing. Analytical methods such as recommended by the IPC are covered, which are simple to use but limited in capability. Finite element modelling methods are reviewed, along with the necessary constitutive laws and fatigue laws for solder, these offer the most accurate predictions at the current time. Research on state-of-the-art damage mechanics methods is also presented, although these have not undergone enough experimental validation to be recommended at present

An extension of Purcell's vector method with applications to panel element equations

The classical Purcell's vector method, for the construction of solutions to dense systems of linear equations is extended to a flexible orthogonalisation procedure. Some properties are revealed of the orthogonalisation procedure in relation to the classical Gauss-Jordan elimination with or without pivoting. Additional properties that are not shared by the classical Gauss-Jordan elimination are exploited. Further properties related to distributed computing are discussed with applications to panel element equations in subsonic compressible aerodynamics. Using an orthogonalisation procedure within panel methods enables a functional decomposition of the sequential panel methods and leads to a two-level parallelism.

Comparison of finite element and finite volume methods application in geometrically nonlinear stress analysis

A novel three-dimensional finite volume (FV) procedure is described in detail for the analysis of geometrically nonlinear problems. The FV procedure is compared with the conventional finite element (FE) Galerkin approach. FV can be considered to be a particular case of the weighted residual method with a unit weighting function, where in the FE Galerkin method we use the shape function as weighting function. A Fortran code has been developed based on the finite volume cell vertex formulation. The formulation is tested on a number of geometrically nonlinear problems. In comparison with FE, the results reveal that FV can reach the FE results in a higher mesh density.

Dynamic load-balancing of finite element applications with the DRAMA library

The DRAMA library, developed within the European Commission funded (ESPRIT) project DRAMA, supports dynamic load-balancing for parallel (message-passing) mesh-based applications. The target applications are those with dynamic and solution-adaptive features. The focus within the DRAMA project was on finite element simulation codes for structural mechanics. An introduction to the DRAMA library will illustrate that the very general cost model and the interface designed specifically for application requirements provide simplified and effective access to a range of parallel partitioners. The main body of the paper will demonstrate the ability to provide dynamic load-balancing for parallel FEM problems that include: adaptive meshing, re-meshing, the need for multi-phase partitioning.

Dynamic multi-partitioning for parallel finite element applications

The central product of the DRAMA (Dynamic Re-Allocation of Meshes for parallel Finite Element Applications) project is a library comprising a variety of tools for dynamic re-partitioning of unstructured Finite Element (FE) applications. The input to the DRAMA library is the computational mesh, and corresponding costs, partitioned into sub-domains. The core library functions then perform a parallel computation of a mesh re-allocation that will re-balance the costs based on the DRAMA cost model. We discuss the basic features of this cost model, which allows a general approach to load identification, modelling and imbalance minimisation. Results from crash simulations are presented which show the necessity for multi-phase/multi-constraint partitioning components

On a flexible elimination algorithm with applications to panel element equations

A flexible elimination algorithm is presented and is applied to the solution of dense systems of linear equations. Properties of the algorithm are exploited in relation to panel element methods for potential flow and subsonic compressible flow. Further properties in relation to distributed computing are also discussed.

Evaluation of distortions in laser welded shipbuilding parts using local-global finite element approach

In recognition of the differences of scale between the welding pool and the heat affected zone along the welding line on one hand, and the overall size of the components being welded on the other, a local-global finite element approach was developed for the evaluation of distortions in laser welded shipbuilding parts. The approach involves the tandem use of a 'local' and a 'global' step. The local step involves a three-dimensional finite element model for the simulation of the laser welding process using the Sysweld finite element code, which takes into account thermal, metallurgical, and mechanical aspects. The simulation of the laser welding process was performed using a non-linear heat transfer analysis, based on a keyhole formation model, and a coupled transient thermomechanical analysis, which takes into account metallurgical transformations using the temperature dependent material properties and the continuous cooling transformation diagram. The size and shape of the keyhole used in the local finite element analysis was evaluated using a keyhole formation model and the Physica finite volume code. The global step involves the transfer of residual plastic strains and the stiffness of the weld obtained from the local model to the global analysis, which then provides the predicted distortions for the whole part. This newly developed methodology was applied to the evaluation of global distortions due to laser welding of stiffeners on a shipbuilding part. The approach has been proved reliable in comparison with experiments and of practical industrial use in terms of computing time and storage.

Optimisation modelling for flip-chip solder joint reliability

This paper details and demonstrates integrated optimisation-reliability modelling for predicting the performance of solder joints in electronic packaging. This integrated modelling approach is used to identify efficiently and quickly the most suitable design parameters for solder joint performance during thermal cycling and is demonstrated on flip-chip components using “no-flow” underfills. To implement “optimisation in reliability” approach, the finite element simulation tool – PHYSICA, is coupled with optimisation and statistical tools. This resulting framework is capable of performing design optimisation procedures in an entirely automated and systematic manner.

Finite element modelling of crack detection tests

Four non-destructive tests for determining the length of fatigue cracks within the solder joints of a 2512 surface mount resistor are investigated. The sensitivity of the tests is obtained using finite element analysis with some experimental validation. Three of the tests are mechanically based and one is thermally based. The mechanical tests all operate by applying different loads to the PCB and monitoring the strain response at the top of the resistor. The thermal test operates by applying a heat source underneath the PCB, and monitoring the temperature response at the top of the resistor. From the modelling work done, two of these tests have shown to be sensitive to cracks. Some experimental results are presented but further work is required to fully validate the simulation results.

Micro-mechanical parameterisations for continuum modelling of granular material using the discrete element method

The present work uses the discrete element method (DEM) to describe assemblies of particulate bulk materials. Working numerical descriptions of entire processes using this scheme are infeasible because of the very large number of elements (1012 or more in a moderately sized industrial silo). However it is possible to capture much of the essential bulk mechanics through selective DEM on important regions of an assembly, thereafter using the information in continuum numerical descriptions of particulate processes. The continuum numerical model uses population balances of the various components in bulk solid mixtures. It depends on constitutive relationships for the internal transfer, creation and/or destruction of components within the mixture. In this paper we show the means of generating such relationships for two important flow phenomena – segregation whereby particles differing in some important property (often size) separate into discrete phases, and degradation, whereby particles break into sub-elements, through impact on each other or shearing. We perform DEM simulations under a range of representative conditions, extracting the important parameters for the relevant transfer, creation and/or destruction of particles in certain classes within the assembly over time. Continuum predictions of segregation and degradation using this scheme are currently being successfully validated against bulk experimental data and are beginning to be used in schemes to improve the design and operation of bulk solids process plant.

Decision support systems for eco-friendly electronic products

This paper discusses an optimisation based decision support system and methodology for electronic packaging and product design and development which is capable of addressing in efficient manner specified environmental, reliability and cost requirements. A study which focuses on the design of a flip-chip package is presented. Different alternatives for the design of the flip-chip package are considered based on existing options for the applied underfill and volume of solder material used to form the interconnects. Variations in these design input parameters have simultaneous effect on package aspects such as cost, environmental impact and reliability. A decision system for the design of the flip-chip that uses numerical optimisation approach is used to identify the package optimal specification which satisfies the imposed requirements. The reliability aspect of interest is the fatigue of solder joints under thermal cycling. Transient nonlinear finite element analysis (FEA) is used to simulate the thermal fatigue damage in solder joints subject to thermal cycling. Simulation results are manipulated within design of experiments and response surface modelling framework to provide numerical model for reliability which can be used to quantify the package reliability. Assessment of the environmental impact of the package materials is performed by using so called Toxic Index (TI). In this paper we demonstrate the evaluation of the environmental impact only for underfill and lead-free solder materials. This evaluation is based on the amount of material per flip-chip package. Cost is the dominant factor in contemporary flip-chip packaging industry. In the optimisation based decision support system for the design of the flip-chip package, cost of materials which varies as a result of variations in the design parameters is considered.

A hybrid Laplace transform/finite difference boundary element method for diffusion problems

The solution process for diffusion problems usually involves the time development separately from the space solution. A finite difference algorithm in time requires a sequential time development in which all previous values must be determined prior to the current value. The Stehfest Laplace transform algorithm, however, allows time solutions without the knowledge of prior values. It is of interest to be able to develop a time-domain decomposition suitable for implementation in a parallel environment. One such possibility is to use the Laplace transform to develop coarse-grained solutions which act as the initial values for a set of fine-grained solutions. The independence of the Laplace transform solutions means that we do indeed have a time-domain decomposition process. Any suitable time solver can be used for the fine-grained solution. To illustrate the technique we shall use an Euler solver in time together with the dual reciprocity boundary element method for the space solution