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.

Mathematical modelling of the behaviour of granular material in a computational fluid dynamics framework using micro-mechanical models

In this paper, a Computational Fluid Dynamics framework is presented for the modelling of key processes which involve granular material (i.e. segregation, degradation, caking). Appropriate physical models and sophisticated algorithms have been developed for the correct representation of the different material components in a granular mixture. The various processes, which arise from the micromechanical properties of the different mixture species can be obtained and parametrised in a DEM / experimental framework, thus enabling the continuum theory to correctly account for the micromechanical properties of a granular system. The present study establishes the link between the micromechanics and continuum theory and demonstrates the model capabilities in simulations of processes which are of great importance to the process engineering industry and involve granular materials in complex geometries.

Macro-Micro Modelling Analysis for High Density Packaged Flip Chips

A wide range of flip chip technologies with solder or adhesives have become dominant solutions for high density packaging applications due to the excellent electrical performance, high I/O density and good thermal performance. This paper discusses the use of modeling technique to predict the reliability of high density packaged flip chips in the humid environment. Reliability assessment is discussed for flip chip package at ultra-fine pitch with anisotropic conductive film (ACF). The purpose of this modeling work is to understand the role that moisture plays in the failure of ACF flip chips. A macro-micro 3D finite element modeling technique was used in order to make the multi-length-scale modeling of the ACF flip chip possible. Modeling results are consistent with the findings in the experimental work

Macro-micro modelling of moisture induced stresses in an ACF flip chip assembly

Purpose – This paper discusses the use of modelling techniques to predict the reliability of an anisotropic conductive film (ACF) flip chip in a humid environment. The purpose of this modelling work is to understand the role that moisture plays in the failure of ACF flip chips. Design/methodology/approach – A 3D macro-micro finite element modelling technique was used to determine the moisture diffusion and moisture-induced stresses inside the ACF flip chip. Findings – The results show that the ACF layer in the flip chip can be expected to be fully saturated with moisture after 3?h at 121°C, 100%RH, 2?atm test conditions. The swelling effect of the adhesive due to this moisture absorption causes predominately tensile stress at the interface between the adhesive and the metallization, which could cause a decrease in the contact area, and therefore an increase in the contact resistance. Originality/value – This paper introduces a macro-micro modelling technique which enables more detailed 3D modelling analysis of an ACF flip chip than previously.

Predicting the behaviour of micro-electronic displays using computational mechanics

Micro-electronic displays are indispensible devices used in high performance applications such as aerospace, medical, marine and industrial sectors.These devices provide an interface to real time mission critical devices and therefore require good optical visual performance and high reliability, all this within varied and challenging environments.

Thermo-mechanical analysis of the packaging process for micro-electronic displays

Micro-electronic displays are sensitive devices and its performance is easily affected by external environmental factors. To enable the display to perform in extreme conditions, the device must be structurally strengthened, the effects of this packaging process was investigated. A thermo-mechanical finite element analysis was used to discover potential problems in the packaging process and to improve the overall design of the device. The main concern from the analysis predicted that displacement of the borosilicate glass and the Y stress of the adhesive are important. Using this information a design which reduced the variation of displacement and kept the stress to a minimum was suggested

Computer modeling of a micro-manufactured one-turn inductor

The results of a finite element computer modelling analysis of a micro-manufactured one-turn magnetic inductor using the software package ANSYS 10.0 are presented. The inductor is designed for a DC-DC converter used in microelectronic devices. It consists of a copper conductor with a rectangular cross-section plated with an insulation layer and a layer of magnetic core. The analysis has focused on the effects of the frequency and the air gaps on the on the inductance values and the Joule losses in the core and conductor. It has been found that an inductor with small multiple air gaps has lower losses than an inductor with a single larger gap

High electric current density-induced interfacial reactions in micro ball grid array (μBGA) solder joints

The effect of a high electric current density on the interfacial reactions of micro ball grid array solder joints was studied at room temperature and at 150 °C. Four types of phenomena were reported. Along with electromigration-induced interfacial intermetallic compound (IMC) formation, dissolution at the Cu under bump metallization (UBM)/bond pad was also noticed. With a detailed investigation, it was found that the narrow and thin metallization at the component side produced “Joule heating” due to its higher resistance, which in turn was responsible for the rapid dissolution of the Cu UBM/bond pad near to the Cu trace. During an “electromigration test” of a solder joint, the heat generation due to Joule heating and the heat dissipation from the package should be considered carefully. When the heat dissipation fails to compete with the Joule heating, the solder joint melts and molten solder accelerates the interfacial reactions in the solder joint. The presence of a liquid phase was demonstrated from microstructural evidence of solder joints after different current stressing (ranging from 0.3 to 2 A) as well as an in situ observation. Electromigration-induced liquid state diffusion of Cu was found to be responsible for the higher growth rate of the IMC on the anode side.

Multiphysics simulation of microwave curing in micro-electronics packaging applications

Purpose – This paper aims to present an open-ended microwave curing system for microelectronics components and a numerical analysis framework for virtual testing and prototyping of the system, enabling design of physical prototypes to be optimized, expediting the development process. Design/methodology/approach – An open-ended microwave oven system able to enhance the cure process for thermosetting polymer materials utilised in microelectronics applications is presented. The system is designed to be mounted on a precision placement machine enabling curing of individual components on a circuit board. The design of the system allows the heating pattern and heating rate to be carefully controlled optimising cure rate and cure quality. A multi-physics analysis approach has been adopted to form a numerical model capable of capturing the complex coupling that exists between physical processes. Electromagnetic analysis has been performed using a Yee finite-difference time-domain scheme, while an unstructured finite volume method has been utilized to perform thermophysical analysis. The two solvers are coupled using a sampling-based cross-mapping algorithm. Findings – The numerical results obtained demonstrate that the numerical model is able to obtain solutions for distribution of temperature, rate of cure, degree of cure and thermally induced stresses within an idealised polymer load heated by the proposed microwave system. Research limitations/implications – The work is limited by the absence of experimentally derived material property data and comparative experimental results. However, the model demonstrates that the proposed microwave system would seem to be a feasible method of expediting the cure rate of polymer materials. Originality/value – The findings of this paper will help to provide an understanding of the behaviour of thermosetting polymer materials during microwave cure processing.

Coupled FDTD-FVM simulation of microwave heating of polymer materials for micro-systems packaging applications

Heating in an idealised polymer load in a novel open-ended variable frequency microwave oven is numerically simulated using a couple solver approach. The frequency-agile microwave oven bonding system (FAMOBS)is developed to meet rapid polymer curing requirements in microelectronics and optoelectronics manufacturing. The heating of and idealised polymer load has been investigated through numerical modelling. Assessment of the system comprises of simulation of electromagnetic fields and of temperature distribution within the load. Initial simulation results are presented and contrasted with experimental analysis of field distribution

Multi-physics modelling for the fabrication, packaging and reliability of micro-systems components

The latest advances in multi-physics modelling both using high fidelity techniques and reduced order and behavioural models will be discussed. Particular focus will be given to the application and validation of these techniques for modelling the fabrication, packaging and subsequent reliability of micro-systems based components. The paper will discuss results from a number of research projects with particular emphasis on the techniques being developed in a major UK Goverment funded project - 3D-MINTEGRATION (www.3d-mintegration.com).

Uncertainty analysis to minimise risk in designing micro-electronics manufacturing processes

A design methodology based on numerical modelling, integrated with optimisation techniques and statistical methods, to aid the process control of micro and nano-electronics based manufacturing processes is presented in this paper. The design methodology is demonstrated for a micro-machining process called Focused Ion Beam (FIB). This process has been modelled to help understand how a pre-defined geometry of micro- and nano- structures can be achieved using this technology. The process performance is characterised on the basis of developed Reduced Order Models (ROM) and are generated using results from a mathematical model of the Focused Ion Beam and Design of Experiment (DoE) methods. Two ion beam sources, Argon and Gallium ions, have been used to compare and quantify the process variable uncertainties that can be observed during the milling process. The evaluations of the process performance takes into account the uncertainties and variations of the process variables and are used to identify their impact on the reliability and quality of the fabricated structure. An optimisation based design task is to identify the optimal process conditions, by varying the process variables, so that certain quality objectives and requirements are achieved and imposed constraints are satisfied. The software tools used and developed to demonstrate the design methodology are also presented.

Modelling and prototyping the conceptual design of 3D CMM micro-probe

This paper details the prototyping of a novel three axial micro probe based on utilisation of piezoelectric sensors and actuators for true three dimensional metrology and measurements at micro- and nanometre scale. Computational mechanics is used first to model and simulate the performance of the conceptual design of the micro-probe. Piezoelectric analysis is conducted to understand performance of three different materials - silicon, glassy carbon, and nickel - and the effect of load parameters (amplitude, frequency, phase angle) on the magnitude of vibrations. Simulations are also used to compare several design options for layout of the lead zirconium titanate (PZT) sensors and to identify the most feasible from fabrication point of view design. The material options for the realisation of the device have been also tested. Direct laser machining was selected as the primary means of production. It is found that a Yb MOPA based fiber laser was capable of providing the necessary precision on glassy carbon (GC), although machining trials on Si and Ni were less successful due to residual thermal effects.To provide the active and sensing elements on the flexures of the probe, PZT thick films are developed and deposited at low temperatures (Lt720 degC) allowing a high quality functional ceramic to be directly integrated with selected materials. Characterisation of the materials has shown that the film has a homogenous and small pore microstructure.

Optimisation methodology for risk mitigation in advanced micro-system electronics manufacturing

This paper presents a design methodology based on numerical modelling, integrated with optimisation techniques and statistical methods, to aid the development of new advanced technologies in the area of micro and nano systems. The design methodology is demonstrated for a micro-machining process called Focused Ion Beam (FIB). This process has been modelled to provide knowledge of how a pre-defined geometry can be achieved through this direct milling. The geometry characterisation is obtained using a Reduced Order Models (ROM), generated from the results of a mathematical model of the Focused Ion Beam, and Design of Experiment (DoE) methods. In this work, the focus is on the design flow methodology which includes an approach on how to include process parameter uncertainties into the process optimisation modelling framework. A discussion on the impact of the process parameters, and their variations, on the quality and performance of the fabricated structure is also presented. The design task is to identify the optimal process conditions, by altering the process parameters, so that certain reliability and confidence of the application is achieved and the imposed constraints are satisfied. The software tools used and developed to demonstrate the design methodology are also presented.