A study of the Sn-Ag-Cu lead-free solder reflow profile has been conducted. The purpose of the work was to determine the Sn-Ag-Cu reflow profile that produced solder bumps with a thin intermetallic compound (IMC) layer and fine microstructure. Two types of reflow profiles were studied. The results of the experiment indicated that the most significant factor in achieving a joint with a thin IMC layer and fine microstructure was the peak temperature. The results suggest that the peak temperature for the Sn-Ag-Cu lead-free solder should be 230°C. The recommended time above liquidus is 40 s for the RSS reflow profile and 50-70 s for the RTS reflow profile.

The purpose of solderability assessment is to predict the effectiveness of soldering process. It is important for companies pursuing zero defects manufacturing because poor solderability is the major cause of two third of soldering failures. The most versatile solderability method is wetting balance method. However, there exist so many indices for wettability in the wetting balance test e.g. time to reach 2/3 values of maximum wetting force, tine to reach zero wetting force, maximum withdrawal force. In this study, three solderability assessment methods, which were the maximum withdrawal force, the wetting balance and the dynamic contact angle (DCA), were evaluated by comparing each other. The wetting balance technique measures the solderability by recording the forces exerted from the specimen after being dipped into the molten solder. Then the force at equilibrium state can be used to calculate a contact angle, which is known as static contact angles. The DCA measures contact angles occurred during advancing and withdrawing of the specimen and the contact angles are known as dynamic contact angles. The maximum withdrawal force uses the maximum force during withdrawal movement and then a contact angle can be calculated. In this study, the maximum withdrawal force method was found to be an objective index for measuring the solderability and the experiment results indicated good agreement between the maximum withdrawal force and the wetting balance method.

The paste printing process accounts for the majority of assembly defects, and most defects originate from poor understanding of the effect of printing process parameters on the printing performance. As the current product miniaturisation trend continues, area array type package solutions are now being designed into products. The assembly of these devices requires the printing of very small solder paste deposits.The printing of solder pastes through small stencil apertures typically results in stencil clogging and incomplete transfer of paste to the PCB pads. At the very narrow aperture sizes required for flip-chip applications, the paste rheology becomes crucial for consistent paste withdrawal. This is because, for smaller paste volumes, surface tension effects become dominant over viscous flow. Proper understanding of the effect of the key material, equipment and process parameters, and their interactions, is crucial for achieving high print yields. During the aperture filling and emptying sub-process, the solder paste experiences forces/stresses as it interacts with the stencil aperture walls and the pad surfaces, which directly impact the paste flow within the apertures. As the substrate and stencil separate, the frictional / adhesive force on the stencil walls competes directly with the adhesives/pull force on the PCB pads, often resulting in incomplete paste transfer or skipping/clogged apertures. In this paper, we investigate the effect of stencil design on the printing process and in particular the effect on paste transfer efficiency.

Soldering technologies continue to evolve to meet the demands of the continuous miniaturisation of electronic products, particularly in the area of solder paste formulations used in the reflow soldering of surface mount devices. Stencil printing continues to be a leading process used for the deposition of solder paste onto printed circuit boards (PCBs) in the volume production of electronic assemblies, despite problems in achieving a consistent print quality at an ultra-fine pitch. In order to eliminate these defects a good understanding of the processes involved in printing is important. Computational simulations may complement experimental print trials and paste characterisation studies, and provide an extra dimension to the understanding of the process. The characteristics and flow properties of solder pastes depend primarily on their chemical and physical composition and good material property data is essential for meaningful results to be obtained by computational simulation.This paper describes paste characterisation and computational simulation studies that have been undertaken through the collaboration of the School of Aeronautical, Mechanical and Manufacturing Engineering at Salford University and the Centre for Numerical Modelling and Process Analysis at the University of Greenwich. The rheological profile of two different paste formulations (lead and lead-free) for sub 100 micron fliip-chip devices are tested and applied to computational simulations of their flow behaviour during the printing process.

This paper presents results on the thixotropic behaviour of two suspensions; solder paste and isotropic conductive adhesives (ICAs). These materials are widely used as bonding medium in the electronics industry. Solder paste are metal alloys suspended in a flux medium while the ICAs consist of silver flakes dispersed in an epoxy resin. The thixotropy behaviour was investigated through two rheological test; (i) hysteresis loop test and (ii) steady shear rate test. In the hysteresis loop test, the shear rate were increased from 0.01 to 10s-1 and then decreased from 10 to 0.01s-1. Meanwhile, in the steady shear rate test, the materials were subjected to a constant shear rate of 0.1, 1 and 10s-1 for a period of 1800 seconds. The solder paste exhibited a higher degree of structural breakdown compared to the ICAs. Both the suspensions showed a high degree of shear thinning behaviour with time. Existing thixotropy model such as Weltman and Hahn were applied to understand the rate of structural change for solder paste and ICAs. The Weltman model (r≥0.95) showed a strong correlation with the experimental data compared to Hahn model (r≤0.95). The rate of structural breakdown increases with the value of B1, from Weltman model. The change in the microstructure of solder paste increases with the B1 but these trends were only observed for isotropic conductive adhesives at lower shear rates.

Solder paste printing has been achieved, over full area array patterns, to ultimately produce 30µm-sized deposits at 60µm pitch using Pb-free solder paste of type-7 particle size distribution (PSD). For a type-6 PSD solder paste, full area array printing was limited to 55µm-sized deposits at 110µm pitch. However, for peripheral printing patterns, 55µm-sized deposits at 90µm pitch were obtained using the type-6 solder paste. The disparities in the behaviour of the two paste types at different geometries can be attributed differences in the sub-processes of the stencil printing. Additionally, both paste types printed satisfactorily and consistently at 125µm pitch in full array patterns over an area of 100 mm2, thus presenting a low cost solution for flip chip Pb-free wafer bumping. The type-6 paste had a tendency to slump at deposit sizes above 60µm, this limited the minimum pitch achievable at full array. On the other hand, the paste release of the type-6 paste from the stencil apertures at these geometries was superior compared to the type-7 paste; this may be attributed to the finer particle paste producing an increased drag force along the stencil aperture walls. Conversely, the type-7 paste was able to fill the smallest aperture openings, ultimately to 30µm, thus producing full array printing patterns at uniquely small pitches. This advancement in the stencil printing process has been made possible by refinements to both solder paste design and stencil manufacturing technology. Adjustments in the solder paste rheology (shear thinning, tackiness and visco-plastic properties), mainly by varying the metal content and flux type, have enabled successful printing at ultra fine pitch geometries. This intern is correlated with printing parameters such as printing speed, pressure, print gap and separation speed to allow for a practical process window. Moreover, advancements in stencil fabrication methods have produced ‘state-of-the-art’ stencils exhibiting very high defined shaped apertures with smooth walls at very fine pitch, thus allowing for improved solder paste release at very small dimensions. The emphasis on this study was to investigate sub process behaviour in the stencil printing of type-6 and type-7 PSD Pb-free solder pastes and to assess the ultimate achievable pitch and web. Differences in the sub process behaviour between the two PSD pastes are also reported. The conclusions satisfy the criterion that interconnects can be produced at ultra small geometries using Pb-free solder paste. Furthermore, the results indicate that type-6 and type-7 solder pastes should be employed separately to specific application geometries.

The stencil printing and reflow performance of two specifically designed fine particle Pbfree solder pastes have been examined. The two solder pastes incorporated the SnAgCu alloy powder of type-6 (IPC) particle size distribution (PSD), however, each paste contained a different specifically designed flux vehicle system. The first Pb-free solder paste (p1) contained a flux type specifically designed for fine pitch stencil printing applications, whilst the second fine particle Pb-free solder paste (p2) contained a flux type designed to allow for optimum reflow soldering performance in the increased temperature profile required for Pb-free. As expected each paste type displayed an improved performance over the other paste type for specific processes. In the reflow soldering process, an inert atmosphere was shown to be a prerequisite, however, p2 displayed optimum reflow behaviour for an oxygen content of around 2000ppm, whilst p1 required an atmosphere with an oxygen content less than 500ppm to obtain acceptable reflow soldering. Conversely, in the stencil printing process, p1 was able to produce consistent solder paste deposits in printing patterns at sub 100µm pitch, whilst the printing performance of p2 at these geometries deteriorated rapidly over a period of 10 minutes. The skipping and inconsistent deposit sizes produced by p2 can be attributed to the blocking of stencil apertures caused by solder paste drying. Rheological measurements performed on each paste type as functions of abandon time have showed that the drying of rheological modifiers in the flux vehicle system increases the viscosity and solid-like properties of the paste. The aim of this study was to show that rheological measurements correlated with results from stencil printing trials can aid the development of solder pastes for specific applications. For paste types designed for enhanced reflow, typically for higher peak temperatures and longer ramp zones, the solid content or activator content in the flux is usually increased. Therefore, rheological modifiers are thus added to compensate for the increased solid content so that stencil printing can be maintained. However, the rheology modifier may cause a detrimental effect to the paste over time, hence, rheological measurements made on different paste types over time can predict if the paste will be ideally suitable for the stencil printing process. The study directly contributed to the aims of a multi-collaborative research project ‘Lead-free soldering for flip chip assembly applications’, supported by the UK’s Engineering & Physical Sciences Research Council (EPSRC) and four industrial project partners: HLA Multicore Solders UK; Celestica Ltd. UK; MBDA UK and Tin Technology UK.

An application of statistic techniques for structure evaluation of packing of equal or distributed spherical particles is presented. The packing of particles generated by computer simulation is cut by a series of equally separated parallel planes, and the area densities of the cross-sections of particles on the cutting planes are used to analyse the packing structure. It is shown that as the number of the cutting planes increases, the mean of the area densities approaches the packing density. Then a time series analysis technique is applied to examine the randomness of the packing. The homogeneity of the packing is evaluated by testing the hypothesis that the particles are uniformly distributed within the packing space. The isotropy of the packing is evaluated both at micro-level, the distribution of projections of centre-to-centre lines between touching particles, and at macro-level, the variances of area densities on the cutting planes perpendicular to different directions. As case studies, the above techniques are applied to evaluate the packing structures of both equal and distributed particles obtained by a collective rearrangement simulation model.

The solder paste printing process is an important process in the assembly of surface mount devices using the reflow soldering technique. There is wide agreement in industry that the paste printing process accounts for the majority of assembly defects, and most defects originate from poor understanding of the effect of printing process parameters on printing performance and the nature of their interactions. The key solder paste printing process parameters considered in this study is the squeegee pressure, squeegee speed, stencil-substrate separation speed and squeegee print direction. Our previous work shows that theses process parameters impact the printing process performance. As the current product miniaturisation trend continue for hand-held consumer products, area array type package solutions [such as chip scale packages and flip chip] are now being designed into products. The assembly of these devices requires the printing of very small solder paste deposits consistently from pad to pad, and from board to board. This paper concerns the determination of the solder paste printing process window for flip chip assembly applications. Five different solder paste formulations [specially formulated for flip-chip assembly] was evaluated as part of a broader study on low cost solder bumped flip-chip assembly. The results have also been used for establishing guidelines for printing solder pastes for both solder bumping and the flip-chip assembly process. The experimental design for the study was based on the Taguchi method. A 2-level and 4 factors orthogonal array was used for investigating the main effects.

Although the primary driver for the current interest in developing lead-free soldering is global market pressure for more environmentally friendly products, the main concern continues to be lead contamination from end-of-life electronic products in landfill sites. In response to existing and impending legislation in Europe and Japan for the elimination of lead from electronic products, the industry has embarked on a number of studies in search of suitable lead-free alternatives. Several reports [1,2] have been published, but there are as yet no drop-in solutions with respect to reflow temperature, joint reliability and assembly costs. Our survey show that the Sn-Ag-Cu alloy is one of the promising lead-free alloys currently being evaluated by industry. There are however a number of issues regarding the use of Sn-Ag-Cu alloys, including the solderability and long-term reliability of the solder joints, which require further study. The lower solderability of Sn-Ag-Cu solder can alter the interface and microstructure of the solder joint formed because of the differing reaction rates between the molten solder and substrate surface. This also has an impact on the nature and extent of the intermetallic compounds formed at the interface, as the intermetallic is generally more brittle than the base metal. This can negatively impact the solder joint reliability. In this paper we report a study on the effect of solder volume on intermetallic layer formation and thickness. For lead-free soldering this could prove to be very important, as a wide range of devices and components of varying joint size,e.g. plastic quad flat pack (PQFP), ball grid array (BGA), chip-scale packaging (CSP), and flip chip, may need to be assembled on a typical board. This means that the nature and thickness of the intermetallic layer formed for each joint size will be different. In the study, solder joints of different sizes representing different devices were used for evaluating the effect of solder volume on intermetallic compound formation.The layer thickness and microstructure were analyzed using scanning electron microscopy (SEM). SEM analysis was also carried out on joint micro-sections, which has undergone temperature cycling to evaluate the effect of intermetallic layer the joint reliability. Our results show that increasing the solder volume (and solder joint size) does not significantly affect the growth of the intermetallic layer thickness. Therefore the intermetallic layer thickness provides the lower limit for solder joint design for ultra-fine pitch flip-chip applications.

High-density packaging devices have unique characteristics which make their assembly, test and repair very difficult. The only realistic method of rework is to replace the defective component with a new or re-balled component. Although a wide range of rework techniques is available, degradation in assembly reliability may accompany the process. The formation of brittle secondary intermetallic compounds following CSP rework can adversely affect the mechanical properties of the joint, particularly when they make up a significant proportion of its thickness. Reports on the effects of different CSP rework techniques on intermetallic layer formation. Two PCB pad-cleaning methods and three flux/paste deposition methods are investigated. The reworked joints are analysed using optical microscopy to determine the extent of intermetallic growth. Their quality is also assessed using shear strength testing prior to, and after, thermal ageing at 1008C to accelerate the growth of intermetallic compounds and evolution of the solder grain structure.

The need to implement high volume production for a Pb-free flip-chip assembly (unpackaged silicon die, with inputs/outputs I/O’s at sub 100µm pitch) has raised interest within the electronics manufacturing industry to find reliable inexpensive manufacturing methods. One method currently being researched is wafer bumping using Pb-free solder paste stencil printing. The introduction of Pb-free materials is being driven by a European directive, Waste from Electronic and Electrical Equipment (WEEE) [1], which necessitates the elimination of lead containing materials from electronics products by January 2008. This has put tremendous pressure on the electronics industry to find a suitable replacement for the widely used tin/lead based solder paste. One material already highlighted is the tin/silver/copper alloy. However, in order to successfully implement the new material into current manufacturing processes, an in-depth understanding of the materials properties is required; as little information is presently known. In this paper we evaluate the rheological properties of certain tin/silver/copper solder pastes currently being developed for low cost flip-chip wafer bumping. Rheological measurements provide useful data for understanding flow behaviour of solder pastes in the stencil printing process. Factors affecting the rheology of solder pastes are alloy type, particle size distribution (PSD), metal content and flux vehicle system. Removal of lead from the solder paste and developments in the flux to accommodate Pb-free materials will inherently affect the flow properties of the solder paste. Therefore, it is essential to the stencil printing process that these new lead-free materials are characterised in a rheological nature. This study, therefore, aims to understand the rheological behaviour of certain lead-free solder pastes for flip-chip assembly applications and to subsequently assist in new formulations replacing lead solders.

At the same solid volume fraction (K) the relative viscosity (-r) of a concentrated noncolloidal bidisperse suspension of hard spherical particles is lower than that of a monodisperse suspension. In this paper a semi-analytical viscosity model of noncolloidal bidisperse suspensions is derived using an integration method. In this model the random loose packing density obtained by computer simulation is taken as the limit of solid volume fraction Km which depends upon both the diameter ratio (5) of large to small particles and the volume fraction of large particles (�=Kl/K). This model shows that at high solid volume fraction, K > 0.40, both 5 and ; significantly influence -r. For example, at K=0.5, it predicts that for monodisperse suspensions -r=70, while for bidisperse suspensions (5=2 and �=0.7) -r=40. Comparison shows that, at high solid volume fraction (0.4-0.5), the relative viscosity predicted by this model is in good agreement with that predicted by the work of Shapiro and Probstein (1992) and of Patlazhan (1993), but is higher than that predicted by the work of others.

Solder paste is one of the most important process materials today in surface mount technology. Stencil printing of solder paste onto PCBs constitutes an important stage in the reflow soldering of surface mount devices. A high proportion of the solder-related defects can be attributed to the stencil printing process. This is likely to continue with the trend toward miniaturization and the implementation of die-size packages. To achieve repeatable solder deposits from board-to-board and pad-to-pad requires an understanding of the paste rheology. One of the key factors that influences solder paste rheology is temperature. A change in temperature will cause the viscosity of the solder paste to change. This change could be ambient or from the stencil printing process itself. This is likely to impact on the performance of the solder paste. In this paper, we present the effect of temperature on the rheological properties of solder paste and the flux vehicle system. Current models show a single variable dependence of viscosity with temperature. The model presented here incorporates shear rates and can be used for any solder paste or non-Newtonian material. The effects of temperature on solder paste flux medium, particle size and distribution, and metal alloy content are also presented.

This article presents the results of an EPSRC-funded project (Microsystems Assembly Technology for the 21st Century, MAT21) carried out by two British Universities (Greenwich and Heriot Watt) and a host of industrial partners (Celestica, DEK, Cookson-SPM, Merlin, Hewlett Packard and Micro-Emissive-Displays) covering the full electronic packaging supply chain. This multi-disciplinary project seeks to produce a low cost, high volume, low temperature (T<100oC) environmentally friendly assembly technology using micro-engineered interconnections at sub-100µm pitch. The continuous strive towards smaller, lighter, and smarter products have driven the need for advanced packaging techniques such as flip-chip assembly [1]. The advantages of flip-chip bonding in mainstream microelectronics are well documented[1,2]; of particular interest for MicroSystems Technology (MST) Packaging is the requirement of a low temperature bonding process. In the MAT21 project, interconnections are achieved by electroforming copper columns that are bonded onto advanced organic substrates [3]. Isotropic Conductive Adhesives (ICAs) are to be bonded onto advanced organic substrates [4] using stencil printing. The primary aim of the project was therefore to develop a process to produce successful and consistent quality deposits using screen printing at sub-100µm pitch. To achieve this, stencils were developed and fabricated at the MicroSystems Engineering Centre (MISEC), Heriot-Watt University, using advanced microengineering techniques. Computational simulations of the printing process (from a fluid mechanics and rheological points of view) and behaviour of the stencils were carried out by the Department of Computing and Mathematical Sciences, University of Greenwich in conjunction with the rheological experiments and characterization studies of the various materials implemented at the School of Engineering, University of Greenwich. Moreover current and developed models were used to predict the reliability of such microsystem assembly processes with the underfill characteristics and to identify process weaknesses. All phases of the project are presented.

Purpose: To investigate how jamming of particles in a solder paste varies as a function of the gap through which the particles flow, and to correlate this with skipping defects during the printing process. Design/methodology/approach: Solder pastes with particle sizes of types 2, 3, 4 and 5 were sheared between the parallel plates of a rheometer. Jamming events that cause the solder particles to be forced against each other were detected by monitoring the electrical current flowing between the plates under a bias of 1.0 V or less. Solder paste printing trials were conducted with the same pastes, and solder paste skipping monitored. Findings: Jamming was detected when the ratio of plate gap to largest particle diameter is reduced to a value between 3.8 and 5.0. Decreasing the gap further results in increased jamming. A strong correlation between levels of skipping and jamming was found. Research limitations/implications: More extensive printing trials are required before rheometric jamming detection can be used to predict printing performance. Practical implications: The common rule of thumb used in solder paste printing that the aperture width should be no smaller than 4-5 particle diameters is justified. Originality/value: This paper presents a new technique for detecting jamming events which are too brief to be detected using normal rheometric techniques, but which have long been thought to be responsible for stochastic skipping defects during printing. Evidence supporting the link between jamming and this type of defect is presented.

The high-intensity, high-resolution x-ray source at the European Synchrotron Radiation Facility (ESRF) has been used in x-ray diffraction (XRD) experiments to detect intermetallic compounds (IMCs) in lead-free solder bumps. The IMCs found in 95.5Sn3.8Ag0.7Cu solder bumps on Cu pads with electroplated-nickel immersion-gold (ENIG) surface finish are consistent with results based on traditional destructive methods. Moreover, after positive identification of the IMCs from the diffraction data, spatial distribution plots over the entire bump were obtained. These spatial distributions for selected intermetallic phases display the layer thickness and confirm the locations of the IMCs. For isothermally aged solder samples, results have shown that much thicker layers of IMCs have grown from the pad interface into the bulk of the solder. Additionally, the XRD technique has also been used in a temperature-resolved mode to observe the formation of IMCs, in situ, during the solidification of the solder joint. The results demonstrate that the XRD technique is very attractive as it allows for nondestructive investigations to be performed on expensive state-of-the-art electronic components, thereby allowing new, lead-free materials to be fully characterized.

In this paper, we apply a Monte Carlo simulation technique to study the microstructure of solder pastes and investigate the influence of solder particle-size distribution on the ultra-fine-pitch stencil printing. First, the microstructures of bulk solder pastes with different particle-size distributions were generated using a random-packing model. Then a statistic model was applied to simulate the packing of solder paste inside the apertures. The numbers of solder particles and solid volume fraction embodied in the apertures were counted. Five particle-size distributions and two aperture shapes (circular and square) were investigated. Simulation results showed that the mean solid volume fraction of the solder particles inside the apertures is lower than that in the bulk solder paste. For the same aperture size and shape, as the particle size increases, the mean solid volume fraction decreases and the standard deciation increases. This implies that to obtain consistent paste deposits in ultra-fine-pitch printing, the particle size must be proportionally reduced with the aperture size. The reasonable size ration of the aperture to the solder particle was found to be around five. Excessive reduction in particle size could not improve the printing quality further, in contrast, it may lead to poor printability due to the increase in the paste viscosity and poor solder joints due to the generation of solder balls in the reflow soldering process.

Random packings of spherical particles have been studied for many years because they serve as useful models for a variety of applications in material industries. A good example is the compaction of ceramic or metallic powders to make green compacts. The mechanical properties of green compacts are signiÆcantly affected by the compaction methods, such as uniaxial or isostatic compaction. In uniaxial compaction, pressure is applied from one direction on the powder aggregate. While in isostatic compaction, the pressure is applied uniformly from all directions on the powder aggregate, and consequently the particles are forced to move toward the center of the aggregate [1, 2]. The main advantage of the isostatic method is that it is possible to form complex shapes with high density and large volumes. Green compacts are characterized by the packing density and the contact number [3]. In recent years, a computer-simulation method has been applied for the study of powder compaction [3, 4].

In the assembly of Printed Circuit Boards (PCBs) using Surface Mount Technology (SMT), solder paste is deposited on the bond pads of the PCBs using stencil/screen printing technique. The last few years have seen the development and introduction of new printing mechanism to meet the miniaturisation challenge of electronic products. The most notable is the development of new printing heads such as the ProFlow [1, 2] and the Rheometric Pumping Head [3]. Unlike the traditional squeegee blade, in these new printing devices the solder paste is contained in a sealed pressurised chamber, and is released during the printing stroke via an opening as the printing head passes over the stencil apertures. The flow profile of the solder paste inside such a chamber plays a key role in determining the volume of solder paste deposited onto the PCB pads. In this paper we investigate the paste flow inside such a chamber and its influence on the aperture filling. Our results show that the paste does not vertically fill the apertures, but has a horizontal velocity component in the printing direction. This horizontal velocity component will lead to insufficient filling of paste at the rear corner of the aperture. To counteract the influence of this undesirable velocity component, we propose to introduce a horizontal shaft perpendicular to the printing direction inside the chamber. During a printing stroke this shaft rotates inside the chamber in the printing direction and drives the paste near the bottom slot to flow against the printing direction. We present an analysis of the paste flow inside such a device and the nature of the aperture filling process. The main parameters that influence the paste flow are the diameter, the rotational speed and the position of the shaft. The key to obtaining sufficient and consistent paste deposits is to minimise the horizontal velocity component of the paste to ensure the paste fills into the aperture vertically, and to maximise the vertical velocity component of the paste to shorten the aperture filling time. The introduction of such a shaft is also expected to significantly reduce the pressure loading on the paste at the top of the chamber.

In this paper we study the short-range correlated percolation and the cluster structure of two-dimensional (2D) random packing of binary disks with size ratio λ in the range of λ. A Monte Carlo simulation model is used to generate the configuration of random packing first. Then a from-neighbor-to-neighbor propagation method is used to identify the number and sizes of the clusters. Results show that for λ=1 the percolation threshold pc lies between the square and triangular site percolation thresholds. As λ increases the percolation threshold pc (the area fraction of small disks) decreases. To characterize the cluster structure at the percolation threshold, we scale the cluster size sc with the cluster radius R as scâ^RD. The fractal dimension D obtained lies between 1.86 and 1.88 and is independent of the size ratio λ. This value is in good agreement with the 2D theoretical fractal dimension which is equal to 91/48.

The wall slip phenomena is known to have a significant effect on the measurement of the viscosity of dense suspensions. In the measurement of the viscosity of solder pastes the effect of wall slip is such that the measured viscosity (also called the apparent viscosity) is much lower than the true viscosity of the paste. Therefore, correction needs to be applied to the measured viscosity in order to obtain the true viscosity of the solder paste. In this paper, we present work on the modeling of the influence of wall slip on viscosity measurement, and a model for predicting the true viscosity based on measurements using parallel plate viscometer. The apparent viscosity values measured at two different plate gaps, but at the same applied shear rate (also called the apparent shear rate), is used for predicting the true viscosity, the wall slip velocity and the thickness of the boundary slip layer. The model was validated using results from solder paste samples measured at three different plate gaps (H=0.5 mm, 1.0 mm and 1.5 mm). Our results show that the predicted values of the true viscosity using the data measured at any two gaps are in reasonably good agreement. The results also show that the influence of the wall slip is significant and that the ratio of the predicted viscosity to the apparent viscosity decreases with increasing apparent shear rate.

A monte Carlo technique is applied to simulate the structure of concentrated suspensions of hard spherical particles that obey lognormal distribution. With this technique, the random loose packing, with packing density m is obtained first, and then the particles in the packing are randomly separated to achieve a specified solid-volume fraction . The simulated structure is evaluated both in the microscale, the neighboring number distribution, and the distribution of gaps between neighboring particles; and in the macroscale, the distribution of the solid-area fractions on a series of parallel cross sections. Results show that, at the same solid-volume fraction, the increase in the standard deviation of particle diameters leads to the decrease in the mean neighboring number and leads to the increase in the mean gap. The mean relative gap obtained from the simulation is larger than that from theoretical prediction, =[(m/)1/3-1]. With particles of lognormal distribution, both the gap sizes and the neighboring numbers distributed over broader ranges than that with equal particles. Results also show that, with equal particles and particles of lognormal distribution, there is no significant differenence between the distributions of the solid-area fractions on the cross sections. The structures obtained in this study are shown to be completely random, homogeneous, and isotropic by statistical tests.

A Monte Carlo simulation model for the random packing of unequal spherical particles is presented in this paper. With this model, the particle radii obeying a given distribution are generated and randomly placed within a cubic packing domain with high packing density and many overlaps. Then a relaxation iteration is applied to reduce or eliminate the overlaps, while the packing space is gradually expanded. The simulation is completed once the mean overlap value falls below a preset value. To simulate the random close packing, a vibration process is applied after the relaxation iteration. For log-normal distributed particles, the effect of particle size standard deviation, and for bidisperse particles, the effects of particle size ratio and the volume fraction of large particles on packing density and on coordination number are investigated. Simulation results show good agreement with that obtained by experiments and by other simulations. The randomness, homogeneity, and isotropy, which have not been evaluated before for packing of distributed particles, are also examined using statistical measures.

Stencil printing of solder paste with sinusoidally vibrated squeegee is a new technique developed in recent years used for the assembly of printed circuit boards (PCB's) in surface mount technology (SMT). Understanding of the behavior of solder paste under the action of vibrating squeegee is needed to optimize the process parameters. Two vibration experiments on solder paste were conducted. In the first experiment, a prototype of vibrating squeegee system was used to simulate the printing process and in the second experiment paste samples were packed in a cylindrical container which was horizontally vibrated. Experimental results validate the prior theoretical predictions. Suitable ranges of vibration parameters were found.

In this paper, the viscoelastic characteristics of solder paste under high frequency (50 Hz-90 Hz) oscillatory shear were investigated by oscillatory shear measurements. Measurement results show that the dynamic viscosity of solder paste decreases as the oscillatory frequency increases, which means the oscillation can help to enhance solder paste fluidity. This proves that in a stencil printing process, the application of a vibrating squeegee can help the paste to fill the apertures. Within the oscillatory frequency range, results show that the solder paste loss modulus is much higher than its storage modulus. With shear stress of 500 Pa, the phase shift (ζ) is around 700, and with shear stress of 1000 Pa it is around 750, so the behaviour of solder paste under oscillatory shear is more like a viscous liquid than a solid. The storage modulus with low shear stress, corresponding to small shear strain, is higher than that with high shear stress, corresponding to large shear strain. This means that the solder paste storage modulus is not only dependent on frequency but is also dependent on shear strain. High oscillatory shear strain can reduce the solder paste deformation recoverability. It suggests that when passing over the apertures, the vibrating squeegee can help to obtain uniform and high solder particle packing density inside the apertures.

Solder paste is a dense suspension (volume fraction of about 50%) of spherical solder alloy particles in a flux/vehicle system. It is known to exhibit viscoelastic properties and under oscillatory shear, the dynamic viscosity has been shown to decrease as the shear frequency increases. This paper presents experimental results of the effect of sinusoidal vibration on solder paste, and its impact on the performance of the paste printing process. In the first experiment, the solder paste sample was horizontally vibrated inside a cylindrical container. Observations of the sample following vibration showed that a thin liquid rich layer was formed on the surface and at the interface between the container and the paste. In the second experiment the sample was placed on a flat plate and as the plate moved towards a vibration squeegee, the sample was pushed by the squeegee blade to produce a paste roll. In both experiments, the vibration frequency and amplitude were varied to observe their effect.