The solder on rubber (SOR) interconnection design and its reliability assessment based on shear strength test and finite element analysis

A novel chip-on-metal structure of the advanced wafer level chip scale package (WLCSP) which has the capability of redistributing the electrical circuit is proposed in this study. In the WLCSP, the solder on rubber (SOR) design expands the chip area and also provides a buffer layer for the deformation energy from the coefficient of thermal expansion (CTE) mismatch. By using the solder ball shear test, the stress/strain-released behavior in the SOR structure is investigated in this research. On the other hand, a three-dimensional nonlinear finite element (FE) model for the ball shear test is established to assist the design of the package. The force-displacement curves from the FE analysis are compared with the experimental results to demonstrate the accuracy of the simulation. Likewise, the issue from element mesh density is also discussed herein. The investigation reveals that the SOR structure could highly decrease the damage in solder bumps from the ball shear test. Furthermore, the transferred stress/strain in the interconnect near the contact pad could be diminished through a suitable layout of redistribution lines.     

基于正交试验的板级电路模块热分析

利用ANSYS的APDL参数化编程语言,建立了灌封电路模块的有限元模型。选取挠性印制电路板(FPCB)厚度、上、下灌封体厚度、空气对流系数和环境温度等7个参数作为关键因素,安排正交试验。结果表明:上、下灌封体厚度等因素都对灌封电路模块工作温度有显著影响,其中空气对流系数的影响最为显著。初始设计的灌封电路模块工作温度为460.94K,通过增加灌封体的厚度,选择高热导率的灌封材料,保证良好的通风散热,控制环境温度,可以将模块的工作温度降到329.11K。     

Reliability evaluations for board-level chip-scale packages under coupled power and thermal cycling test conditions

To evaluate conjointly the effects of ambient temperature fluctuation and operation bias on the reliability of board-level electronic packages, a coupled power and thermal cycling test has been proposed. In this study, the sequential thermal–mechanical coupling analysis, which solves in turn the transient temperature field and subsequent thermomechanical deformations, is performed to investigate thermal characteristics along with fatigue reliability of board-level thin-profile fine-pitch ball grid array chip-scale packages under coupled power and thermal cycling test conditions. Effects of different power cycling durations are studied. A pure thermal cycling condition is also examined and compared. Numerical results indicate that, for the coupled power and thermal cycling test, a shorter power cycling duration in general leads to a shorter fatigue life. However, the temperature compensation effect elongates the fatigue life under certain power cycling durations.     

Improvements of solder ball shear strength of a wafer-level CSP using a novel Cu stud technology

The solder ball shear test has been widely adopted in the electronics industry to estimate the strength of solder ball attachment of advanced electronic packages. A solder ball with low shear strength is usually considered as a weak solder joint in package reliability testing. Consequently, demands for increasing the solder ball shear strength have risen in recent years. This work attempts to enhance the solder ball shear strength of the wafer level chip scale package (WLCSP) by forming a Cu stud on the surface of the solder pad. The novel Cu stud design technology has been achieved by using a simple semiconductor manufacturing process. To investigate the impact of Cu stud, a three-dimensional (3-D) nonlinear finite element method is used for Cu stud design. Furthermore, the shear force-displacement curves, obtained by computational analysis, are compared with the experimental results to demonstrate the accuracy of the finite element models. This investigation also explores the effects of various parameters including the Cu stud's dimension, shape, and material properties on solder ball shear strength. The analytical results establish that a suitable size of Cu stud in a solder ball can effectively enhance the ball's shear strength.     

Residual stress evaluation in resin-molded IC chips using finite element analysis and piezoresistive gauges

The high residual stress in a resin-molded electronic package sometimes makes the electronic functions unstable. Therefore the residual stress in electronic packages, especially on the top surfaces of semiconductor chips, should be evaluated. The objective of this study is to present a simple method for evaluating residual stress in resin-molded semiconductor chips using a combination of experimental and numerical methods. The actual residual stress of the packaging process was measured by using test chips that included piezoresistive gauges. A linear thermoelastic finite element analysis was then carried out using a three-dimensional model. The finite element analysis was performed under a stress-free temperature determined by the temperature dependence of the residual stress, which was experimentally measured by using the piezoresistive test chips. The measured residual stress using the test chips agreed well with the results of the finite element analysis. It was therefore confirmed that the present evaluation method, combining experimental and numerical methods, is reliable and reasonable.     

Optimal design for micro-thermoelectric generators using finite element analysis

To fabricate micro-thermoelectric generators (μTEGs), one must design the optimal structure of the μTEGs and achieve thermoelectric thin films with excellent properties. This study investigated the role of the dimensions of μTEGs, including the length of the thermoelements, thickness of the substrates, and cross-sectional area of the thermoelements. To evaluate the power generated by μTEGs and their efficiency, three-dimensional models of μTEGs were subjected to finite element analysis. Three-dimensional models are more accurate than one-dimensional models, since the directions of the heat flux and electrical current are not parallel in μTEGs. The governing equations were derived from the Seebeck effect and Peltier effect, which show thermoelectric energy conversion. In the simulation, the substrate, n-type material, and p-type material were assumed to be silicon, Bi₂Te₃, and Sb₂Te₃, respectively. We calculated the thermoelectric power generated by the μTEGs and their thermoelectric energy conversion efficiency. These two evaluation indices represent the performance of μTEGs. The thermoelectric simulation produced design guidelines for high-performance μTEGs.     

Vibration reliability test and finite element analysis for flip chip solder joints

Vibration fatigue test and analysis methodology for flip chip solder joint fatigue life assessment have been developed by performing vibration tests with constant G-level and varying G-level input excitation. The linear cumulative damage analysis method (Miner’s rule) predicts non-conservative result for vibration fatigue life of flip chip solder joint. Finite element analysis (FEA) using a global-local-beam modeling method was used to calculate the natural frequency and were compared to experimental data. A quasi-static finite element analysis method was developed to investigate solder joint stress strain behavior for solder joint vibration fatigue life prediction. Harmonic finite element analysis was also carried out to predict solder joint fatigue life. Results from quasi-static analysis and harmonic analysis were compared. Based on Miner’s rule and stress amplitude results from FEA results, different assumed cumulative damage index (CDI) factors were investigated in fatigue life prediction.     

Finite element simulation of a nondestructive shear test for TABbonds

The viability of using a nondestructive micro-shear test to resolve interfacial features in integrated circuits incorporating TAB (tape automated bonding) technology has been confirmed using finite element method (FEM) simulations. Both two- and three-dimensional finite element models were built to determine whether the size and location of interfacial features such as dead zones (nonbonded regions), delaminations and inclusions could be identified by applying one or more forces to the surfaces of a bond and monitoring the resulting deflections. By monitoring the localized Von Mises stress in the model, it was shown that the applied surface forces did not cause irreversible yield within the bond, and could therefore be considered nondestructive. The models, created in NASTRAN, consisted of two- or three-dimensional brick shaped elements (of length 12.5 μm per side) whose material properties were set to either copper (representing the lead) or gold (representing the bump). Non-bonded regions within the bond were simulated by either removing elements adjacent to the lead/bump interface, or by implementing gap elements between interfacial nodes. Inclusions were modeled by setting the material parameters of elements adjacent to the interface to those of silicon dioxide. The input force was applied either directly through the surface nodes of the lead, or through a force tool which contacted the lead surface via gap elements. Other issues considered include the relationship between lead overhang length and the bond force deflection curve, as well as the surface force and displacement profiles generated on the bond under the force tool     

Reliability of a cascade system with normal stress and exponential strength

In this paper we study the reliability of an N-cascade system whose stress and strength follow normal and exponential distributions, respectively. In this system we can observe that reliability increases for lower values of strength parameter (λ) and stress parameter (μ). Marginal reliability rate also increases at higher values of λ. Hence we conclude that the addition of components by a cascade system gives a significant improvement.     

Reliability of a cascade system with exponential strength and gamma stress

In this paper an expression for the reliability of an n-cascade system is allowed when the strengths of the components follows an exponential distribution and the imminent stress is impinged on the first component with a gamma distribution. Also the stress on the successive components are acted by deterministic but unequal factors. The results are observed for the cases when the parameter p takes higher values, one can infer that the systems with larger parameters value and lesser attenuation factors are more reliable.     

Correlation studies for component level ball impact shear test and board level drop test

This paper presents a comprehensive study of the resistance of solder joints to failure when subjected to strain rates that simulate the conditions of drop-impact on a portable electronic product. Two test methods are used in this study: the board level drop/shock test (BLDT) and the component level ball impact shear test (BIST). The performance of (i) 12 material combinations consisting of six solder alloys and two pad finishes; and (ii) 11 manufacturing variations covering three vendors, two finishes, three immersion gold thicknesses and three thermal aged conditions, were investigated using these two test methods, and analysis of correlations between the methods was performed. Quantitative correlation and sensitivity coefficients for the failure modes and the measured characteristic parameters - number of drops to failure for BLDT and peak load, total fracture energy, and energy-to-peak load for BIST - were evaluated. The lack of universal correlations between the two test methods has ruled out the use of BIST for evaluating solder joint materials, but BIST is recommended as a test method for quality assurance in view of the strong correlation between the measured parameters and the failure mode. The total fracture energy parameter is preferred over the peak load and energy-to-peak load due to its higher sensitivity and reduced susceptibility to measurement error.     

Combining vibration test with finite element analysis for the fatigue life estimation of PBGA components

The study develops a methodology that combines the vibration failure test, finite element analysis (FEA), and theoretical formulation for the calculation of the electronic component’s fatigue life under vibration loading. A specially designed plastic ball grid array (PBGA) component with built-in daisy chain circuits is mounted on a printed wiring board (PWB) as the test vehicle for the vibration test. It is then excited by a sinusoidal vibration whose frequency equals the fundamental frequency of the test vehicle and tested until the component fails. Because the solder balls are too small for direct measurement of their stresses, FEA is used for obtaining the stresses instead. Thus, the real displacements in the vibration test are then inputted to the FEA model when performing the stress analysis. Consequently, the stress versus failure cycles (S–N) curve is constructed by correlating both the obtained stresses on the solder balls and the number of failure cycles in the vibration test. Furthermore, the Miner’s rule is applied in calculating the fatigue damage index for those test components when failed. Finally, a formula for the prediction of the component failure cycle is deduced from all these procedures studied. It is also examined later by firstly predicting the fatigue failure cycle of a component and then conducting a vibration test for the same component for the verification purposes. The field test results have proven to be consistent with predicted results. It is then believed that the methodology is effective in predicting component’s life and may be applied further in improving the reliability of electronic systems.     

基于有限元分析的直流电机控制策略

无轴承无刷直流电机集成了直流和交流电机的优点,具有重要的实际应用价值,针对传统悬浮力控制方法存在工作复杂、逆变器通断频繁等缺陷,为了提高磁悬浮力的控制效果,提出了基于有限元分析的无轴承无刷直流电机悬浮力控制策略。首先对无轴承无刷直流电机的结构以及悬浮力产生的原理进行了分析,然后采用有限元分析法对电机转矩和悬浮力进行计算,从而实现无轴承无刷直流电机控制,最后采用Matlab/Simulink工具对其性能进行测试与验证。结果表明,本文策略可以提高转子悬浮的稳定性,能够保证无轴承无刷直流电机的正常运行。     

某型号天线座壳体强度刚度有限元分析

根据该型号雷达天线座图纸，进行了适当的简化，建立了天线座的有限元模型。同时，运用ANSYS分析软件，按工作状态和保全状态两种受力状态进行了强度与刚度校核，不仅从理论上验证了天线座换材料后在任何一种状态下都是满足设计条件的，而且为今后的天线座设计工作提供了有指导意义的依据。     

High-speed nonlinear finite element analysis for surgical simulation using graphics processing units

The use of biomechanical modelling, especially in conjunction with finite element analysis, has become common in many areas of medical image analysis and surgical simulation. Clinical employment of such techniques is hindered by conflicting requirements for high fidelity in the modelling approach, and fast solution speeds. We report the development of techniques for high-speed nonlinear finite element analysis for surgical simulation. We use a fully nonlinear total Lagrangian explicit finite element formulation which offers significant computational advantages for soft tissue simulation. However, the key contribution of the work is the presentation of a fast graphics processing unit (GPU) solution scheme for the finite element equations. To the best of our knowledge, this represents the first GPU implementation of a nonlinear finite element solver. We show that the present explicit finite element scheme is well suited to solution via highly parallel graphics hardware, and that even a midrange GPU allows significant solution speed gains (up to 16.8 times) compared with equivalent CPU implementations. For the models tested the scheme allows real-time solution of models with up to 16 000 tetrahedral elements. The use of GPUs for such purposes offers a cost-effective high-performance alternative to expensive multi-CPU machines, and may have important applications in medical image analysis and surgical simulation.     

Analysis of Cu-wire pull and shear test failure modes under ageing cycles and finite element modelling of Si-crack propagation

In microelectronic packaging, wire bonding is the predominant method for making electrical connections. Copper is increasingly substituting gold as interconnection material since it is a much cheaper alternative and it also offers several physical advantages.Adequate and reliable mechanical integrity of the connection is usually checked by process controls based onto “wire pull” and “ball bond shear” tests. In this paper the two methods are compared in terms of sensitiveness in detecting a latent weakness of the bond-pad structure, either induced by inappropriate wire bonding process or cumulated during reliability ageing. The failure modes (in terms of frequency and maximum test load) observed at the ball bond interface have been investigated on two different batches of a same chip, obtained from different wire-bonding recipes and including both unstressed and aged units. Cross-sections of the samples, submitted to pull and shear both in destructive and non-destructive tests, have allowed us to investigate the relationship between the bond morphological characteristics (metal deformation and potential micro-damages induced by copper bonding) and the weak points for fracture propagation inside the bond-pad inner layers and the silicon substrate.Besides the experimental activities, fracture mechanics and the finite element method have been employed to model the pull and shear tests. The aims of the finite element modelling have been to predict the reduction of test maximum load in defective ball bonds and the crack growth angle adopting a mixed-mode criterion. Good results have been obtained by the numerical fracture analysis, which can then support the reliability characterization and mechanical improvement of the bond.     

Design and analysis of coplanar waveguide optical modulator using finite element method

An analysis is given on the finite element method (FEM) for calculating the various parameters of optical modulators and a computer program is written to solve the finite element equation. Based on this method, a Mach-Zehnder type electro-optic modulator with coplanar waveguide (CPW) electrode is designed and fabricated. When compared with the Fourier series method, small differences on the 3-dB bandwidth, characteristic impedance and half-wave voltage, etc. are obtained.     

Efficient singular element for finite element analysis of quasi-TEMtransmission lines and waveguides with sharp metal edges

The FEM presents a slow rate of convergence when it is used in the analysis of quasi-TEM transmission lines or homogeneous waveguides with field singularities. In order to improve this drawback, mesh techniques or vector elements that cope with the singularities can be used. A different solution is to employ scalar singular elements although, most of those that have been used are only compatible with first-order ordinary elements or can only be used with field singularities of order O(r^-1/2) and O(r^-1/3). In this paper, we present an improvement on the rate of convergence of FEM by employing a scalar singular element, which can be utilized for any order of singularity, is compatible with quadratic or higher order standard elements and is also easy to implement in standard finite element codes. Several transmission lines and waveguides with sharp metal edges have been analysed with a reduced number of degrees of freedom that compares well with other FEM approaches. We also show that electromagnetic fields computed using the proposed singular element have very good agreement with the ones theoretically expected from the singular edge condition     

Features of a Scan and Clock Resource chip for providing access to board-level test functions

The architecture and some of the specific features of a Scan and Clock Resource (SCR) chip are described. This chip is currently being used in a high-end workstation product to provide access to the testability features of the individual chips and/or printed circuit boards. Using a board-level controller to gain access to the testability features of system components and interfacing the controller to a diagnostics processor (or external tester) is emerging as a common strategy for designing testable digital systems. Based upon experience gained from such an application, controller features that are deemed useful are discussed.This paper is an enhanced version of the author's earlier paper titled Towards a Standard Approach for Controlling Board-Level Test Functions, presented at the IEEE International Test Conference, ITC'90, Washington D.C., September 1990.     

The waiting time distribution for a TDMA model with a finite buffer and state-dependent service

We obtain detailed analytic formulas for the density and probability distribution of the waiting time in a time-division multiple-access (TDMA) model with a finite buffer and state-dependent service. On successive intervals of length equal to the duration of a slot, the density is expressed as a linear combination of beta densities with positive coefficients. A recursive scheme, obtained by a matrix-analytic derivation, allows for the highly efficient computations of the coefficient sequences. An expression for the mean waiting time is derived using the classical queueing formula L=/spl lambda/W. We also demonstrate that our methodology provides a concise treatment of various special cases that have been studied over the past half century.