Investigation on flip chip solder joint fatigue with cure-dependent underfill properties

A cure-dependent viscoelastic constitutive relation is applied to describe the curing process of epoxy underfill in flip chip on board (FCOB). The chemical shrinkage of the epoxy underfill during the curing process is applied via incremental initial strains. Thus, the stress and strain build-up, caused by the simultaneous increase in stiffness and shrinkage during the curing process, are simulated. Accelerated fatigue experiments with thermal cycles from -55/spl deg/C to 80/spl deg/C are carried out for a specially designed flip chip configuration. Based on the obtained curing induced initial stress and strain fields, thermo-mechanical predictions are presented for the test carriers. The solder bumps are modeled with temperature dependent visco-plastic properties. A combination of a Coffin-Manson based fatigue relation and a creep fatigue model is used as fatigue failure criterion. The results show that the finite element method (FEM)-based fatigue life predictions match better with the experimental results, if the curing induced initial stress state is taken into account. The effect of cure-induced hydrostatic stress is qualitatively investigated by using a modified energy partitioning damage model with a correction factor in the creep damage formulation to take into account the effect of the hydrostatic stress.     

Numerical modeling of warpage induced in QFN array molding process

Warpage is a critical issue for QFN array molding process. In this paper, a cure-dependent viscoelastic constitutive model is established to model the cure-induced warpage in array molding process. For the relaxation modulus functions of the packaging polymer, the equilibrium moduli are modeled with a model based on scaling analysis and the relaxation behavior of the transient part is described by the cure-dependent relaxation amplitude and reduced relaxation times which are based on the time-conversion superposition principle. The cure-dependent parameters are characterized by using an integrated approach of dynamical mechanical analysis (DMA) and differential scanning calorimetry (DSC) measurements. Finite element modeling is carried out for three configurations of a carrier package map mould and the warpage induced during the curing process and cooling down is predicted. The results show that warpage induced during the curing process has significant contribution on the total warpage of the map.     

Effect of filler concentration of rubbery shear and bulk modulus of molding compounds

In the electronics industry epoxy molding compounds, underfills and adhesives are used for the packaging of electronic components. These materials are applied in liquid form, cured at elevated temperatures and then cooled down to room temperature. During these processing steps residual stresses are built up resulting from both cure and thermal shrinkage. In order to minimize these stresses inorganic fillers are added. These fillers have several opposing effects on the residual stresses because they decrease the cure shrinkage and thermal contraction but increase the modulus below and above the glass transition temperature. In this paper an extensive study on the cure-dependent rubbery moduli of a series of silica spheres filled epoxy resins is carried out both experimentally and theoretically. Low frequency dynamic mechanical analysis (DMA) was used to measure the rubbery modulus build-up during cure. A model based on scaling analysis was applied to describe the evolution of the rubbery shear modulus. The effect of the filler percentage on the rubbery shear and bulk moduli as well as the coefficients of thermal expansion were measured and compared with models from the theory of particulate-filled composites.     

Controlling warpage of molded package for inkjet manufacturing

A system consisting of four silicon dies and several discrete components was encapsulated with epoxy mold material and the package was used for the evaluation of inkjet manufacturing in electronics. Experimental samples showed that the molding process induces thermo-mechanical stresses that warp the package after the mold resin is cured at elevated temperature. The molding process was modeled using the finite element method (FEM), and different package structures were simulated to see how those affect the final warpage of the package. Material properties of the mold material were measured and used in the FE model. The viscoelastic behavior of mold material was modeled with a sum of Prony series terms and a time-temperature shift factor was used to include the temperature effect. To verify the modeling assumptions, the surface profile of an experimental package was measured with an optical profilometer and the measurements were compared with the simulated profile. A good correlation was found between the measured and simulated profile of the package. The simulations with different package structures showed that e.g. an additional film placed on top of the mold resin reduces significantly the warpage of the package.     

Electrical Contact Resistance Theory for Anisotropic Conductive Films Considering Electron Tunneling and Particle Flattening

This study models the electrical contact resistance (ECR) between two surfaces separated by an anisotropic conductive film. The film is made up of an epoxy with conductive spherical particles(metallic) dispersed within. In practical situations the particles are often heavily loaded and will undergo severe plastic deformation and may essentially be flattened out. In between the particles and the surfaces there may also be an ultra-thin insulating film (consisting of epoxy) which causes considerable electrical resistance between the surfaces. In the past this effect has been neglected and the predicted ECR was much lower than that measured experimentally. This added resistance is considered using electron tunneling theory. The severe plastic deformation of the spherical particles is modeled using a new expanded elasto-plastic spherical contact model. This work also investigates the effect of compression of the separating epoxy film on the electrical contact resistance. The model finds that the high experimental ECR measurements can be accounted for by including the existence of a thin insulating film through the electron tunneling model     

无铅倒装焊封装工艺中的芯片应力及开裂分析

采用粘塑性Garofalo-Arrhenius模型描述无铅焊料的非弹性力学行为,确定了Sn3.5Ag焊料该模型的材料参数。采用与固化过程相关的粘弹性力学模型描述倒装焊底充胶的力学行为。利用有限元仿真的方法,模拟了无铅倒装封装器件封装的工艺及可靠性测试。结果表明:由于无铅技术在封装中的引入,芯片破裂的可能性随之增加,破裂出现时裂纹的尺寸更小。     

Electrothermal compact macromodel of monolithic switching voltage regulator MC34063A

In this paper a new electrothermal compact macromodel of the monolithic switching voltage regulator MC34063A for SPICE is proposed. This macromodel, valid for the transient analysis, is composed of two essential parts: the electrical model consisting of the most important fundamental blocks as: the oscillator, the comparator, the RS flip-flop, the output stage as well as the lumped thermal model. The correctness of the macromodel is verified experimentally. The values of the macromodel parameters are determined from the measurements and the catalogue data. Some of the calculated characteristics are compared with the measuring results.     

Impedance boundary conditions in ultrasonics

A generalized impedance boundary condition (GIBC) is developed to approximate the scattering of a plane acoustic wave from a bone structure such as a rib. In particular, the rib and surrounding tissue are modeled as a viscoelastic cylinder of infinite length immersed in an infinite, inviscid fluid medium. In order to determine the scattered pressure wave, appropriate boundary conditions are imposed on the relevant differential equations at the fluid-solid surface. The exact solution is then used to develop first- and second-order impedance boundary conditions applicable at the surface of the cylinder. Numerical results demonstrate the improved accuracy of the second order condition     

Estimation of sideslip angle and cornering stiffness of an articulated vehicle using a constrained lateral dynamics model

In this paper, a constrained lateral dynamics model of articulated vehicles and an algorithm for estimating sideslip angle and cornering stiffness are proposed. The articulated vehicle was modeled using the bicycle model, linear tire model, and modified Dug-off model. The normal force of each axle included in the model was estimated based on the longitudinal load transfer model. Physical constraints were applied to reduce model states. Accurate sideslip angle and cornering stiffness are essential for vehicle control safety and autonomous driving performance. The sideslip angle and cornering stiffness were simultaneously estimated using a dual linear time-varying (LTV) Kalman filter. The observability matrix guaranteed the convergence of the proposed estimation algorithm. The estimation performance was verified by simulation with TruckSim and an experiment using an articulated bus.     

Warpage simulation for the reconstituted wafer used in fan-out wafer level packaging

Fan-out packaging technology involves processing redistribution interconnects on reconstituted wafer, which takes the form of an array of silicon dies embedded in epoxy molding compound (EMC). Yields of the redistribution interconnect processes are significantly affected by the warpage of the reconstituted wafer. The warpage can be attributed to the crosslinking reaction and viscoelastic relaxation of the EMC, and to the thermal expansion mismatch between dissimilar materials during the reconstitution thermal processes. In this study, the coupled chemical-thermomechanical deformation mechanism of a commercial EMC was characterized and incorporated in a finite element model for considering the warpage evolution during the reconstitution thermal processes. Results of the analyses indicate that the warpage is strongly influenced by the volume percentage of Si in the reconstituted wafer and the viscoelastic relaxation of the EMC. On the other hand, contribution from the chemical shrinkage of the commercial EMC on warpage is insignificant. As such, evaluations based on the comprehensive chemical-thermomechanical model considering the full process history can be approximated by the estimations from a simplified viscoelastic warpage model considering only the thermal excursion.     

Vector one-way wave absorbing boundary conditions for FEMapplications

In the paper a derivation is presented which leads to a new and general class of vector absorbing boundary conditions (ABCs) for use with the finite element method (FEM). The derivation is based on a vector one-way wave equation and a polynomial approximation of the vector radical. It is shown that wide-angle absorbing boundary conditions, as proposed in Halpern and Trefethen (1988) for optimal absorption of out-going waves, can be obtained in vector form. Vector plane waves are used to evaluate the accuracy and the reflection performance of these boundary conditions in a wide range of incidence angles. The implementation of the vector ABCs in a FEM formulation is also provided to show how up to the fifth-order absorbing accuracy can be achieved with derivatives only up to the second-order. A possible formulation is described which not only yields a third-order accuracy with first-order derivatives, but also retains the symmetry of the FEM matrix     

Modeling and analysis of power distribution networks for Gigabit applications

As the operating frequency of digital systems increases and voltage swing decreases, it becomes very important to characterize and analyze power distribution networks (PDNs) accurately. This paper presents the modeling, simulation, and characterization of the PDN in a high-speed printed circuit board (PCB) designed for chip-to-chip communication at a data rate of 3.2 Gbps. The test board consists of transmitter and receiver chips wirebonded onto plastic ball grid array (PGBA) packages on a PCB. In this paper, a hybrid method has been applied for analysis, which consists of the transmission matrix method (TMM) in the frequency domain and macromodeling method in the time domain. As an initial step, power/ground planes have been modeled using TMM. Then, the macromodel of the power/ground planes has been generated at the desired ports using macromodeling. Finally, the macromodel of the planes, transmission lines, and nonlinear drivers have been simulated in standard SPICE-based circuit simulators for computing power supply noise. In addition to noise computation, the self and transfer impedances of power/ground planes have been computed and the effect of decoupling capacitors on power supply noise has been analyzed. The methods discussed have been validated using hardware measurements.     

导电胶的力学性能研究

导电胶主要是由环氧树脂基体和导电粒子组成的复合导电聚合物,其力学性能主要是由聚合物基体决定,基体是粘弹性材料,具有时间和温度依赖性。文章建立了一个基于时间-温度、时间-固化度的宏观粘弹性本构关系来描述导电胶在固化过程中的粘弹性行为,通过动态力学试验（DMA）表征导电胶的粘弹性行为,测定导电胶的粘弹性参数。通过对导电胶粘弹性行为表征,能更好的优化固化工艺参数。     

Adaptive Solution Space Projection for Fast and Robust Wideband Finite-Element Simulation of Microwave Components

A fast and robust wideband finite element method (FEM) is presented for simulation of various microwave components. Port boundary conditions are derived by means of the eigenfunction expansion and then incorporated into the functional, which is discretized and solved by the high-order FEM. To achieve an efficient and reliable wideband simulation, a multipoint model order reduction technique, called the solution space projection method, is applied. The method requires neither the construction of a port-boundary-condition matrix polynomial, nor the calculation of frequency derivatives of solution vectors in its basic version. Thus, the method not only saves memory, but also can deal with various kinds of boundary conditions that may have arbitrary frequency dependence or are described by a set of discrete vectors over the frequency band.     

Cure shrinkage measurement of nonconductive adhesives by means of a thermomechanical analyzer

The conductivity of a nonconductive adhesive (NCA) flip chip interconnect is completely dependent on the direct mechanical contact between the integrated circuit (IC) bump and substrate pad. Cure shrinkage of NCA is critical for the formation of the final contact force in the contacts. However, measurement of the cure shrinkage during cross-linking reaction is fairly difficult. This paper introduces a new, yet simple, approach to measure cure shrinkage of adhesives using a thermo-mechanical analyzer. Isothermal studies of shrinkage change as a function of curing show four distinct regions. First, the thickness of the epoxy decreases due to decreasing viscosity and applied load, followed by a stage where the dimension change is constant as the cross-linking reaction is yet to set in. Once cross-linking begins, the shrinkage reaches a maximum followed by a plateau where the cross-linking reaction has completed. Sharp changes of the slope of cure shrinkage versus degree of cure were observed to coincide with gelation and vitrification. After gelation, a linear relationship between the cure shrinkage and degree of cure was observed to extend until the occurrence of vitrification, which quenches the cross-linking reaction. Applied load in the range of 0.05 N was found to be optimal to minimize measurement errors.     

Finite element modeling of electrode-skin contact impedance inelectrical impedance tomography

In electrical impedance tomography (EIT), the measured voltages are sensitive to electrode-skin contact impedance because the contact impedance and the current density through it are both high. Large electrodes were used to provide a more uniform current distribution and reduce the contact impedance. A large electrode differs from a point electrode in that it has shunting and edge effects that cannot be modeled by a single resistor. The finite-element method (FEM) was used to study the electric field distributions underneath an electrode, and three models were developed: a FEM model, a simplified FEM model, and a weighted load model. The FEM models considered both shunting and edge effects and closely matched the experimental measurements. It is concluded that FEM models of electrodes can be used to improve the performance of an electrical impedance tomography reconstruction algorithm     

A combined FEM/MoM approach to analyze the plane wave diffractionby arbitrary gratings

The diffraction of TE- and TM-polarized plane waves by planar gratings is numerically analyzed using a combined finite-element-method/method-of-moments (FEM/MoM) algorithm based on the generalized network formulation. The interior region, treated using the FEM, is truncated to a single unit cell with the introduction of an exact periodic boundary condition, which is enforced as a natural boundary condition. Using the FEM to compute the fields within the periodic structure allows gratings of arbitrary cross section and material composition to be efficiently modeled     

Finite-element method coupled with method of lines for the analysis of planar or quasi-planar transmission lines

A full-wave analysis incorporating the finite-element method (FEM) and the method of lines (MoL) is presented in this paper to investigate a planar or quasi-planar transmission-line structure containing complex geometric/material features. For a transmission-line structure being considered, the regions containing complex media are modeled by the FEM while those consisting of simple media with simple geometry are analyzed using the MoL. From the field solutions calculated by MoL, the boundary conditions are constructed. The boundary integrals involved in finite-element analysis are then carried out using these boundary conditions. Since the finite-element analysis is employed only in the complex parts of the structures, while other parts are handled by the MoL, this approach not only retains the major advantage of the FEM in simulating complex structures but also becomes more efficient than the conventional finite-element analysis. Good agreement between the calculated results and those reported in the available literature is obtained and thus validates the present approach. Furthermore, proficient computational efficiency of this method is demonstrated by examining its convergence property. Finally, a number of relevant transmission-line structures are analyzed to illustrate the applications of this approach.     

Modélisation d’une antenne-réseau et traitement optimal

An array antenna is modeled after a linear multipole filter, one part of which is connected to a distant source, radiating in a specified direction, while the relations between the other parts are characterized by the antenna admittance matrix. This modeling technique is applied to an array of parallel linear wire antennas. It is shown how the array admittance matrix can be evaluated numerically by a discrete quantization of the Maxwell’s equations with the proper boundary conditions (Harrington’s method of moments). The admittance matrix is then used to formulate the optimum signal processing for transmission (maximization of antenna gain, with or without constraints) and for reception (maximization of signalto-noise ratio). Along with the model of the array antenna that is submitted, a method of signal processing is developed in which accurate estimates are included of the losses that occur within the array elements as well as of the coupling between elements and of the noise arising in the receiving system. The antenna designer can thus optimize the geometric configuration of the array and study the phenomenon of superdirectivity with a more realistic approach than was hitherto possible.