A challenge in evaluating the mechanical reliability of heterogeneously integrated packages is associated with the dense arrangements of dissimilar materials. In evaluating cracking or debonding risks under typical thermal or mechanical stresses, the scale-dependent inelastic behaviors of these materials result in distinctly different energy dissipation modes. An energy-ratebased fracture mechanics analysis was applied in this study to investigate the effects of these time- and temperature-dependent behaviors on the fracture driving forces. The results show that the viscoelastic damping of polymer-based packaging materials increases significantly and becomes the primary energy dissipation mode as the temperature increases or the crack growth rate decreases. The energy dissipation due to viscoplastic deformation of Cu interconnect is also significant when it is arranged in a compliant setting. Because of the substantial energy dissipations through these time-dependent deformation mechanisms, the total driving forces required to propagate cracking defects in these structures would be much higher than the intrinsic bonding energy of the interface or material of interest.

High-pin-count, large-body, ball grid array (BGA) packages used in high-performance computing (HPC) applications are typically subjected to large heatsink compressive loads under typical service conditions. The higher assembly warpage due to the larger body size, combined with the mechanical compression, results in complex deformation and stress that affect the reliability. Experimental and numerical analyses were conducted to investigate the interaction between thermal and mechanical loads on the collapse of BGA solder joints and the associated risk of bridging failure in a large flip-chip BGA. A series of compressive characterizations was performed to develop the time-dependent inelastic constitutive model of the SAC305 solder joint. A process-dependent finite element model with viscoplastic solder properties was applied to simulate the evolution of deformation and stress in the assembly under surface-mount reflow, compression fixture installation, and thermal aging conditions. The numerical results were validated with experimental data. It was shown that the combined effects of warpage due to thermal deformation mismatch in the board-level assembly and contact bending of the heatsink attachment result in significant compressive stress concentration at the corners of the solder joint array. An efficient procedure that first identifies the geometry-dependent BGA pressure profile using a process-dependent global model and then calculates solder collapse at the critical location using a single-joint model was proposed to evaluate the risk of bridging failure for large-body packages. A set of empirical equations was also developed to simplify the estimation of solder collapse and bridging failure lifetime.

A fracture mechanics-based 3-D global-local finite element model is developed to investigate the debonding growth driving force of the redistribution layer (RDL) Cu-trace and polyimide (PI)-dielectric layers in a 2.5-D package. The driving forces for crack growth at the Cu-PI interface and through PI under temperature cycling thermal stresses are estimated. Results of the global analysis of the 2.5D package showed that the stress concentration regions in the RDL are at the corners of the logic and HBM chiplets. From the perspective of the overall package configuration, the high-risk area of cracking failure is mainly around the periphery of each chiplet, as opposed to being judged only by the distance to the neutral point at the package center. Additionally, the RDL stress around the corner defect is mainly in shear, and the crack growth driving force is Mode-II and -III dominant. The shear stress-induced rotations of the RDL Cu lines lead to variation in the crack driving force across each Cu line. Comparing the debond driving forces of each RDL layer interface, it was shown that the thermal stress-induced defect growth in RDL is more likely to occur in layers close to the Si die than in layers close to the laminate substrate. This trend can be attributed to the high deformation mismatch between the Si die and the RDL. For RDL defect underneath the logic die, as the location of the defect moves closer to the corner of the die, the strain energy release rate increases, the Mode-I stress intensity factor decreases, and the Mode-II and -III stress intensity factors increase.

One of the challenges in evaluating the thermomechanical reliability of the chiplet package is related to the highly heterogeneous, inelastic, and multiscale natures of the package-level interconnects. A physics-based holistic analysis would require a significant amount of computing resources. To overcome this difficulty, a viscoplastic homogenization process was developed and incorporated into a multiscale model of a 2.5-D chiplet package for evaluating the damage accumulations in the redistribution layer (RDL) Cu traces. From the comparison of the homogenized RDL model and the benchmark high-resolution RDL model, it was shown that the homogenized model can describe the time- and temperature-dependent inelastic behaviors of the RDL while requiring less than 3% of the solution time. From the thermomechanical analyses of an RDL-based 2.5-D chiplet package by using the proposed multiscale approach, it was shown that the RDL trace underneath the outer corner of the logic die is the damage hotspot when the package is under solder reflow process, package- or board-level temperature cycling (T/C) conditions. In addition, the results indicate that the RDL Cu trace failure driving force for the board-level T/C test condition is higher than that for the package-level T/C test condition.

In this paper, a fracture mechanics model for the driving force of the debonding of Si sidewall-underfill interface in a fan-out (FO) chiplet package under solder reflow condition is presented. The numerical finite element (FE) based model considers the coupled hygro-thermo-mechanical response of the chiplet package under moisture sensitivity level (MSL) test condition. The model simulates the transient moisture diffusion and the subsequent vapor pressure development in the polymeric materials, and then evaluates the related hygroscopic and thermomechanical stresses in the package. In addition, the fracture mechanics parameters for the interface debond including the strain energy release rate and the phase angle are obtained from a 3-D virtual crack closure procedure. From the simulation results for a FO two-die package, it was shown that the primary debond driving forces of the Si-underfill interface at elevated temperatures are the CTE-mismatch related thermal stress and the crack-face vapor pressure. On the other hand, the moisture swelling does not contribute much to the debond growth. The estimated debond driving force would exceed the moisture-weakened fracture toughness of the interface if the defect size reaches a certain threshold. In addition to the comprehensive procedure that models the coupled hygro-thermo-mechanical driving force for interface debond growth at reflow temperature, a simplified model for evaluating the debonding risk was also presented. The simplified model ignores the transient moisture diffusion process and adopts an equivalent coefficient of thermal expansion for considering both thermal and moisture effects. By comparing to the results of the comprehensive model, it was shown that the simplified model is feasible as a first-order evaluation of the crack driving force under reflow condition.

Multilayer ceramic capacitors (MLCCs) are essential passive elements for circuit boards and could be treated as metal/ceramic laminated structures. Due to thermo-mechanical mismatch and the high temperature experienced during fabrication, considerable stress could be induced. Consequently, structural failures such as delamination between layers or crack propagation in ceramics are frequently reported due to the brittle nature of materials. In this work, essential structural integrity assessment flow for characterizing fracture properties of MLCC are developed and the corresponding fracture properties characterization are conducted after different processing conditions in prior to serve for device longevity design based on indentation techniques. Elastic modulus and hardness, and consequently, the dependence of both fracture toughness and residual stress w.r.t. sintering temperatures are obtained. The results should be useful for optimizing processing parameters such as sintering temperatures and durations for both performance improvement and carbon emission reduction.

Polymer compounds including epoxy molding compound and underfills are widely used in high-performance multi-die package designs. In addition to the issue of thermal expansion mismatch to Si dies, the moisture absorbing nature of these compounds leads to hygroscopic swelling, interface adhesion degradation, and vapor pressure build up at high temperatures. In this study, the debonding of Si-underfill interface in a fan-out package was considered by using fracture mechanics approach. The interface fracture toughness was first measured by using four-point bending test. A numerical procedure was implemented as finite element post-process for vapor pressure calculation. Virtual crack closure procedure was applied to evaluate the crack driving force under hygro-thermo-mechanical load at reflow condition. Failure driving forces associated with vapor pressure, thermal expansion mismatch and moisture swelling were compared. The results indicate that the Si-underfill debond driving force at the Si-sidewall is significantly higher if vapor pressure is present.

The oscillatory crack-tip field in the classical interface fracture mechanics solution often leads to complications in identifying the mode mixity in bimaterial interface fracture problems. In this paper, a non-singular series solution for the continuum problem of a crack on the cohesive-spring interface under mixed-mode loading is presented and compared to the classical oscillatory solution. A Gaussian process regression model was also developed to enable quick evaluation of the phase angle for interface delamination characterization by using mixed-mode bending fracture test.

Interface debonding is one of the critical failure modes in fan-in or fan-out Cu-polyimide (PI) redistribution interconnect. Because of the time-dependent inelastic constitutive characteristics of Cu and PI, the energy absorptions through the inelastic deformations of these materials would affect the debond driving force, and should be considered in the analysis of the risk of interface debonding under process or in-service conditions. In this study, a numerical procedure was developed for evaluating the debond driving force for the Cu-PI interface. The procedure focuses on the quantitative estimation of each energy absorption modes including viscoelastic damping, viscoplastic dissipations, and debond separation. The procedure was applied to investigate the driving forces of a Cu-PI interface crack under either mechanical or thermal loads. It was shown that the dominant modes of energy dissipations are significantly different under Mode-I and mixed-mode loading conditions. In particularly, the energy dissipation through viscoplastic deformation of Cu is insignificant under Mode-I condition, but it is the dominant energy dissipation mode under mixed-mode condition. On the other hand, the contribution of viscoelastic damping on energy dissipation during debond growth is limited for both Mode-I and mixed-moded condition. Because typical thermal processes for redistribution interconnect lead to mixed-moded stress condition for the Cu-PI interface, the viscoplastic deformation of Cu plays an important role in the overall debond energy dissipation, and should be considered in the design optimization for interconnect reliability.

The problem of an edge-split bilayer beam consisted of bonded dissimilar materials under mixed-mode bending (MMB) is investigated by using a structural mechanics procedure. In this analytical procedure, the bilayer beam is modeled as two Timoshenko beams joined by using interface tensile and shear springs, and the fracture mechanics parameters including the strain energy release rate and phase angle are estimated from the spring responses. Numerical examples of bilayer beams consisted of isotropic or orthotropic bimaterials and with symmetric or asymmetric dimensions are presented and compared to continuum based finite-element solutions with either cohesive-zone or perfectly-bonded interface models. It is shown that the strain energy release rates obtained from these models are in good agreement. The phase angles obtained from the analytical model and the cohesive-zone-interface based continuum model are also consistent with each other, and agree to the crack-tip deformation. On the other hand, the phase angles obtained from the oscillating crack-tip fields related to the perfectly-bonded interface do not match to the crack-tip deformation as well as the cohesive-zone interface models. Consequently, it is recommended to characterize the mode-mixity dependent interfacial adhesion and fatigue responses by using the fracture mechanics parameters obtained by using the analytical solution for the MMB fracture problem.

A moisture-dependent viscoelastic model of polyimide dielectric thin film was developed from experimental characterizations of the moisture diffusion and the moisture-dependent viscoelastic behaviors. In the moisture diffusion characterization, a series of moisture absorption experiments were carried out by using vapor sorption analyzer. A dual-stage diffusion model was established from the experimental results. The constitutive behaviors of PI thin film under various ambient humidity conditions were obtained from dynamic mechanical analyzer. A master curve of the hygro-thermo-viscoelastic modulus was constructed by fitting to the characterization results with a time-temperature-moisture superposition model. In the hygro-thermo-viscoelastic model of PI thin film, a vertical scale factor was introduced to represent both temperature and moisture effects on the viscoelastic modulus in the glassy regime below the glass transition point. For investigating the influence of moisture on the stress development in fan-out package, a global-local finite element model was developed to consider moisture absorption and the corresponding stress in redistribution-layer interconnect.

Multilayered fan-in or fan-out (FO) redistribution interconnects are used extensively in advanced package designs for many state-of-theart high-performance computing and portable applications. A common feature of the various redistribution interconnect designs is the high density of materials interfaces between metal conductors and ceramic or polymeric dielectrics. While the design offers significant benefit in electrical performance, the lack of strong bonds between the dissimilar materials leads to a higher risk in delamination failure under process and reliability test conditions. In the estimations of the mechanical or thermomechanical debond driving forces, an important factor to be considered is the time-dependent inelastic behaviors of metals and polymers. Under thermal or mechanical loading conditions, the energy dissipation in the layered structure is not only through the breaking of the weak chemical bonds at the dissimilar materials interface, but also through the viscoelastic and viscoplastic deformations of the polymer and metals around the interface. From the perspectives of the thermomechanical reliability and structural design of the redistribution interconnect, it is important to evaluate the contributions of the inelastic energy absorptions of the metal and polymer and their effects on the interface debond growth.In this study, the influences of the viscoelastic behavior of polyimide (PI) dielectric and the viscoplastic behavior of Cu metallization on the debonding driving force of the redistribution interconnect is considered. The thermoviscoelastic constitutive behavior of the PI thin film was modelled by using a generalized Maxwell model with time-temperature superposition scheme. The viscoplastic behavior the Cu interconnect was considered by using the Anand model. A finite-element based numerical model was developed to evaluate the debonding growth at the Cu-PI interface. The model was first applied to evaluate the energy dissipations of the inelastic materials and their influences on the debonding strain energy release rate under either Mode-I or mixed-mode loading conditions. The effects of temperature and loading rate on the partition of energy dissipation through interface separation, viscoelastic and viscoplastic deformations were also discussed. The model was then applied to investigate an interface crack in redistribution interconnect under thermomechanical load. The numerical procedure developed in this study can be implemented to enable a quick evaluation of the interconnect geometry and materials selection for package design and process development.

In this study, the risk of debonding failure of the Cu-polyimide structure prepared by using realistic redistribution processes were investigated. The constitutive behavior of the polyimide thin film was first evaluated under tensile loading conditions at various temperatures. It was shown that the polyimide thin film with low glass transition temperature exhibits obvious viscoelastic response. A generalized Maxwell model was adopted to describe the thermoviscoelastic behavior. The debonding growth behavior of the Cu-polyimide interface was then investigated by using the double cantilever beam fracture mechanics tests. A finite-element based numerical model was then developed to evaluate the debonding growth at the Cu-polyimide interface and to investigate the effects of inelastic energy dissipations in the Cu and polyimide layers on the debonding response of the layered structure. The model can be applied to consider complex fan-out designs and would allow development of design rules for extending the Cu-polyimide based redistribution interconnect technology to the regimes of higher I/O densities.

A viscoplastic model based on the Chaboche framework was developed to consider the behaviors of Sn3.0Ag0.5Cu solder under tensile, creep, relaxation and cyclic conditions at a wide range of temperatures. The experimentally-observed strong softening responses, especially at lower strain rates and higher temperatures, were modeled by incorporating evolutionary dynamic recovery parameters, which depend both on the accumulated viscoplastic strain and the strain memory surface. Temperature rate terms were also included to consider the thermomechanical response. The viscoplastic model parameters were obtained by using a two-step procedure and validated to experimental data by using Runge-Kutta and finite element simulations.

An implicit integration scheme was developed for simulating the viscoplastic constitutive behavior of Sn3.0Ag0.5Cusolder and programmed into a user material subroutine of the finite element software ANSYS.The numerical procedure first solves the essential state variables by using a three-level iterative procedure, and updates the remaining stress and state variables accordingly.The numerical implementation was applied to consider the responses of solder joints in an electronic assembly under temperature cycling condition.The viscoplastic strain energy density accumulation over one temperature cycle was identified as a feasible parameter for evaluating the thermomechanical reliability of the solder joints.

The present work aims to examine the heat transfer effectiveness of laminar forced convection for water-based Nano-PCM emulsion flow through a pipe. Over a finite length of the wall, the pipe is uniformly heated with a uniform heating flux. An approximate enthalpy model is employed for the formulation of the energy equation to present the phase-change process of the Nano-PCM emulsion. Efficiency of utilizing the water-based Nano-PCM emulsion to substitute its base fluid as the working fluid in a uniform heating pipe was then demarcated quantitatively for different dimensionless parameters including the mass concentration of the Nano-PCM particles, ωpcmp, and the modified Stefan number,Stebf∗. Predicted results show that the surface-averaged cooling efficiency of the nanofluid appears increasingly promoted with its Nano-PCM particle fraction under decreasingStebf∗. The local heat transfer coefficient can be improved more than 20 times as the phase change fluid with ωpcmp = 10% and Stebf∗ = 0.01 is used. The local heat transfer improvement for the phase change nanofluid over the water is directly related to the mass fraction of Nano-PCM particle. The averaged heat transfer effectiveness of water-based Nano-PCM emulsion flow is considerably increased with its Nano-PCM particle fraction under decreasing Stebf∗.

The driving force of the silicon-underfill interface delamination was evaluated with the consideration of the underfill viscoelastic behavior. The viscoelastic constitutive behavior of the underfill was first characterized under quasi-static loading conditions at various temperatures. It was shown that the underfill exhibits an obvious viscoelastic response at temperatures in typical packaging process and reliability test conditions. A generalized Maxwell model was adopted to describe the thermoviscoelastic behavior. A finite-element based numerical procedure was developed to evaluate the debonding growth at the interface. The evolutions of the fracture mechanics parameters including the strain energy release rate and the stress intensity factors were first calculated for a bimaterial interface crack in an infinite medium, and compared to analytical solution to validate the accuracy of the numerical procedure. The model was then applied to investigate the effects of inelastic deformation of the underfill on the debonding characteristics of the underfill-silicon interface. The numerical procedure can be applied to enable a quick evaluation of the interconnect geometry and materials selection for package design and process development. It would also allow the development of design rules for extending the package-level interconnect technology to the regimes of higher I/O densities.

To prevent glass cracking from external mechanical damages, chemically strengthened glass is usually employed. The cutting of strengthened glass becomes critical due to their residual tensile stress induced in the inner core of glass attributed to the ion exchange process. This paper describes a novel technique for dealing cutting interior holes and separation of strengthened ultrathin glass for the display unit of mobile communication and computational devices. This method integrates picosecond laser ablation with quenching induced thermo-shock for accomplishing such a task. Essential analyses are performed based on fracture mechanics and finite element method to provide the scientific basis of such an approach. Experimental results indicate that with a proper temperature control, the proposed method could achieve successful separations for various enclosed shapes with the associated surface roughness satisfying the requirement. (C) 2019 Elsevier B.V. All rights reserved.

A novel viscoplastic model was developed for simulating the constitutive behavior of SAC305 (Sn3.0Ag0.5Cu) solder. The model incorporates dynamic recovery functions in the kinematic hardening rule for modeling the cyclic-softening behavior of the solder. The unified viscoplastic model was discretized by following the backward Euler integration scheme and implemented as a user-defined material subroutine (USERMAT) in ANSYS. Validation of the numerical model was conducted by simulating the solder rod responses under either strain-or stress-controlled cycling and compared to experimental measurements. It was shown that the numerical simulation is capable of predicting the softening response under cyclic straining and the ratcheting response under cyclic stressing. An ANSYS model for wafer-level package (WLP) under board-level temperature cyclic condition was also developed to simulate the ball grid array (BGA) solder joint response. From the simulation, the viscoplastic strain energy density accumulation over one temperature cycle was identified as a feasible parameter for evaluating the thermomechanical reliability of the of solder joints in electronic assembly.