Copper pillar μbumps are increasingly being used in heterogeneously integrated semiconductor packages as first-level interconnects to achieve higher interconnect densities than traditional solder bumps. The role of thermomechanical reliability in the co-design process of Cu-pillar microbumps has therefore received increased scrutiny in the literature.In this study, the impact of various design parameters and manufacturing variability on the thermomechanical stresses of the Au-Cu interface in μbumps with Cu pillars bonded to Au pads is assessed using finite element modeling techniques. The severity of the interface stresses is an indicator of the reliability of the interface. The design parameters being considered in this study are: (i) standoff height variability due to die misalignment during manufacturing; (ii) interconnect feature dimensions (Cu pillar diameter and Au pad thickness); and (iii) interconnect pitch.These parametric studies are conducted by using a two-step global-local finite element modeling approach that maps the effect of various design/manufacturing features on thermomechanical reliability. The global model of a semiconductor package, with linear-elastic approximations, simplified geometry, and coarse finite element mesh, is used to identify regions of criticality and to generate local displacement histories near those critical regions. The local displacement fields are then transferred to the boundary nodes of a local model of the critical region(s), consisting of more granularity and fidelity in terms of local geometric details, finer computational spatial resolution, and nonlinear viscoplastic material properties. The stress severity at the interface between the Cu pillar and the Au pad is assessed using equivalent and peel strains at the interface, estimated with finite element modeling.

Electronics packaging increasingly relies on heterogeneous integration with high-density solder interconnects, where the thermomechanical reliability depends strongly on the creep behavior of solder alloy under varying thermal cycling ramp rates. The small length scale results in oligocrystalline joints whose deformation depends on grain-scale anisotropic mechanics. This study develops a continuum-scale anisotropic framework to predict variability of SAC305 solder joint deformation during different loading conditions. A modified Hill–Darveaux creep model with separate Hill constants for primary and secondary creep is calibrated using virtual data from a dislocation-mechanics-based crystal viscoplasticity model. The formulation is implemented through user material (UMAT) definitions in Abaqus. Simulations compare responses with and without primary creep to quantify its influence on variability of deformation and creep work in oligocrystalline solder geometry.

Microstrip patch antennas are widely used in wireless systems due to their low profile, lightweight structure, and compatibility with planar and conformal electronics. In this work, we report the fabrication and characterization of carbon nanotube-graphene oxide (CNT-GO) based 3D-printed rectangular patch antennas that can be integrated onto curvilinear and deformable surfaces. The printed antennas are only a few micrometers thick and exhibit strong high-frequency performance. Reflection coefficient $\left(\mathbf{S}_{\mathbf{1 1}}\right)$ measurements show ultra-wideband behavior, remaining below -10 dB over 12-39 GHz on flat FR4 substrates, while antennas on curvilinear and bendable polylactic acid (PLA) substrates operate across ~7-22 GHz and ~5-25 GHz, respectively. Radiation efficiency was experimentally evaluated, and antenna gain was analyzed via performance after prolonged temperature cycling. These results highlight the potential of CNT-GO printed antennas for lightweight, conformal radio frequency (RF) components in millimeter-wave communications, wearable electronics, and flexible wireless systems.

Real-time, high-throughput applications such as AI/ML and connected vehicles require advanced packaging with heterogeneous integration for high performance and thin form factors. Underfills delaminate or crack due to interfacial stresses and stress concentrations, motivating modeling approaches to capture resulting failure modes and effects. While cracks in the underfill (bulk and interfacial) will not immediately affect the operational performance of the package, it will reduce the overall reliability of the electronic package because of the changes in the load distribution. It is necessary to have a simplified modelling scheme to quantify the effect of underfill cracks on the stress distribution in the die, μbumps, and redistribution layers (RDL) of the substrate. A multiscale global-local finite element thermal cycling simulation in the range between -55 and 125 °C is conducted in this paper to assess the effect of the underfill interfacial delamination on the thermomechanical reliability of an advanced heterogeneously integrated multi-chiplet semiconductor package on an ultra-fine pitch organic substrate. A global model with simplified geometry, a coarse mesh, and linear elastic material properties is first developed for the overall package. Local models of the critical region with more detailed geometric features, finer meshes, and nonlinear viscoplastic material properties are seeded with cracks of varying sizes at the underfill interfaces. Stress, strain, and energy distributions are compared in the die, μbump, and RDL, before and after underfill-RDL delamination.

As advanced packaging demands higher interconnect density, Redistribution Layer (RDL) technologies must accommodate progressively smaller line widths and tighter spacing. However, this scaling intensifies reliability challenges, making ultrafine RDLs highly vulnerable to progressive crack growth and delamination. Currently, macroscopic experimental methods like the Double Cantilever Beam (DCB) test are employed to measure fracture energy and extract parameters for Cohesive Zone Modeling (CZM). Yet, as RDLs transition to sub-micron regimes, adapting classical fracture-mechanics tests becomes challenging because the target interface is often buried deep within a multi-material stack, making it difficult to control the crack path and isolate specific fracture planes. To overcome these metrology limitations, this paper presents a Molecular Dynamics (MD) approach to extract intrinsic interfacial traction-separation behavior at the nanoscale. Because MD and macroscopic experiments operate at very different scales, the atomistic results are transformed through scaling coefficients to produce CZM parameters that are MD-informed and experimentally consistent in energy. Ultimately, this multiscale framework demonstrates the importance of accurately assessing package reliability by bridging nanoscale interfacial behavior with macroscale predictive design-for-reliability in next-generation RDL stacks

Thermomechanical reliability of SnAgCu (SAC) is a significant aspect of heterogeneous integration, due to miniaturization and the corresponding increase in interconnect power density. Traditional approaches to the modeling of thermomechanical fatigue in solder interconnects usually rely on isotropic, uniform, secondary creep properties of solder joints. A majority of the solder interconnect modeling literature has focused on steady-state creep behavior. Although limited in quantity, there is some important evidence in the literature to suggest that primary creep can also be an important contributor to cyclic thermo-mechanical fatigue in solder interconnects. In this study, the contribution of primary creep in to thermal cycling fatigue of SAC305 is analyzed using grain-scale transient finite element modeling. Simplified thermal cycling simulations are conducted between -40 and 125C. The effect of different ramp rates are considered. The anisotropic continuum model used for each solder grain is the Hill-Darveaux model, which considers both primary and secondary creep in a single unified approach. Hill-Darveaux model constants are obtained from multi-scale dislocation-mechanics crystal viscoplasticity (DMCV) models. Single-crystal solder joints with different grain orientations are considered for conducting simulations.

This study considers the response of printed hybrid electronic (PHE) assemblies to extreme mechanical shock (50,000 g base excitation) at multiple elevated temperatures (25-125 degrees C). Passive components were recessed into milled cavities in injection-molded polysulfone beams using a unique 'mill-and-fill' method. The components were interconnected to printed silver traces using printed solder, with circuits then formed from the silver traces. The populated beam specimens were subjected to drop testing in a clamped-clamped configuration without secondary impact using an accelerated-fall drop tower with dual mass shock amplifier (DMSA), resulting in strain magnitudes in the polysulfone substrate of similar to 30,000 mu m/m at rates up to similar to 200 /s. A finite element model of the fully populated assembly was used to estimate plastic strain history at the failure site in the sintered silver. Circuit failure occurred due to component separation from the substrate caused by cracking within the sintered silver beneath the soldered interconnect - a failure mode common across all temperatures. Maximum plastic strain magnitudes in the sintered silver were similar to 0.11 m/m at rates of similar to 1000 /s. Total number of drops to failure was recorded in four different component locations at all temperatures. These results, together with transient nonlinear finite element simulation data, were then integrated by means of a cumulative damage model, to generate a low-cycle fatigue curve for sintered silver from 25 to 125 degrees C.

A single-stage dual-active-bridge direct current-alternating current (DC-AC) micro-inverter prototype with Gallium Nitride (GaN) primary switching devices was assembled and subjected to environmental reliability testing. Testing consisted of an unpowered temperature cycling with an amplitude ranging from −40 °C to 105 °C. Electrical performance characterization was performed during the accelerated testing at regular intervals until a failure was observed. Nondestructive failure analysis was performed on the board to determine the failure modes and mechanisms, and it revealed that the failure occurred due to solder bump delamination at the gate, source, and drain pads. To better understand the failure mechanism and predict the fatigue life of the assembled GaN field effective transistors (FET), thermo-mechanical simulation was performed using finite element analysis (FEA), where the submodeling feature was used to track the location of the GaN device on the board, and the average strain energy accumulation at the critical solder joint for each set of temperature cycles was simulated. Garofalo creep model was used to capture the creep deformation during thermal cycling, and Syed's Energy-based fatigue model for SAC305 solder was used to determine the life of the land grid array (LGA) package. The model constants were calibrated using the experimental failure time. This study was then extended to examine the effects of encapsulation materials on the life of the primary devices. The results reveal that encapsulation significantly increases the fatigue life of the Gallium Nitride field effective transistors (GaN FET) for all encapsulation materials.

Additive manufacturing provides a pathway for manufacturing of printed hybrid electronic (PHE) assemblies in novel non-planar (curvilinear and 3D) form factors. In particular, PHEs may combine conventionally manufactured microelectronics components and circuit elements with additively manufactured features. Aerosol jet printing (AJP) is one of the leading additive manufacturing methods for PHEs. It is therefore critical to better understand the reliability aspects of using AJP-based PHEs to fully leverage the possibilities offered by this technology. This paper evaluates the reliability of nano -particle based metallic conductors in aerosol jet printed electronics (AJPE) under temperature cycling (TC) conditions for various substrates and supports the rapidly growing field of PHEs. PHE samples specifically designed and fabricated for this study consisting of substrates made of three different PCB materials (Glass-FR4, Kevlar-polyimide, Ceramic) were cycled to failure between -40 degrees C and +125 degrees C. Finite element analysis (FEA) was used to quantify the different thermomechanical strain levels experienced by the conductor on the different substrate materials. The corresponding number of temperature cycles to failure were measured from the test and Weibull characteristic life was estimated for each substrate type. Failure analysis revealed that across all three substrates, the transition region connecting the printed traces to copper pads was where most of the failures occurred. The local geometric complexities at the transition region between the printed and conventional elements resulted in localized stressors. The FEA results confirm this strain concentration site. The failure experimental results, when combined with the local thermomechanical strain history at the failure site (estimated by the FEA), give useful insights into the design considerations needed for producing reliable AJPEs.

Electronics, when exposed to temperature-humidity-bias (THB) conditions are subject to degradation and failure by a mechanism called electrochemical migration (ECM). This is a phenomenon where neighboring conductors can, under an appropriate applied bias voltage and in the presence of an electrolyte, experience metallic migration via dendritic filament growth. ECM can induce failure in electronics by causing a degradation in the surface insulation resistance of the materials between conductors, leading to various degradation/failure modes such as leakage currents, dielectric breakdown and ultimately short-circuit. This paper investigates the reliability of aerosol-jet printed (AJP) metallic silver nano-particle conductors (Ag-NP) under THB conditions, leading to ECM failure. An earlier study by this group on Ag-NP AJP test coupons showed dendritic filament growth, with intricate dendrite morphologies under different combinations of temperature, humidity, and electric bias levels in THB experiments. That prior study also reported the dendrite density to scale with the electrical field strength applied across neighboring conductors. In the current paper, that prior work is expanded upon, to better quantify the dependence of the ECM dendrite density on the field strength for AJP AgNP conductors under THB conditions. A novel methodology for conducting an image processing analysis quantifying the dendrite density is proposed. A correlation between the dendrite density and electrical field impedance level is found. This paper lays the foundation for a future physics-of-failure (PoF) based ECM model for printed electronics using AJP.

In this study, we report our development of a new highly conductive and extremely stable 3D printable (or directly writable) metal-free ink for printed electronics applications. The ink consists of carbon nanotubes (CNTs) and functionalized (with p-phenylenediamine or PPD) graphene oxide and exhibits conductivity that is nearly 1 order of magnitude greater than that of the previously reported CNT-GO inks. Comprehensive characterization of the CNT-GO-PPD ink reveals its optimal rheological properties (making it 3D printable or direct writable), uniform deposition characteristics, and remarkably high conductivity (among the very best in metal-free carbon-based inks). We conduct molecular dynamics (MD) simulations and, from the equilibrium structure of the CNT-GO-PPD system (revealed by such simulations), explain the manner in which the PPD and CNT molecules simultaneously adsorb on the GO flakes to ensure significantly large conductivity of the CNT-GO-PPD ink. The ink can be directly written on various substrates and for creating complex geometries. Additionally, the traces printed with this ink demonstrate temperature sensing and humidity sensing capabilities and at the same time show excellent reliability and stability across a broad range of temperatures and humidity levels, establishing the ink's potential for advancing the field of printed electronics.

SAC solder joints contain few anisotropic viscoplastic grains and each grain contains pro-eutectic beta-Tin dendrites surrounded by a Tin-Silver eutectic region. Grains are separated by viscoplastic grain boundaries. Over the past decade, crystal viscoplasticity (CV) models developed by this group have considered deformation mechanisms at each length scale due to dislocation creep, to determine viscoplastic deformation of single grains. The effect of the evolution of the microstructure on creep behavior of solder grains has also been captured using a combination of multi-scale-CV modeling and finite element grain-scale modeling. Studies conducted by multiple researchers indicate that the evolution of solder joint microstructure takes place during thermal cycling in two ways: (i) ripening of Ag-Sn intermetallic structure in the eutectic region and breakdown of dendritic structure in the pro-eutectic region within each grain, due to higher diffusion rates at elevated temperature; and (ii) localized recrystallization of larger grains to form finer grain structure in regions that see a combination of cyclic stress and elevated temperature. Effect of factor (i) above on creep behavior of solder has been previously presented by the authors. The current paper presents simulation of localized recrystallization of single crystal solder joint into finer grains. Progressive thermal cycling, causes progressive increase in the region of recrystallization, which reduces the overall creep resistance of oligocrystalline solder joints. Reduction in the creep resistance causes progressive reduction in the fatigue resistance of solder joint.

The advantages of printed hybrid electronic assemblies are of considerable interest to designers of electromechanical systems, especially for applications in extreme environments. This study considered the reliability of electrical components embedded into polymeric substrates and interconnected with printed conductors as elements of printed hybrid electronic (PHE) assemblies subject to extreme acceleration levels experienced during mechanical shock. Passive components were recessed into cavities in injection-molded polysulfone beams by way of a unique "mill-and-fill" method combining traditional subtractive milling with extrusion-based paste printing. The components were interconnected to printed silver traces using printed solder, with circuits then formed from the silver traces. The populated beam specimens were subjected to drop testing in a clamped-clamped configuration without secondary impact using an accelerated-fall drop tower with shock amplifier. Excitation acceleration levels ranged from 25,000 to 100,000 g, resulting in substrate strain magnitudes of up to 50,000 mu m/m at rates up to similar to 1000/s. Repeated shocks induced cracking within the sintered silver traces adjacent to the components, eventually causing component separation from the substrate. Experimentally calibrated bare substrate and fully populated assembly modeling was used to assess substrate response and stress levels within the traces, with plastic strain magnitudes as high as 120,000 mu m/m at rates of up to similar to 1200/s. Based on experiments and modeling, a low-cycle fatigue curve for sintered silver was generated.

The response of printed hybrid electronic (PHE) assemblies to mechanical shock was previously assessed experimentally but, as with much experimental work, the relevance of these results was limited by the specific intended application. The primary failure mode observed was physical separation of embedded components caused by fractures within sub-surface sintered silver traces and interconnections. This current study focuses on physics-based modeling of these failures, to facilitate extrapolation to other use conditions for broader integration of PHE assemblies within the electronics community, especially for applications experiencing repeated high-g mechanical shock. Modeling efforts integrated all elements of the tested PHE circuit, consisting of molded polysulfone substrates, printed nano-particle ink silver traces, embedded passive components, and printed tin-bismuth soldered interconnects. Circuits were manufactured using a novel 'mill-and-fill' hybrid method on a beam measuring 3.2 mm thick, 12.7 mm wide, and 63.5 mm long. The beam was secured by clamped-clamped fixturing along both short edges and subjected to drop testing with no secondary impact. Embedded components were located at regions of maximum bending flexure within the substrate. Simulated base excitation shock levels were based on experimental drop tower testing and ranged from 25,000 g to 100,000 g with pulse durations less than .1 ms. A two-step hierarchical multiscale finite element modeling approach was used, with fully populated models relying on 3D solid elements with explicit dynamic solving and nonlinear effects to account for high peak strain magnitudes (similar to 18%) and strain rates (similar to 1,000 /s) in the sintered silver. Validation of a bare substrate model was accomplished prior to maturation of the fully populated model by means of comparing measured and modeled strain response of the substrate in the time domain and frequency domain up to 10 kHz. Given the observed failure sites within the sintered silver traces from experimental work, the maximum stresses and strains at these sites were generated from modeling as a function of base acceleration magnitude and component location on the beam. These values were then compared against experimental cycles to failure data for several different substrate and component geometries with cycles to failure including cumulative damage effects. These geometries included two different strain locations on the beam (edge and center) and two different orientations of the silver trace (longitudinal or transverse) relative to the beam axis. The end result was a geometry- and application-agnostic low-cycle (below 10(3) cycles) fatigue curve for printed silver traces suitable for applications with repeated loads or as an element of subsequent cumulative damage models. Additional work is ongoing to incorporate the added effects of elevated temperature (up to 125 degrees C) on the mechanical response of the substrates and silver traces during a mechanical shock.

In this paper, we develop multifunctional, physically soft, mechanically compliant, and magnetically responsive PDMS films, with embedded Fe3O4 nanoparticles, that show robust magnetic properties over a significant range of mechanical deformation. First, we establish that the magnetic properties, namely the saturation magnetization (M s), remanent magnetization (M r), and intrinsic coercivity (H ci) of these PDMS films in highly deformed configurations, i.e. in folded, twisted (with different twist angles), and bent (flexed) configurations, show very little degradation compared to those obtained in undeformed configurations. Next, the films were subjected to repetitive cycles of zero-to-max deformation (R = 0) and the saturation magnetization of the films was shown to not exhibit any significant degree of progressive degradation as a function of cyclic deformation history. These findings confirm the excellent robustness and cyclic durability of magnetic properties shown by these magnetic and compliant PDMS films and point to their suitability for wearable electronics applications.

A single-stage dual-active-bridge DC-AC microinverter prototype board with Gallium Nitride (GaN) primary switching devices was designed and assembled for environmental reliability testing. An unpowered temperature cycling test was conducted with an amplitude ranging from -40 to 105 degrees C at a ramp rate of 5 degrees C/min. The electrical testing revealed a failure in the board between 800 and 1000 hours, which was located at the primary devices. Non-destructive failure analysis was performed on the board to determine the failure modes and mechanisms. Using a Confocal Scanning Acoustic Microscope (C-SAM) with a 75MHz transducer, it was determined that failure was located at the solder bumps, and the scans revealed that two of four primary devices, EPC2001C, experienced a solder bump delamination at the gate, source, and drain pads. Hence, it is concluded that the delamination occurred due to coefficient of thermal expansion (CTE) mismatch between substrate and die. To understand the failure mechanism and predict the fatigue life of the assembled GaNFET, Finite Element Analysis (FEA) simulation was performed using ANSYS structural models, where thesub-modeling feature was used to track the location of the GaN device on the board, and a total of five temperature cycles were simulated to determine the average strain energy of the critical solder joint. The Garofalo creep model was used to capture the creep deformation during thermal cycling. Syed's Energy-based fatigue model for SAC305 solder was used to determine thelife of the land grid array package assembly of the EPC2001C, and the model constants were calibrated using the experimental failure time. Furthermore, this study was extended to examine the effects of encapsulation materials on the life of the primary switching devices. The encapsulation materials were studied in three distinct configurations: solely potting, solely underfill, and a hybrid combination of potting and underfill. The results reveal that the encapsulation materials significantly increase the fatigue life of the GaNFET.

The objective of this work is to develop a microstructure-based simulation approach to assess the fatigue life of solder joints that are used by the microelectronics industry. The developed approach can generate solder joints with random grain morphologies by means of 3D Voronoi tessellation. The anisotropic material behavior of each grain is described by the Garofalo creep equation combined with Hill's definition of the equivalent stress for anisotropic materials. Grain boundaries are implemented as interface elements, with an isotropic creep constitutive model. The stochastic variability in the creep response of solder joints was qualitatively estimated by generating 100 unique solder joints containing 5 to 9 grains, each having a random material orientation. These joints were independently loaded with a realistic stress level for microelectronic products during thermal cycling. The volume-averaged creep strain energy density in the solder joints was used to predict the fatigue life of the solder joints. The results showed a factor of similar to 4 difference in expected lifetime of the individual solder joints. Next, nine randomly picked solder joints from the above-mentioned pool of 100 were sandwiched between a silicon die and a printed circuit board to form a simulation model of a Wafer-Level Chip-Scale package (WLCSP). The creep strain energy density in the joints was computed for 34 unique cases of the WLCSP. A factor of similar to 2.5 between the highest and lowest estimate for the solder joint life was found. The slope of the corresponding Weibull distribution equals similar to 6, which falls within the slopes typical reported for solder joint reliability of WLCSPs.

This study assessed the performance of printed hybrid electronic (PHE) assemblies subject to simultaneous exposure to elevated temperatures (up to 150 degrees C) and extreme mechanical shock (up to 100,000 g). The test specimens were rectangular beams measuring 3.2 mm thick, 12.7 mm wide, and 63.5 mm long, fabricated using injection molding from various polysulfone polymers. Several different electronic circuit elements - traces, passive components, and interconnects - were embedded into the largest flat surface of these substrates using a novel 'mill-and-fill' method. This method used conventional 5-axis CNC milling to generate pockets and channels into which the electrical elements were embedded. Traces were extrusionprinted with silver paste. The components used were 0-ohm resistors. Interconnects were formed using extrusion-printed tinbismuth solder. Testing was accomplished using an accelerated-freefall drop tower equipped with a shock amplifier and integrated furnace. Acceleration pulses (half-sine shape) ranged from 25,000 g to 100,000 g with pulse durations of similar to.03-.1 ms and velocity changes of 6-25 m/s. Elevated temperatures ranged from 88 degrees C to 150 degrees C in addition to room temperature (25 degrees C). The specimens were fixtured in a clamped-clamped configuration (largest flat face upright) and did not experience any secondary impact. Tests were instrumented with accelerometers, thermocouples / RTDs, and strain gauges with sampling grates of 1 MHz. Thermal cameras and high-speed optical cameras were also used. At the highest acceleration levels, peak strain values measured >14,000 microstrain. Drop degradation assessment was based on changes in electrical performance metric (such as overall circuit resistance) or based on structural failure of circuit elements. Measurements were made either in real time during the drop event or intermittently after a select number of drops. Global and meso-scale modeling was conducted to validate measured strain response data, facilitate generation of a damage accumulation model, explain observed failure modes, and predict physical and electrical response for future geometries and applications. Component separation and interconnect failure were the primary failure modes observed. As expected, number of cycles to failure decreased with increasing acceleration level and increasing temperature. The polysulfone beams themselves survived at all tested temperatures and most acceleration levels except for 100,000 g. Optical microscopy observations throughout testing showed cracking present in sintered silver traces, but this was not the sole predictor of circuit failure. Additional work is ongoing to further explore the causes for these failure modes and understand the implications of the physical response on different embedded components and specimen geometries.

SnAgCu solder joint has oligocrystalline (few large grains) structure and due to body-centered tetragonal (BCT) structure, each grain shows strongly anisotropic behavior. Modelling anisotropic behavior of grain scale solder joints has been extensively researched by this group. In this paper, anisotropic grain-scale plasticity model is used to predict variability of solder joint fatigue durability under sine sweep vibration excitation. Solder experiences different levels of cyclic stress for different grain orientations. Stress-based high cycle fatigue (HCF) model (Basquin’s model) and Miner’s rule are used for determining the variability of vibration durability of solder joints for different orientations and compared with experimental results.

Grain morphology of SnAgCu (SAC) solder alloys is known to evolve throughout their life due to recrystallization caused by mechanical and/or thermal cycling. Changes in grain morphology affect the overall anisotropic mechanical behavior of few-grained (oligocrystalline) SAC solder joints. The recrystallization occurs preferentially and locally in high deformation regions in solder joints, resulting in the formation of small grains and new grain boundaries. This behavior has been studied experimentally by different researchers and various attempts have been made to model the recrystallization in solder joints under different cycling conditions. The objectives of this article are to: (i) demonstrate a procedure for explicit modeling of recrystallization in critical regions of anisotropic oligocrystalline solder joints, using multi-level nested Voronoi tessellation techniques; and (ii) demonstrate the effects of the recrystallization on solder joint creep response, using anisotropic Hill-Garofalo representation of each grain and an isotropic Mises-Garofalo representation of the intervening grain boundaries.