Xin-Ping Zhang

Modeling of Ni4Ti3 precipitation during stress-free and stress-assisted aging of bi-crystalline NiTi shape memory alloys

Abstract The phase field method was applied to study the microstructure evolution of Ni4Ti3 precipitates during stress-free and stress-assisted aging of bi-crystalline NiTi shape memory alloys (SAMs) with two different initial Ni-contents of 51.5% and 52.5% (mole fraction), respectively. The simulation results show that, during stress-free aging of the NiTi alloy with a low supersaturation of Ni (i.e., Ti-51.5%Ni), the Ni4Ti3 precipitates exhibit a heterogeneous distribution with a high number density of particles at the grain boundary, leaving most of the grain interiors free of precipitates; while for the NiTi alloy with a high supersaturation of Ni (i.e., Ti-52.5%Ni), the Ni4Ti3 precipitates show a homogeneous distribution across the entire simulation system. The stress-assisted aging can give rise to homogeneous distribution of the precipitates, regardless of the initial Ni-content; however, the distribution of variant type within the two grains is heterogeneous.

Phase transformation and damping behavior of lightweight porous TiNiCu alloys fabricated by powder metallurgy process

Abstract Porous TiNiCu ternary shape memory alloys (SMAs) were successfully fabricated by powder metallurgy method. The microstructure, martensitic transformation behavior, damping performance and mechanical properties of the fabricated alloys were intensively studied. It is found that the apparent density of alloys decreases with increasing the Cu content, the porous Ti50Ni40Cu10 alloy exhibits wide endothermic and exothermic peaks arisen from the hysteresis of martensitic transformations, while the porous Ti50Ni30Cu20 alloy shows much stronger and narrower endothermic and exothermic peaks owing to the B2-B19 transformation taking place easily. Moreover, the porous Ti50Ni40Cu10 alloy shows a lower shape recovery rate than the porous Ti50Ni50 alloy, while the porous Ti50Ni30Cu20 alloy behaves reversely. In addition, the damping capacity (or internal friction, IF) of the porous TiNiCu alloys increases with increasing the Cu content. The porous Ti50Ni30Cu20 alloy has very high equivalent internal friction, with the maximum equivalent internal friction value five times higher than that of the porous Ti50Ni50 alloy.

FE simulation of size effects on interface fracture characteristics of microscale lead-free solder interconnects

Understanding of interface fracture behavior of the solder joints has long been significant in reliability evaluation of electronic components and packages. The experimental and finite element methods were employed to characterize the fracture performance of “Cu wire/solder/Cu wire” sandwich structured butt microscale solder joints with different sizes (75 to 425μm in thickness and 200 to 300μm in diameter). In particular, linear elastic and elastic-plastic fracture mechanics approaches were used to quantitatively characterize the fracture performance of the predefined crack at the solder/IMC interface of both Pb-free (Sn-3.0Ag-0.5Cu) and Pb-contained (Sn-37Pb) solder joints. The simulation results show that the crack tip stress intensity factors (SIFs) for the crack at the solder/IMC interface, both KII and KI, decrease with decreasing thickness of the solder joint and increasing the loading rate; and this is coincident with the experimental results. Also, it has been seen that KII is greater than KI probably owing to the effect of Poisson contraction of the solder metal near the interfaces. It has also been shown that with increasing thickness of the solder joint, the orientation evolution of the high energy release rate area may result in the change in fracture position from the solder/IMC interface to the middle part of the joints.

Creep behavior of Cu/Sn-3.0Ag-0.5Cu/Cu solder joints under tensile stress coupled with DC current stressing

Creep behavior of microscale Cu/Sn-3.0Ag-0.5Cu/Cu joints with different thicknesses under electric current stressing was studied in comparison with those without current stressing. The effect of current stressing on creep mechanism was characterized by calculation of the stress exponent (n) of the steady-state creep rate and fractographic analysis of fractured joints. Results show that creep curves of solder joints under current stressing consist of three distinct stages, namely the primary, secondary and tertiary stages. With increasing current density, the steady-state creep rate increases significantly while the creep lifetime decreases. The higher the electric current density is, the higher the steady-state creep rate is and the lower the creep lifetime is. The decrease of joint thickness leads to decrease in steady-state creep rate and increase in creep lifetime under current stressing. The steady-state creep rate of solder joints with a large thickness is more sensitive to the change of the applied tensile stress than that with a small thickness. The value of the stress exponent (n) varies with the current density and joint thickness. Decrease in joint thickness brings about the change of the fracture location from the middle of the solder matrix to the transition region between the solder/Cu6Sn5 interface and solder matrix, and correspondingly the fracture mode tends to transform from ductile to a mixed ductile-brittle mode of fracture.

Phase Field Simulation of Segregation of the Bi-Riched Phase in Cu/Sn-Bi/Cu Solder Interconnects under Electric Current Stressing

The migration and segregation of Bi atoms in Cu/Sn-Bi/Cu solder interconnects under electric current stressing usually induce the formation of Bi-riched layers at the anode side, which can cause the failure of solder interconnects easily. In our study, the microstructure evolution of the eutectic Sn-Bi solder in a Cu/Sn-Bi/Cu flip chip solder joint and a right-angle Cu/Sn-Bi/Cu solder interconnect is simulated by phase field method. Further, the phase field equation is coupled with the Laplace equation governing the electric potential to simulate the segregation of the Bi-riched phase in Cu/Sn-Bi/Cu solder interconnects, in which the Bi-riched phase and Sn-riched phase inhomogeneously distribute. The coarsening behavior of the eutectic microstructure can also be seen in the simulation results, and the phases grow and become coarse along multiple directions in the flip chip solder interconnect compared with that in the right-angle solder interconnect. Under electric current stressing, Bi atoms migrate towards the anode side, while Sn atoms move in the opposite direction, and finally a segregated layer of Bi-riched phase is formed at the anode side, which is consistent with the experimental studies. The phase separation first occurs near the bottom corner of the right-angle solder interconnect. Moreover, the inhomogeneity of microstructures can influence the current density distribution, and the electromigration and segregation of the Bi-riched phase can induce the increase of both the voltage and resistance.

Morphological evolution and migration behavior of the microvoid in Sn/Cu interconnects under electrical field studied by phase-field simulation

Microvoids usually form at the interface between the Sn-based solder and Cu substrate during aging process. The existence and growth (electromigration and coalescence) of the microvoids can decrease the reliability of solder joints, in particular for the joints undergoing electrical current stressing of high density. In this paper, a diffuse interface model is employed to simulate the morphological evolution and migration behavior of microvoids in the solder interconnect consisting of the Sn-based solder and Cu substrate (i.e., Sn/Cu system), under electrical fields. Simulations take into account the coupled effect of surface diffusion and electrical field. The order parameter equation and electrical field equation are solved by using the finite difference method. The validity of this method is confirmed by the agreement of the evolution of noncircular microvoids driven by surface energy with that predicted theoretically. Simulation results show that the electrical field has significant influence on the morphological evolution of microvoids. The circular microvoids migrate from the region with high electric potential to the region with low potential under electrical field. Moreover, the migration velocity of the microvoid is constant. With increasing the voltage, the migration rate increases and under a high voltage the severe migration of microvoid may lead to a failure of the solder interconnect by the electromigration or coalescence of microvoids.

Hermetic packaging of Kovar alloy and low-carbon steel structure in hybrid integrated circuit (HIC) system using parallel seam welding process

This work aims to characterize the microstructure and temperature field of the hermetic packaging structure by welding the cover made of Kovar alloy and the base made of a low-carbon low-alloy steel (i.e., #10 steel) using parallel seam welding (PSW) process. The microstructure of welded joints and distribution of elements were analyzed by scanning electron microscopy (SEM) equipped with energy dispersive spectrometer (EDS). Welding mechanism of PSW is discussed and temperature field of PSW is studied by a nonlinear transient finite element analysis. In FEM simulation, the surface contact pair is created to form weld beam and the heat generated by a pulse current is taken as a moving heat source. The results show that the maximum temperature in the weldment is 1105.3 °C, which is below the melting point of Kovar alloy and #10 steel (both in 1400~1500°C). The cross-sectional microstructure analysis results of the welded joint show that welded junction is localized between the plating layers of two base materials, both Kovar alloy and #10 steel did not melt during the welding process. Numerical simulation value of the temperature at the plating coat layer on Kovar side is larger than that on #10 steel because of boundary conditions and thermal conductivity. Same phenomenon can be seen at the location 3 mm away from the weldment. The temperature on the node of Kovar with a distance of 5 mm from the weldment is 796 °C.

Electromigration induced microstructure evolution and damage in asymmetric Cu/Sn-58Bi/Cu solder interconnect under current stressing

Abstract The electromigration induced microstructure evolution and damage in asymmetric Cu/Sn-58Bi/Cu solder interconnects were investigated by in-situ SEM observation, focused ion beam (FIB) microanalysis and finite element (FE) simulation. The SEM results show that the electromigration-induced local degradation of microstructures, i.e., segregation of Bi-rich phase and formation of microcracks, in the asymmetric solder interconnects is much severer than that in the symmetrical ones. FIB-SEM microanalysis reveals that the microregional heterogeneity in electrical resistance along different electron flowing paths is the key factor leading to non-uniform current distribution and the resultant electromigration damage. Theoretical analysis and FE simulation results manifest that the current crowding easily occurs at the local part with smaller resistance in an asymmetric solder interconnect. All results indicate that the asymmetric shape of the solder interconnect brings about the difference of the electrical resistance between the different microregions and further results in the severe electromigration damage.

Study of critical factors influencing the solidification undercooling behavior of Sn-3.0Ag-0.5Cu (SAC) lead-free solder and SAC/Cu joints

The solidification behavior of Sn-3.0Ag-0.5Cu solders and Sn-3.0Ag-0.5Cu/Cu joints was investigated by using differential scanning calorimetry (DSC) incorporated into the reflow process. The critical factors influencing the undercooling behavior of the solders and joints, such as the solder size, composition and substrate size, were examined. The results show that the type of the primary solidification phase and its volume fraction are the dominant factors affecting the undercooling of the solders and joints, and the degree of undercooling of the solders and joints increases inversely with the solder volume (joint size). For the same solder size (volume), when Cu6Sn5 is the primary solidification phase, the degree of undercooling of Sn-3.0Ag-xCu(x≥0.5wt.%)/Cu joints increases with increasing the substrate size and decreases with increasing the volume fraction of Cu6Sn5. The factors influencing the undercooling of solder joints are complicated, and the composition of the solder matrix is the dominant factor affecting the undercooling of the Sn-3.0Ag-xCu/Cu joints made of the solders with hypoeutectic compositions, while the substrate size plays the dominant role when the Cu content exceeds its eutectic composition.

Microstructure Simulation and Thermo-Mechanical Behavior Analysis of Copper Filled Through Silicon Vias Using Coupled Phase Field and Finite Element Methods

High thermo-mechanical stresses are usually induced in through silicon via (TSV) structures due to the mismatch of coefficients of thermal expansion (CTE) between copper and silicon in Cu filled TSVs, which has brought an increasing concern for the reliability problems during fabrication process and operation of electronic devices. The size, shape and orientation of Cu grains in TSVs and their effects on thermo-mechanical behavior of TSVs can not be ignored, especially with the continuous miniaturization and increasing integration of 3D ICs. In this study, the dynamic evolution characteristics of grain growth in a Cu filled TSV are simulated by a two-dimensional phase field model firstly, and then the thermo-mechanical behavior of the TSV with different grain morphologies under annealing condition is investigated by finite element method (FEM), and finally the interaction effects of grain growth and thermo-mechanical behavior in the TSV during operation of electronic devices are studied.