A wavelet analysis on digital microstructure in microbumps

© 2015 IEEE. Heterogeneous three-dimensional system integration is the ultimate goal for packaging and integration, where materials are pushed to their physical limits. In this context, the microstructure of packaging materials, which exhibits a multi-scale nature, will be carefully designed and tightly controlled in both manufacturing and in-service conditions to ensure long-term reliability of the electronic products. A multi-level discrete wavelet transform using the haar wavelet is conducted on the dendritic structures, simulated with a phase field model, during solidification in microbumps with different sizes and geometries. The statistical data, e.g. the mean, standard deviation and energy, of the detail coefficients from the wavelet analysis reveal a wealthy of information on the features of the dendritic structure and its evolution during solidification at multiple resolutions. The size and geometry effects on the microstructure formed in the microbumps can thus be quantified by such data. Further studies using techniques such as principle component analysis and Radon transform can be conducted to evaluate the consistence of the result

Effects of stress and electromigration on microstructural evolution in microbumps of three-dimensional integrated circuits

Due to geometric scaling, the heterogeneous and anisotropic microstructures present in through-silicon vias and microbumps must be considered in the stress management of 3-D integrated circuits. In this paper, a phase field model is developed to investigate the effects of stress and electromigration on microstructural evolution in a Cu/Sn-microbump/Cu structure at 150 °C. External compressive stress is observed to accelerate the growth of Cu3Sn grains and cause the separation of continuous interfacial Cu 6 Sn 5 grains by β-Sn grains, whereas tensile stress promotes the growth of Cu 6 Sn 5 grains and the formation of a continuous Cu 6 Sn 5 layer. The roughness of the β-Sn-Cu 6 Sn 5 interface under compressive stress is greater than that under tensile stress. The morphological evolution of the β-Sn grains is also affected by stress. An external shear or compressive stress favors the growth of the β-Sn grains with their c-axis particular to the Y -direction. Furthermore, the interdiffusion flux driven by electromigration increases the roughness of the interfacial Cu 6 Sn 5 grains at the cathode. The strain caused by electromigration results in larger β-Sn grains, enabling faster interdiffusion along the current direction. The preferential growth of the β-Sn grains under stress or electromigration decreases the shear modulus of microbumps

Processing-structure-protrusion relationship of 3D Cu TSVs: control at the atomic scale

A phase-field-crystal model is used to investigate the processing-structure-protrusion relationship of blind Cu through-silicon vias (TSVs) at the atomic scale. A higher temperature results in a larger TSV protrusion. Deformation via dislocation motion dominates at temperatures lower than around 300∘C, while both diffusional and dislocation creep occur at temperatures greater than around 300∘C. TSVs with smaller sidewall roughness Ra and wavelength λa exhibit larger protrusions. Moreover, different protrusion profiles are observed for TSVs with different grain structures. Both protrusions and intrusions are observed when a single grain is placed near the TSV top end, while the top surface protrudes near both edges when it contains more grains. Under symmetric loading, coalescence of the grains occurs near the top end, and a symmetric grain structure can accelerate this process. The strain distributions in TSVs are calculated, and the eigenstrain projection along the vertical direction can be considered an index to predict the TSV protrusion tendency

Protrusion of Cu-TSV under different strain states

A phase-field-crystal (PFC) model is used to investigate the protrusion of blind TSVs under different strain states. The direction of loading applied to the TSVs has an effect on the protrusion, which is closely related to the copper grains and their orientations at the TSV edges. A nonlinear relation between protrusion and strain rate has been found, which can be explained by different mechanisms of deformation. A higher strain occurring near the top end of the TSVs leads to a larger protrusion of the bind TSVs

Mechanisms of copper protrusion in through-silicon-via structures at the nanoscale

Thermal stress-induced copper protrusion is frequently observed in through-silicon-vias (TSVs) based three-dimensional (3D) system integration. In this study, the detailed process of Cu protrusion is reproduced on the atomic scale using a two-mode phase-field-crystal (PFC) model, and the mechanisms of protrusion are identified. To simulate thermal loading, a “penalty term” is added to the governing equation of the PFC model. The application of loading on the TSVs induces copper grain deformation and grain boundary migration at the nanoscale. Furthermore, the simulation results suggest that the Cu protrusion is resulted from diffusional creep, involving both Nabarro-Herring creep and Coble creep. The obtained power index of diffusional creep is around 2.16, suggesting that lattice diffusion contributes more to protrusion than grain boundary diffusion does. The protrusion height in micron-scale TSVs predicted by extrapolating the relationship between the protrusion height and diameter of nanoscale TSVs agrees with the experimental data

Multiscale microstructures and microstructural effects on the reliability of microbumps in three-dimensional integration

The dimensions of microbumps in three-dimensional integration reach microscopic scales and thus necessitate a study of the multiscale microstructures in microbumps. Here, we present simulated mesoscale and atomic-scale microstructures of microbumps using phase field and phase field crystal models. Coupled microstructure, mechanical stress, and electromigration modeling was performed to highlight the microstructural effects on the reliability of microbumps. The results suggest that the size and geometry of microbumps can influence both the mesoscale and atomic-scale microstructural formation during solidification. An external stress imposed on the microbump can cause ordered phase growth along the boundaries of the microbump. Mesoscale microstructures formed in the microbumps from solidification, solid state phase separation, and coarsening processes suggest that the microstructures in smaller microbumps are more heterogeneous. Due to the differences in microstructures, the von Mises stress distributions in microbumps of different sizes and geometries vary. In addition, a combined effect resulting from the connectivity of the phase morphology and the amount of interface present in the mesoscale microstructure can influence the electromigration reliability of microbumps

Multiscale microstructures and microstructural effects on the reliability of microbumps in three-dimensional integration

The dimensions of microbumps in three-dimensional integration reach microscopic scales and thus necessitate a study of the multiscale microstructures in microbumps. Here, we present simulated mesoscale and atomic-scale microstructures of microbumps using phase field and phase field crystal models. Coupled microstructure, mechanical stress, and electromigration modeling was performed to highlight the microstructural effects on the reliability of microbumps. The results suggest that the size and geometry of microbumps can influence both the mesoscale and atomic-scale microstructural formation during solidification. An external stress imposed on the microbump can cause ordered phase growth along the boundaries of the microbump. Mesoscale microstructures formed in the microbumps from solidification, solid state phase separation, and coarsening processes suggest that the microstructures in smaller microbumps are more heterogeneous. Due to the differences in microstructures, the von Mises stress distributions in microbumps of different sizes and geometries vary. In addition, a combined effect resulting from the connectivity of the phase morphology and the amount of interface present in the mesoscale microstructure can influence the electromigration reliability of microbumps

Quantitative characterisation of multi scale microstructures in interconnects for multi-chip stacking

Geometric scaling of the conventional silicon MOSFET following Moore’s law down to the 14nm or even lower dimension technology node presents many fundamental challenges. Therefore, three-dimensional integrated circuit (3-D IC) architectures emerge as a game changer to the continuation of the Moore’s law. Staking multiple chips by the through-silicon-vias and microbumps has been proved to be a viable technology. However, 3-D ICs are facing challenges in design, materials and reliability issues. This paper introduces a microstructure-based multiphysics modeling platform that integrates multiscale microstructural evolution modeling, quantification of microstructural features, and modeling of microstructure-level responses of the 3-D interconnects under thermal, mechanical and electrical fields. Multiscale microstructures formed in the interconnects during processes of solidification, aging, and electromigration under effects from geometries and external stresses are presented first. Different methods such as singular value decomposition (SVD), wavelet multi-resolution analysis, and radon transformation are then used to quantification of the microstructural characteristics in 3-D interconnects. Based on the quantified microstructural index, an effort to establish a microstructure-interconnect performance relationship is introduced. Finally, the response of microstructure under multiphysics fields and its implications to design reliable 3-D interconnects are discussed

A method for quantification of the effects of size and geometry on the microstructure of miniature interconnects

Because the heterogeneity of microstructure has significant effects on the material properties of ultrafine interconnects, it should be quantified, to facilitate high-fidelity prediction of reliability. To address this challenge, a method based on autocorrelation and singular value decomposition is proposed for quantitative characterization of microstructure. The method was validated by developing a quantitative relationship between reported microstructure and tensile strength for SnAgCuRE solders reported in the literature. The method was used to study the effects of size and geometry in ultrafine Sn37Pb interconnects on microstructure and von Mises stress, which were obtained simultaneously by coupling a phase-field model with an elastic mechanical model. By use of this method the degree of heterogeneity of the microstructure in relation to preferred growth directions of the phases was quantified by use of a scalar microstructure index. It was found that microstructure heterogeneity increases with decreasing standoff height, and is higher for hourglass-shaped solder joints. The average von Mises stress was found to be positively related to the microstructure index. The strong correlation between microstructure index and average von Mises stress was confirmed by nonlinear regression analysis using an artificial neural network. This indicates that the mechanical behavior of ultrafine interconnects can be predicted more accurately on the basis of the microstructure index

Microstructural evolution and protrusion simulations of Cu-TSVs under different loading conditions

Thermal stress-induced protrusions of copper through-silicon-vias (Cu-TSVs) during thermal processing pose substantial reliability concerns in three-dimensional (3D) system integration. In this study, a phase-field-crystal (PFC) model is used to investigate the protrusions and microstructural evolutions of blind Cu-TSVs under different loading conditions. Protrusions are observed only when the TSVs are under εx, εy, and γxy, whereas no protrusions are observed when the TSVs are subjected to pure shear strains γyx. The simulation results suggest that the grains in the top layer of a TSV contribute more to both the protrusion profile and the protrusion height than the grains in the lower layers. Moreover, the protrusion is larger when the misorientation among the grains is larger and the grain size along the y-direction is smaller. In addition, a phenomenological model linking protrusion and microstructural factors and a visual guide from the viewpoint of plastic flow are provided to understand the origins of Cu-TSV protrusion