Finite Element Modeling Strategies for Studying Mechanical Design Tradeoffs in Heterogeneously Integrated Packages

Abstract

The limits of area scaling leading to a slowdown of Moore’s law dictum on transistor scaling has driven significant 2.5D and 3D heterogeneously integrated package development. A general modeling strategy that enables efficient design trade-offs decisions to steer early product development of complex heterogeneously integrated packages is largely missing in the existing literature. Efficient numerical modeling strategies are necessary to carry out fast analysis, which in turn will enable quick early design decisions. Since finite element analysis is the most common numerical modeling technique for electronic packages, in this paper, finite element modeling strategies are systematically developed that have general applicability for complex heterogeneously integrated packages. The challenges addressed in the paper include (1) CAD geometry import, cleanup, model construction, and verification (2) structural modeling complexity and analysis speed trade-offs, including the choice of using shell elements instead of solid elements, and using beam elements for vertical interconnects (3) using rigid bars, beams and springs to interconnect various components modeled using shell or solid elements and (4) analyzing mechanical responses driven by the heatsink assembly process through enforced forces versus enforced displacements. The computational cost of the modeling alternatives is systematically evaluated on a complex heterogeneously integrated package consisting of an optical module mounted on a substrate using elastomeric contacts and integrated with a large Field Programmable Gate Array (FPGA) die assembled onto the substrate using C4 solder joints. The final modeling approximations ensure analysis times of the order a minute on a desktop computer to enable quick early design decisions to be influenced with "reasonable" design-oriented analysis accuracy. A parametric study is then carried out by systematically evaluating heatsink clamping spring design choices and exploring their impact on the deformation of the package. The modeling approach developed here is expected to be generally valid for making early design decisions in a wide variety of heterogeneously integrated packages that are currently being developed in the industry.