A nested finite element methodology for virtual qualification of area-array microelectronic interconnect assemblies.

摘要

A N&barbelow;ested F&barbelow;inite E&barbelow;lement M&barbelow;ethodology (NFEM) is proposed in this dissertation, for capturing localized stress gradients in complex structures, without a significant increase in computational time and degrees of freedom. A single main finite element is refined locally by superposing nested sub-elements to capture local gradients of stress and strain. The local discretization offers a distinct advantage in terms of reducing the degrees of freedom as no further sub-division of a main element is required except at the point of interest. This innovative discretization is made possible because of the re-formulation of the potential energy with a “cut-and-replace” technique, which involves replacing a cut volume of a main element with an equivalent volume of a nested sub-element containing enhanced displacement fields. The nested sub-elements, apart from capturing the sharp gradients of the displacement field, can also be used to model material heterogeneities. The material of the sub-elements could range from plastic domains to voids to rigid inclusions.; The NFEM tool is developed to perform thermomechanical elastic-creep analysis and vibration-induced elasto-plastic analysis of two emerging area-array interconnect assemblies: flip chip on board assembly (FCOB) and chip scale ball grid array assembly (CSP-BGA). The various practical applications of the nested sub-element method are illustrated through these case studies. This dissertation focuses on the durability of solder interconnects as these are potential weak links in the assemblies. Load-stepping and/or time-stepping techniques are used to obtain piece-wise linear approximations to the nonlinear elasto-plastic and elastic-creep deformation histories. The stress, strain and energy density fields are calculated for each increment and are accumulated throughout the loading and unloading history. An energy partitioning fatigue model is used to estimate fatigue endurance of the solder joint, based on cyclic energy densities obtained from NFEM. The accuracy of the proposed method is found to be comparable to conventional finite element results (generated with significantly higher mesh density) and, where applicable, to experimental results. Computational time of NFEM for the case studies analyzed in this dissertation is observed to be significantly lower than conventional finite element analysis. This work also demonstrates the ability of NFEM to model solder defects such as (a) voids, (b) solder volume and (c) component misalignment.