Analytical Modeling of Cyclic Thermal Stress and Strain in Plated-Through-Vias With Defects

A previously published analytical model for thermal stress and strain in idealized plated-through-vias (PTVs) has been adapted to conduct elastic-plastic analyses of vias with geometric defects using elastic stress concentration factors calculated earlier. The von Mises stress amplitude, at the mid-plane of the perfect via and at the defect (Δσ
₀
and Δσ, respectively), and the cumulative plastic von Mises strain, also at the mid-plane of a perfect via and at a defect (ε
₀
^pl
and ε
^pl
, respectively), compared well with results of finite element analyses (FEAs). Four types of PTV defects were evaluated: barrel thickness reduction, occasional waviness, continuous waviness, and wicking. This model provides a relatively simple alternative to FEA to calculate stresses and strains in vias with defects as well as in perfect vias subjected to multiple thermal cycles. This model provides a tool to investigate quickly the influence of possible PTV design dimensions and defects under thermal cycling conditions (i.e., which are particularly damaging in a given situation). It is much easier than FEA for parametric studies like this. It also provides a means for calculating damage metrics, such as the cumulative von Mises strain, which can then be empirically correlated with the cycles to failure data from thermal cycling tests of PTVs.