Prediction of microelectronic substrate warpage using homogenized finite element models

The focus of this study was to numerically predict effective thermo-mechanical properties and substrate warpage of high-density microelectronic substrates used in organic CPU packages. Microelectronic substrates are typically composed of several polymer, fiber-weave, and copper layers and are filled with a variety of complex features, such as electric traces, plated-through-holes, micro-vias, and adhesion holes. When subjected to temperature changes, these substrates may warp, driven by the mismatch in coefficients of thermal expansion (CTE) of the constituent materials. This study focused on predicting substrate warpage in an isothermal condition. The numerical approach consisted of three major tasks: estimating homogenized (effective) thermo-mechanical properties of the features; calculating effective properties of discretized layers using the effective properties of the features; and assembling the layers to create two-dimensional (2D) finite element (FE) plate models and to calculate warpage of the substrates. The effective properties of the features were extracted from three-dimensional (3D) unit cell FE models, and closed-form approximate expressions were developed using the numerical results, curve fitting, and some simple bounds. The numerical approach was applied to predict warpage of production substrates, analyzed, and validated against experimentally measured stiffness and CTEs. In this paper, the homogenization approach, numerical predictions, and experimental validation are discussed.