On the Assumption Used for the Time-Dependent Warpage Analysis of Encapsulated Semiconductor Packages Available to Purchase

When a linear viscoelastic (LVE) analysis is to be implemented, the time-dependent shear and bulk moduli, $G(t)$ and $K(t)$⁠, are required. In practice, however, only the time-dependent behavior under uniaxial loading, $E(t)$⁠, is often available for the analysis simply because it can be measured routinely using commercial tools such as a dynamic mechanical analyzer (DMA) or a universal tensile testing machine. When only $E(t)$ is available for an LVE analysis, some assumption has to be made to satisfy the input requirements of an LVE analysis. The most widely used assumption is “time-independent” Poisson's ratio, which implies that the approximated relaxation behavior under shear and hydrostatic loadings would be proportional to the relaxation behavior under uniaxial loading. The effect of the assumption on warpage prediction is investigated. First, the experimentally measured Young's and bulk modulus master curves, $E(t)$ and $K(t)$⁠, are presented, from which all viscoelastic properties are determined. The approximated $G(t)$ and $K(t)$ master curves are then calculated from the experimentally measured $E(t)$ and the assumed constant Poisson's ratios. Both sets of properties are used in two critical applications to examine the effect of the assumption on warpage prediction quantitatively: (1) fan-out wafer-level package (FO-WLP) and (2) stacked-die package. Some modeling guidelines are also provided when the assumption must be used.