The thermomechanical behavior of multilayer structures is a subject of perennial interest. Stoney’s
formula has long been one of the most important tools for understanding thermomechanical stress
for single-layered structures like spin-coated polyimides or deposited metal thin film on substrates.
In today’s microelectronics, however, as multilayer substrates have become widely available, the
‘‘modified version’’ of Stoney’s formula for multilayer applications is not only useful but necessary.
While the majority of reports in the literature have focused on single-layer analysis, in this study, we
examined an extended usage of Stoney’s formula for multilayer analysis. A simple model, the
multilayer-modified Stoney’s formula, which predicts the stress contribution of each individual
layer is proposed and verified through experiments and numerical analysis. Using various kinds of
materials employed in a typical lamination-based multichip module technology, the
thermomechanical behavior of the lamination-based multilayer substrates was measured by a laser
profilometry during thermal cycling. The measured values were compared with calculated values
using the multilayer-modified Stoney’s formula.