Geometric and material nonlinearity during the deformation of micron-scale thin-film bilayers subject to thermal loading

We study, by experiments and modeling, the linear and geometric nonlinear behavior of thin-film bilayer mechanical structures subjected to thermal loading due to combined creep and stress relaxation. On the experimental side, we designed and fabricated a series of micron-scale gold ( thick)/polysilicon(1.5 and thick) beams and plates and initially thermal cycled them between room temperature and 190°C to stabilize the gold microstructure over this temperature range. After the initial thermal cycle, they are heated to 190°C where they are relatively flat, and then cooled to 120°C. During this temperature drop the thin film structures undergo linear and possibly geometrically nonlinear deformation depending on their size. They are then held at 120°C for about four weeks. During the thermal loading history we measured, using interferometry, full-field deformed shapes of the structures, from which curvature was determined. During the isothermal hold, creep and stress relaxation are observed in all of the structures, as manifested in significant curvature changes. We observe that both material and structural phenomena contribute to the observed deformation response. The interplay between the two is apparent in the plates where the initial cooling caused them to buckle, but the creep and stress relaxation then caused them to substantially unbuckle. We attempted to model the inelastic deformation by assuming simple power-law creep in the gold , and assuming that the polysilicon did not relax at the modest temperature of 120°C. In order to accurately account for the dependence of curvature and stress on position, we carried out the calculations using the finite element method. We find that with such a simple model we can qualitatively describe all of the observed phenomena, however, some quantitative discrepancies exist. Finally, we carried out a parametric study of the effects of the structure shape and the power-law creep constants on the deformation, and studied the evolution of the stress state in the films both through the thickness and in the plane of the beams and plates. Regarding the stress state, initially a significant stress gradient exists through the thickness of the films. Over time it becomes more uniform, and nearly constant in the creeping/relaxing metal film, but the gradient remains in the polysilicon film (that does not creep or relax).