Deformation and structural stability of layered plate microstructures subjected to thermal loading

We study the deformation and stability of gold-polysilicon MEMS plate microstructures fabricated by the MUMPS surface micromachining process and subjected to uniform temperature changes. We measured, using an interferometric microscope, full-field deformed shapes of a series of square and circular gold (0.5 μm thick)/polysilicon (1.5 μm thick) plate microstructures with characteristic lengths l (square side length and circle diameter) ranging from l=150 to 300 μm. From these measurements we determined the pointwise and average curvature of the deformed plates. Although the curvature generally varies with position, the deformation response of the plates can be broadly characterized in terms of the spatial average curvature as a function of temperature change. In terms of this, three deformation regimes were observed: (i) linear thermoelastic response independent of plate size; (ii) geometrically nonlinear thermoelastic response that depends on plate size; and (iii) bifurcations in the curvature-temperature response that also depend on plate size. We modeled the deformation response both analytically and with the finite element method; in the former we assume spatially constant curvature, while in the latter, we relax this assumption. Good qualitative and quantitative agreement is obtained between predictions and measurements in all three deformation regimes, although the details of bifurcation are less accurately predicted than the linear and nonlinear response. This is attributed to their strong sensitivity to slight imperfections, which is discussed in some detail. Good agreement is also obtained between measurements and predictions of the spatial nonuniformity of the curvature across the plate. Although it is not the focus of this study, the predictions, when coupled with curvature measurements, can be used inversely to determine elastic and thermal expansion properties of the materials in a layered plate microstructure.