Using Micro-Raman Spectroscopy to Assess MEMS Si/SiO2 Membranes Exhibiting Negative Spring Constant Behavior

Abstract

We introduce a novel micro-mechanical structure that exhibits two regions of stable linear positive and negative stiffness. Springs, cantilevers, beams and any other geometry that display an increasing return force that is proportional to the displacement can be considered to have a "Hookean" positive spring constant, or stiffness. Less well known is the opposite characteristic of a reducing return force for a given deflection, or negative stiffness. Unfortunately many simple negative stiffness structures exhibit unstable buckling and require additional moving components during deflection to avoid deforming out of its useful shape. In Micro-Electro-Mechanical Systems (MEMS) devices, buckling caused by stress at the interface of silicon and thermally grown SiO2 causes tensile and compressive forces that will warp structures if the silicon layer is thin enough. The 1 mm 2 membrane structures presented here utilizes this effect but overcome this limitation and empirically demonstrates linearity in both regions. The Si/SiO2 membranes presented deflect ~17 μm from their pre-released position. The load deflection curves produced exhibit positive linear stiffness with an inflection point holding nearly constant with a slight negative stiffness. Depositing a 0.05 μm titanium and 0.3 μm layer of gold on top of the Si/SiO2 membrane reduces the initial deflection to ~13.5 μm. However, the load deflection curve produced illustrates both a linear positive and negative spring constant with a fairly sharp inflection point. These results are potentially useful to selectively tune the spring constant of mechanical structures used in MEMS. The structures presented are manufactured using typical micromachining techniques and can be fabricated in-situ with other MEMS devices.

Isolating the negative stiffness region of a buckled Si/SiO2membrane

“…Recently, buckling in MEMS has been used for its ability to display linear regressive spring constant behavior [6], similar to behavior seen in the disk spring [7], which can be explained by the following. Suppose that a buckled membrane is loaded normal to the planar surface.…”