Modeling of stress-induced curvature in surface-micromachined devices

This paper compares measured to modeled stress-induced curvature of simple piston micromirrors. Two similar flexure-beam micromirror designs were fabricated using the 11th DARPA-supported Multi-User MEMS Processes (MUMPs) run. The test devices vary only in the MUMPs layers used for fabrication. In one case the mirror plate (upper electrode) is the 1.5 mu m thick Poly2 layer. The other mirror design employs stacked Poly1 and Poly2 layers for a total thickness of 3.5 mu m. Both mirror structures are covered with the standard MUMPs metallization of similar to 200 Angstrom of chromium and 0.5 mu m of gold. Curvature of these devices was measured to within +/- 5 nm with a computer controlled microscope laser interferometer system. As intended, the increased thickness of the stacked polysilicon layers reduces the mirror curvature by a factor of 4. The two micromirror designs were modeled using IntelliCAD, a commercial CAD system for MEMS. The basis of analysis was the finite element method. Simulated results using MUMPs II film parameters showed qualitative agreement with measured data, but obvious quantitative differences. Subsequent remeasurement of the metal stress and use of the new value significantly improved model agreement with the measured data. The paper explores the effect of several film parameters on the modeled structures. Implications for MEMS film metrology, and test structures are considered.