Bent-beam strain sensors

We examine a new class of sensitive and compact passive strain sensors that utilize a pair of narrow bent beams with an apex at their mid-points. The narrow beams amplify and transform deformations caused by residual stress into opposing displacements of the apices, where vernier scales are positioned to quantify the deformation. An analytical method to correlate vernier readings to residual stress is outlined, and its results are corroborated by finite-element modeling. It is shown that tensile and compressive residual stress levels below 10 MPa, corresponding to strains below 6×10^-5 can be measured in a 1.5-μm-thick layer of polysilicon using a pair of beams that are 2 μm wide, 200 μm long, and bent 0.05 radians (2.86°) to the long axis of the device. Experimental data is presented from bent-beam strain sensors that were fabricated from boron-doped single crystal silicon using the dissolved wafer process and from polycrystalline silicon using surface micromachining. Measurements from these devices agree well with those obtained by other methods