A nonlinear stiffness softening mechanism for low-bias, high-sensitivity MEMS accelerometers with extended dynamic range

The small dimensions of microfabricated devices present challenges in applications such as inertial sensing, where a larger proofmass is necessary for enhanced sensitivity. An effective approach to addressing the limitations of linear sensing is to use nonlinear mechanisms that adapt the device's response according to different operating conditions. This paper introduces a new nonlinear spring mechanism for use in microsensors that harnesses the buckling phenomenon to achieve stiffness softening. The proposed mechanism utilizes a micro-arm to apply an eccentric axial load to an inclined beam, causing it to buckle in a controlled manner under a specified load. Once buckled, linear springs dominate the response of the system. We demonstrate that this method results in a smaller bias displacement compared to previously reported techniques based on snap-through behaviour, leading to potential reductions in device size and improvements in operational range. The behaviour is analytically modelled and verified through simulations. A prototype device was designed and microfabricated to experimentally validate the design principles. Compared to pre-curved nonlinear springs, the proposed design results in an 11-fold reduction in bias force, a 100-fold reduction in bias displacement, and a reduction in mechanical stiffness by a factor of 520. These results were verified through experiments conducted on a microfabricated accelerometer with an on-chip optical interferometer. Test results reveal an extended linear range of better than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>150</mml:mn> <mml:mspace></mml:mspace> <mml:mi>mg</mml:mi></mml:mrow> </mml:math> , a bias force of 0.3 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>mN</mml:mi></mml:math> , and a bias displacement of 10 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>μm</mml:mi></mml:math> , measured with an integrated optical interferometer with a displacement noise floor of 40 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>pm</mml:mi> <mml:mo>/</mml:mo> <mml:msqrt><mml:mi>Hz</mml:mi></mml:msqrt> </mml:mrow> </mml:math> at 2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Hz</mml:mi></mml:math> and sensitivity of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup><mml:mrow><mml:mn>194</mml:mn></mml:mrow> <mml:mo>∘</mml:mo></mml:msup> <mml:mo>/</mml:mo> <mml:mi>mg</mml:mi></mml:mrow> </mml:math> .