Analysis of local deformation effects in resistive strain sensing of a submicron-thickness AFM cantilever

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Incorporating resistive strain-sensing elements into MEMS devices is a long-standing approach for electronic detection of the device deformation. As the need for more sensitivity trends the device dimensions downwards, the size of the strain-sensor may become comparable to the device size, which can have significant impact on the mechanical behaviour of the device. To study this effect, we modelled a submicron-thickness silicon nitride AFM cantilever with strain-sensing element. Using finite element analysis, we calculated the strain in the sensor elements for a deflected cantilever. The sensor element contributes to a local stiffening effect in the device structure which lowers the strain in the sensor. By varying the sensor geometry, we investigated the degree to which this effect impacts the strain. Minimizing the sensor size increases the strain, but the reduction in sensor cross-sectional area increases the resistance and expected sensor noise. The optimal sensor geometry must therefore account for this effect. We used our analysis to optimize geometric variations of nanogranular tunnelling resistor (NTR) strain sensors arranged in a Wheatstone bridge on a silicon nitride AFM cantilever. We varied the dimensions of each sensor element to maintain a constant cross-sectional area but maximize the strain in the sensor element. Through this approach, we expect a 45% increase in strain in the sensor and corresponding 20% increase in the Wheatstone bridge signal. Our results provide an important consideration in the design geometry of resistive strainsensing elements in MEMS devices.