Topology optimization for piezoresistive nanomechanical surface stress sensors in anisotropic <111> orientations.

MEMS-based piezoresistive nanomechanical sensors are compact sensing platforms widely employed in vapor sensing, environmental monitoring, and biosensing. Despite their extensive utility, their lower sensitivity relative to their optical readout counterparts has been a limiting factor, constraining the wider application of this technology. Prior research has suggested that alternative silicon orientations, such as 〈111〉 orientations in (110) wafers, can significantly improve the sensitivity of piezoresistive sensors. However, the complexity of optimizing two-dimensional stress distribution and handling anisotropic elasticity has made device design a formidable task, leaving this promising avenue largely unexplored. To address this challenge, we employ density-based topology optimization to generate a series of optimized designs for piezoresistive nanomechanical sensors manufactured along 〈111〉 orientations. Our study reveals a transition in optimized designs from a double-cantilever configuration to a suspended platform configuration, dictated by the stiffness ratio between the immobilization layer and the silicon layer. This transition is attributed to the shift in the neutral plane and the prevailing stress relaxation mechanism.