Topology optimization for piezoresistive nanomechanical surface stress sensors in anisotropic 〈111〉 orientations

Abstract

Microelectromechanical systems (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. The properties of the immobilization layer—the functional coating on the sensor—are parametrically varied to explore optimal designs. 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. In addition, we scrutinize the effects of piezoresistor geometry and find that the optimized designs depend asymmetrically on the piezoresistor position, a characteristic stemming from the anisotropic elasticity in 〈111〉 orientations. These optimized designs, verified by finite element analysis (FEA), demonstrate a notable improvement in sensitivity of more than 20% when benchmarked against traditional rectangular designs and equivalent optimized designs in conventional orientations, thereby validating the effectiveness of the present model. This study provides crucial knowledge for the design of piezoresistive biosensors, facilitating more efficient geometric design in future sensor development.