In silico modeling and investigation of self-heating effects in composite nano cantilever biosensors with integrated piezoresistors

Over the years, piezoresistive nano cantilever sensors have been extensively investigated for various biological sensing applications. Piezoresistive cantilever sensor is a composite structure with different materials constituting its various layers. Design and modeling of such sensors become challenging since their response is governed by the interplay between their geometrical and constituent material parameters. Even though, piezoresistive nano cantilever biosensors have several advantages, they suffer from a limitation in the form of self-heating induced inaccuracy which is seldom considered in design stages. Although, a few simplified mathematical models have been reported which incorporate the self-heating effect, several assumptions made in the modeling stages result in inaccuracy in predicting sensor terminal response. In this paper, we model and investigate the effect of self-heating on the thermo-electro-mechanical response of piezoresistive cantilever sensors as a function of the relative geometries of the piezoresistor and the cantilever platform. Finite element method (FEM) based numerical computations are used to model the target-receptor interactions induced surface stress response in steady state and maximize the electrical sensitivity to thermal sensitivity ratio of the sensor. Simulation results show that the conduction mode of heat transfer is the dominant heat transfer mechanism. Furthermore, the isolation and immobilization layers play a critical role in determining the thermal sensitivity of the sensor. It is found that the shorter and wider cantilever platforms are more suitable to reduce self-heating induced inaccuracies. In addition, results depict that the piezoresistor width plays a more dominant role in determining the thermal drift induced inaccuracies compared to the piezoresistor length. It is found that for surface stress sensors at large piezoresistor width, the electrical sensitivity to thermal sensitivity ratio improves.