Effect of temperature and elastic constant correction on piezoresistivity of silicon nanobeams

A strain k.p model is used to investigate lattice temperature dependence of the piezoresistivity of p-doped silicon nanobeam sensor in the range of 100-600 K based on the self-consistent solution of the Schodinger and Poisson equations. Based on quasiharmonic approximation, an analytical semi-continuum model is presented to describe the effect of size and temperature on elastic constants of the silicon nanobeam sensor by using Keating model. A quantitative comparison of the piezoresistive coefficient calculated with and without considering elastic constant correction indicates it is crucial to incorporate elastic constant correction in order to quantify the piezoresistivity of the silicon nanobeam. Our calculations demonstrate that size-dependent elastic constant correction is more important than temperature-dependent elastic constant correction, however, lattice temperature can lead to considerable changes in the piezoresistive coefficient due to the large redistribution of the carriers between the heavy hole and light hole subbands, which may impact the application of the nanobeam as sensors. Fortunately, the interaction of a piezoresistive effect with hole quantization effect results in a remarkable enhanced electromechanical properties, exhibiting a promising application in mechanical sensors.