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

A strain k⋅p model is used to investigate lattice temperature dependence of the piezoresistivity of p-doped silicon nanobeams in the range of 100–600 K, based on the self-consistent solution to the coupled Schrödinger–Poisson equations. According to quasiharmonic approximation, an analytical semicontinuum atomistic lattice model is presented to describe the effect of size and temperature on elastic constants of the silicon nanobeam by using the anharmonic Keating model. The result presented here indicates the piezoresistive coefficient of the silicon nanobeam, which is dependent on quantum confinement effects, has a negative and nonlinear temperature coefficient. A quantitative comparison of the piezoresistive coefficients calculated with and without considering the elastic constant correction shows that it is crucial to incorporate the size-dependent elastic constant correction in order to quantify the piezoresistivity.