Quantifying the size-dependent effect of the residual surface stress on the resonantfrequencies of silicon nanowires if finite deformation kinematics are considered

Abstract

There are two major objectives to the present work. The first objective is to demonstratethat, in contrast to predictions from linear surface elastic theory, when nonlinear, finitedeformation kinematics are considered, the residual surface stress does impact the resonantfrequencies of silicon nanowires. The second objective of this work is to delineate,as a function of nanowire size, the relative contributions of both the residual(strain-independent) and the surface elastic (strain-dependent) parts of the surface stress tothe nanowire resonant frequencies. Both goals are accomplished by using the recentlydeveloped surface Cauchy–Born model, which accounts for nanoscale surface stressesthrough a nonlinear, finite deformation continuum mechanics model that leads to thesolution of a standard finite element eigenvalue problem for the nanowire resonantfrequencies. In addition to demonstrating that the residual surface stress does impact theresonant frequencies of silicon nanowires, we further show that there is a strong sizedependence to its effect; in particular, we find that consideration of the residual surfacestress alone leads to significant errors in predictions of the nanowire resonant frequency,with an increase in error with decreasing nanowire size. Correspondingly, thestrain-dependent part of the surface stress is found to have an increasingly importanteffect on the resonant frequencies of the nanowires with decreasing nanowire size.