Three-point bending analysis of doubly clamped silicon nanowire beams; Young's modulus, initial stress, and crystal orientation

A non-linear model is introduced describing the force-deflection relation of doubly clamped beams, including initial stress. Several approximations for the exact model are developed and compared, revealing the importance of considering the initial stress during 3-point bending measurements analysis. A novel approximation is found to be better than others, and both the exact model and this approximation are in perfect agreement with finite element simulations. A brief experimental example of silicon nanowires is presented in which the Young's modulus, the initial stress, and the crystallographic growth orientation are extracted by 3-point bending analysis.