Position-dependent deflection (PPD) of a nanobeam: a new method to determine the Young's modulus of nanoscale matter

In this approach, a nanowire beam is fixed at two ends and an AFM is used to apply a force F(x) where x locates the position along the beam and the beam deflection $\delta $z(x) is measured simultaneously. This situation is realized by placing a nanobeam over a trench fabricated on a Silicon substrate via photolithography followed by metal evaporation, lift-off and XeF$_{2}$ etching. The AFM tip force-distance curve is first obtained from experiments on the rigid substrate. The slope of the AFM force-distance obtained when the tip contacts the beam is then measured and the Young's modulus Y is obtained from the change in slope using the Euler-Bernoulli (E-B) equation. The beam dimensions are also required: the beam height and length via AFM and the beam width and length by SEM. We believe this method can be used in any other nano-beam systems to measure the Young's modulus. Results for rectangular ZnS beams ($\sim $100nm x 100 nm x 5$\mu $m long) will be presented that demonstrate the potential for this method. Values for Y lower than reported for the bulk are obtained (i.e. Y(nano) $\sim $ 70{\%} Y(bulk)). This work was supported, in part, by NSF-NIRT DMR-0304178