**Acknowledgements**

Two approaches have been explored to study scale-dependent elastic behavior: experimental and theoretical, however a discrepancy exists between the two approaches. The scale at which the scale-dependence starts in experimental measurements is different from that estimated theoretically. Various techniques involving resonance frequency, tensile tests in TEM, atomic force microscopy and nanoindentation have been used to characterize the effective Young's modulus of silicon nanocantilevers and nanowires. Each method involves different assump‐ tions, sources of errors and interpretations. We proposed the use of the electrostatic pull-in instability method in order to avoid most of the issues with other existing methods, as described in Section 3. Using molecular dynamics calculations and the semi-continuum approaches (Section 4) the surface effects on the elastic behavior of silicon nanocantilevers have been investigated. Direct comparison between the surface effects simulations with experi‐ mental data from the reliable EPI method showed that although surface effects influence the effective Young's modulus of silicon to some extent, they alone are insufficient to explain the

180 Advances in Micro/Nano Electromechanical Systems and Fabrication Technologies

Another important influence is caused by native oxide layers that exist at the surfaces of the silicon nanocantilevers. The native oxide layers influence the effective Young's modulus of silicon in 3 ways. Through: 1) its distinct elastic response; 2) unknown interactions between the oxide and the silicon at the interface; and, 3) consumption of silicon during oxidation; during oxidation for every unit of silicon oxide 0.44 units of the silicon surface is "consumed". We assumed that the effect of native oxide on the surface elasticity of silicon, or the interface elasticity of Si-SiO2, is not significant compared to the distinct elastic response of the native oxide. Taking the native oxide layers into consideration reduced the difference between experimental measurements and theoretical predictions, yet there was still a considerable

One of the important issues which was confirmed experimentally, but had not previously been considered in theoretical modeling, was accounting for the fact that experimentally tested nanocantilevers and nanowires are not defect free. Molecular dynamics calculations have been carried out to determine the effects of defects on the effective Young's modulus of silicon nanocantilevers. The conclusion is that the scale effect observed in silicon nanocantilevers can be explained by a contribution of surface effects, native oxide layers and defects. Taking these into account, the gap between the experimental measurements and theory can be closed.

There are a number of issues that are recommended for future research on the size effects:

**•** The electrostatic pull-in instability method has its own limitations; the application of electrostatic load requires a fairly conductive device and a counter electrode. This implies that the method is only applicable to conductive materials. Moreover, stiction prevention by additional stopper is necessary to ensure the release of the cantilever for multiple measurements. Another fact, that is believed to be minor, but has to be investigated in detail, is the influence of the electric field (electrostatic charges) used in EPI method on the measured value of the effective Young's modulus of nanocantilevers and nanowires.

**•** Future work on the silicon native oxide layer and its properties will help to explain in more detail the observed size effects. The scale-dependent elastic behavior of silicon native oxide

experimental observations.

difference (Fig. 14).

This book chapter was financially supported by Enabling Technology program (ETP) for Materials Technology, Dr. L.J.M.G. Dortmans, of Netherlands Organization for Scientific Applied Research (TNO). The authors would like to thank Dr. T.S.D. O'Mahoney and Dr. A. Bossche for their supports, helps and valuable suggestions.
