**6. Summary, conclusions and recommendations**

**Figure 20.** Snapshots of middle layers of silicon (a) [110] nanoplate without defect, (b) [110] nanoplate with a defect in the centre, (c) and (d) [100] nanoplates with patterned defects. Each individual atom is coloured by its stiffness con‐

The experimental observations, which were described earlier in this section, indicate that the defect density (*Ad/A0*) is between 0.005% to 0.12%, depending on the thickness of the silicon device layer [38]. Taking into account the range of experimentally observed defect density and the results presented in Fig. 19, one can include the effect of defects in the scale-dependent *Ê*. The results including the effects of surface elasticity, native oxide layers and fabricationinduced defects were calculated for the thicknesses that were experimentally measured. The results are presented in Fig. 21. Due to variations in the defects' density, an upper and lower limit of the influence of defects is introduced in the figure. The shaded area in the figure demonstrates the extent that defects influence *Ê*. Further quantification of the defects' density versus the thickness of nanocantilevers has to be done. It can be seen, that taking the defects into account, could explain the observed gap between experimental measurements and

tribution. Blue colours denote atoms of higher stiffness.

178 Advances in Micro/Nano Electromechanical Systems and Fabrication Technologies

theoretical calculations.

The main observations, investigations and discussions to be drawn from the chapter are summarized and concluded in this section.

Silicon based nanodevices are widely used in sensing and actuating applications. For reliable design of such devices, a thorough knowledge of the mechanical properties of these nano‐ structures is of vital importance. In order to improve the sensitivity, significant research efforts have been directed towards reducing the size of the nanostructures. However, decreasing the size causes the mechanical behavior and the elastic behavior to deviate from the bulk value, known as "scale-dependence" phenomenon.

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 experimental observations.

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 difference (Fig. 14).

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:


layershas tobe investigated.Propermeasurementsondeterminationofthe thickness andthe Young'smodulusof siliconnativeoxide layerasafunctionof siliconthickness is recommend‐ ed as further research. In this work, we assumed that the effect of native oxide on the surface elasticity of silicon, or the interface elasticity of Si-SiO2 is not significant. However, a system‐ aticcomputationalstudyontheinterfaceofSi-SiO2 isessentialtodeterminetheextenttowhich this factor affects the elastic behavior. One of the limiting factors for studying the interface of Si-SiO2 isthelackofaproperpotentialforSi-SiO2 inMDcalculations.Therefore,futureresearch for developing a reliable potential for silicon native oxide and its interface with silicon is also necessary to enable direct comparison with experiments.

In order to better explain the influence of HF defects on the effective Young's modulus of silicon nanosystems, future work on the quantitative determination of the defects and defect density as a function of silicon thickness is necessary. Moreover, the inevitable random distribution of defects, arising from nanocantilever and nanowire synthesis has to be taken into account.
