Relative stiffness of irregularly perforated plates

The size-dependent elastic behavior of silicon nanocantilevers and nanowires, specifically the effective Young's modulus, has been determined by experimental measurements and theoretical investigations. The size dependence becomes more significant as the devices scale down from micro-to nano-dimensions, which has mainly been attributed to surface effects. However, discrepancies between experimental measurements and computational investigations show that there could be other influences besides surface effects. In this paper, we try to determine to what extent the surface effects, such as surface stress, surface elasticity, surface contamination and native oxide layers, influence the effective Young's modulus of silicon nanocantilevers. For this purpose, silicon cantilevers were fabricated in the top device layer of silicon on insulator (SOI) wafers, which were thinned down to 14 nm. The effective Young's modulus was extracted with the electrostatic pull-in instability method, recently developed by the authors (H Sadeghian et al 2009 Appl. Phys. Lett. 94 221903). In this work, the drop in the effective Young's modulus was measured to be significant at around 150 nm thick cantilevers. The comparison between theoretical models and experimental measurements demonstrates that, although the surface effects influence the effective Young's modulus of silicon to some extent, they alone are insufficient to explain why the effective Young's modulus decreases prematurely. It was observed that the fabrication-induced defects abruptly increased when the device layer was thinned to below 100 nm. These defects became visible as pinholes during HF-etching. It is speculated that they could be the origin of the reduced effective Young's modulus experimentally observed in ultra-thin silicon cantilevers.

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“…In order to approximate the effect of defects and pinholes on the Ẽ, an analytical solution, described in [45] is used as…”

Section: Fabrication-induced Defectsmentioning

confidence: 99%

Effects of size and defects on the elasticity of silicon nanocantilevers

Sadeghian

Yang

Goosen

et al. 2010

J. Micromech. Microeng.

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“…As shown in figures 4 and 5 the MD results were compared with an analytical solution based on continuum theory [28], shown as a solid line. Comparison between the MD results and the analytical solution shows a very good agreement, even for very small defects.…”

mentioning

confidence: 99%

On the size-dependent elasticity of silicon nanocantilevers: impact of defects

Sadeghian¹,

Goosen²,

Bossche³

et al. 2011

J. Phys. D: Appl. Phys.

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Recent measurements have indicated that the elastic behaviour of silicon nanocantilevers and nanowires is size-dependent. Several theoretical models have been proposed to explain this phenomenon, mainly focused on surface stress effects. However, discrepancies are found between experiments and theories, indicating that there could be other influences in addition to surface effects. One of the important issues, which was experimentally confirmed and has not been considered, is accounting for the fact that experimentally tested nanocantilevers and nanowires are not defect free. In this paper molecular dynamics (MD) is utilized to study the effects of defects on the elasticity of silicon. The effective Young's modulusẼ of [1 0 0] and [1 1 0] oriented silicon nanoplates is extracted in the presence of defects, showing that such defects significantly influence the size-dependent behaviour inẼ. The MD results are compared with the results of continuum theory, showing that continuum theory holds, even for very small defects. Taking into account the surface effects, native oxide layers together with fabrication-induced defects, the experimental measurements can be explained. The studied example involved nanocantilevers, but can be extended to nanowires.

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“…In order to approximate the effect of defects on the effective Young's modulus, an analytical solution, described in Ref. [12] is used as…”

Section: Resultsmentioning

confidence: 99%

“…4 The Young's modulus of the SiNWs with different cross-sections as a function of the concentration of defects.In this paper, our MD results are compared with an analytical solution based on continuum theory. In order to approximate the effect of defects on the effective Young's modulus, an analytical solution, described in Ref [12]. is used as…”

mentioning

confidence: 99%

Influence of Defects on the Young's Modulus of [110] Silicon Nanowires with Different Cross Sections

Zhang

Liu

2015

KEM

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The size dependence becomes more significant as the devices scale down from micro-to nanodimensions, which is generally attributed to surface effects due to the very high surface-to-bulk ratios in nanoscale structures. However, significant discrepancies between experimental measurements and computational studies indicate that there could be other influences besides surface effects, such as the influences of native oxide layer, fabrication-induced defects and boundary conditions. In this paper, our purpose is to investigate mainly the influence of fabrication-induced defects on the elasticity of [110] silicon nanowires (SiNWs) with different cross sections. We accomplish this by using the molecular dynamics (MD) simulation. Our MD results show that the H-passivated [110] SiNWs without surface defects is slightly elastically softer than bulk, which is in good agreement with other literature MD values. However, the effective Young’s modulus of SiNWs with surface defects can significantly decreases as the defects increase. This softening behavior of [110] SiNWs is severe, which indicates the importance of surface defects. It is noted that the influence of defects on the Young's Modulus of SiNWs strongly depended on the distribution and morphology of defects as well as the cross-sectional shapes of SiNWs. It is observed that the influence of defects on square SiNWs is significantly different from those of hexagonal and triangle SiNWs. Our work reveals that fabrication-induced surface defects could be one of the important origins of the reduced effective Young’s modulus experimentally observed in ultra-thin SiNWs. Therefore, the effect of defects on the characterization of the mechanical properties of nanowire must be carefully considered.

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Relative stiffness of irregularly perforated plates

Cited by 9 publications

References 0 publications

Effects of size and defects on the elasticity of silicon nanocantilevers

Effects of size and defects on the elasticity of silicon nanocantilevers

On the size-dependent elasticity of silicon nanocantilevers: impact of defects

Influence of Defects on the Young's Modulus of [110] Silicon Nanowires with Different Cross Sections

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