Effects of size and defects on the elasticity of silicon nanocantilevers

Abstract

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.

Surface effect on resonant properties of nanowires predicted by an elastic theory for nanomaterials

“…It is found that the effective Young's modulus of a fixed-fixed nanowire shows an oppositely sizedependent behavior to that of a cantilever one. [3][4][5][6][7][8] It increases with a decreasing characteristic size for fixed-fixed nanowires, while decreases for cantilever ones. Such a behavior cannot be predicted by the classical beam theory, a proper one considering surface effect should be developed.…”

“…[43][44][45] All the theoretical predictions agree well with the experimental and numerical results. [3][4][5]7,[46][47][48][49] In the present paper, the resonant vibration of both fixed-fixed nanowires and cantilevered ones is investigated with the new developed elastic theory for nanomaterials and theoretical predictions are further compared with the existing numerical results. Geometrical factors governing the size dependent characteristics of resonant frequency are also discussed, which could provide a theoretical guidance for the design of nanowire resonators and sensors in NEMs.…”

Nonlinear oscillation of nanoelectro-mechanical resonators using energy balance method: considering the size effect and the van der Waals force

“…As NEMSs are very small in size, the size effect plays a considerable role on the behavior of these devices. Sadeghian et al (2010) experimentally examined the size-dependent elastic behavior of silicon NEMS, and Beni et al (2011) utilized the modified couple stress theory to study the size dependency for NEMS.…”

On-wafer time-dependent high reproducibility nano-force tensile testing

“…It also increased the understanding of why the mechanics at the micro-and nanoscale differs from that at the macroscale. Size-effects in the elastic response [6], (temperature dependent) plastic yield strength [7][8][9][10] and cyclic fatigue [11][12][13] of thin films have received considerable attention. Small scale time-dependent mechanics, such as thin film creep, did not attract substantial research efforts yet.…”