Surface effect on size dependent Young’s modulus of nanowires: Exponentially decreased surface elasticity model

Li, Jiangang; Lei, Xiao; Ding, Jing; Gao, Zhixiang; Wang, Hua; Shi, Yanling

doi:10.1016/j.matlet.2021.131001

Cited by 7 publications

(3 citation statements)

References 10 publications

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“…The CS model thus assumes an abrupt change of properties from core to the surface. Hence, the M-CS model was introduced to consider a gradual transition between core and surface properties [25][26][27]. So far, the surface state in the M-CS approach has been utilized for Si with unreconstructed surface state only, while the presence of a native oxide surface in Si NWs is widely reported in experimental observations [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

An analytical-atomistic model for elastic behavior of silicon nanowires

Zare Pakzad,

Nasr Esfahani,

Erdem Alaca

2024

J. Phys. Mater.

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Silicon nanowires entail significant potential as sensors in nanoelectromechanical systems. Despite its crucial impact in such applications, inconsistent trends in mechanical behavior reported in computational and experimental studies remain unexplained. Hence, scale effect in even the most fundamental elastic properties requires clarification. This work introduces a multiscale model to bridge the existing gap between atomistic simulations and experimental observations encountered around a critical dimension of 10 nm. The combined approach of this work is based on molecular dynamics and modified core-shell model and captures the scale effect over a substantial size range. The evolution of the modulus of elasticity is thus studied and linked to nanowire critical dimension through the parameterization of surface inhomogeneity. The developed method is also validated through an analysis of native oxide revealing an average modulus of elasticity of 75 GPa. The method’s applicability can be extended to similar one-dimensional structures with unique surface states.

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Section: Introductionmentioning

confidence: 99%

An analytical-atomistic model for elastic behavior of silicon nanowires

Zare Pakzad,

Nasr Esfahani,

Erdem Alaca

2024

J. Phys. Mater.

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“…The initial core-surface model by Gurtin and Murdoch is an idealized model as it ignores the surface layer thickness and thus describes the surface as a stretchable but not a bendable structure. ,− This approach is further improved by a series of core–shell models, ,, where the NW cross section is considered as a composite structure composed of a bulk core and a surface layer of finite thickness, each with its distinct set of elastic constants. , The definition of the effective bending rigidity is another cause of further discrepancy among nanomechanical models. , The term originates from the local geometric nonlinearity of strains through incremental deformation theory. , Ignoring its dependence on parameters such as surface-induced residual stresses renders YL and modified YL models incapable of capturing surface stress effects emanating from NW side surfaces . These effects are significant upon large deformation of NWs leading to axial reorientations and phase transformations. , Consequently, the effectiveness of available nanomechanical models ,,− in predicting NW bending behavior is directly related to the extent of their parameter sets.…”

Section: Introductionmentioning

confidence: 99%

Nanomechanical Modeling of the Bending Response of Silicon Nanowires

Zare Pakzad,

Nasr Esfahani,

Tasdemir

et al. 2023

ACS Appl. Nano Mater.

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Understanding the mechanical behavior of silicon nanowires is essential for the implementation of advanced nanoscale devices. Although bending tests are predominantly used for this purpose, their findings should be properly interpreted through modeling. Various modeling approaches tend to ignore parts of the effective parameter set involved in the rather complex bending response. This oversimplification is the main reason behind the spread of the modulus of elasticity and strength data in the literature. Addressing this challenge, a surface-based nanomechanical model is introduced in this study. The proposed model considers two important factors that have so far remained neglected despite their significance: (i) intrinsic stresses composed of the initial residual stress and surface-induced residual stress and (ii) anisotropic implementation of surface stress and elasticity. The modeling study is consolidated with molecular dynamics-based study of the native oxide surface through reactive force fields and a series of nanoscale characterization work through in situ three-point bending test and Raman spectroscopy. The treatment of the test data through a series of models with increasing complexity demonstrates a spread of 85 GPa for the modulus of elasticity and points to the origins of ambiguity regarding silicon nanowire properties, which are some of the most commonly employed nanoscale building blocks. A similar conclusion is reached for strength with variations of up to 3 GPa estimated by the aforementioned nanomechanical models. Precise consideration of the nanowire surface state is thus critical to comprehending the mechanical behavior of silicon nanowires accurately. Overall, this study highlights the need for a multiscale theoretical framework to fully understand the size-dependent mechanical behavior of silicon nanowires, with fortifying effects on the design and reliability assessment of future nanoelectromechanical systems.

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“…Furthermore, various core-shell models have been developed as structural frameworks that comprise a core with the modulus of the bulk material and a surface shell [31][32][33]. These models are utilized to interpret and analyze the impact of surface properties on the overall behavior of the NWs [17,34,35]. Silicon (Si) NWs have been extensively investigated as fundamental components in semiconductor manufacturing due to their unique properties [13,14,36].…”

Section: Introductionmentioning

confidence: 99%