Effect of Surface Layer on Young’s Modulus of Ultrathin Nanofilms: A Theoretical Model

Abstract:

The existing discrepancy between theoretical models and experimental results in describing the elastic properties of ultra-thin nanofilms (less than 10 nm) is primarily attributed to the oversight of the surface layer thickness impact. To address this, a new model incorporating a surface layer with thickness is proposed in this article. Utilizing a layered model, the Young’s modulus of nanofilms approaches that of bulk materials as the film thickness becomes infinitely large, equating to the Young’s modulus of the bulk material in both layered and unlayered models. The dimensional unit of the surface elastic coefficient in the layered model differs from that of the unlayered model, approximately by the thickness of the film. Numerically, the former is more than double the latter. Predictions using the layered model for ultra-thin films comprising only two surface layers reveal a hardening effect in materials such as Si, Ge, InAs, and GaAs. The increase in Young’s modulus for these materials is 20.81%, 95.28%, 79.03%, and 84.04%, respectively, compared to their bulk counterparts. Moreover, a continuous increase in the Young’s modulus is observed as the thickness further decreases.

• Periodical: Defect and Diffusion Forum (Volume 436)
• Pages: 163-174
• DOI: https://doi.org/10.4028/p-2bO6SL
• Online since: September 2024
• Authors: Yi'ao Jia, Yehejong Saqier, Bai Narsu*
• Keywords: Surface Effect, Ultrathin Nanofilm, Young’s Modulus

References

[1] Eom, K., Park, H.S., Yoon, D. S., Kwon, T., Nanomechanical resonators and their applications in biological/chemical detection: Nanomechanics principles. Physics Reports, 503.4-5 (2011) 115-163.

DOI: 10.1016/j.physrep.2011.03.002

[2] A. Boisen, S. Dohn, S.S. Keller, S. Schmid, M. Tenje, Cantilever-like micromechanical sensors. Reports on Progress in Physics, 74.3 (2011) 036101.

DOI: 10.1088/0034-4885/74/3/036101

[3] J. Mei, L. Li, Frequency self-tuning of carbon nanotube resonator with application in mass sensors. Sensors and Actuators B: Chemical, 188 (2013) 661-668.

DOI: 10.1016/j.snb.2013.07.030

[4] E. P. M. Amorim, E. Z. da Silva, Helical Gold Nanowires Make Longer Linear Atomic Chains, Phys. Rev. Lett. 101 (2008) 125502.

DOI: 10.1103/physrevlett.101.125502

[5] Q. F. Gu, G. Krauss, F. Gramm, A. Cervellino, W. Steurer, Unexpected High Stiffness of Ag and Au Nanoparticles, Phys. Rev. Lett. 100 (2008) 045502.

DOI: 10.1103/physrevlett.100.045502

[6] M. Lebrat, S. Häusler, P. Fabritius, D. Husmann, L. Corman, T. Esslinger, Quantized Conductance through a Spin-Selective Atomic Point Contact, Phys. Rev. Lett. 123 (2019) 193605.

DOI: 10.1103/physrevlett.123.193605

[7] J. Zhang, M. Tomitori, T. Arai, Y. Oshima, Surface Effect on Young's Modulus of Sub-Two-Nanometer Gold [111] Nanocontacts. Phys. Rev. Lett. 128 (2022) 146101-14.

DOI: 10.1103/physrevlett.128.146101

[8] S. D. Bennett, J. Maassen, A. A. Clerk, Scattering Approach to Backaction in Coherent Nanoelectromechanical Systems, Phys. Rev. Lett. 105 (2010) 217206.

DOI: 10.1103/physrevlett.106.199902

[9] X. Li, T. Ono, Y. Wang, M. Esashi, Ultrathin single-crystalline-silicon cantilever resonators: Fabrication technology and significant specimen size effect on Young's modulus, Appl. Phys. Lett. 83 (2003) 3081.

DOI: 10.1063/1.1618369

[10] C. Q. Chen, Y. Shi, Y. S. Zhang, J. Zhu, Y. J. Yan, Size Dependence of Young's Modulus in ZnO Nanowires, Phys. Rev. Lett. 96 (2006) 075505.

DOI: 10.1103/physrevlett.96.075505

[11] A. Sánchez-Iglesias, B. Rivas-Murias, M. Grzelczak, J. Pérez-Juste, L. M. Liz-Marzán, F. Rivadulla, M.A. Correa-Duarte, Highly transparent and conductive films of densely aligned ultrathin Au nanowire monolayers, Nano Lett. 12 (2012) 6066.

DOI: 10.1021/nl3021522

[12] S. Gong, W. Schwalb, Y. Wang, Y. Chen, Y. Tang, J. Si, B. Shirinzadeh, W. Cheng, A wearable and highly sensitive pressure sensor with ultrathin gold nanowires, Nat. Commun. 5 (2014) 3132.

DOI: 10.1038/ncomms4132

[13] R.E. Miller, V. B. Shenoy, Size-dependent elastic properties of nanosized structural elements. Nanotechnology, 11.3 (2000) 139.

DOI: 10.1088/0957-4484/11/3/301

[14] M.E. Gurtin, A. Ian Murdoch, A continuum theory of elastic material surfaces. Archive for rational mechanics and analysis, 57 (1975) 291-323.

DOI: 10.1007/bf00261375

[15] M.E. Gurtin, A.I. Murdoch, Surface stress in solids. International journal of Solids and Structures, 14.6 (1978) 431-440.

DOI: 10.1016/0020-7683(78)90008-2

[16] J. F. Nye, John Frederick. Physical properties of crystals: their representation by tensors and matrices. Oxford university press, 1985.

[17] N. W. Ashcroft, N. D. Mermin. Solid State Physics (HRW Internat. ed.), 1987.

[18] D. Sander, The correlation between mechanical stress and magnetic anisotropy in ultrathin films, Reports on Progress in Physics 62.5 (1999) 809.

DOI: 10.1088/0034-4885/62/5/204

[19] M. Liu, F. Liu, Quantum manifestation of elastic constants in nanofilms. Nanotechnology, 25.13 (2014) 135706.

DOI: 10.1088/0957-4484/25/13/135706

[20] M. De Jong, W. Chen, T. Angsten, A. Jain, R. Notestine, A. Gamst, M. Asta, Charting the complete elastic properties of inorganic crystalline compounds. Scientific data, 2.1 (2015)1-13.

DOI: 10.1038/sdata.2015.9

[21] C. Deneke, C. Müller, N.Y. Phillipp, O.G. Schmidt, Diameter scalability of rolled-up In (Ga) As/GaAs nanotubes. Semiconductor science and technology, 17.12 (2002), 1278.

DOI: 10.1088/0268-1242/17/12/312