Nanometer Scale Size and Cross-sectional Dependence of Elastic Modulus of Silicon Pillars
Carly McKown
Bredesen Center for Interdisciplinary Research and Graduate Education, University of Tennessee
This page shows visualizations of 5nm wide, 10nm long fixed-free Silicon Cantilever beams with different cross-sectional shapes
For transport phenomena and sensors, creating structures with tunable natural frequency is essential. Many sensors use cantilever beam structures and interpret results based on beam position. In transport phenomena, biomimetic pillars in nano-, micro- and hierarchal scales have been developed to direct droplet and solid movement, especially under external vibrational forces. In terms of transport phenomena, vibrational induced pillared structures can be used to carry liquids and solids across a surface. A key aspect of this mechanism is creating the largest possible pillar displacement through hitting the resonance frequency. However, smaller structures tend to have higher resonance frequencies, which can be impractical to reach.
Based on free-fixed cantilever beam theory, other than changing pillar dimensions, one would need to increase material density or lower elastic modulus. On the bulk scale, this could only be done by changing the pillar material. However, for nanoscale structures, elastic modulus of cantilever beams have been empirically and computationally demonstrated to decrease with decreasing beam thickness[1]. To investigate other possible dimensional nanoscale dimensional dependence, a series of simulations were used to determine elastic properties of 2nm, 5nm and 8nm wide pillars at different lengths. The simulations were run for both square and circular beam cross-sections. Through these simulations, no clear trend on pillar length was determined. However, based on average elastic modulus for each of the three beam widths, circular cross-sections led to smaller elastic moduli than their square counterparts. While derived elastic moduli were larger than the ~50GPa Li et al reported for a 12nm beam thickness[1], the trend that circular cross-sections lead to lower elastic moduli is still valid.
While the elastic properties LAMMPS code were primarily based on LAMMPS ELASTIC example codes, the visualizations below are self-written code to simulate a fixed-free cantilever beam with an applied force of 0.001eV/angstrom at the end. These visualizations display the practical difference between the two cross-sectional types.
Interactive Structure
Color Legend:
- Silver= Silicon
References
1. X. Li, T. Ono, Y. Wang, and M. Esashi, "Ultrathin single-crystalline-silicon cantilever resonators: Fabrication technology and significant specimen size effect on Young's modulus," Applied Physics Letters, vol. 83, pp. 3081-3083, 2003.10.1016/j.jnucmat.2013.07.001
posted: April 2016.
updated: April 2016.