Elastic properties of nanomechanical resonators

The Project was initiated within the A06 project of the SFB 767 'Controlled nanosystems'.

The oscillation behaviour of (Si) nanomechanical resonators in the bridge geometry (nano bridges) is investigated by molecular dynamics simulations using (semi-) empirical interaction potentials like Stillinger-Weber for Si. After setting up the initial structure using a diamond lattice for Si and a (2x1) symmetric dimer surface reconstruction, the end points of the bridges are fixed and a constant force is applied over all atoms in order to achieve a transverse deflection. The force is then turned off resulting in a free oscillation of the bridges.

Besides varying the size of the bridges, the effects of temperature and external stretching fields are explored. The results show a decline of the oscillation frequencies with rising temperature and a strong increase of the damping coefficient, a strong increase of the frequencies with external stress (stretching) and a decline of frequencies with length. Other materials (e.g. NiTi memory alloys) are explored as well.

Besides the bridge also the membrane geometry was investigated. An example for an elevated one, where drum modes are visible at the beginning, is shown in the video below.

Drum modes

Synchronization of nanobridges

The synchronization of two coupled silicon nanobridges is investigated by molecular dynamics simulations using the open source code LAMMPS, whereby one bridge is extended in length so that a mismatch in the autonomous frequencies is generated.  An in time sinusoidal and spatial homogeneous  external force is applied to one of the bridges  with a frequency fitting the autonomous one of the driven bridge. The center-of-mass movement of the oscillators is then studied with respect to the synchronization in frequency and phase by different temperatures.
The results show a step-like, monotonous mismatch of the phase difference at low temperatures with several equidistant plateaus. At high temperatures, however, a constant phase difference is explored. Additionally a mismatch in the frequency of the force and the autonomous frequency of the driven oscillator was generated and varied to study the influence of the forces strength on the synchronization. It is shown, that a higher detuning needs an accordingly stronger external force to achieve a synchronous oscillation.

a) New publications

  • Article
  • Book
  • Dissertation
  • Thesis
  • Proceedings
  • Other
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b) Completed work

  1. K. Scholz, diploma thesis: Simulation elastischer Eigenschaften von Nanobrücken (2011).
  2. M. Ring, master thesis: Computer simulations of the dynamics of nanomembranes (2013).
  3. F. Müller, master thesis: Molekulardynamik-Simulation zur atomistischen Kopplung von Silizium-Nanobrücken (2016).

d) References

e) External links (programs, potentials ...)

  1. LAMMPS. S. Plimpton, J. Comput. Phys. 117, 1 (1995). (http://lammps.sandia.gov)
  2. General potentials LAMMPS http://www.ctcms.nist.gov/potentials/
  3.  EAM-potentials of FCC metals H. W. Sheng, M. J. Kramer, A. Cadien, T. Fujita, and M. W.
    Chen, Phys. Rev. B 83, 134118 (2011). (https://sites.google.com/site/eampotentials/)

f) Books