Phonons are lattice vibration arising from collective atomic motion and one of the questions popping up is whether the associated physical properties can be explained by the particle picture or by the wave nature of these excitations. Why does this matter? It matters since it is intimately related to energy dissipation, rendering inadequate attempts to transmit useful signals, from few GHz to 100s of THz impacting, e.g., information processing.
We investigated propagating phonons in two-dimensional silicon crystals with various positional disorder of otherwise periodically positioned holes, to ascertain to what degree disorder matters in their propagation, since they carry most of the heat in semiconductors materials, underpinning today’s (opto)electronics and nanoelectronics. We used a state-of-the-art pump-and-probe spectroscopy (see fig. 1) and a home-built two-laser Raman thermometry (2LRT) set up to extract the thermal conductivity. We measure at room temperature and simulate by finite element methods. We found that disorder lowers phonon energies and facilitates their in-plane propagation becoming impervious to disorder. Surprisingly, disorder was found to be unaffected by disorder. We thus propose a practical criterion for predicting phonon coherence as a function of roughness and disorder:
(i) phonon coherence is unaffected if the roughness R is smaller than 1/25 of the phonon wavelength and
(ii) phonon coherence is destroyed if R is greater than 1/10 of the phonon wavelength.
Our results have repercussions well beyond our own research in nano-scale thermal transport and thermoelectricity. They provide a hint to the factors affecting vibrational energy transport in condensed matter with variations in the nm-scale, the length scale of acoustic phonons relevant to electronics but also to biology.
Reference
Wagner MR, Graczykowski B, Reparaz JS, El Sachat A, Sledzinska M, Alzina F & Sotomayor Torres CM 2016, ‘Two-Dimensional Phononic Crystals: Disorder Matters’, Nano Letters, 16 (9) 5661 – 5668.
Fig. 1. Schematics of the silicon membrane and of the patterned two-dimensional phononic crystal (left), the femtosecond pump-and-probe experiments (middle) and results of the FEM simulation of the response of the phononic crystal in terms of displacements, ascribed to specific phonons.
