Three-dimensional phonon population anisotropy in silicon nanomembranes.

Nanoscale single-crystals possess modified phonon dispersions due to the truncation of the crystal. The introduction of surfaces alters the population of phonons relative to the bulk and introduces anisotropy arising from the breaking of translational symmetry. Such modifications exist throughout the Brillouin zone, even in structures with dimensions of several nanometers, posing a challenge to the characterization of vibrational properties and leading to uncertainty in predicting the thermal, optical, and electronic properties of nanomaterials. Synchrotron x-ray thermal diffuse scattering studies find that freestanding Si nanomembranes with thicknesses as large as 21 nm exhibit a higher scattering intensity per unit thickness than bulk silicon. In addition, the anisotropy arising from the finite thickness of these membranes produces particularly intense scattering along reciprocal-space directions normal to the membrane surface compared to corresponding in-plane directions. These results reveal the dimensions at which calculations of materials properties and device characteristics based on bulk phonon dispersions require consideration of the nanoscale size of the crystal.