Vibrational modes of GaN nanowires in the gigahertz range

Abstract

Brillouin-light-scattering measurements and finite-element modeling of vibrational spectra in the range of 5-40 GHz are presented for an array of monocrystalline GaN nanowires with hexagonal cross sections. Analysis of the spectra is substantially complicated by the presence of a distribution of nanowire diameters. The measurements and calculations reveal a variety of modes with simple flexural, higher-order flexural, approximately 'plane-strain', approximately longitudinal and torsional displacement patterns that are similar to the corresponding modes of isotropic cylinders. The largest peaks in the spectra with acoustic angular wavenumbers in the range of 4 to ~15 μm(-1) were determined to arise from modes with relatively large transverse displacements, consistent with inelastic light scattering arising predominantly from surface ripple. These dominant modes have finite frequencies in the limit of zero wavenumber, corresponding to transverse standing waves. At higher wavenumbers, the spectra provide evidence for increased scattering through elasto-optic coupling, especially with respect to the emergence of a peak from a mode analogous to the longitudinal guided modes of thin films.

Direct observation of confined acoustic phonon polarization branches in free-standing semiconductor nanowires

“…Various modifications of Brillouin spectroscopy3435 are gaining popularity for investigating acoustic phonon and magnon energies in phononic crystals and other materials3136373839404142434445. Changing the angle of light incidence, α , with respect to the substrate allowed us to vary the probing phonon wave-vector, q , and determine the dispersion near the BZ center.…”

“…This approach is ambiguous owing to the difficulty of separating the phonon confinement effects from the phonon—boundary scattering. A Brillouin spectroscopy study of GaN nanowires made an important step forward in investigating confined phonons31. However, a large distribution in NW diameters, and discrepancy between the experimental and calculated dispersion left the question open.…”

Vibrational properties of semiconductor nanowires and nanowire heterostructures: ensembles and single nanowires

“…Phonon confinement effects have been clearly identified in Si NWs with diameters smaller than 10 nm 3. The lowest frequency region of the spectrum, corresponding to acoustic modes, is also altered, with the appearance of modes that involve the vibration of the nanowire as a whole 16, 17. From these, the radial breathing modes recently observed in CdSe and CdSe/ZnS core‐shell nanowire ensembles with diameters below 6 nm strongly depend on NW size 16.…”

Ultrasonic and Spectroscopic Techniques for the Measurement of the Elastic Properties of Nanoscale Materials

“…Measurements were compared to a finite elements simulation; the analysis had to take into account the dispersion of the diameters, with an average value of 190 nm and a variance of 40 nm. Several branches of the dispersion relation could however be identified [74].…”

“…A periodic pattern, of periodicity λ ∥ ,canbe obtained either by two beams which interfere at the surface of the sample [84] or by a hyperbolic diffraction grating [85]. The strain field generated by the pulse is the superposition of a broad, non-oscillating feature, due to the overall heating, whose decay is governed by heat diffusion, and an oscillating feature [74,86,87]. The oscillating signal is due to the SAWs which are launched in opposite directions, and which form a standing wave, of periodicity λ ∥ , which is eventually damped.…”