Abstract
We present a detailed experimental and theoretical study of the acoustic phonon modes in rolled-up multilayers with thickness of the layers in the nanometre and diameters in the micrometre range. We compare our results to planar, unrolled multilayers grown by molecular beam epitaxy. For the planar multilayers the experimentally obtained acoustic modes exhibit properties of a superlattice and match well to calculations obtained by the Rytov model. The rolled-up superlattice tubes show intriguing differences compared to the planar structures which can be attributed to the imperfect adhesion between individual tube windings. A transfer matrix method including a massless spring accounting for the imperfect adhesion between the layers yields good agreement between experiment and calculations for up to five windings. Areas with sufficient mechanical coupling between all windings can be distinguished by their acoustic mode spectrum from areas where individual windings are only partially in contact. This allows the spatially resolved characterization of individual tubes with micrometre spatial resolution where areas with varying interface adhesion can be identified.
Highlights
Well established techniques to experimentally study the acoustic phonons and eigenmodes of nanostructures are static Raman and Brillouin spectroscopy which can provide access to the acoustic dynamics in the rolled-up superlattices[20,21,22,23]
We present a study of the acoustic phonon modes of the rolled-up multilayers and compare the results to planar multilayers grown by MBE
The experimental results are corroborated by calculations of the phonon mode spectra obtained via a transfer matrix method and the Rytov model
Summary
An important step to implement the fabrication process has been achieved by producing crystalline superlattices without the need of growing the full layer stack by molecular beam epitaxy (MBE) but instead by growth of a strained bilayer of two materials which - upon release from the substrate - undergoes a rolling-up process[1, 2]. The frequency resolution which has been achieved with these techniques on single structures, is very limited so far We circumvent these limitations by using an optical pump-probe setup as a non-invasive characterization method[24] which renders invasive and destructive methods, e.g., focused ion beam based characterization in combination with SEM imaging, unnecessary. By removing the sacrificial layer the bilayer is released, which directly results in its roll-up into several windings (sample Ar, Fig. 1, middle part). In this way we obtain direct access to the dynamics of coherent acoustic phonons in the system
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