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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.

Interface Adhesion and Structural Characterization of Rolled-up GaAs/In0.2Ga0.8As Multilayer Tubes by Coherent Phonon Spectroscopy