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We analyze fluctuation of the layer thicknesses and its influence on thestrain state of (In,Ga)As/(Al,Ga)As micro-tubes containing quantum wellstructures. In those structures a curved high-mobility two-dimensional electrongas (HM2DEG) is established. The layer thickness fluctuation studied by atomicforce microscopy, x-ray scattering, and spatially resolved cathodoluminescencespectroscopy occurs on two different lateral length scales. On the shorterlength scale of about 0.01~$\mu$m, we found from atomic force micrographs andthe broadening of the satellite maxima in x-ray diffraction curves a very smallvalue of the mean square roughness of 0.1~nm. However, on a longer length scaleof about 1.0~$\mu$m, step bunching during epitaxial growth resulted in layerthickness inhomogeneities of up to 2~nm. The resulting fluctuation of thestrain in the micro-tubes leads to a local variation of the chemical potential,which results in the fluctuation of the carrier density as well. This leads toa phase cancelation of the Shubnikov-de-Haas oscillations in the curved HM2DEGand a reduction of the single-electron scattering time, while the electronmobility in the structures remains high. The estimated fluctuation of thecarrier density agrees well with the energy fluctuation measured in thecathodoluminescence spectra of the free-electron transition of the quantumwell.

Inhomogeneous micro-strain in cylindrical semiconductor heterostructures and its influence on the adiabatic motion of electrons