Imaging of three-dimensional (Si,Ge) nanostructures by off-axis electron holography

Quantitative phase mapping in transmission electron microscopy is applied to image the three-dimensional (3D) morphology of (Si,Ge) islands grown on Si substrates. The phase shift of the transmitted electrons induced by the crystal inner potential was recorded by using off-axis electron holography. The analysis of the experimental data requires the knowledge of the mean inner potential (MIP) of the (Si,Ge) solid solution. The MIP was calculated using different models of isolated or bonded atoms, which are based on the interpolation of first principle data. The results are compared with structure modeling and related MIP calculations applying classical molecular dynamics (MD) simulations. For MD simulations bond order potentials were applied, which can take into consideration both electronic effects and elastic relaxations. The calculated mean inner potential is used to transform the phase shifts into thickness mapping for the reconstruction of the 3D island morphology. Both, phase shift due to dynamical electron diffraction and structural relaxation influence the resulting 3D reconstruction.