Dynamical effects in strain measurements by dark-field electron holography.

Here, we study the effect of dynamic scattering on the projected geometric phase and strain maps reconstructed using dark-field electron holography (DFEH) for non-uniformly strained crystals. The investigated structure consists of a {SiGe/Si} superlattice grown on a (001)-Si substrate. The three-dimensional strain field within the thin TEM lamella is modelled by the finite element method. The observed projected strain is simulated in two ways by multiplying the strain at each depth in the crystal by a weighting function determined from a recently developed analytical two-beam dynamical theory, and by simply taking the average value. We demonstrate that the experimental results need to be understood in terms of the dynamical theory and good agreement is found between the experimental and simulated results. Discrepancies do remain for certain cases and are likely to be from an imprecision in the actual two-beam diffraction conditions, notably the deviation parameter, and points to limitations in the 2-beam approximation. Finally, a route towards a 3D reconstruction of strain fields is proposed.

Composition and local strain mapping in Au-catalyzed axial Si/Ge nanowires.

For most applications, heterostructures in nanowires (NWs) with lattice mismatched materials are required and promise certain advantages thanks to lateral strain relaxation. The formation of Si/Ge axial heterojunctions is a challenging task to obtain straight, defect free and extended NWs. And the control of the interface will determine the future device properties. This paper reports the growth and analysis of NWs consisting of an axial Si/Ge heterostructure grown by a vapor-liquid-solid process. The composition gradient and the strain distribution at the heterointerface were measured by advanced quantitative electron microscopy methods with a resolution at the nanometer scale. The transition from pure Ge to pure Si shows an exponential slope with a transition width of 21 nm for a NW diameter of 31 nm. Although diffuse, the heterointerface makes possible strain engineering along the axis of the NW. The interface is dislocation-free and a tensile out-of-plane strain is noticeable in the Ge section of the NW, indicating a lattice accommodation. Experimental results were compared to finite element calculations.