Lattice bending in three-dimensional Ge microcrystals studied by X-ray nanodiffraction and modelling

Extending the functionality of ubiquitous Si-based microelectronic devices often requires combining materials with different lattice parameters and thermal expansion coefficients. In this paper, scanning X-ray nanodiffraction is used to map the lattice bending produced by thermal strain relaxation in heteroepitaxial Ge microcrystals of various heights grown on high aspect ratio Si pillars. The local crystal lattice tilt and curvature are obtained from experimental three-dimensional reciprocal space maps and compared with diffraction patterns simulated by means of the finite element method. The simulations are in good agreement with the experimental data for various positions of the focused X-ray beam inside a Ge microcrystal. Both experiment and simulations reveal that the crystal lattice bending induced by thermal strain relaxation vanishes with increasing Ge crystal height.