Atomic structures of Si and Ge Σ = 13 [0 0 1] tilt grain boundaries studied by high-resolution electron microscopy and atomistic simulations

Abstract

By combining high-resolution electron microscopy and atomistic simulations, the atomic structures of several interfaces, {5 1 0}, {2 3 0} and {8 1 0}/{7 4 0}, in germanium and in silicon Σ = 13 [0 0 1] tilt grain boundaries (TGBs) are studied using bicrystals prepared in two different ways from the melt. The interfaces are characterized by either transmission electron microscopy or scanning transmission electron microscopy (STEM). The Si TGB shows only one interface, {1 5 0} with one interfacial structure. The Ge TGB contains many facets. In Ge, observations performed in two perpendicular directions, [0 0 1] and [ 5 0], confirm that the {5 1 0} interface has two different structures. One structure, called M-structure, is periodic along [0 0 1] and has tetracoordinated atoms. The other structure, called U-structure, is more peculiar as it contains a fixed part surrounding a variable complex core. High-resolution STEM, realised in modern microscopes equipped with a probe Cs-corrector, is a very effective technique for structure determination of grain boundaries (GBs). However, current limitations for high-resolution study of GBs are the structural changes under the electron beam and the limited number of crystallographic axes suitable for atomic-resolution imaging. The structures of GB atomistic models can be ordered according to their calculated energies. It appears that energies calculated using empirical potentials, like Tersoff or Stillinger-Weber potentials, do not give the same classification as ab initio calculations and cannot be used to determine the structure of lowest energy. This structure is the M-structure, the structure observed in the Si bicrystal.