Atomic structure of a $1T$-TiSe$_2$ surface layer from photoelectron and Auger electron holography data

A three-dimensional ($3D$) reconstruction of the atomic structure of the (100) surface of a $1T$-TiSe$_2$ layered dichalcogenide crystal has been performed from X-ray photoelectron and Auger electron diffraction data. The diffraction patterns of the emission of Auger electrons of Se(LMM) selenium and photoelectrons of Ti2$p$ titanium have been considered as holographic diagrams. Being processed with the scattering pattern extraction algorithm using the maximum entropy method (SPEA-MEM), they provide individual $3D$ images of the nearest environment of selenium and titanium atoms in the TiSe$_2$ lattice. Using reconstructed $3D$ images, the positions of $128$ atoms in the $2\times2\times1.5$-nm region of the surface layer of TiSe$_2$ have been determined. The structure of the surface has a $1T$ polytype. Interatomic distances in the layer and van der Waals gap are larger than the respective parameters in the bulk of the crystal. It is assumed that titanium layers in two Se-Ti-Se upper surface structural units are displaced along the [001] axis. The structure of the surface layer can be described by a unit cell of the P3 space group with the parameters $a=3.85$ Å and $c=14.4$ Å.