  We report the preparation of high-quality single crystal of Bi$_2$Se$_3$, a
well-known topological insulator and its Ti-doped compositions using Bridgeman
technique. Prepared single crystals were characterized by x-ray diffraction
(XRD) to check the crystalline structure and energy dispersive analysis of
x-rays for composition analysis. The XRD data of Ti-doped compounds show a
small shift with respect to normal Bi$_2$Se$_3$ indicating changes in the
lattice parameters while the structure type remained unchanged; this also
establishes that Ti goes to the intended substitution sites. All the above
analysis establishes successful preparation of these crystals with high quality
using Bridgman technique. We carried out x-ray photo-emission spectroscopy to
study the composition via investigating the core level spectra. Bi$_2$Se$_3$
spectra exhibit sharp and distinct features for the core levels and absence of
impurity features. The core level spectra of the Ti-doped sample exhibit
distinct signal due to Ti core levels. The analysis of the spectral features
reveal signature of plasmon excitation and final state satellites; a signature
of finite electron correlation effect in the electronic structure.
