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.
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