We report molecular beam epitaxy growth of Sr-doped Bi$_2$Se$_3$ films on (111) BaF$_2$ substrate, aimed to realize unusual superconducting properties inherent to Sr$_x$Bi$_2$Se$_3$ single crystals. Despite wide range of the compositions, we do not achieve superconductivity. To explore the reason for that we study structural, morphological and electronic properties of the films and compare them to the corresponding properties of the single crystals. The dependence of the c-lattice constant in the films on Sr content appears to be more than an order of magnitude stronger than in the crystals. Correspondingly, all other properties also differ substantially, indicating that Sr atoms get different positions in lattices. We argue that these structural discrepancies come from essential differences in growth conditions. Our research calls for more detailed structural studies and novel growth approaches for design of superconducting Sr$_x$Bi$_2$Se$_3$ thin films.
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