  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.
