  Bi(0001) films with thicknesses up to several bilayers (BLs) are grown on
Se-terminated Bi$_2$Se$_3$(0001) surfaces, and low energy electron diffraction
(LEED), low energy ion scattering (LEIS) and atomic force microscopy (AFM) are
used to investigate the surface composition, topography and atomic structure.
For a single deposited Bi BL, the lattice constant matches that of the
substrate and the Bi atoms adjacent to the uppermost Se atoms are located at
fcc-like sites. When a 2nd Bi bilayer is deposited, it is incommensurate with
the substrate. As the thickness of the deposited Bi film increases further, the
lattice parameter evolves to that of bulk Bi(0001). After annealing a multiple
BL film at 120{\deg}C, the first commensurate Bi BL remains intact, but the
additional BLs aggregate to form thicker islands of Bi. These results show that
a single Bi BL on Bi$_2$Se$_3$ is a particularly stable structure. After
annealing to 490{\deg}C, all of the excess Bi desorbs and the Se-terminated
Bi$_2$Se$_3$ surface is restored.
