  Using kinetic Monte Carlo simulations, we develop a framework to relate
morphological properties and microscopic dynamics during island growth,
coalescence, and initial formation of continuous heteroepitaxial films. The
average island width is controlled by adatom mobility on the substrate.
Subsequent evolution strongly depends on the Ehrlich-Schw\"{o}ebel energy
barrier $E_{ES}$ of the deposited material. As $E_{ES}$ decreases, islands
becomes taller and their coalescence is delayed. For small islands and large
$E_{ES}$, the global roughness increases as $W\sim{\text{thickness}}^{1/2}$ and
the local roughness increases at short scales (apparent anomalous scaling)
before and after island coalescence. If the islands are wide, $W$ may have a
plateau for large $E_{ES}$ and has a maximum for small $E_{ES}$ when the
islands coalesce. This framework is applied to atomic-force microscopy data of
the initial stages of CdTe deposition on Kapton: a maximum of $W$ during island
coalescence indicates negligible ES barrier, consistently with scaling
properties of much thicker films, and the diffusion coefficient
${10}^{-7}{\text{--}}{10}^{-5}{\text{cm}}^2/{\text s}$ on the Kapton surface at
$150\,^{\circ}\mathrm{C}$ is estimated. Applications of the framework to other
materials are suggested, in which the expected roles of ES barriers are
highlighted.
