A persistent challenge in the field of spintronics is the search for suitable materials that enable the circumvention of the impedance mismatch preventing efficient spin-injection from metallic ferromagnetic conductors into semiconductors. One promising material is europium sulfide (EuS), a ferromagnetic semiconductor below the Curie temperature of 16.5 K. Investigation and optimization of the conditions required for high-quality growth of epitaxial EuS films on suitable substrates are thus of particular interest for the creation of efficient devices. We present the results of a growth-mode study employing atomic force microscopy and spot-profile analysis low-energy electron diffraction (SPA-LEED) of epitaxial EuS thin films deposited by electron-beam evaporation on InAs(100) substrates with varying combinations of, respectively, growth and annealing temperatures, Tg and Ta, from room temperature to 400 °C. We observed Stranski-Krastanov-like growth featuring low-roughness surfaces with root mean square values between 0.4 – 0.9 nm for all temperature combinations. An increased tendency for nucleation into grains and islands was observed for higher Ta from 300 – 400 °C. The corresponding nucleation mode, defined by varying degrees of 2D and 3D nucleation, was dependent on Tg. A 2D island growth mode was observed for Tg = 150 °C and Ta = 400 °C featuring a sharp and bright SPA-LEED pattern. This suggests the formation of a highly ordered, smooth surface for these growth conditions thereby providing a good starting point for optimization attempts for potential future devices.