The authors have established a robust set of growth conditions for homoepitaxy of high-quality InAs with a (111)A crystallographic orientation by molecular beam epitaxy (MBE). By tuning the substrate temperature, the authors obtain a transition from a 2D island growth mode to step-flow growth. Optimized MBE parameters (substrate temperature ¼ 500 C, growth rate ¼ 0:12 ML=s, and V=III ratio ! 40) lead to the growth of extremely smooth InAs(111)A films, free from hillocks and other 3D surface imperfections. The authors see a correlation between InAs surface smoothness and optical quality, as measured by photoluminescence spectroscopy. This work establishes InAs(111)A as a platform for future research into other materials from the 6.1 Å family of semiconductors grown with a (111) orientation.