We studied InAs epitaxial growth by molecular beam epitaxy on a Se-terminated GaAs surface as well as on an As-stabilized GaAs surface by in situ synchrotron radiation photoelectron spectroscopy (SRPES), in situ reflection high-energy electron diffraction, high-resolution scanning electron microscopy, and cross-sectional transmission electron microscopy to evaluate the electronic and structural properties of the InAs epitaxial nanocrystals. While an InAs layer grew on the As-stabilized GaAs substrate in the Stranski-Krastanov growth mode, InAs nanocrystal islands formed on the Se-terminated GaAs surfaces at the very early growth stages. InAs nanocrystals with a lateral width of about 70-80 nm, a density of about 2x10(9) cm(-2), and a height of about 20 nm were reproducibly grown on Se-terminated GaAs. The SRPES deconvoluted results indicate that although band bending is reduced by the Se treatment, it reappears at the heterointerface between InAs nanocrystals and the Se-treated GaAs surface during InAs deposition due to the lattice mismatch.