Novel behavior in semiconductor hetero-epitaxial growth such as InAs/GaAs is systematically investigated using ab initio-based approach incorporating temperature T and beam equivalent pressure p. The calculated In adsorption-desorption boundary curve elucidates that In atoms can adsorb on the InAs(111) A-(2 x 2) with In-vacancy wetting layer (WL) surface with simultaneous As adsorption similarly to homo-epitaxial growth. On the InAs(001)-(2 x 4)alpha 2 WL surface, however, In atoms hardly adsorb on the (001) WL in contrast with In adsorption on homo-epitaxial surface without strain. These results suggest that strain accumulated in the WL is not significant for the hetero-epitaxial growth on the InAs (111) A but strongly affects the growth process on the InAs(001) at the initial growth stage. It is also found that the InAs(001)-(2 x 3) WL surface fully covered by As dimers is unstable while the (n x 3) surfaces (n = 4, 6, and 8) with (n - 1) dimers and one missing dimer is more stable at the conventional molecular beam epitaxial growth conditions. It should be noted that In atoms are incorporated through In-As dimer formation with As desorption below InAs coverage theta similar to 0.9 monolayer (ML) on the (n x 3) surfaces. This suggests that the growth dose not proceed at theta > 0.9 ML without strain relaxation on the InAs/GaAs(001). (C) 2017 Elsevier B.V. All rights reserved.