Here, we compare the stabilities of different III-V crystals configurations on stepped Si substrates, with or without anti-phase boundaries, for abrupt and compensated interfaces, using density functional theory. Thermodynamic stability of the different heterostructures is analyzed with an atomic scale description of charge densities distribution and mechanical strain. We show that the configuration where a III-V crystal adapts to a Si monoatomic step through change of charge compensation at the hetero-interface is much more stable than the configuration in which an antiphase boundary is formed. This study thus demonstrates that antiphase boundaries commonly observed in III-V/Si samples are not originating from Si monoatomic step edges but from inevitable kinetically driven coalescence of monophase 3D III-V islands.