The catalyst-free growth of the GaAs nanowire is based on preferential one-dimensional growth along the <111>B direction of the zinc-blende-structure GaAs, which originates from the formation of facets depending on the temperature and pressure. However, the driving force for preferential growth has yet to be fully elucidated. In this study, the adsorption-desorption behavior for several low-index surfaces was investigated in terms of temperature, pressure, and surface reconstruction using ab-initio thermodynamics. It was found that the As adsorption on the (111)B surface is highly favorable compared to that on the other surfaces under the experimental conditions, where the growth of the GaAs nanowires was successful without catalyst. Based on the thorough calculations and a comparison of the results with those of previous experiments, the driving force behind the preferential one-dimensional growth along the <111>B direction is confirmed to be the preferential adsorption of As on the (111)B surface under the specific temperature and pressure condition. In particular, the Ga-vacancy α(2×2) reconstruction of the (111)B surface, which was calculated to be stable at high temperature, is identified to provide the preferential adsorption sites for the incoming vapor sources. Unlabelled Image • Stable reconstruction of GaAs (111)B changes depending on temperature and pressure. • Ga adsorption on (111)B is favorable under all temperature and pressure considered. • As adsorption on (111)B is favorable under specific temperature and pressure. • Preference of As adsorption on (111)B is not much affected by pre-adsorbed Ga. • As adsorption on (111)B is the limiting factor of GaAs <111>B nanowire growth. [ABSTRACT FROM AUTHOR]