About A Fundamental Uncertainty Of The Contact Angle Of The Catalyst Drop On The Top Of The Nanowire

In this paper, we aim to explain a fundamental uncertainty of the contact angle of the drops catalyzing vapor-liquid-solid growth of semiconductor nanowires (NWs). We developed the concepts about the crystallization processes occurring near the triple-phase boundary as well as the conditions of equilibrium wetting of NW top surface singular with a catalyst liquid drop characterized by the NW contact angle. We demonstrated that due to either dissolution of the crystallizable substance or its precipitation from the liquid catalyst drop on the NW tip, the wetting perimeter of the drop is not fixed and the drop can take an equilibrium shape with the NW contact angle, which does not satisfy Young's equation. The NW contact angle corresponds to the indifferent equilibrium of the catalyst droplet because of the wetting hysteresis. We proposed that the fundamental uncertainty of the NW contact angle of the catalyst drop saturated with a crystallizable substance at the NW tip is a result of the interaction of two opposing competing processes: the spheroidization of the catalytic liquid during the gravity neutralization and the wetting. We concluded that the steady-state NW contact angle of the drop depends on the free surface energies of the solid/liquid and liquid/vapor phase boundaries but does not depend on the free surface energy of the vertical sidewalls of the NWs. In this paper, we also proposed a new method to find the free surface energies of phase boundaries by the shape of the catalyst droplet on the NW tip as well as on the substrate. The paper also presents the results of obtaining the interphase free energy of the boundaries in Si-Au, Si-Cu, Ge-Au, GaAs-Au, InAs-Au, SiC-Fe, InP-Au, and so on systems.