On the Stability of Catalyst Drops at the Vapor-Liquid-Solid Contact during the Nanowires Growth

Abstract

The paper provides a physical justification for the wettability conditions for a crystalline surface of a limited area by a small-volume catalytic liquid at the end of a growing nanowires (NW) characterized by a contact angle β, which contributes to a fundamental understanding of the nature of the contact angle of catalyst drops at the top of the NW. It is shown that under the conditions of stationary growth of NWs with a transverse singular face, there are only values of the angles β and γ (the angle of inclination of the side surface of the crystal to this face), which correspond to the minimum increment of the free energy of the three-phase system αLVcosβ + αSL = αSVcosγ and determine the stability of the catalyst drop at the top of the NW. With the growth of cylindrical NWs, the conditions of indifferent equilibrium are realized at the drop wetting perimeter. A drop, due to the dissolution of a crystallizing substance or its separation from a liquid solution, can take an equilibrium shape with a contact angle β that does not satisfy the equilibrium contact angle condition θ in the Young equation. A concentric break (rib) at the NW tip should increase the observed wetting angle θ and lead to contact angle hysteresis. The restrictions imposed on the value of the contact angle of a stable catalyst drop at the top of the NW are determined. The catalyst drop will take an equilibrium shape if the hysteresis angle β is in the range θ < β ≤ θ' + γ (θ' is the wetting angle of the NW side walls). For the growth of semiconductor NWs in the form of a straight cylinder, γ = 90° and therefore always β > 90°. It is shown that the direction of displacement of the three-phase line relative to the droplet surface is determined by the growth angle φ0: for the nonwetting growth mode of NWs (with a transverse face) φ0 = β – γ; for the wetting growth mode (with the end surface curved near the three-phase line)