About the Shape of the Crystallization Front of the Semiconductor Nanowires

Abstract

During the nanowire (NW) formation, the growth steps reaching the crystallization front (CF) under the catalytic drop are either absorbed by the three-phase line or accumulated in front of it, curving the surface of the front. In this paper, we have analyzed the conditions leading to a change of shape of the crystallization front of the NWs under the catalyst drop as well as the reasons for the formation of atomically smooth (singular) and curved (nonsingular) regions. A model explaining the curvature of the crystallization front under the drop in the process of NW growth is proposed. The model demonstrates that under conditions of good wettability of the crystalline surface with a catalytic liquid and nucleation at regular places of the growing NW face, a metastable equilibrium at the CF near the three-phase line is achieved due to the thermodynamic size effect of reduction of overcooling (supersaturation). This metastable equilibrium results in the curvature of the CF. The CF curvature depends on the NW radius and the level of overcooling (supersaturation) in the droplet. During this process, the low-index inclined facets adjacent to the wetting perimeter of the catalyst drop may appear on the curved CF.

Vapor–Liquid–Solid Growth of Nanowires under the Conditions of External Faceting

“…[6] Here, it is necessary to mention that with the decreasing of the wetting perimeter of a nanodroplet, the linear energy of the three-phase contact interface α χ ¼ χ r increases, where χ is the linear tension, and r is the NWs radius. [21,22] This means that with the decreasing of the wetting perimeter of a nanodroplet, the angle condition θ 0 < θ(hkl) is unstable. However, to simplify our analysis we will not consider linear effects.…”

“…In the case of the large angles of θ 0 and φ (wetting scenario of NWs growth, θ 0 > θ), [15,22] the growth steps emerging under the droplet cannot be absorbed by the TPL due to the energetic disadvantage of the process: dα ¼ α À α SL > 0, where α ¼ α S À α L cosφ and α S À α L cosφ > α SL . Those steps will accumulate in front of the TPL, forming a curved stepped surface of the NWs' crystallization front (Figure 1b).…”

“…On the contrary, at small values of α L , the inequality dα < 0 may not be executed. [22] At a sufficiently large inclination angle ψ, the stepped curved surface of the crystallization front under the droplet will be at the equilibrium conditions as at large curvature of the surface of the front, the supersaturation above it will tend to zero due to the Kelvin size effect. [3] In addition to the thermodynamical equilibrium along the curved surface, the condition of the thermodynamic equilibrium must also be satisfied at the TPL itself.…”

“…[3] In addition to the thermodynamical equilibrium along the curved surface, the condition of the thermodynamic equilibrium must also be satisfied at the TPL itself. [23] The equilibrium at the TPL is achieved if the sum of the vector forces, corresponding to the free energies of interfaces liquid/vapor α L , solid/vapor α S, and solid/liquid α SL and their projections on coordinate axes, is zero [22] Àα L sinϕ 0 þ α SL cosψ ¼ 0…”