Model of step propagation and step bunching at the sidewalls of nanowires

Controlling the shape of a tapered nanowire: lessons from the Burton-Cabrera-Frank model

“…In this series of papers, the sticking of adatoms at steps was assumed to be large. A final numerical calculation was performed for chosen values of the characteristic parameters describing the dynamics of steps: it allowed the authors to demonstrate the possibility of a cylinder shape with radial growth, of a "pencil shape" due to step bunching, and of tapering [22,23]. The nucleation of steps was shown to take place at or near the basis of the NW.…”

“…The two coefficients A and B are determined by the boundary conditions at the steps: if, for the sake of simplicity, we assume no Ehrlich-Schwöbel effect [31], the symmetry imposes B = 0 if the position is measured from the center of the terrace. The parameter A is determined by the fact that the current related to the gradient of adatoms balances the incorporation of adatoms on both sides at the step: ∓D∇n(±l s ) = β[n(±l s ) − n eq ], where the parameter β sets the efficiency of trapping at the step [22,35], and n eq is determined by the sublimation rate V sub of the material, n eq = V sub τ . The sublimation process involves the release of an atom already incorporated, generally at a step edge, adding thus an adatom to the neighboring terrace [33], which then diffuses and may be desorbed or re-incorporated.…”

The onset of tapering in the early stage of growth of a nanowire

“…The pencil-shape of III-V nanowires 12 has attracted a lot of attention from theoreticians. The most precise description of the radial growth involves the nucleation and propagation of atomic steps along the nanowire sidewalls 13,14 . The pencil shape ("P" in Fig.…”

“…These profiles will be discussed later on. (b) Same as (a), taking into account the incorporation at step edges (Burton-Cabrera-Frank model 8,13,14 ).…”

Radial Growth of Self-Catalyzed GaAs Nanowires and the Evolution of the Liquid Ga-Droplet Studied by Time-Resolved in Situ X-ray Diffraction

“…axial NW heterostructures, 25 and for advanced device applications. [26][27][28] Hence, current efforts aim at the control, 5,7,[29][30][31] and understanding 8,9,[32][33][34][35][36][37][38][39][40][41] of radial growth processes responsible for tapering. Of particular interest here are self-stabilizing growth processes that are closely linked to the liquid Ga-droplet.…”