Disassembly of Faceted Macrosteps in the Step Droplet Zone in Non-Equilibrium Steady State

Abstract

A Wulff figure-the polar graph of the surface tension of a crystal-with a discontinuity was calculated by applying the density matrix renormalization group method to the p-RSOS model, a restricted solid-on-solid model with a point-contact-type step-step attraction. In the step droplet zone in this model, the surface tension is discontinuous around the (111) surface and continuous around the (001) surface. The vicinal surface of 4H-SiC crystal in a Si-Cr-C solution is thought to be in the step droplet zone. The dependence of the vicinal surface growth rate and the macrostep size n on the driving force ∆µ for a typical state in the step droplet zone in non-equilibrium steady state was calculated using the Monte Carlo method. In contrast to the known step bunching phenomenon, the size of the macrostep was found to decrease with increasing driving force. The detachment of elementary steps from a macrostep was investigated, and it was found that n satisfies a scaling function. Moreover, kinetic roughening was observed for |∆µ| > ∆µ R , where ∆µ R is the crossover driving force above which the macrostep disappears.

Relationship between Macrostep Height and Surface Velocity for a Reaction-Limited Crystal Growth Process

“…Step attachment/detachment model In the case that two surfaces coexist, elementary steps will attach to or detach from the edge of the faceted side surface. The effect of ∆µ on the vicinal surface morphology for |∆µ| < ∆µ R was assessed by considering a step-attachment-detachment model as n evolved over time [22]. This was calculated as…”

“…Thus, if |∆µ| < ∆µ R , then n + can be expressed as n + = ρ 1 v 1 , where ρ 1 and v 1 are the step density and the step velocity of the elementary steps, respectively. Based on the step-attachment-detachment model, surface velocity V can be expressed using more microscopic quantities, as [22,23]…”

“…The resulting energy gain leads to the step-step attraction. Although the p-RSOS model involves a simple lattice, the vicinal surface of the model exhibits a variety of surface configurations with respect to the self-assembling/disassembling of macrosteps depending on the temperature and the driving force for crystal growth [20][21][22][23].…”

Computer Simulations: Essential Tools for Crystal Growth Studies

“…They proposed a theoretical approach that can be used to model the nucleation and growth of small particles for which experimental studies are difficult to perform. Akutsu studied the surface tension, growth rate, and size of macrosteps on the surface of 4H-SiC crystals using the restricted solid-on-solid model [11]. The effects of the driving force on the size of a faceted macrostep and on the growth rate of the vicinal surface were discussed.…”

“…Ito and Akiyama [10] and Akutsu [11] used MC simulations. Elts et al also used a kinetic MC method, which is a simulation method for the mesoscale growth or dissolution of a crystal [7].…”