Spiral Growth and Step Edge Barriers

Abstract

The growth of spiral mounds containing a screw dislocation is compared to the growth of wedding cakes by two-dimensional nucleation. Using phase field simulations and homoepitaxial growth experiments on the Pt(111) surface we show that both structures attain the same large scale shape when a significant step-edge barrier suppresses interlayer transport. The higher vertical growth rate of the spiral mounds on Pt(111) reflects the different incorporation mechanisms for atoms in the top region and can be formally represented by an enhanced apparent step-edge barrier.

Thin interface analysis of a phase-field model for epitaxial growth with nucleation and Ehrlich–Schwoebel effects

“…Therefore, in our opinions, models with an extra nucleation term are lack of quantitative and not suitable for the larger scale simulations. We emphases that Redinger et al [31] have studied spiral growth with step edge barriers, which can be comparable with the growth of wedding cakes by two-dimensional nucleation. Since no extra term is needed to the phase-field model, their conclusions and results are more rational and quantitative.…”

Phase-field modeling of anomalous spiral step growth on Si(001) surface

“…In the presence of an Ehrlich-Schwoebel barrier, the spiral step growth deviates from the uniform step spacing and forms a typical mound shape with steep edges. 3 Both regimes can be found in practical applications; the models however neglect the influence of the strain field resulting from the screw dislocation. Taking these effects into account might lead to anomalous spiral step motion as recently found on a Si͑001͒ surface.…”

“…Phasefield approach has already been applied to conventional spiral growth, surface phase transition, and island growth, where complex factors such as anisotropy, attachment kinetics, Ehrlich-Schwoebel barrier, and nucleation kinetics are incorporated successfully. 2,3,[8][9][10][11][12][13] Here, we extend the phasefield description of the step motion by considering the surface phase switching between ͑1 ϫ 2͒ and ͑2 ϫ 1͒ during the surface growth and sublimation. Our simulations reproduce the anomalous spiral motion on the Si͑001͒ surface.…”

Phase-field modeling of epitaxial growth with the Ehrlich-Schwoebel barrier: Model validation and application

“…According to BCF theory, this model suggests that steps/terraces are quantitatively represented by a continuous variable order parameter (called the phase-field , which is an integer on terraces and a decimal at steps). Because explicit tracking of the fronts is obviously not required, this model has become a comprehensive and quantitative description of the dynamic processes of crystal growth [20].…”

“…The phase-field model [17][18][19][20][21][22][23][24], which is based on the Ginzberg-Landau theory of phase transition, has been widely applied as a novel and promising method for continuous simulation of epitaxial growth. It becomes popular because it applies to a wide range of simulation scales, i. e., a mesoscopic scale of simulations.…”