Evolution of terrace size distributions during thin-film growth by step-mediated epitaxy

Abstract

Under certain conditions the process of thin-film epitaxy can be envisioned as atom deposition onto a crystalline substrate with subsequent surface diffusion along the surface terraces and eventual atomic bonding at a surface step. This process of step-mediated growth is currently being explored as a mechanism to form two-dimensional periodic structures. Such schemes require a periodic step distribution, i.e., uniform terrace lengths, to succeed. In this paper we use a model based on step-mediated growth to present an analytical derivation of the approach to uniform terrace lengths on a stepped surface, given a terrace length distribution of finite width at the outset. The results show that growth interruption is of no advantage and that in general the approach to uniform terrace lengths is quite slow. The width of the terrace length distribution varies approximately as the inverse 4th root of the deposited coverage. This will only occur if the atoms attach themselves predominately at the up-step of each terrace. Otherwise, the width of the distribution will grow without bounds. The model further predicts characteristic oscillations of terrace lengths in the vicinity of multiple height steps.

Anomalous Temperature-Dependent Bimodal Size Evolution of InAs Quantum Dots on Vicinal GaAs(100) Substrates

“…Our seemingly surprise results can be explained by taking into account the presence of the multi atomic steps on the substrates. At low growth temperature (below 520 o C), the energy barrier [12] at the step kinks can limit the migration of adatoms within two nearby steps effectively. Since nucleation on steps is energetically favorable, the multiatomic steps provide a large amount of nucleation sites and enable the formation of smaller critical nuclei for island growth [14], which results in small average diameters and high island densities, as observed in our QD growth.…”

“…The small QDs formed on step edges are not in thermal equilibrium and will subsequently develop into the energetically favorable large QDs. However, on the vicinal substrate, the migration of adatoms from a terrace to another terrace across the steps is prohibited due to the energy barrier formed at the step kinks [12]. This leads to a lower surface diffusion length, which slows down the transformation of the small QDs into the energetically favorable dots and in this case bimodal distribution of QDs appears.…”

Effects of controlled ambidirectional nucleation on the heteroepitaxial growth of m-GaN on m-sapphire

“…Many grain boundaries are observed in m-GaN films grown on m-sapphires off-cut toward the ͗0001͘ direction ͓Fig. Assuming the film grows by step-flow mode, 14 adatoms attach preferentially at the step edge which is energetically the lowest position in terms of SPE, the growth will start from step edge. 2͑b͔͒, respectively.…”

Second Layer Nucleation and the Shape of Wedding Cakes

“…Convergence of the time between nucleation events, and the top terrace size at nucleation, as a function of 1Convergence of numerically generated wedding cakes to the asymptotic shape function Φ(x). The symbols show the coverage profile rescaled according to(25).…”