A layer-by-layer growth mechanism for three-dimensional island nucleation in strained heteroepitaxy

Abstract

A theoretic model of layer-by-layer growth for heleroepilaxial films is introduced in this thesis, in order to explain the morphological evolution of strained hctcrocpitaxial films. The energetics related to island formation are analyzed. There are two main energy terms which contribute to the total free energy for the whole system: strain energy and island step free energy. We have investigated two-dimensional (2D) circular single layer islands and stacked three-dimensional (3D) circular islands with n layers (n >= 2). The island strain energy is calculated by using a small-slop approximation, and the step free energy is calculated by using a ball and spring model. Moreover, we have considered the entropic repulsion between two adjacent steps. This model can explain the following observations from simulation results using kinetic Monte Carlo method under slow deposition conditions. At the early stage of a deposition process, only 2D islands exist. Next, 3D island formation follows a layer-by-layer growth mode. Only if an n-layer island grows laterally larger can a new layer of atoms nucleate on lop. There is an equilibrium shape for an n-layer island: the separation between the steps at adjacent layer decreases when the number of layers of the island increases accompanying deposition. Good agreement is found between the model and the Kinetic Monte Carlo simulation results.