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Title: Layer-by-layer nucleation mechanism for quantum dot formation in strained heteroepitaxy
Authors: Xiang, R
Lung, MT
Lam, CH 
Keywords: Axisymmetric
Critical radius
Elastic strain energy
Facetted surfaces
Fast kinetics
Island formation
Lateral expansion
Nucleation energy
Nucleation mechanism
Quantum Dot
Spontaneous formation
Three-dimensional (3D) islands
Total free energy
Issue Date: 2-Aug-2010
Publisher: American Physical Society
Source: Physical review E, statistical, nonlinear, and soft matter physics, 2 Aug. 2010, v. 82, no. 2, 021601, p.1-8 How to cite?
Journal: Physical review E, statistical, nonlinear, and soft matter physics 
Abstract: We study the spontaneous formation of quantum dots in the form of three-dimensional (3D) islands on facetted surfaces in heteroepitaxy. Island development from fast kinetic Monte Carlo (KMC) simulations at low deposition rates is found to follow a layer-by-layer nucleation pathway characterized by energetics driven continuous lateral expansion interrupted by a sequence of independent two-dimensional (2D) upper-layer nucleation events. The process involves only unstable 2D upper-layer nuclei but no unstable 3D nucleus. We have calculated analytically the elastic strain energy of an island in the form of an axisymmetric stepped mound using a small-slope approximation. The total free energy of a system with a 3D island and an adatom bath is obtained. Our theory explains island formation via a free energy driven layer-by-layer nucleation mechanism. Upper-layer nucleation energy barrier, nucleation time, critical radius, and island step spacings are estimated. The relevance of entropic step-step repulsion is discussed. Our theory satisfactorily explains the 3D KMC simulations and may describe the initial evolution of islands in the form of stepped mounds observed in experiments.
ISSN: 1539-3755 (print)
1550-2376 (online)
DOI: 10.1103/PhysRevE.82.021601
Rights: © 2010 The American Physical Society. The Journal's web site is located at
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