Layer-by-layer nucleation mechanism for quantum dot formation in strained heteroepitaxy

Ruoxi Xiang, M. T. Lung, Chi Hang Lam

Research output: Journal article publicationJournal articleAcademic researchpeer-review

15 Citations (Scopus)


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.
Original languageEnglish
Article number021601
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number2
Publication statusPublished - 2 Aug 2010

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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