# Stranski-Krastanov mechanism of growth and the effect of misfit sign on quantum dots nucleation

## TL;DR

This paper analyzes the thermodynamics of the Stranski-Krastanov growth mode, highlighting how the sign of lattice misfit influences quantum dot nucleation, island stability, and growth mechanisms.

## Contribution

It provides a detailed thermodynamic model explaining how misfit sign affects growth modes and island formation in epitaxial quantum dots.

## Key findings

- Critical island size diverges at a specific misfit value.
- Different transformation mechanisms occur in tensile vs. compressed overlayers.
- Monolayer islands are precursors to 3D island formation.

## Abstract

The thermodynamics of the Stranski-Krastanov mode of epitaxial growth and the effect of the sign of the lattice misfit are discussed. The Stranski-Krastanov mode of growth represents a sequence of layer-by-layer or Frank-van der Merwe growth followed by the formation of three-dimensional (3D) islands or Volmer-Weber growth. The occurrence of both growth modes mentioned above is in compliance with the wettability criterion of Bauer. The positive wetting function required for the occurrence of the Volmer-Weber growth is originated by the vertical displacements of the atoms close to the edges of the two-dimensional (2D) islands as a result of the relaxation of the lattice misfit. The monolayer high islands become unstable against bilayer islands, bilayer islands in turn become unstable against trilayer islands, etc. beyond some critical islands sizes. Monolayer islands appear as necessary precursors of three-dimensional (3D) islands. The critical island size for mono-bilayer transformation increases steeply with decreasing lattice misfit and diverges at a critical value of the misfit. This value divides the regions of Frank-van der Merwe and Stranski-Krastanov modes in a phase diagram of coordinates wetting-misfit. The transformation of monolayer to multilayer islands takes place either by consecutive nucleation and growth of 2D islands (layer-by-layer transformation), or by nucleation and lateral (2D) growth of multilayer islands (multilayer 2D transformation). The former occurs in the case of "stiff" overlayer materials and mostly in compressed overlayers. The latter takes place in the case of "soft" materials like Pb and In, mostly in tensile overlayers. Tensile films show non-nucleation transformation compared with the nucleation-like behavior of compressed films.