Entropy-Driven Effects in Self-Organized Formation of Quantum Dots

Finite-temperature thermodynamic theory is developed for equilibrium arrays of two-dimensional monolayer-high islands in heteroepitaxial systems at submonolayer coverage. It is shown that the entropy contribution to the Helmholtz free energy of the system favors formation of smaller islands at higher temperatures which results in a decrease of the average number of atoms in the islands (the island volume) with temperature. The characteristic temperature T char , at which the island volume is significantly decreased compared to its value at T = 0 K, is found to be far below the characteristic energy of the island formation and to lie in a region of several hundreds of K. Such a temperature dependence can be the basis for decisive experiments aimed at distinguishing between thermodynamic and kinetic effects in the formation of arrays of 2D islands. Results of high resolution electron microscopy and photoluminescence spectroscopy of a submonolayer InAs/GaAs(001) system are in agreement with the theory. It confirms that the formation of a sub-monolayer array of InAs/GaAs(001) islands is predominantly influenced by thermodynamics.