Critical coverage for strain-induced formation of InAs quantum dots

The critical coverage ${\theta }_C$ for the strain-induced transformation of initial two-dimensional (2D) InAs or InGaAs growth islands into quantum-dot-like three-dimensional (3D) islands is studied with in situ electron diffraction under variation of the flux F, temperature T, and lattice mismatch $\delta$ given by the Ga content in InGaAs films. The experimental data are compared to calculations based on a kinetic rate model with layer dependent strain energy inside the islands. With the growth model, the lateral size distribution and the height of the islands is calculated, as well as ${\theta }_C.$ Good agreement between experiments and rate equation results is obtained for the influence of $\delta$ and F on ${\theta }_C,$ whereas the T dependencies show a contradictory behavior. This is explained by a temperature-dependent intermixing between the deposited In and Ga from the substrate. Considering this effect in the calculations allows a determination of the temperature-dependent Ga content. Additional calculation results point out that the island diameter shrinks during the 2D to 3D transition and that the island shape is not in equilibrium during growth.