REDUCED EFFECTIVE MISFIT IN LATERALLY LIMITED STRUCTURES SUCH AS EPITAXIAL ISLANDS

Numerical finite element calculations have been reported to determine a correction function Φ that describes the reduction of the misfit that occurs when laterally limited structures such as faceted islands or mesa structures are grown on a substrate. The reduction of the average strain energy density is calculated in these three-dimensional islands and compared to the constant strain energy density in a continuous layer. Ratios Φ are obtained from the calculation of different island geometries, i.e., different facet angles γ and different aspect ratios island width l to island height h. These discrete values are fitted by a function which can easily be applied to the full range of aspect ratios (l/h>0) and facet angles (0°<γ<90°). Faceted Ge(Si) islands on Si(001) substrate, grown from the solution in the Stranski-Krastanov growth mode, serve as an example for the calculation. Experimental and theoretical values for the critical thickness of these islands agree well. This result demonstrates the drastic influence of islanding on misfit strain distribution in island and substrate as well and, consequently, on the strong increase of the critical thickness as determined by the mechanical equilibrium theory of Matthews and Blakeslee. © 1995 American Institute of Physics.