Strain profiles in pyramidal quantum dots by means of atomistic simulation

The minimum energy configurations of the atomic structure of a Ge island on a Si(001) substrate are calculated by using the conjugate gradient minimiz ation of the potential energy of the system. The island is assumed to be co vered or uncovered by a Si layer and assumed to be of pyramidal shape with the sidewalls of {110} or {105} facets; the base length of the island range s from 5.43 to 10.9 nm. Two empirical potentials, the Keating and Stillinge r-Weber potentials, are used. At the interfaces between the regions occupie d by the atoms of different species, the potential parameters for such bond ings are properly adopted. The strain profiles along the three selected pat hs within the structure and along the cap surface are calculated. While the profiles of the normal strain component epsilon (xx) obtained by the two p otentials are in good agreement with each other except within the substrate and at the edges of the island in the uncovered structures, the two profil es of the normal strain component epsilon (zz) show a considerable differen ce in their magnitude, and the use of the Stillinger-Weber potential is rec ommended for the islands of the small sizes below 10 nm. The validity of th e valence force field model with the Keating potential for such small islan ds is questionable although this model is widely recognized to be applicabl e to the calculation of strains in the quantum dot structures. The strain r elaxation in the uncovered island is discussed through the comparison with that in the covered island. The strain profile along the cap surface explai ns vertical self-organization of stacked dots. (C) 2001 American Institute of Physics.