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A possible mechanism for the formation of a 90{\deg} misfit dislocation atthe Ge/Si(001) interface through homogeneous nucleation is identified fromatomic scale calculations where a minimum energy path connecting the coherentepitaxial state and a final state with a 90{\deg} misfit dislocation is foundusing the nudged elastic band method. The initial path is generated using arepulsive bias activation procedure in a model system including 75000 atoms.The energy along the path exhibits two maxima in the energy. The first maximumoccurs as a 60{\deg} dislocation nucleates. The intermediate minimumcorresponds to an extended 60{\deg} dislocation. The subsequent energy maximumoccurs as a second 60{\deg} dislocation nucleates in a complementary, mirrorglide plane, simultaneously starting from the surface and from the first60{\deg} dislocation. The activation energy of the nucleation of the seconddislocation is 30% lower than that of the first one showing that the formationof the second 60{\deg} dislocation is aided by the presence of the first one.The simulations represent a step towards unraveling the formation mechanism of90{\deg} dislocations, an important issue in the design of growth proceduresfor strain released Ge overlayers on Si(100) surfaces, and more generallyillustrate an approach that can be used to gain insight into the mechanism ofcomplex nucleation paths of extended defects in solids.

Minimum energy path for the nucleation of misfit dislocations in Ge/Si(001) heteroepitaxy