  A possible mechanism for the formation of a 90{\deg} misfit dislocation at
the Ge/Si(001) interface through homogeneous nucleation is identified from
atomic scale calculations where a minimum energy path connecting the coherent
epitaxial state and a final state with a 90{\deg} misfit dislocation is found
using the nudged elastic band method. The initial path is generated using a
repulsive bias activation procedure in a model system including 75000 atoms.
The energy along the path exhibits two maxima in the energy. The first maximum
occurs as a 60{\deg} dislocation nucleates. The intermediate minimum
corresponds to an extended 60{\deg} dislocation. The subsequent energy maximum
occurs as a second 60{\deg} dislocation nucleates in a complementary, mirror
glide plane, simultaneously starting from the surface and from the first
60{\deg} dislocation. The activation energy of the nucleation of the second
dislocation is 30% lower than that of the first one showing that the formation
of the second 60{\deg} dislocation is aided by the presence of the first one.
The simulations represent a step towards unraveling the formation mechanism of
90{\deg} dislocations, an important issue in the design of growth procedures
for strain released Ge overlayers on Si(100) surfaces, and more generally
illustrate an approach that can be used to gain insight into the mechanism of
complex nucleation paths of extended defects in solids.
