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Global optimization of transition paths in complex atomic scale systems isaddressed in the context of misfit dislocation formation in a strained Ge filmon Si(001). Such paths contain multiple intermediate minima connected byminimum energy paths on the energy surface emerging from the atomicinteractions in the system. The challenge is to find which intermediate statesto include and to construct a path going through these intermediates in such away that the overall activation energy for the transition is minimal. In thenumerical approach presented here, intermediate minima are constructed byheredity transformations of known minimum energy structures and by identifyinglocal minima in minimum energy paths calculated using a modified version of thenudged elastic band method. Several mechanisms for the formation of a 90{\deg}misfit dislocation at the Ge-Si interface are identified when this method isused to construct transition paths connecting a homogeneously strained Ge filmand a film containing a misfit dislocation. One of these mechanisms which hasnot been reported in the literature is detailed. The activation energy for thispath is calculated to be 26% smaller than the activation energy for half loopformation of a full, isolated 60{\deg} dislocation. An extension of the commonneighbor analysis method involving characterization of the geometricalarrangement of second nearest neighbors is used to identify and visualize thedislocations and stacking faults.

Global transition path search for dislocation formation in Ge on Si(001)