Multiplication of dislocations inSi1−xGexlayers on Si(001)

A mechanism describing how dislocations in epitaxial layers multiply is presented. It is shown that a single threading dislocation can give rise to an array of dislocation sources, where each source generates a separate dislocation loop perpendicular to the primary misfit dislocation. The conditions controlling the activation of these sources are discussed in detail. Most notably, it is demonstrated that a minimum layer thickness, referred to as the ‘‘multiplication thickness,’’ is required to accommodate the cross-slip processes that are necessary for source activation. An experimental value of 0.67 μm for the multiplication thickness ${\mathit{h}}_{\mathit{x}}$ is measured from a single ${\mathrm{Si}}_{0.87}$ ${\mathrm{Ge}}_{0.13}$ layer on Si(001), and a general expression for ${\mathit{h}}_{\mathit{x}}$ is developed. The dislocation patterns produced by this mechanism are also considered, as are the implications of such a mechanism in light of the established view of strain relaxation.