The Hagen-Strunk multiplication mechanism of misfit dislocations in lattice-mismatched hetero-epitaxial layers was investigated within the realm of elasticity theory. A necessary condition for the mechanism was proposed by considering the equilibrium of the forces that were exerted on a dislocation segment, and resulted from the annihilation of 2 crossing misfit dislocations. Under these conditions, the critical layer thicknesses at which Hagen-Strunk multiplication ceased were calculated for the present systems. These critical thicknesses were smaller than the critical Matthews-Blakeslee values. This suggested that multiplication due to the Hagen-Strunk mechanism was not likely to occur in hetero-epitaxial layers.

Y.Obayashi, K.Shintani: Philosophical Magazine Letters, 1997, 76[1], 1-7