Properties of an array of dislocations in a strained epitaxial layer

The energy of a general array of dislocations in an epitaxial layer is formulated and expressed in terms of per unit area of interface. Several limiting cases are used to verify the solution and the results are compared to other independent treatments. The critical thickness required for the generation of an isolated dislocation is found by solving for the layer thickness which corresponds to a zero value of the formation energy. The critical dislocation density at a given thickness is also determined. An additional work required for sequential generation of dislocations in an epitaxial layer arises from dislocation-dislocation interaction and has to be expressed in terms of per unit length of dislocation line. The work hardening effect is found to increase sharply with decreasing distance between the fresh and the pre-existing dislocations once the distance falls below approximately twenty times the layer thickness. The additional work achieves the level of the self energy of an isolated dislocation when the distance between the fresh and the nearest pre-existing dislocation is comparable to twice the layer thickness.