CALCULATION OF CRITICAL-LAYER-THICKNESS AND STRAIN RELAXATION IN GEXSI1-X STRAINED LAYERS WITH INTERACTING 60 AND 90-DEGREES DISLOCATIONS

In view of the recent experimental evidence that 90-degrees dislocations also play a significant role in relaxing strain in the GexSi1-x strained layers, properties of the layers containing these dislocations are examined theoretically. The important results are: (1) the expression for the critical thickness h(c) derived by Van der Merwe neglecting dislocation interactions is valid for the 90-degrees dislocations but not for 60-degrees dislocations when dislocation interactions are included in the theory; (2) the critical layer thickness for 90-degrees dislocations is always smaller than that for 60-degrees dislocations. Typically, for x = 0.1, h(c) = 127 angstrom for 90-degrees dislocations as compared to 236 angstrom for 60-degrees dislocations; (3) For layers in equilibrium, and for a given thickness h > h(c) the number of dislocations introduced is smaller, the total energy lower, and the strain relaxation larger for 90-degrees dislocations as compared to 60-degrees dislocations. These results suggest that in thermodynamic equilibrium, 90-degrees dislocations should be preferred for strain relaxation. Recent experimental results are consistent with this finding; (4) in recent literature, the energy of a dislocation array has been calculated by taking into account only nearest neighbour interactions. We find that this method gives large error in the value of the total energy and strain relaxation; (5) effect of non-periodic distribution of dislocations on the energy of the strained layer is examined briefly. Approximating the non-periodic array with average spacing pBAR with a periodic array with dislocation spacing p = pBAR gives large errors in the calculated values of the energy and strain relaxation. Calculations show that for h > h(c), the equilibrium strain relaxation is smaller for non-periodic distribution. The excess stress, which determines the driving force and the strain relaxation when a thick metastable layer is annealed, is larger for 90-degrees dislocations than for 60-degrees dislocations.