Simulation of the Process of Strain Relaxation in Si1—xGex/Si(100) Heterostructures

For a series of metastable Si1—xGex/Si(100) (0.25 < x ≤ 0.3) heterostructures, the plastic strain relaxation during post-growth annealing at temperatures between 850 and 900 °C is studied by in situ X-ray diffraction. This method measures in particular the later stages of the strain relaxation process, when the mean distance between parallel misfit dislocations is already below 1 μm. The obtained relaxation curves are simulated by means of a model proposed by Gosling, Jain, and Harker. Their theoretical analysis led to two coupled rate equations for the degree of plastic relaxation and the number of mobile threading dislocations. The latter may be changed by dislocation nucleation, multiplication, and blocking. We show that a reasonable fitting of the experimental values is only possible if the model is appropriately modified. In particular, the blocking rate has to be changed to a continuous instead of the proposed abrupt decrease of the number of mobile dislocations. This empirically found deviation from the Gosling model may be explained in terms of a number of inter-related factors, which effectively reduce the number of mobile dislocations.