Elastic Strain Relaxation in Si 1-x Ge x Layers Epitaxially Grown on Si Substrates

We have investigated the elastic strain relaxation in Si 1-x Ge x layers grown by the molecular beam epitaxy (MBE) technique and in situ controlled with RHEED. Up to ≈0.8% critical lattice mismatch (about 20% Ge) uniform strained and flat layers were grown both on (111) and on (001) Si substrates. Calculations of the elastic constants evidenced a tetragonal distortion about 50% higher on (001) than on (111) in the same experimental conditions. At higher misfits (and/or thicknesses) a growth instability was evidenced only on (001) Si substrates. Si 1-x Ge x layers there displayed a surface layer undulation. On the contrary, Si 1-x Ge x layers grown on (111) Si substrates remained smooth throughout the growth up to the plastic relaxation of the layers. To determine stress fields in the Si 1-x Ge x layers, a high spatial resolution convergent beam electron diffraction (CBED) experiment was performed with a field effect analytical microscope. The CBED technique was applied to two typical cases: totally strained layer and undulated dislocation-free layer. In the latter case, CBED patterns recorded on nanometer scale areas of an undulation crest (cross-section sample) showed a gradual elastic relaxation mainly directed along the growth axis (z). Moreover a triclinic distortion of the unit cell was pointed out. These results were confirmed on a plane view sample. In conclusion, our results show that the driving force for the undulation is not the in-plane elastic relaxation since CBED experiments proved an important elastic relaxation of the (001) Si 1-x Ge x layers along the z axis. This was in agreement with the calculations of the elastic constants. We think that this could be at the origin of the undulation.