The critical thickness of silicon-germanium layers grown by liquid phase epitaxy

Silicon-germanium layers are grown from metallic solution on (100) and (111) silicon substrates. On (111) Si, coherently strained dislocation-free SiGe layers are obtained with thicknesses larger than predicted by the current models of misfit-induced strain relaxation. A comprehensive characterisation by imaging, diffraction, and analytical electron microscopy techniques is carried out to determine the critical thickness, study the onset of plastic relaxation, and explain the particular growth mechanisms leading to an unexpectedly high thickness of elastically strained SiGe layers. A vertical Ge concentration gradient and the formation of step edges on the layers, where lateral strain relaxes locally, explain the high critical thickness. The model of Matthews and Blakeslee is modified in order to match the experimental observations for solution-grown SiGe layers.