Misfit dislocations in finite lateral size Si1-xGex films grown by selective epitaxy

Abstract

In this paper, the reduction of misfit dislocation density on small pads of selectively grown Si1-xGex films is studied experimentally and theoretically. The experiments were performed mainly on Si1-xGex layers with x=0.12 grown on patterned substrates with pad sizes of 10×10 to 104×104 μm2. The misfit dislocations were detected by optical and transmission electron microscopy. It was observed that on small pads, misfit dislocations are generated at a significantly higher critical thickness than on extended areas, while pads of size 10×10 μm2 or smaller showed no evidence of misfit dislocations at all. The theoretical analysis was performed in two steps. First, an elastic strain model was used to calculate the pad size dependence of the critical thickness. The main hypothesis of the model is that the density of misfit dislocations is solely affected by the elastic relaxation at the edges of small epitaxial areas. This equilibrium model can explain only the experimentally observed absence of misfit dislocations on small pads; however, it predicts a critical thickness for finite sizes much lower than the observed one. Second, a kinetic approach was further performed, in which the relaxation is supposed to be due to nucleation of misfit dislocations at defects and self-multiplication. The best fit with the experimental results was obtained for time constants for generation from defects of 600 min and for self-multiplication of 7 min and a gliding velocity of 12 μm/min. While the onset of relaxation seems to be due generation at defects, the self-multiplication process determines to a great extend the density of misfit dislocations.