Brittle-to-ductile transition and strain relaxation in Si$_{1-x}$Ge$_x$ linearly graded buffers
The strain-relaxation mechanism of a set of Si$_{0.6}$Ge$_{0.4}$ linearly graded buffers (LGBs), grown following different temperature profiles, has been investigated by means of defect-etching and variable-temperature high-resolution X-ray diffraction (VT-HRXRD). Defect-etching experiments demonstrate that a sharp increase of threading dislocation density (TDD) from $3 \times 10^{5}$\,cm$^{-2}$ to $1.2 \times 10^{6}$\,cm$^{-2}$ takes place when the final growth temperature exceeds a critical value T$_c\approx 530^\circ$C. VT-HRXRD measurements show that in low TDD samples extra relaxation takes place for annealing temperatures larger than T$_c$, thanks to the nucleation of new dislocations. These results indicate that, below T$_c$, strain relaxation is driven by the gliding of existing dislocations while above T$_c$ new dislocations are nucleated, suggesting a link with our results and the brittle-to-ductile transition in Si$_{1-x}$Ge$_x$ alloys.