Brittle-to-ductile transition and strain relaxation in Si$_{1-x}$Ge$_x$ linearly graded buffers

TL;DR

The paper investigates how Si$_{1-x}$Ge$_x$ linearly graded buffers (LGBs) relieve strain and how the relaxation mechanism transitions from dislocation glide to nucleation as growth temperature increases. Using LEPECVD to grow $Si_{0.6}Ge_{0.4}$ LGBs with a fixed final composition but different temperature profiles, the authors combine defect-etching, AFM, and temperature-dependent high-resolution X-ray diffraction to distinguish glide-dominated and nucleation-driven relaxation. A sharp change in threading dislocation density (TDD) around $T_c \,\approx\ 530^\circ$C accompanies a switch from glide to nucleation, with annealing experiments confirming nucleation as the primary route to extra relaxation above $T_c$. The work links this relaxation behavior to the brittle-to-ductile transition (BDT) in SiGe, offering a tunable approach to control strain and motivating further BDT-related epitaxial studies, with data publicly available at Zenodo.

Abstract

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.

Figures (6)

• Figure 1: Variation of temperature (left axis) and composition (right axis) during growth for the set of LGBs featuring ${x_f=0.4}$ and different final temperatures. The gray area shows an estimation the brittle -ductile transition temperature in Si$_{1-x}$Ge$_x$.
• Figure 2: Structural characterization of sample A5. a) Room temperature RSM around the (224) diffraction peak showing the continuous variation of composition between the Si substrate and the Si$_{0.6}$Ge$_{0.4}$ relaxed buffer. b) AFM image of the cross-hatch pattern.
• Figure 3: Threading dislocation density in Si$_{0.6}$Ge$_{0.4}$ LGBs. (a) TDD vs. final temperature. The plot reports the density of so-called field TDs, i.e. dislocations not piled-up in clusters, and the total number of TDs. The roughness dependence on the final temperature can be read on the right-hand y-axis. Panels (b) and (c) show representative optical micro-graphs obtained after defect etching of samples A1 (T$_f=510\,^\circ$C) and A5 (T$_f=580\,^\circ$C), respectively.
• Figure 4: Degree of relaxation at different post-growth annealing temperatures as measured by VT-HRXRD. For each of the A-samples ($x_f=0.4$) listed in Tab. \ref{['tab:samples']} the relaxation has been measured during a 1st heating ramp (empty circles), cool-down (empty diamonds) and a 2nd heating ramp and cool-down (stars)
• Figure 5: Total (filled circles) and field (empty circles) density of TDs in Si$_{1-x}$Ge$_{x}$ LGBs with increasing Ge content. The low T data-points refer to samples A1, B1, C1, and D, the high T data-points to A5, B5, and C5 described in Tab. \ref{['tab:samples']}.