Strain relaxation in AlGaN under tensile plane stress

Relaxation of tensile strain in ${\mathrm{Al}}_x{\mathrm{Ga}}_{\text{1−x}}$ N layers of different compositions epitaxially grown on GaN/sapphire is investigated. Extended crack channels along $\text{〈2}\overline{11}\text{0〉}$ directions are formed if the aluminum content exceeds a critical value, which decreases with increasing layer thickness. This process is found to limit the average strain energy density to a maximum value of 4 ${\mathrm{J/m}}^2.$ By calculating the stress distribution between cracks and the strain energy release rate for crack propagation, the relaxed strain as measured by x-ray diffraction is correlated to the crack density, and the onsets of crack channeling and layer decohesion are fitted to a fracture toughness of 9 ${\mathrm{J/m}}^2.$ Moreover, the crack opening at the surface is found to linearly increase with the stress. Annealing of samples above the growth temperature introduces additional tensile stress due to the mismatch in thermal expansion coefficients between the layer and substrate. This stress is shown to relieve not only by the formation of additional cracks but also by the extension of cracks into the GaN layer and a thermal activated change in the defect structure.