Misfit stress relaxation in $\alpha$-Ga$_{2}$O$_{3}$/$\alpha$-Al$_{2}$O$_{3}$ heterostructures via formation of misfit dislocations

A theoretical model of misfit stress relaxation in film/substrate $\alpha$-Ga$_{2}$O$_{3}$/$\alpha$-Al$_{2}$O$_{3}$ heterostructures with allowance for lattice anisotropy of heterostructure materials is proposed. Nucleation of misfit dislocations as a result of basal or prismatic slip in $\alpha$-Ga$_{2}$O$_{3}$/$\alpha$-Al$_{2}$O$_{3}$ heterostructures with different film orientations is considered. Dependences of critical thickness $h_c$ (above this thickness nucleation of misfit dislocations is favorable) on angle $\vartheta$ between the polar $c$-axis and the normal to the film growth plane for $\alpha$-Ga$_{2}$O$_{3}$/$\alpha$-Al$_{2}$O$_{3}$ heterostructures are obtained. It is shown that consideration of elastic constant $C_{14}$ in these models of relaxation in $\alpha$-Ga$_{2}$O$_{3}$/$\alpha$-Al$_{2}$O$_{3}$ heterostructures is unnecessary.