Strain states and relaxation for $$\alpha$$-(Al$$_x$$Ga$$_1-x$$)$$_2$$O$$_3$$ thin films on prismatic planes of $$\alpha$$-Al$$_2$$O$$_3$$ in the full composition range: Fundamental difference of a- and m-epitaxial planes in the manifestation of shear strain and lattice tilt

Abstract Pseudomorphic and relaxed $$\alpha$$-(Al$$_x$$Ga$$_1-x$$)$$_2$$O$$_3$$ thin films are grown by combinatorial pulsed laser deposition in the entire composition range on prismatic a- and m-plane $$\alpha$$-Al$$_2$$O$$_3$$ substrates. Pseudomorphic growth on m-plane sapphire has been achieved for $$x \ge 0.45$$. A distinct difference between the a- and m-epitaxial plane is observed in reciprocal space map measurements being in agreement with continuum elasticity theory for rhombohedral heterostructures. While pseudomorphic layers on m-plane sapphire show a pronounced shear strain $$e'_5$$ along the c-axis direction, relaxed layers exhibit a global lattice tilt in the same direction. Both effects are not present on the a-epitaxial plane. Out-of-plane lattice constants as well as $$e'_5$$ are modeled as function of x employing elasticity theory, confirming theoretical values of the elastic stiffness tensor for $$\alpha$$-Ga$$_2$$O$$_3$$, especially the non-zero value of the $$C₁₄$$ component. Possible pyramidal slip systems for strain relaxation in c-axis direction are examined to explain and numerically model the difference in lattice tilt for the two substrate orientations. Graphic abstract