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

Abstract Pseudomorphic and relaxed $$\alpha$$ α -(Al$$_x$$ x Ga$$_{1-x}$$ 1 - x )$$_2$$ 2 O$$_3$$ 3 thin films are grown by combinatorial pulsed laser deposition in the entire composition range on prismatic a- and m-plane $$\alpha$$ α -Al$$_2$$ 2 O$$_3$$ 3 substrates. Pseudomorphic growth on m-plane sapphire has been achieved for $$x \ge 0.45$$ x ≥ 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 $$e'_5$$ 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 $$e'_5$$ e 5 ′ are modeled as function of x employing elasticity theory, confirming theoretical values of the elastic stiffness tensor for $$\alpha$$ α -Ga$$_2$$ 2 O$$_3$$ 3 , especially the non-zero value of the $$C_{14}$$ C 14 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