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 $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -(Al $$_x$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mi>x</mml:mi> </mml:msub> </mml:math> Ga $$_{1-x}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:mi>x</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mn>2</mml:mn> </mml:msub> </mml:math> O $$_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mn>3</mml:mn> </mml:msub> </mml:math> thin films are grown by combinatorial pulsed laser deposition in the entire composition range on prismatic a- and m-plane $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -Al $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mn>2</mml:mn> </mml:msub> </mml:math> O $$_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mn>3</mml:mn> </mml:msub> </mml:math> substrates. Pseudomorphic growth on m-plane sapphire has been achieved for $$x \ge 0.45$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>0.45</mml:mn> </mml:mrow> </mml:math> . 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 $$e'_5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>e</mml:mi> <mml:mn>5</mml:mn> <mml:mo>′</mml:mo> </mml:msubsup> </mml:math> 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 $$e'_5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>e</mml:mi> <mml:mn>5</mml:mn> <mml:mo>′</mml:mo> </mml:msubsup> </mml:math> are modeled as function of x employing elasticity theory, confirming theoretical values of the elastic stiffness tensor for $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -Ga $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mn>2</mml:mn> </mml:msub> </mml:math> O $$_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mn>3</mml:mn> </mml:msub> </mml:math> , especially the non-zero value of the $$C_{14}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>C</mml:mi> <mml:mn>14</mml:mn> </mml:msub> </mml:math> 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

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