Work

Strain-stress relationships for coherent in-plane strain in heterostructures with monoclinic crystal systems: β - ( Al x Ga 1 − x ) 2 O 3 on ( h 0 l ) β - Ga 2 O 3 as example

Year: 2025

Type: article

Abstract: In this work, we derive the relationship between the states of strain and stress in pseudomorphic epitaxial layers on a substrate with differing equilibrium lattice parameters under symmetry-conserving conditions for the case of monoclinic crystal symmetry. We compare surface vectors across the template-epitaxial layer interface and impose conditions of a stress-free epitaxial layer. As a result, we demonstrate the theoretical existence of up to three possible unit cells that can establish on a given template. We demonstrate this approach for the special case of symmetry-conserving strain in a class of templates with ( h 0 l ) surface orientations. We use β - ( Al x Ga 1 − x ) 2 O 3 on ( h 0 l ) β - Ga 2 O 3 as an example. We discuss the effects of the composition x and surface orientation on the formation of three elastically stable unit cells, their strain and stress tensors, unit-cell axes, unit-cell volumes, lattice spacings, elastic potential energies, and stress-free directions. The previous paradigm for epitaxial layer growth, where the only stress-free direction is perpendicular to the growing surface, is not generally valid for low-symmetry materials. In the example here, we find that, in addition to the stress-free growth direction for crystallographic planes with low Miller indices, two possible competing domains can exist with stress-free directions oblique to the surface of the template for almost all planes ( h 0 l ) . We further demonstrate the effect of the orientation-dependent differently strained domains and calculate the strain-shifted anisotropic band-to-band transitions for β - ( Al 0.1 Ga 0.9 ) 2 O 3 on ( h 0 l ) β - Ga 2 O 3 . We also provide examples of x-ray diffraction analyses, which may help guide the search for the occurrence of such differently strained unit cells in epitaxial layers grown by experiment, here taking the ( 2 ¯ 01 ) surface orientation as case for demonstration.

Source: Physical Review Applied

DOI: 10.1103/5gx2-kn6m