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Strain-stress relationships for coherent in-plane strain in heterostructures with monoclinic crystal systems : β-(AlxGa1−x)2O3 on (h0l)β-Ga2O3 as example

Schubert, Mathias LU orcid ; Korlacki, Rafał ; Khayam, Sina ; Traouli, Yousra ; Sorensen, Preston ; Papamichail, Alexis and Darakchieva, Vanya LU (2025) In Physical Review Applied 24(4).
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 (h0l) surface orientations. We use β-(AlxGa1−x)2O3 on... (More)

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 (h0l) surface orientations. We use β-(AlxGa1−x)2O3 on (h0l)β-Ga2O3 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 (h0l). We further demonstrate the effect of the orientation-dependent differently strained domains and calculate the strain-shifted anisotropic band-to-band transitions for β-(Al0.1Ga0.9)2O3 on (h0l)β-Ga2O3. 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.

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author
; ; ; ; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review Applied
volume
24
issue
4
article number
044075
publisher
American Physical Society
external identifiers
  • scopus:105024852128
ISSN
2331-7019
DOI
10.1103/5gx2-kn6m
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2025 authors. Published by the American Physical Society.
id
6fdc4e7f-f739-49e2-ad41-34357cc13694
date added to LUP
2026-02-23 13:25:00
date last changed
2026-03-04 09:31:13
@article{6fdc4e7f-f739-49e2-ad41-34357cc13694,
  abstract     = {{<p>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 (h0l) surface orientations. We use β-(Al<sub>x</sub>Ga<sub>1−x</sub>)<sub>2</sub>O<sub>3</sub> on (h0l)β-Ga<sub>2</sub>O<sub>3</sub> 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 (h0l). 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<sub>0.1</sub>Ga<sub>0.9</sub>)<sub>2</sub>O<sub>3</sub> on (h0l)β-Ga<sub>2</sub>O<sub>3</sub>. 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.</p>}},
  author       = {{Schubert, Mathias and Korlacki, Rafał and Khayam, Sina and Traouli, Yousra and Sorensen, Preston and Papamichail, Alexis and Darakchieva, Vanya}},
  issn         = {{2331-7019}},
  language     = {{eng}},
  month        = {{10}},
  number       = {{4}},
  publisher    = {{American Physical Society}},
  series       = {{Physical Review Applied}},
  title        = {{Strain-stress relationships for coherent in-plane strain in heterostructures with monoclinic crystal systems : β-(Al<sub>x</sub>Ga<sub>1−x</sub>)<sub>2</sub>O<sub>3</sub> on (h0l)β-Ga<sub>2</sub>O<sub>3</sub> as example}},
  url          = {{http://dx.doi.org/10.1103/5gx2-kn6m}},
  doi          = {{10.1103/5gx2-kn6m}},
  volume       = {{24}},
  year         = {{2025}},
}