Stress–strain state in α-Ga₂O₃ epitaxial films on α-Al₂O₃ substrates

Abstract

We consider the stress–strain state in α-Ga2O3/α-Al2O3 heterostructures, in which both constituting phases belong to trigonal crystal system. We utilize the hexagonal geometry (hexagonal cell) to account for structural features of the materials and include in the analysis the complete set of six elastic constants Cij being typical for materials with rhombohedral crystal structure that differs from materials with hexagonal one by the presence of an additional constant C14. This allows us to derive analytical formulas for elastic strains and mechanical stresses in pseudomorphic α-Ga2O3 films on α-Al2O3 substrates with various growth orientations assuming nonzero constant C14.

Misfit Stress Relaxation in α-Ga2O3/α-Al2O3 Heterostructures via Formation of Misfit Dislocations

“…This is primarily related to the high level of misfit stress in the heterostructure under consideration. It was shown in [24] that the strain level in the α-Ga 2 O 3 /α-Al 2 O 3 heterostructure is approximately MDs were also observed in α-Ga 2 O 3 /α-Al 2 O 3 heterostructures with the film thicknesses of 686 nm [30], 350 nm [31], and 35-90 nm [32]. The experimentally observed values of the α-Ga 2 O 3 film thicknesses lie above the corresponding curves shown in Fig.…”

“…The stress-strain state in the α-Ga 2 O 3 /α-Al 2 O 3 heterostructure with allowance for the anisotropy of materials and arbitrary film orientation was considered in [23]. However, analytical formulas for the misfit stress in an α-Ga 2 O 3 film were not reported in [23]; therefore, the misfit stress tensor determined in [24] is used in our calculations: σ '' '' Film Film Film Substrate Substrate Substrate…”

“…Note that the approach proposed in [23] makes it possible to determine the stress-strain state in the α-Ga 2 O 3 /α-Al 2 O 3 heterostructure with allowance for azimuthal angle φ (along with angle ϑ). In [24], we analyzed a particular case: φ = 0°. However, as was shown in [26] by an example of α-(Al 0.9 Ga 0.1 ) 2 O 3 films formed on α-Al 2 O 3 substrates with different growth planes (( ) at φ = -30° and ( ) at φ = 30°), consideration of azimuthal angle φ barely changes the elastic strain field of the film (by no more than 7%).…”

A Most General and Facile Recipe for the Calculation of Heteroepitaxial Strain

“…We note that ϵ 0 13 6 ¼ 0 for ϕ ¼ 0, in disagreement with previous studies. [21][22][23][24] The graphic result in a previous study [3] also shows that generally ϵ 0 13 6 ¼ 0 for strained rhombohedral heterostructures (ϵ 0 13 ¼ 0 for θ ¼ 0, AEπ=2 and for ϕ ¼ π=6 þ nπ=3, n ∈ ℤ). Thus, the analytical formulas for ϵ 0 11 and ϵ 0 22 in a previous study [21] are not equivalent to the ones given here for ϕ ¼ 0.…”

Comment on “Stress-strain state in α-Ga2O3 epitaxial films on α-Al2O3 substrates” [Appl. Phys. Express 13, 075502 (2020)]

“…In a recent paper, 1) analytical formulas for the strain in lattice-mismatched rhombohedral heterostructures are provided. The authors explicitly relate their result to the case f = 0 of Ref.…”