Lattice parameters and elastic properties for strain analysis in <i>κ</i>-(In<i>x</i>Ga1−<i>x</i>)2O3/<i>κ</i>-Ga2O3/Al2O3 heterostructures from density functional theory, x-ray diffraction, and scanning precession nanobeam electron diffraction

Abstract

In this publication, we study strain in κ-(InxGa1−x)2O3/κ-Ga2O3/Al2O3 heterostructures grown by plasma-assisted molecular beam epitaxy using a combination of density functional theory (DFT), x-ray diffraction (XRD), nanobeam electron diffraction (NBED), and energy-dispersive x-ray spectroscopy (EDX) for layers with low (2%) and high (18%) In concentration. Lattice parameters and elastic moduli were computed using the density functional theory formalism. The strain between κ-(InxGa1−x)2O3 and κ-Ga2O3 as well as Al2O3 and κ-Ga2O3 was measured in two different zone axes by NBED. Due to the quasi-hexagonality of the κ-phase, this yields an approximation for the full strain tensor. The obtained NBED results are supported by reciprocal space maps from XRD measurements. The relaxation of the layers was analyzed by comparing the measured strain data with those computed from the DFT lattice parameters and elastic moduli using the element concentrations measured by EDX, thus allowing for direct validation of the theoretical calculations by experimental data. This analysis results in satisfactory agreement and reveals that the layer with a low In concentration is fully strained (measured εzz=0.0037, computed εzz=0.0039), whereas the layer with high In concentration is fully relaxed (measured εzz=0.0222, computed εzz=0.0219). NBED, XRD, and theoretical predictions agree within their respective error margins for the strain between κ-(InxGa1−x)2O3 and κ-Ga2O3. Overall, the absolute value of the strain between κ-Ga2O3 and Al2O3 was measured to be smaller by NBED (measured εzz=−0.0628) and XRD than it was computed from literature lattice parameters (εzz=−0.0716).