Adsorption-controlled Plasma-Assisted Molecular Beam Epitaxy of LaInO3 on DyScO3 (110): Growth Window, Strain Relaxation, and Domain Pattern

${\mathrm{LaInO}}_{3}$ is a lattice-matched barrier material for the confinement of two-dimensional electron gases at the interface with the perovskite ${\mathrm{BaSnO}}_{3}$, which is known for its high room-temperature electron mobility. Here, we report the adsorption-controlled growth of epitaxial ${\mathrm{LaInO}}_{3}$ by molecular beam epitaxy (MBE), a growth method that has demonstrated the highest electron mobilities in ${\mathrm{SrTiO}}_{3}$ and ${\mathrm{BaSnO}}_{3}$ thin films. The adsorption-controlled growth was monitored using line-of-sight quadrupole mass spectrometry. In a thermodynamics of MBE diagram, the experimental growth window was found to be significantly narrower than the theoretically predicted one. We found the critical thickness for strain relaxation of the ${\mathrm{LaInO}}_{3}$ layer on ${\mathrm{DyScO}}_{3}$(110) substrates (lattice mismatch $\ensuremath{\approx}\ensuremath{-}4%$) to be 1 nm using in situ reflection high-energy electron diffraction analysis. The substrate and film possess an orthorhombic crystal structure which can be approximated by a pseudocubic lattice. X-ray-diffraction analysis revealed the pseudocube-on-pseudocube epitaxial relationship of the ${\mathrm{LaInO}}_{3}$ films to the ${\mathrm{DyScO}}_{3}$ substrates. This relation was confirmed by transmission electron microscopy, which further resolved the presence of rotational orthorhombic domains, the majority of which have a $c$ axis that coincides with that of the substrate. Raman spectroscopy further confirmed the presence of a ${\mathrm{LaInO}}_{3}$ layer. Our findings provide the missing building block for the realization of two-dimensional electron gases with high room-temperature electron mobilities at the MBE-grown heterointerface with ${\mathrm{BaSnO}}_{3}$.