Investigating the ranges of (meta)stable phase formation in (InxGa1-x)2O3: Impact of the cation coordination

We investigate the phase diagram of the heterostructural solid solution (InxGa1-x)(2)O-3 both computationally, by combining cluster expansion and density functional theory, and experimentally, by means of transmission electron microscopy (TEM) measurements of pulsed laser deposited (PLD) heteroepitaxial thin films. The shapes of the Gibbs free energy curves for the monoclinic, hexagonal, and cubic bixbyite alloy as a function of composition can be explained in terms of the preferred cation coordination environments of indium and gallium. We show by atomically resolved scanning TEM that the strong preference of indium for sixfold coordination results in ordered monoclinic and hexagonal lattices. This ordering impacts the configurational entropy in the solid solution and thereby the (InxGa1-x)(2)O-3 phase diagram. The resulting phase diagram is characterized by very limited solubilities of gallium and indium in the monoclinic, hexagonal, and cubic ground state phases, respectively, but exhibits wide metastable ranges at realistic growth temperatures. On the indium rich side of the phase diagram a wide miscibility gap up to temperatures higher than 1400 K is found, which results in phase separated layers. The experimentally observed indium solubilities in the PLD samples are in the range of x = 0.45 and x = 0.55 for monoclinic and hexagonal single-phase films, while for phase separated films we find x = 0.5 for the monoclinic phase, x = 0.65-0.7 for the hexagonal phase and x >= 0.9 for the cubic phase. These values are consistent with the computed metastable ranges for each phase.