Indium defects and their diffusion in monoclinic (In_x­Ga_1-x)₂O₃

Measurements on thin film (In_xGa_1-x)₂O₃ are compared to hybrid density functional theory calculations to study how defects relate to an increase in n-type conductivity. XRD shows that the films are monoclinic up to 10% In (x = 0.1), and a lack of broadening indicates that the inclusion of In does not introduce an appreciable amount of dislocation defects. Theory predicts expansion of the lattice due to the inclusion of indium which results in a reduction of the electronic band gap as a function of In concentration; Tauc plots confirm this as the electronic band gap decreases from 4.9 eV to 4.63 eV as In concentration increases to 10%. Hall and magnetoresistance measurements reveal an increase in n-type conductivity as the In concentration is increased from x=0 in pure Ga₂O₃ to x=0.1 in In_0.1Ga_0.9O₃, a somewhat anomalous behavior as In and Ga are isoelectronic. Formation energy calculations reveal, however that a stable In-based defect complex comprised of a substitutional In (In_Ga) and interstitial In (In_i) may form spontaneously in a +2 charge state, resulting in a near conduction band edge, singly occupied band gap level 0.2 eV below the band edge. There also exists a (+/0) transition state due to this defect 0.5 eV above the conduction band edge, which can be attributed to the increase in n-type conductivity seen in experiment. Diffusion paths and mechanisms from hybrid density functional theory nudged elastic band calculations will also be discussed.