  Transparent conducting oxides (TCOs) play an essential role in modern
optoelectronic devices through their combination of electrical conductivity and
optical transparency. We review recent progress in our understanding of
multi-component TCOs formed from solid-solutions of ZnO, In2O3, Ga2O3 and
Al2O3, with a particular emphasis on the contributions of materials modelling,
primarily based on Density Functional Theory. In particular, we highlight three
major results from our work: (i) the fundamental principles governing the
crystal structures of multi-component oxide structures including (In2O3)(ZnO)n,
named IZO, and (In2O3)m(Ga2O3)l(ZnO)n, named IGZO; (ii) the relationship
between elemental composition and optical and electrical behaviour, including
valence band alignments; (iii) the high-performance of amorphous oxide
semiconductors. From these advances, the challenge of the rational design of
novel electroceramic materials is discussed.
