**3. Crystal chemistry of ITO**

Crystalline indium oxide has the bixbyite structure consisting of an 80-atom unit cell with the Ia3 space group and a 1-nm lattice parameter in an arrangement that is based on the stacking of InO6 coordination groups. The structure is closely related to fluorite, which is a face-centered cubic array of cations with all the tetrahedral interstitial positions occupied with anions. The bixbyite structure is similar to fluorite except that the MO8 coordination units (oxygen position on the corners of a cube and M located near the center of the cube) of fluorite are replaced with units that have oxygen missing from either the body or the face diagonal. The removal of two oxygen ions from the metal-centered cube to form the InO6 coordination units of bixbyite forces the displacement of the cation from the center of the cube. In this way, indium is distributed in two nonequivalent sites with one-fourth of the indium atoms positioned at the center of a trigonally distorted oxygen octahedron (diagonally missing O). The remaining three-fourths of the indium atoms are positioned at the center of a more distorted octahedron that forms with the removal of two oxygen atoms from the face of the octahedron. These MO6 coordination units are stacked such that onefourth of the oxygen ions are missing from each {100} plane to form the complete bixbyite structure. A minimum in the thin-film resistivity is found in the ITO system when the oxygen partial pressure during deposition is optimized. This is because doping arises from two sources, four-valent tin substituting for three-valent indium in the crystal and the creation of doubly charged oxygen vacancies. This is due to an oxygen-dependent competition between substitutional Sn and Sn in the form of neutral oxide complexes that do not contribute carriers. Amorphous ITO that has been optimized with respect to oxygen content during deposition has a characteristic carrier mobility (40 cm2/V s) that is only slightly less than that of crystalline films of the same composition. This is in sharp contrast to amorphous covalent semiconductors such as Si, where carrier transport is severely limited by the disorder of the amorphous phase. In semiconducting oxides formed from heavy-metal cations with (n-1)d10ns0 (n ≤4) electronic configurations, it appears that the degenerate band conduction is not band-tail limited.
