Electrical Properties of Titanium Dioxide Semiconductors

Measurements have been made of the electrical resistivity and Hall coefficient of semiconducting rutile both in the form of ceramics and single crystals from -190°C to +500°C. The samples were reduced in pure hydrogen for various times and temperatures to provide a range of resistivities, all corresponding to rather large numbers of charge carriers. The single crystal samples were measured in different orientations to study the directional dependence of resistivity and mobility. From these measurements the variations of mobility and charge carrier concentration with temperature have been determined. The mobility data can be satisfactorily described in terms of an electron scattering by the optical modes of lattice vibration predominant at high temperatures combined with a scattering by ionized impurities predominant at low temperatures. The low values of the mobility in all samples indicate an anomalously large effective electron mass. In the crystalline samples the mobility in the $c$ direction is approximately twice as great as in the $a$ direction. The data on the temperature dependence of the electron concentration may be represented by a sum of two Boltzmann terms, indicating two types of donor centers. It is suggested that these centers may be oxygen ion vacancies at which one or two electrons are trapped as ${\mathrm{Ti}}^{+3\mathrm{}}$ ions. An energy level diagram is proposed which explains many of the electrical and optical observations on rutile semiconductors.