The current state of polaron theory as applicable to transition metal oxides is reviewed, including problems such as impurity conduction where disorder plays a role. An estimate is given of the conditions under which polaron formation leads to an enhancement of the mass but no hopping energy. The binding energy of a polaron to a donor or acceptor in narrow-band semiconductors is discussed. The experimental evidence about the conductivity of TiO 2 and NiO is reviewed. Impurity conduction in NiO and conduction in glasses containing transition metal ions is discussed and it is emphasized that the activation energy for hopping nearly all vanishes at low temperatures. Pollak's theory of a.c. impurity conductivity is reviewed and applied to the problem of dielectric loss in these materials.

Polarons in crystalline and non-crystalline materials

(1967). Electrons in disordered structures. Advances in Physics: Vol. 16, No. 61, pp. 49-144.

Electrons in disordered structures

The paper examines states in the gap in amorphous silicon and chalcogenides and their effect on photoconductivity, luminescence and drift mobility. It is supposed that carriers in an ‘ideal’ glassy semiconductor without defects would move by hopping at the band edge at low temperatures and by excitation to a mobility edge at high temperatures, and that the carriers do not form polarons; the results of Spear and co-workers (e.g. Spear 1974 a) for glow-discharge-deposited silicon and of Nagels, Callearts and Denayer (1974) for quenched As2Te3 containing silicon are considered. The effectively zero value of the Hall coefficient in the hopping regime is discussed. States in the gap are supposed to be due to dangling bonds which may form pairs at divacancies; if the concentration is high, these may have a predominating effect on the conductivity and in this case polaron-type hopping could occur, both for chalcogenides and for silicon. For the chalcogenides (in contrast to silicon), it is proposed, ada...

States in the gap and recombination in amorphous semiconductors

In this paper an attempt is made to establish the nature of free charge carriers and of charge carriers bound to centres in p-type NiO, CoO and MnO and in n-type MnO and α-Fe2O3. For free charge carriers, d.c. conductivity, Seebeck coefficient and Hall effect are considered. Effects arising from inhomogeneous conduction and impurity conduction are discussed. Impurity conduction appears to have a strong influence on transport properties in the case of α-Fe2O3, less so in NiO, whereas no influence of this effect has been found in CoO and MnO. It is shown that NiO and CoO do not exhibit the features characteristic of small-polaron conductors but rather can be consistently conceived of as large-polaron band semiconductors. It is suggested that magnetic resistance due to exchange coupling between charge-carrier spin and cation spins plays an important role. The anomalous behaviour of the Hall effect in NiO and α-Fe2O3 is extensively discussed. In contradistinction to NiO, CoO and n-type MnO, free char...

Small-polaron versus band conduction in some transition-metal oxides

The minimum metallic conductivity in disordered materials, proposed by the author in previous papers, is evaluated in the light of the revised criterion for Anderson localization given by Edwards and Thouless (1972). The experimental evidence resulting from the recent work of Allen and Adkins (1972) is reviewed, as is also the discussion by Cohen (1971) and Eggarter (1972) based on percolation theory. This and other evidence suggests strongly that a minimum metallic conductivity does exist having approximately the calculated value.

L Friedman

Papers

Studies of polaron motion: Part III: The Hall mobility of the small polaron