N. F. Mott

Conduction in non-crystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors

Abstract The experimental evidence concerning the density of states in amorphous semiconductors and the ranges of energy in which states are localized is reviewed; this includes d.c. and a.c. conductivity, drift mobility and optical absorption. There is evidence that for some chalcogenide semiconductors the model proposed by Cohen, Fritzsche and Ovshinsky (1969) should be modified by introducing a band of localized states, near the centre of the gap. The values of C, when the d.c. conductivity is expressed as C exp (- E/kT), are considered. The behaviour of the optical absorption coefficient near the absorption edge and its relation to exciton formation are discussed. Finally, an interpretation of some results on photoconductivity is offered.

The theory of impurity conduction

Abstract : Contents: The model and general discussion of impurity conduction. The impurity wave functions. Observations of impurity conduction. Methods of calculating the electrical conductivity at low concentrations. The properties of a one-dimensional disordered lattice. The interaction of localized carriers with lattice vibrations. Calculations of impurity conduction. Dependence of the transition concentration on degree of compensation. Concentration at which the transition occurs. Resistivity in the region of metallic conduction.

Polarons in crystalline and non-crystalline materials

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. Pollaks theory of a.c. impurity conductivity is reviewed and applied to the problem of dielectric loss in these materials.

States in the gap and recombination in amorphous semiconductors

Abstract 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...

The transition to the metallic state

Abstract An account is given of the theory that a crystalline or non-crystalline array of atoms will make a transition from the metallic to the non-metallic state as the interatomic distance is varied. Experimental evidence relevant to the theory is summarized. Wigners (1938) suggestion that an electron gas might crystallize at sufficiently low densities is examined, and an experiment suggested by which it might be tested.

Conduction in non-crystalline systems

Abstract The present author (1967, 1968) has used the work of Anderson (1958) to deduce that under certain conditions the conductivity due to a degenerate gas of electrons in a disordered lattice tends to zero with temperature, even though the density of states N(EF ) at the Fermi energy EF is finite. Neither Andersons conclusions nor those of the present author have been universally accepted, and this paper examines in detail the method of Mott (1968) which shows that, for a very disordered Anderson lattice, the conductivity at frequency ω behaves (apart from a logarithmic term) like ω2 for small values of ω, and therefore tends to zero with ω. The method is the laborious one of examining all configurations of the ensemble and showing that any non-zero contributions to tend to zero exponentially as the volume ω of the specimen considered tends to infinity. Some discussion is given of the energy Ec which separates localized from non-localized states and of the behaviour of for va...

The Anderson Transition

An outline is given of the electrical properties expected in a disordered solid or fluid which shows a metal-insulator transition of Anderson type. This is one in which the Fermi energy of the electrons passes through a mobility edge separating extended states from states localized by disorder, as the composition or some other parameter is changed. Some of the experimental evidence for this kind of transition is described. In particular, a relatively detailed account is given of the two dimensional inversion layer system in which the relevant parameters may be varied in a single device by direct electrical means.

Rare-earth compounds with mixed valencies

Abstract This paper reviews the properties of certain rare-earth compounds in which the 4f band has mixed valency, notably SmB6 and the high-pressure forms of SmS, SmSe and SmTe. The metal-insulator transitions of the last three materials under pressure are discussed. It is suggested that the low-pressure form of SmS is an excitonic insulator. In SmB6 and high-pressure SmS a very small gap separates occupied from unoccupied states, this in our view being due to hybridization of 4f and 5d bands. The electrical properties are discussed; if kT is greater than the gap energy, then the gap does not affect the metallic behaviour. Finally metallic compounds such as CeAl3 are described, in which there is no magnetic ordering at low temperatures, and it is suggested that this must always occur if the Kondo temperature is higher than the RKKY interaction. In this case, as in compounds with mixed valency, the Fermi energy will pass through the 4f band, and there is a very large enhancement of the effective mass. The...

The metal-insulator transition in extrinsic semiconductors

Abstract The main purpose of this article is to describe the electrical and magnetic properties of extrinsic semiconductors when the concentration of donors varies, particularly for concentrations near that for which a metal-insulator transition takes place. Since the donor centres are distributed at random in space, the combined effects of correlation and Anderson localization have to be considered. As an introduction, in § 1 we give an outline of our present understanding of the transition in some crystalline materials, particularly V2O3. For this the metallic phase, a highly correlated electron gas, is discussed, as is also the question of a discontinuous change in the number of current carriers. In § 2 we discuss Si : P and similar materials. For uncompensated samples, the material near the transition is to be described by overlapping Hubbard bands, and the metal-insulator transition occurs when the states at the Fermi energy show Anderson localization. Just on the insulator side of the transition con...

Introductory talk; Conduction in non-crystalline materials

Abstract The present position of the theory of conduction in non-crystalline materials is reviewed. Particular attention is given to the behaviour at the mobility edge, the Hall effect, hopping at low temperatures, the metal-non-metal transition in a non-crystalline system and to the effect of correlation and of a random concentration of vacancies on the properties of vanadium monoxide.