Transport properties of electrons in energy band tails

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Abstract
Transport properties of electrons in energy band tails of disordered semiconductors are studied experimentally using a material system in which (i) the width and shape of the band-tail are approximately known and (ii) the Fermi energy is controllable. The material is heavily-doped, closely-compensated, crystalline n-GaAs whose compensation ratio can be made arbitrarily close to unity by the use of two techniques that are described in detail. This control of the Fermi level through compensation permits the measurement of the transport properties of electrons at various energies in the band-tail. Using band tails having a width of ∼50 meV, measurements have been made of the temperature dependence of the d.c. conductivity and Hall coefficient, the frequency dependence of the a.c. conductivity and the electric field dependence of the d.c. conductivity (the last two at low temperatures). The evidence demonstrates the progressively greater localization of states deeper in the tails. No sign is found of a sharp mobility edge. There is a number of close similarities to the properties of amorphous semiconductors but some significant differences. The frequency dependence of the a.c. conductivity at low temperatures is essentially identical with that of amorphous semiconductors in accord with the general interpretation that conductivity at low temperatures takes place by electron hopping among localized states near the Fermi energy. The detailed temperature dependence of the d.c. conductivity at low temperatures is log σ=σ 0 exp [−(T 0/T)1/2], thus disagreeing with a theoretical expectation that the exponent for low temperature hopping conduction should be 1/4. At low temperatures, the electric field dependence of the conductivity shows a variation as σ∼exp (bF/T) over a considerable range extending down to field strengths close to 1 V/cm. This closely resembles recent observations on amorphous semiconductors but the range of field strengths here is lower by several orders of magnitude.