Showing papers on "Variable-range hopping published in 1972"

A percolation treatment of dc hopping conduction

Abstract: It is shown that the current paths considered by Miller and Abrahams in their theory of hopping conduction must be modified for large enough samples, such as are met under most experimental conditions. A possible exception is the case of transverse measurements on thin amorphous films. A percolation model for hopping conduction is set up using Miller and Abrahams' impedance representation of the problem. Approximate solutions for the model yield expressions for dc hopping conductivity. It is found that the density of states functions effects the temperature dependence of the conductivity. When the density of states is constant within a certain region around the Fermi level Mott's T − 1 4 law is obtained. For a density appropriate for impurity conduction at small compensations an activated conductivity is obtained. When the density of states increases as the nth power of the distance from the Fermi energy the logarithm of the resistivity is a linear function of Tsu−(n+1)/(n+4). Some comparison of the theory with experiments on impurity conduction and on amorphous semiconductors is made.

Frequency-dependence of conductivity in hopping systems

Abstract: A critical review is given of the experimental evidence relating to the frequency dependence of the electrical conductivity, σ (ω), in solids in which the flow of current occurs by hopping of localized carriers, whether electrons or ions. It is pointed out that the same dependence is found in semiconducting amorphous systems and in a wide class of insulators, giving σ α ωn, where 0.5 < n < 1, depending upon temperature. Evidence for a region in which σ α ω2 is considered to be of dubious reliability. It is pointed out that the conventional theoretical approach to the treatment of the frequency dependence of conductivity leaves certain gaps in our understanding of the physical processes taking place. An alternative approach is developed in which a stochastic sequence of hopping current pulses is Fourier-analyzed to give a frequency dependence of the power-law type found experimentally. The analysis leads to the conclusion that no exponent significantly higher than unity is to be expected - in agreement with all available evidence, and the ω2 region is possible as a consequence of the dielectric relaxation in the host matrix in which hopping takes place or of the corresponding hopping process by carriers tightly bound to fixed sites in the matrix. The new theoretical approach enables high-field ac behaviour to be analyzed and experimental results are given to illustrate the discussion. It is also pointed out that the frequency dependence of conductivity is an essential consequence of hopping conduction and not of the disorder of the structure. It is therefore predicted theoretically that similar results should be obtainable in ordered systems in which hopping is known to take place and some experimental results are quoted to support this claim.

Variable range hopping in a non-uniform density of states

Abstract: An expression is derived for the conductivity due to variable range hopping in a density of states which varies as a power of the energy from the Fermi level. The derivation is also given for the case of two-dimensional hopping.

Electrical conduction in heavily doped germanium

Abstract: Samples of germanium in the doping range 1 × 1017 to 5 × 1017 cm−3 donors, with 25% compensation, have been investigated. The electrical receptivity-has been measured from 300 to below 0·2 K in most cases, and the Hall effect from 300 to 2·0 K. In all cases, activated conduction of some form is seen at low temperatures. This is interpreted in the more heavily doped samples as being initially due to activation to a mobility edge in the impurity band, going over to hopping (variable range) around the Fermi energy at very low temperatures as suggested by Mott. The behavior of the more lightly doped samples is consistent with the ideas of Mott and Davis on impurity conduction, each sample showing regions of different, constant activation energy even down to very low temperatures. The magnitude of the conductivities observed in the variable range hopping region is compared with the values suggested by theoretical considerations.

Correlation effects in hopping conduction: Hopping as a multi-electron transition

Abstract: The treatment of hopping between localized states as a one electron transition breaks down at high densities. We have treated the problem in terms of a correlated two electron (one phonon) transition. We neglect exchange effects. The correlation effect consists of the movement of two (or more) electrons simultaneously whenever it lowers the energy difference between initial and final state of the system. This is seen to lower the activation energy over the one electron process, an effect noticeable at low temperatures, moderate densities, and moderate compensation in impurity conduction. The onset of the effect is seen to occur at a density on the order of ( 3 4 π) (e 2 a/2kTK)− 3 2 for a temperature T, where K is the dielectric constant of the host medium and a is the Bohr radius of an impurity state.

On the Hall effect in hopping impurity conduction

Abstract: The green function approach is used for the calculation of the AC transverse conductivity in the hopping regime of the impurity conduction. This approach enables the author to clarify what type of absorption contributes to the Hall effect. The result is that only the direct (resonant) absorption occurs. On the other hand, he finds out what approximations are involved in Holstein's early calculations. He concludes that these approximations are not achieved by the experimental circumstances, a fact which explains the discrepancy between the Holstein theory and experiments. Another problem discussed is the way of calculation of the conductivity in the hopping regime. It is explained why it is correct to calculate the induced dipole moment rather than the current.