Conduction In Granular Metals Research Articles

Notes on the hopping conduction in granular metals

A calculation is done to determine the critical volume fraction of percolation and the range of temperature for which hopping conduction follows the law log sigma approximately T-12/. It is shown that the critical volume fraction Vc does not have a universal value, but varies as the system is changed. The theoretical exponential law for the DC conductivity shows a good agreement with the experimental law when the metallic concentration is high.

Potential disorder in granular metal systems: the field effect in discontinuous metal films

The authors show that the conventional model for the basic physics of conduction in granular metals is unable to account for low-temperature field-effect measurements on discontinuous metal films. They discuss the physics of electrical contact between metals and insulators and show that it results in potential disorder that is large in comparison with other relevant energies. They explore the idea of electrostatic relaxation in the insulator and show that it correctly accounts for the small field effect that is observed and for its dependence on temperature and the activation energy for conduction. They have verified the role of electrostatic relaxation by direct experiments in which the relaxation processes are modified with the predicted consequences. They assert that potential disorder must play a dominant role as regards electrical transport in all granular systems.

The temperature dependence of the electrical resistivity of granular metals

A simple percolation model of the hopping conduction in granular metals is proposed. The separation between the grains, in this model, is a random variable uncorrelated with the activation energy, the latter being dominated by the intragrain level splitting. The model is capable of reproducing the resistivity exp ( T 0 T ) 1 2 law over a wide temperature range, in spite of the narrow range of the grain diameters, explaining the recent observations of Choi et al.

Low-field hopping conductivity in granular metals

The hopping conductivity of granular metals is known to be of the form sigma varies as exp (-(T0/T)12/) in the temperature range 20K<or=T<280K. A theoretical derivation of this relation using the critical percolation conductance method as developed in the context of the variable range hopping mechanism of conduction in amorphous systems, is discussed. Use is made of the empirical fact that the ratio of intergrain separation and grain size is nearly constant for macroscopically homogeneous samples. It is also assumed that the hopping of electrons is predominantly between nearest neighbours. Extension of the treatment to thin films and comparison with previous theoretical work is briefly discussed.

Hopping Conductivity in Granular Metals

We present evidence that in granular metals the observed temperature dependence of the low-field conductivity, $\mathrm{exp}(\ensuremath{-}\frac{b}{{T}^{\ensuremath{\alpha}}})$ with $\ensuremath{\alpha}=\frac{1}{2}$, can be ascribed to a relationship $s{E}_{c}=\mathrm{const}$ between $s$, the separation of neighboring metal grains, and ${E}_{c}$, the electrostatic energy required to create a positive-negative charged pair of grains. This relationship results from simple considerations of the structure of granular metals. The predictions of the theory, for both the high- and the low-field electrical conductivity, are in excellent accord with experimental results in granular Ni-Si${\mathrm{O}}_{2}$ films.

Voltage-Induced Tunneling Conduction in Granular Metals at Low Temperatures

We have observed a new conduction mechanism in granular metals at low temperatures and high electric fields $\mathcal{E}$ characterized by a field-dependent conductivity ${\ensuremath{\sigma}}_{0}\mathrm{exp}(\frac{\ensuremath{-}{\mathcal{E}}_{0}}{\mathcal{E}})$. A theory based on a simple model of field-induced electron-hole generation in the bulk of the granular metal predicts the observed field dependence and gives expressions for ${\ensuremath{\sigma}}_{0}$ and ${\mathcal{E}}_{0}$ which are functions of the granular-metal parameters: metal grain size, and thickness and height of the tunneling barriers separating the metal grains. Agreement between theory and experiment is satisfactory.