Transport Properties of Square Lattice of Metallic Nanogranules Embeded in Insulator (Bulletin of Pure and Applied Sciences – Physics, 2022)
We have made theoretical studies of transport properties of square lattice of metallic  nanogranules embedded insulting layers. We have developed an extension of the  classical Sheng-Abeles model for a single layer of identical spherical particles located  in sites of a simple square lattice with three possible charging states of granule and  three kinetics processes, creation of a pair on neighbor granules, recombination of  such a pair and charge translation from a charged to neighbor neutral granule. This  model neglecting the effect of disorder within a layer and of multilayered structures,  revealed a variety of possible kinetic and thermodynamical regimes. Effective kinetic  equations for averaged charge densities were derived for the characteristics area of  the granular sample, the contact areas beneath metallic currents leads and free area  between these leads. From these kinetic equations, it was shown that the tunnel  conduction in the free area did not produce any notable charge accumulation and  the conduction regime was purely ohmic. Some conduction in the contact area  became impossible without charge accumulation, leading to a generally non-ohmic  conduction regime, since the contact area dominated in the overall resistance. The  calculated I-V curves and temperature dependences were found in a good  agreement with available experimental data and obtained theoretical results.