Electrostatic energy of a disordered system of metallic granules

Charge state of a disordered system of metallic nanoparticles

“…(3), is the inverse matrix of capacities of the systems. Since in our case the distances between particles are commen surable with their sizes, and the particles cannot be considered as point charges, the inverse matrix ele ments were calculated with allowance for corrections caused by polarization of the particles in a dipole approximation [8]. Energies were calculated using the approach described in [15]: (4) where n i is the initial number of electrons on granules.…”

“…However, in real disordered structures, the average activation energy is significantly lower than the charge energy of an isolated particle, which leads to a sub stantial increase in the tunneling probability. The main cause is the mutual polarization of the particles that is the stronger the higher is the particle density in the structure [8]. The increase in the particle density means the decrease in the gap sizes between the parti cles, and this also increases the tunneling probability.…”

Field effect in granular metal films

“…In this expression e is unit charge, C −1 i j is the inverse matrix of capacitance of the system (in the case of dense system this matrix should be calculated taking into account polarization effects [18]) and…”

“…As one can see from figure 3, the major tendency is the enhancement of the modulation depth with the decrease of film thickness except for the special case of a single-layer film in dual-gate configuration. The origin of such behaviour is related to the fact that the mean value of the granules' effective charging energy [18], E c = 1 2 e 2 C −1 ii , is lower than E c0 because of the polarization of the surrounding granules. Since this effect is due to the long-range Coulomb interaction, it is less efficient in thin films and this is why the mean charging energy increases in thin films.…”