Monte Carlo simulation of current–voltage characteristics in metal–insulator–metal thin film structures

Abstract

Many metal–insulator–metal (MIM) thin film sandwich structures exhibit an electroforming process, following which the resulting direct current (DC) current–voltage I–V characteristic exhibits ohmic conduction and voltage-controlled differential negative resistance (VCNR) at low and high voltages, respectively. One of the more successful models of these phenomena is the filamentary model, in which it is assumed that the electroforming process establishes a population of ohmic filaments within the insulating matrix, which span the metal contacts. The VCNR behaviour results from the progressive cessation of conduction in individual filaments owing to Joule heating effects. Early work showed that by postulating plausible probability distributions of filament resistances, I–V characteristics typical of those obtained experimentally could be derived. More recently more realistic normal distributions of filament resistances, radii and cross-sectional areas have been considered, and these too have yielded characteristics in accordance with experiment. In the present work normal distributions of filament resistances and radii are considered, but in contrast to previous work a novel method using a Monte Carlo simulation was employed. Furthermore, the effects of using a combination of two different filament resistivity values were explored. Variations in conductance and shifts in the current peak were explicable using existing theory. The approach adopted in this work lends itself to the exploration of more complex filament distributions, and therefore to a better representation of the underlying filament population, including those having a multivariate distribution.