A 3-dimensional Wentzel–Krammers–Brillouin calculation of the charging and retention times of metal nanoparticles in a dielectric matrix

Abstract When an assembly of metallic nanoparticles (mNPs) is found in a dielectric matrix over a Si substrate with an applied bias the mNPs are filled with electrons (or holes depending on the polarity of the bias.) It is customary to calculate the times for either charging (i.e. programming) or discharging when the bias is removed (i.e. retention) by either (i) simple capacitor models or (ii) solving the three dimensional (3D) Poisson equation and using a simplified 1D Wentzel–Krammers–Brillouin (WKB) model for the current despite the 3D nature of the potential profile. In this paper we use a fully 3D self-consistent method in which both potential and current are calculated by a 3D Poisson and a 3D WKB method respectively. The methodology has been applied in other cases and we now apply it to Non-Volatile-Memory structures with Pt NPs in a SiO 2 /HfO 2 matrix fabricated by our group and reported in this paper.