Effects of control oxide material on the charging times of metal nanoparticles inside non-volatile memories: A 3-dimensional WKB calculation

Abstract

We have investigated the influence of different control oxide materials on the charging times of metal nanoparticles (mNP) inside a [Si/SiO2/(mNP)/Control-Oxide/gate] non-volatile memory (NVM) in which the control oxide can have a higher dielectric constant ε than that of SiO2 like HfO2 or Al2O3 as is the case in practice frequently. Our calculations are performed for both N-type and P-type substrates. We have used a previously published 3-dimensional Wentzel–Krammers–Brillouin (WKB) method of ours, which does not contain such adjustable parameters as effective area or capture cross-section which other 1-dimensional theories use. To obtain the total time for the charging of the NVM to saturation we calculate the times that successive electrons take to be incorporated into an mNP under a given applied voltage and a given duration of the charging pulse, each time updating the tunneling potential due to the incorporation of the extra electron into the mNP. We obtain an exponential dependence of these charging times on the dielectric constant of the control oxide for which we offer a simple explanation. The change with substrate type is on the other hand less pronounced. Our results are confirmed by experiment. In particular, when our method is applied to NVMs with SiO2 and HfO2 as the control oxide we obtain good agreement with experiment without using such adjustable parameter as effective area of emission. We finally show that if the fraction of the substrate area that is covered with mNP is used to estimate this parameter the error involved will be quite significant, i.e. a factor of 5 approximately.