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

• The charging of metal nanoparticles inside NVM was investigated by a 3-D WKB theory.
• This 3-D theory does not contain arbitrary parameters as 1-D theories do.
• The charging times tn by n electrons were calculated for different control oxides.
• An exponential dependence of tn on the oxide material was found and explained.
• Agreement with experimental results was obtained for all relevant gate voltages.

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.

The charging times of metal nanoparticles inside NVMs — calculated by a 3-D WKB method with no arbitrary parameters — depend exponentially on the control oxide (CO) material. Good agreement with experiment is obtained with SiO2 as CO with the charging performed at constant voltage (left) and with HfO2 as CO when the charging is performed at constant pulse time but variable pulse height (right).Figure optionsDownload as PowerPoint slide