The over-erase phenomenon in the polysilicon-oxide-silicon nitride-oxide-silicon (SONOS) memory structure is minimized by using hafnium oxide or hafnium aluminum oxide to replace silicon nitride as the charge storage layer (the resulting structures are termed SOHOS devices, where the "H" denotes the high dielectric constant material instead of silicon nitride). Unlike SONOS devices, SOHOS structures show a reduced over-erase phenomenon and self-limiting charge storage behavior under both erase and program operations. These are attributed to the differences in band offset and the crystallinity of the charge storage layer.