Non-volatile memory devices and arrays are described that facilitate the use of band-gap engineered gate stacks with asymmetric tunnel barriers in reverse and normal mode floating node memory cells in NOR or NAND memory architectures that allow for direct tunnel programming and erase, while maintaining high charge blocking barriers and deep carrier trapping sites for good charge retention. The low voltage direct tunneling program and erase capability reduces damage to the gate stack and the crystal lattice from high energy carriers, reducing write fatigue and enhancing device lifespan. The low voltage direct tunnel program and erase capability also enables size reduction through low voltage design and further device feature scaling. Memory cells of the present invention also allow multiple bit storage. These characteristics allow memory device embodiments of the present invention to operate within the definition of a universal memory, capable of replacing both DRAM and ROM in a system.