Non-volatile memory devices and arrays are described that utilize back-side trapped floating node memory cells with band-gap engineered gate stacks with asymmetric tunnel barriers. Embodiments of the present invention allow for direct tunneling programming and efficient erase with electrons and holes, while maintaining high charge blocking barriers and deep carrier trapping sites for good charge retention and reduces the possibility of damage to the channel/insulator interface. The direct tunneling program and efficient erase capability reduces damage to the gate stack and the crystal lattice from high energy carriers, reducing write fatigue and leakage issues and enhancing device lifespan. Memory device embodiments of the present invention are presented that are arranged in NOR or NAND memory architecture arrays. Memory cell embodiments of the present invention also allow multiple levels of bit storage in a single memory cell, and allow for programming and erase with reduced voltages.