Abstract: A non-volatile memory device includes an improved method for erasing a block of stack-gate single transistor flash memory cells. The memory performs an efficient and controllable mode of programming, referred to as block convergence. During an erase operation, one or more electrical erase pulses of fixed number, duration and voltage waveform are applied to memory cells in an addressable block of the memory device array. The erase pulse(s) fully erase all bits in the block. A block convergence operation is applied simultaneously to all cells in the block. The block convergence operation brings a threshold voltage of cells, which may have become over-erased during the erase operation, to a controlled level. A reverse-bias pulse, capable of inducing band-to-band tunnelling across one junction in the structure of the flash memory cells, is applied to a first junction. The other junction receives either a reverse bias or floating potential.