Flash memory devices include a memory array having a plurality of NAND strings of EEPROM cells therein. A word line driver is provided to improve programming efficiency. The word line driver is electrically coupled to the memory array by a plurality of word lines. The word line driver includes a plurality of pass voltage switches. These switches have outputs electrically coupled by diodes to the plurality of word lines. Methods of programming flash memory devices include applying a pass voltage to a plurality of unselected word lines in a non-volatile memory array while simultaneously applying a sequentially ramped program voltage to a selected word line in the non-volatile memory array. The sequentially ramped program voltage has a minimum value that is clamped by a word line driver to a level not less than a value of the pass voltage.