A method of fabricating an E.sup.2 PROM or a flash memory cell having a sharp tip or thin wedge at one of its gates, e.g., the floating gate, for the erasure of electrical charges stored in the floating gate. A recess is formed between a first polysilicon gate and the substrate by removing portions of an insulating layer interposed between the first gate and the substrate. Another insulating layer, e.g., thermal oxide, is formed on the exposed portions of the first gate and the substrate, and partially fills the recess. A second polysilicon layer is formed on the thermal oxide and patterned to form a floating gate. The partially filled recess causes a sharp polysilicon tip or thin wedge to be formed as part of the floating gate. This sharp tip or thin wedge can generate a high electrical field that facilitates the removal of the stored electrical charges from the floating gate.