Multiple bits of data can be programmed into a single EPROM or FLASH memory cell by applying one of a number of programming voltages to the control gate of a memory cell that forms a punchthrough current during programming. The punchthrough current forms substrate hot electrons which, in addition to the channel hot electrons, accumulate on the floating gate. The charge on the floating gate converges to a stable threshold value which is linearly related to the programming voltage utilized. In addition, by utilizing the substrate hot electrons, a much lower control gate voltage can be utilized during programming.