Multiple logic levels can be simultaneously programmed into any combination of memory cells in a column of an alternate-metal virtual-ground (AMG) EPROM or flash memory array by applying one of a corresponding number of programming voltages to the word lines that correspond with the cells to be programmed. In the present invention, the memory cells in the array form a punchthrough current during programming which, in turn, leads to the formation of an increased number of substrate hot electrons. By utilizing the substrate hot electrons formed from the punchthrough current in addition to the channel hot electrons, much lower control gate voltages can be utilized during programming.