A memory device includes a plurality of memory cells arranged in series in the semiconductor body, such as a NAND string, having a plurality of word lines. A selected memory cell is programmed by hot carrier injection. The program operation is based on metering a flow of carriers between a first semiconductor body region on a first side of the selected cell in the NAND string and a second semiconductor body region on a second side of the selected cell. A program potential higher than a hot carrier injection barrier level is applied to the selected cell, and then the drain to source voltage across the selected cell and the flow of carriers in the selected cell reach a level sufficient to support hot carrier injection, which is controlled by a combination of a switch cell adjacent the selected cell and modulation of a source side voltage applied to the NAND string.