A semiconductor memory device has a low-resistivity semiconductor substrate on which a higher-resistivity semiconductor layer of the same conductivity type is formed. Memory cell transistors are formed in the semiconductor layer. A diffusion region, also of the same conductivity type, is formed below the memory cell transistors. The resistivity of the diffusion region is lower than the resistivity of the semiconductor layer. In the programming of data into the memory cell transistors by hot electron injection, the diffusion region reduces the voltage drop due to current flow from the part of the semiconductor layer near the memory cell transistors into the semiconductor substrate, thereby reducing unwanted elevation of the potential of the semiconductor layer.