A semiconductor memory element has MOS transistor for writing by a drain-avalanche hot electron. The MOS transistor has a semiconductor substrate, a first semiconductor layer formed on the semiconductor substrate, a floating gate provided on the first semiconductor layer through intermediation of a first insulating film, a channel region formed in a surface of the first semiconductor layer under the floating gate, and source region and a drain region provided on the first semiconductor layer so as to be in contact with the channel region. The channel region has a distribution of at least two kinds of carrier densities provided in at least two portions thereof disposed in parallel along a direction connecting the source region and the drain region.