A non-volatile semiconductor memory device comprising a first conductive semiconductor having steps on a surface thereof, a second conductive semiconductor region formed on an upper portion and a bottom portion of each of the steps and being separated in a direction perpendicular to the main surface of the first conductive semiconductor to function as a source or a drain, a gate dielectric film containing therein charge storage means which is spatially discrete and being formed on the first conductive semiconductor so as to coat at least a sidewall of each of the steps, and a gate electrode formed on the gate dielectric film. Accordingly, there are provided a non-volatile semiconductor memory device which suffers almost no deterioration in the properties and can perform the operation of recording of 2 bits per unit memory device even when the size of the semiconductor memory device in the semiconductor substrate is scaled down, and a process for fabricating the non-volatile semiconductor memory device.