Semiconductor element and semiconductor memory device using the same

A semiconductor element comprising:

• a source region, a drain region, a channel forming region connecting said source region and said drain region and a gate applying an electric field to said channel forming region, and a carrier confinement region isolated by said channel forming region and by a potential barrier between said channel forming region and the carrier confinement region,
• wherein said carrier confinement region is formed of a conductor or semiconductor grains disposed between said channel forming region and said gate and surrounded by an insulator, and further wherein said carrier confinement region is smaller in width than said gate, and said carrier confinement region satisfies a condition as given by q2/2Ctt>kT where Ctt represents a total capacitance existing around said carrier confinement region, k represents Boltzmann's constant, T represents a temperature in degree Kelvin, and q represents a charge of an electron.