Single electron memory - a mathematical model

Single electron memory (SEM) has received a lot of interest in research circles because of its promise for ultra-large scale integration. Room temperature SEM have to be fabricated at the nanometer scale and require a quantum mechanical treatment for their modeling. We have developed a semi-classical mathematical model for an electron tunneling into the memory node of a single tunnel junction SEM. We have used the 1D Schrodinger equation and elementary statistical physics and electromagnetics. We proceed by assuming the channel (reservoir) electrons to be a non-interacting free electron system, and show how an applied bias can increase the probability of electron tunneling. We have applied the model to an SEM reported in Futatsugi et al. (1998) and have found it to be in excellent agreement with the said characteristics with respect to the voltage at which a tunneling transition should take place