A NUMERICAL STUDY OF THE DYNAMICS AND STATISTICS OF SINGLE-ELECTRON SYSTEMS

We describe a new and efficient method for the numerical study of the dynamics and statistics of single electron systems presenting arbitrar y combinations of small tunnel junctions, capacitances, and voltage so urces. The method is based on numerical solution of a linear matrix eq uation for the vector of probabilities of various electric charge stat es of the system, with iterative refining of the operational set of st ates. The method is able to describe very small deviations from the '' classical'' behavior of a system, due to the finite speed of applied s ignals, thermal activation, and macroscopic quantum tunneling of charg e (cotunneling). As an illustration, probability of dynamic and static errors in two single electron memory cells with 6 and 8 tunnel juncti ons have been calculated as a function of bias voltage, temperature, a nd switching speed. (C) 1995 American Institute of Physics.