A numerical study of the dynamics and statistics of single electron systems

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Abstract
We describe a new and efficient method for the numerical study of the dynamics and statistics of single electron systems presenting arbitrary combinations of small tunnel junctions, capacitances, and voltage sources. The method is based on numerical solution of a linear matrix equation for the vector of probabilities of various electric charge states of the system, with iterative refining of the operational set of states. The method is able to describe very small deviations from the ‘‘classical’’ behavior of a system, due to the finite speed of applied signals, thermal activation, and macroscopic quantum tunneling of charge (cotunneling). As an illustration, probability of dynamic and static errors in two single electron memory cells with 6 and 8 tunnel junctions have been calculated as a function of bias voltage, temperature, and switching speed.