Conventional treatments of the dynamics of mesoscopic normal tunnel junctions mainly reduce the problem to a stochastic master equation and finally resort to computer simulation. This paper presents a new methodology based on probability-density functions to solve the problem in a fully analytic manner. Analytic expressions of the charge distribution across the junction, current-voltage characteristics, and the degree of randomness of the single-electron-tunneling oscillations are obtained under an arbitrary bias condition, where the degree of randomness is defined as the ratio of the standard deviation of dwell times to their mean value. In particular, the minimum degree of randomness achievable under the constant-current-bias condition is found to be (${\mathit{R}}_{\mathit{T}}$${\mathit{CI}}_{\mathrm{dc}}$/e${)}^{1/2}$, where e is the electronic charge, ${\mathit{R}}_{\mathit{T}}$ is the tunnel resistance, C is the junction capacitance, and ${\mathit{I}}_{\mathrm{dc}}$ is the bias current.

• Received 8 February 1990

DOI:https://doi.org/10.1103/PhysRevB.42.3087