Master-equation-based approach to stochastic processes in few-electron systems and advanced considerations for practical applications

Abstract

This paper revisits the master-equation-based approach to physical parameters to characterize transport in three-dimensional and low-dimensional few-electron systems. Advanced expressions of the electron density are theoretically derived at equilibrium for a system having traps. It is revealed that electron density at equilibrium is slightly higher than that without any interface traps as a result of the influence of dynamic trapping/detrapping processes. The capture time constant of electrons applicable to practical systems having traps, such as silicon-related materials, is also theoretically derived. The theoretical model is examined by numerical calculations and experimental results. In wire-type metal–oxide–semiconductor devices, the capture-time constant model roughly reproduces its inverse-temperature dependence. The effective activation energy of the capture time constant is not significantly influenced by that of the emission time constant. In the conductive filaments of silicon oxide film created by electrical stress, the capture-time constant model basically reproduces its inverse-temperature dependence. The effective activation energy of the capture time constant is not significantly influenced by that of the emission time constant but is influenced by the cross-sectional area of the filament and the electron density in the filament. The capture-time constant model semi-quantitatively reproduces the experimentally observed bias dependence of the silicon oxide film. Numerical calculation results suggest that the carrier transit time assumed in the model depends on the physical properties of the materials used. Given the goal of this study, the theoretical approach basically produces successful results.