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

Yasuhisa Omura

doi:10.1063/5.0064633

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.

Highlights

In the 1950s and 1960s, generation–recombination (G–R) noise was analyzed theoretically and the carrier density fluctuation was found to be directly related to the G–R phenomenon.[1]
The following important results were obtained by comparing numerical calculation results with past experimental results
(i) When some traps exist at the oxide/semiconductor interface, the electron density at equilibrium is slightly higher than that without any interface traps

Summary

INTRODUCTION

In the 1950s and 1960s, generation–recombination (G–R) noise was analyzed theoretically and the carrier density fluctuation was found to be directly related to the G–R phenomenon.[1]. This study revisits the mathematical formulation for the conventional master-equation-based approach[18] in order to identify new findings on electron transport characteristics that can explain recent experimental findings on RTN signals in scaled semiconductor devices and on the behaviors of insulating films showing resistance switching and to elucidate physical mechanisms of such phenomena observed in scaled MOSFETs because the electronic industry must target the successful development of future lowvoltage semiconductor devices. This paper first reviews the conventional calculation process based on the master-equation-based approach from the point of view of few-electron systems. It can be thought that this viewpoint is very rewarding in terms of analyzing RTN signals in low-dimensional semiconductor devices and the aspect of conductive filaments in insulating films and in characterizing various carrier-density fluctuations in future scaled semiconductor devices.[20]. This paper, does not discuss spin-dependent phenomena[21] from the first step for simplicity because few-electron systems are assumed, so the electronic transitions between the conduction band and traps are mostly unrestricted

Master equation and its possible solution

Models for generation and recombination processes and equilibrium states

DISCUSSION

Case of nano-wire-type MOS devices such as the gate-all-around structure

On the activation energy of time constants

CONCLUSION