Universal Tunnel Mass and Charge Trapping in $[( \hbox{SiO}_{2})_{1-x} (\hbox{Si}_{3}\hbox{N}_{4})_{x}]_{1-y}\hbox{Si}_{y}$ Film

Although the tunnel mass is indispensable to predict the gate leakage current of electron devices, it has been regarded as an adjustable parameter to fit the calculated leakage current with the measured ones. This appears useful because it enables calculation of the tunnel current while ignoring some details in advanced device modeling, even though it has veiled the intuitive nature of the modeling. More concretely, the adjustable tunnel mass pushes us to ignore the related issues that should carefully be considered. In this paper, we extract the tunnel masses for electrons and holes from an individual experiment and find that they are 0.85m ₀, where m ₀ is the rest electron mass, irrespective of the molecular compound ratio between Si₃N₄ and SiO₂ and the film thickness. This suggests a convincing model for charge trapping in [(SiO₂)_1-x(Si₃N₄)_x]_1-ySi_y including interfacial transition layers. It is also found that the leakage mechanism is the direct tunneling enhanced by the trapped positive charge.

I. Introduction

The Miniaturization of electron devices has increased the significance of direct tunneling (DT) gate leakage current, which has been well modeled assuming the effective mass of tunneling electrons, i.e., the tunnel mass. It is, however, noted that the effective mass approximation is used in the tunnel barrier of very thin gate dielectrics where Bloch's theorem is not satisfied, although this approximation is valid in the conduction band where Bloch's theorem is assumed to be valid.