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

Abstract

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 0.85 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> is the rest electron mass, irrespective of the molecular compound ratio between Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> and SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and the film thickness. This suggests a convincing model for charge trapping in [(SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> (Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> ) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> ] <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-y</sub> Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</sub> including interfacial transition layers. It is also found that the leakage mechanism is the direct tunneling enhanced by the trapped positive charge.