Semi-Analytical Modeling of Short-Channel Effects in Si and Ge Symmetrical Double-Gate MOSFETs

Abstract

A simple analytical expression of the 2-D potential distribution along the channel of silicon symmetrical double-gate (DG) MOSFETs in weak inversion is derived. The analytical solution of the potential distribution is compared with the numerical solution of the 2-D Poisson's equation in terms of the channel length <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> , the silicon thickness <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Si</sub> , and the gate oxide thickness <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">OX</sub> . The obtained results show that the analytical solution describes, with good accuracy, the potential distribution along the channel at different positions from the gate interfaces for well-designed devices when the ratio of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Si</sub> is ges 2-3. Based on the 2-D extra potential induced in the silicon film due to short-channel effects (SCEs), a semi-analytical expression for the subthreshold drain current of short-channel devices is derived. From the obtained subthreshold characteristics, the extracted device parameters of the subthreshold slope, drain-induced barrier lowering, and threshold voltage are discussed. Application of the proposed model to devices with silicon replaced by germanium demonstrates that the germanium DG MOSFETs are more prone to SCEs.