Comparison of Random-Dopant-Induced Threshold Voltage Fluctuation in Nanoscale Single-, Double-, and Surrounding-Gate Field-Effect Transistors

Abstract

In this study, we explore random-dopant-induced threshold voltage fluctuation by solving a quantum correction model. Fluctuation of the threshold voltage for three nanoscale transistors, single-, double-, and surrounding-gate (SG, DG, and AG) metal–oxide–semiconductor field-effect transistors (MOSFETs) are computationally compared. To calculate the variance of the threshold voltages of the SG, DG, and AG MOSFETs, a quantum correction model under equilibrium conditions is expanded and numerically solved using perturbation and monotone iterative methods. Fluctuation of the threshold voltage resulting from the random dopant, gate oxide thickness, channel film thickness, gate channel length, and device width are calculated for the three devices. Quantum mechanical and classical results give similar predictions for fluctuation of the threshold voltage with respect to different parameters including the dimensions of the device and the channel doping. Fluctuation increases when the channel doping concentration, channel film thickness, and gate oxide thickness increase. On the other hand, it decreases when the channel length and device width increase. Calculation results of the quantum correction model are quantitatively higher than those of classical estimation in accordance with different quantum confinement effects in nanoscale SG, DG, and AG MOSFETs. It is found that the AG MOSFET has the smallest threshold voltage fluctuation among the three device structures due to its good channel controllability. In contrast to the conventional quantum Monte Carlo approach and the small-signal analysis of the Schrödinger–Poisson equations, this computationally cost-effective quantum correction approach shows acceptable accuracy and is ready for industrial technology computer-aided design application.