Computationally Efficient Band Structure-Based Approach for Accurately Determining Electrostatics and Source-to-Drain Tunneling Current in UTB MOSFETs

The ability of Ultra-Thin-Body (UTB) MOS devices to enable channel length scaling can only be realistically assessed by accurately taking key physical effects such as Quantum Confinement effects (QCEs) and Short channel effects (SCEs) into account. QCEs can accurately be considered only through a full band structure-based approach, which tends to be computationally inefficient, particularly at higher channel thicknesses, and is further exacerbated when required to be used to calculate 2-D channel electrostatics. Therefore, in this work, we propose a methodology to efficiently simulate the channel electrostatics of a UTB Double Gate MOSFET by solving the 1-D band structure with the 2-D Poisson’s equation self consistently, determined by using the $sp^{3}d^{5}s^{*}$ semi-empirical tight-binding approach only over those k-points that are likely to have a significant effect on the electrostatics. By showing that determining the 1-D Band structure at the source-channel junction is adequate to accurately determine the 2-D channel electrostatics, we show that this approach remains computationally tractable even at higher channel lengths. By following this approach, we obtain the 2-D profile of important device parameters such as electron density and channel potential, which, in turn, enables the determination of the thermionic current density and source-to-drain tunneling current density for a wide range of device parameters using Tsu-Esaki and WKB formalism respectively. Furthermore, the effect of phonon scattering, which is likely to manifest at longer channel lengths, is also incorporated in the drain current calculation, thus making this approach widely applicable.