Quasi-Compact Model of Direct Source-to-Drain Tunneling Current in Ultrashort-Channel Nanosheet MOSFETs by Wavelet Transform

Abstract

We present an analytical approach for the calculation of direct source-to-drain tunneling (DSDT) probability of electrons in gate-all-around (GAA) silicon nanosheet (SiNS) MOSFETs. The used method is based on the wavelet transform and leads to a quasi-compact model (QCM) for the DSDT current of ultrashort-channel devices. Among them, we introduce a four-piece parabolic approximation method for the conduction band edge and present analytical expressions for the tunneling distances of electrons with different energy levels. The development of a QCM is achieved by limiting the number of interpolation points for the tunneling current density to seven specific electron energies, distributed around the energy level that makes the largest contribution to the tunneling current. A further simplification is achieved by the Gaussian approximation of the tunneling current density in transverse direction so that only the center and surface potentials ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi _ {\text {C}}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi _ {\text {S}}$ </tex-math></inline-formula> ) at the barrier are of interest for the modeling. For comparison, all those approximations are also implemented in the Wentzel–Kramer–Brillouin (WKB) approximation. Furthermore, the approach is verified by nonequilibrium Green’s function (NEGF) simulation.