Equivalent DG Dimensions Concept for Compact Modeling of Short-Channel and Thin Body GAA MOSFETs Including Quantum Confinement

In this work, short-channel effects (SCEs) in cylindrical gate-all-around (GAA) MOSFETs with intrinsic or lightly doped channels are analytically described by using the conformal mapping technique for 2-D double-gate (DG) FETs. An equivalent capacitor model leads to an equivalent channel length concept, which allows to correctly determine the SCEs relevant center and surface potentials ( $\Phi _{{C}} $ and $\Phi _{{S}} $ ) at the potential barrier. Furthermore, we make use of the rotational symmetry of GAA FETs and modify a compact drain current model of a DG device to use it for GAA transistors. Also, a mathematical correlation regarding quantum confinement for thin body transistors is derived, which shows that the mostly unwanted quantum effects occur in GAA structures already for thicker channels compared to DG transistors. Both transistor types experience a comparable influence with regard to quantization if the channel thickness of GAA FETs is 53% more than that of DG FETs. The dc behavior of our adapted model is verified with 3-D TCAD simulation data and applied to experimental data of ultrascaled silicon on insulator (SOI) omega-gate nanowire N-MOSFETs.