Compact modeling of multi-gate transistors

Scaling of the classical planar MOSFET below 20 nm gate length is facing not only technological difficulties but also limitations imposed by short channel effects, gate and junction leakage current due to quantum tunneling, high body doping induced threshold voltage variation, and carrier mobility degradation. Non-classical multiple-gate structures such as double-gate (DG) FinFETs and surrounding gate field-effect-transistors (SGFETs) have good electrostatic integrity and are an alternative to planar MOSFETs for below 20 nm technology nodes. Circuit design with these devices need compact models for SPICE simulation. In this work physics based compact models for the common-gate symmetric DG-FinFET, independent-gate asymmetric DG-FinFET, and SGFET are developed. Despite the complex device structure and boundary conditions for the Poisson-Boltzmann equation, the core structure of the DG-FinFET and SGFET models, are maintained similar to the surface potential based compact models for planar MOSFETs such as SP and PSP. TCAD simulations show differences between the transient behavior and the capacitance-voltage characteristics of bulk and SOI FinFETs if the gate-voltage swing includes the accumulation region. This effect can be captured by a compact model of FinFETs only if it includes the contribution of both types of carriers in the Poisson-Boltzmann equation. An accurate implicit input voltage equation valid in all regions of operation is proposed for common-gate symmetric DG-FinFETs with intrinsic or lightly doped bodies. A closed-form algorithm is developed for solving the new input voltage equation including ambipolar effects. The algorithm is verified for both the surface potential and its derivatives and includes a previously published analytical approximation for surface potential as a special case when ambipolar effects can be neglected. The symmetric linearization method for common-gate symmetric DG-FinFETs is developed in a form free of the charge-sheet approximation present in its original formulation for bulk MOSFETs. The accuracy of the proposed technique is verified by comparison with exact results. An alternative and computationally efficient description of the boundary between the trigonometric and hyperbolic solutions of the Poisson-Boltzmann equation for the independent-gate asymmetric DG-FinFET is developed in terms of the Lambert W function. Efficient numerical algorithm is proposed for solving the input voltage equation. Analytical expressions for terminal charges of an independent-gate asymmetric DG-FinFET are derived. The new charge model is C-infinity continuous, valid for weak as well as for strong inversion condition of both the channels and does not involve the charge-sheet approximation. This is accomplished by developing the symmetric linearization method in a form that does not require identical boundary conditions at the two Si-SiO2 interfaces and allows for volume inversion in the DG-FinFET. Verification of the model is performed with both numerical computations and 2D TCAD simulations under a wide range of biasing conditions. The model is implemented in a standard circuit simulator through Verilog-A code. Simulation examples for both digital and analog circuits verify good model convergence and demonstrate the capabilities of new circuit topologies that can be implemented using independent-gate asymmetric DG-FinFETs.