Analytical model for random dopant fluctuation in double-gate MOSFET in the subthreshold region using macroscopic modeling method

An analytical model is proposed for the random dopant fluctuation (RDF) in a symmetric double-gate metal-oxidesemiconductor field-effect-transistor (DG MOSFET) in the subthreshold region. Unintended impurity dopants cannot be absolutely prevented during the device fabrication; hence, it is important to analytically model the fluctuations in the electrical characteristics caused by these impurity dopants. Therefore, a macroscopic modeling method is applied to represent the impurity dopants in DG MOSFETs. With this method, the two-dimensional (2D) Poisson equation is separated into a basic analytical DG MOSFET model with channel doping concentration NA and an impurity-dopant-related term with local doping concentration NRD confined in a specific rectangular area. To solve the second term, the manually solvable 2D Green's function for DG MOSFETs is used. Through calculation of the channel potential (ϕ(x, y)), the variations in the drive current (IDS) and threshold voltage (Vth) are extracted from the analytical model. All results from the analytical model for an impurity dopant in a DG MOSFET are examined by comparisons with the commercially available 2D numerical simulation results, with respect to various oxide thicknesses (tox), channel lengths (L), and location of impurity dopants.