Quasi-3D modeling of surface potential and threshold voltage of Triple Metal Quadruple Gate MOSFETs

In this paper we present electrostatic model of 3D Triple Metal Quadruple Gate (TMQG) MOSFET of rectangular cross-section based on quasi-3D method. The analytical equations for channel potential and characteristic length have been derived by decomposing TMQG into two 2D perpendicular cross-sections (triple metal double gate, TMDG) and the effective characteristic length of TMQG is found using equivalent number of gates (ENG) method. For each of the TMDG, 2D Poisson's equation is solved by parabolic approximation and proper boundary conditions to calculate channel potential. The threshold voltage expression is developed using inversion carrier charge sheet density method. The developed models for channel potential and threshold voltage are validated using numerical simulations of TMQG. The developed model provides the design guidelines for TMQG with improved HCEs and SCEs.