Quantum mechanical compact modeling of symmetric double-gate MOSFETs using variational approach

A physics-based analytical model for symmetrically biased double-gate (DG) MOSFETs considering quantum mechanical effects is proposed. Schrödinger's and Poisson's equations are solved simultaneously using a variational approach. Solving the Poisson and Schrödinger equations simultaneously reveals quantum mechanical effects (QME) that influence the performance of DG MOSFETs. The inversion charge and electrical potential distributions perpendicular to the channel are expressed in closed forms. We systematically evaluated and analyzed the potentials and inversion charges, taking QME into consideration, in Si based double gate devices. The effect of silicon thickness variation in inversion-layer charge and potentials are quantitatively defined. The analytical solutions provide good physical insight into the quantization caused by quantum confinement under various gate biases.