A Compact Model of Quantum Electron Density at the Subthreshold Region for Double-Gate Junctionless Transistors

A compact model of quantum electron density at the subthreshold region is derived for junctionless (JL) double-gate (DG) FETs. The proposed quantum model is obtained under two different quantum confinement conditions. One is for a case of a thick channel and a heavily doped channel, where quantum confinement effects (QCEs) are modeled by a 1-D quantum harmonic oscillator. The other is for a case of a thin channel, where QCEs are modeled by the use of a 1-D quantum well surrounded by high potential barriers and an energy correction term coming from the depletion charge. It is shown that, regardless of the channel thickness, the quantum confinement is higher in JL than in inversion-mode (IM) DG FETs. However, for a thin channel, the quantum threshold voltage shift is less severe in JL than in IM DG FETs. The proposed model gives an analytical expression for the threshold voltage shift due to QCEs, which can be used as a quantum correction term for compact modeling.