We present a subthreshold swing model for a symmetric junctionless double gate MOSFET. The scale length λ₁ required to obtain the potential distribution using the Poisson's equation is a criterion for analyzing the short channel effect by an analytical model. In general, if the channel length L_g satisfies L_g ＞ 1.5λ₁, it is known that the analytical model can be sufficiently used to analyze short channel effects. The scale length varies depending on the channel and oxide thickness as well as the dielectric constant of the channel and the oxide film. In this paper, we obtain the scale length for a constant permittivity (silicon and silicon dioxide), and derive the relationship between the scale length and the channel length satisfying the error range within 5%, compared with a numerical method. As a result, when the thickness of the oxide film is reduced to 1 nm, even in the case of L_g ＜ λ₁, the analytical subthreshold swing model proposed in this paper is observed to satisfy the error range of 5%. However, if the oxide thickness is increased to 3 nm and the channel thickness decreased to 6 nm, the analytical model can be used only for the channel length of L_g ＞ 1.8 λ₁.

An analytical threshold voltage model is proposed to analyze the threshold voltage roll-off and drain-induced barrier lowering (DIBL) for a junction-based double-gate (JBDG) MOSFET and a junction-less double-gate (JLDG) MOSFET. We used the series-type potential distribution function derived from the Poisson equation, and observed that it is sufficient to use n＝1 due to the drastic decrease in eigenvalues when increasing the n of the series-type potential function. The threshold voltage derived from this threshold voltage model was in good agreement with the result of TCAD simulation. The threshold voltage roll-off of the JBDG MOSFET was about 57% better than that of the JLDG MOSFET for a channel length of 25 nm, channel thickness of 10 nm, and oxide thickness of 2 nm. The DIBL of the JBDG MOSFET was about 12% better than that of the JLDG MOSFET, at a gate metal work-function of 5 eV. It was also found that decreasing the work-function of the gate metal significantly reduces the DIBL.