An analytical threshold voltage model is presented to observe the change in threshold voltage shift ΔV_th of a junctionless double gate MOSFET using ferroelectric-metal-SiO₂ as a gate oxide film. The negative capacitance transistors using ferroelectric have the characteristics of increasing on-current and lowering off-current. The change in the threshold voltage of the transistor affects the power dissipation. Therefore, the change in the threshold voltage as a function of theferroelectric thickness is analyzed. The presented threshold voltage model is in a good agreement with the results of TCAD. As a results of our analysis using this analytical threshold voltage model, the change in the threshold voltage with respect to the change in the ferroelectric thickness showed that the threshold voltage increased with the increase of the absolute value of charges in the employed ferroelectric. This suggests that it is possible to obtain an optimum ferroelectric thickness at which the threshold voltage shift becomes 0 V by the voltage across the ferroelectric even when the channel length is reduced. It was also found that the ferroelectric thickness increased as the silicon thickness increased when the channel length was less than 30 nm, but the ferroelectric thickness decreased as the silicon thickness increased when the channel length was 30 nm or more in order to satisfy ΔV_th=0.

The subthreshold swing (SS) of an asymmetric junctionless double gate (AJLDG) MOSFET is analyzed by the use of Gaussian function. In the asymmetric structure, the thickness of the top/bottom oxide film and the flat-band voltages of top gate (Vfbf) and bottom gate (Vfbb) could be made differently, so the change in the SS for these factors is analyzed with the projected range and standard projected deviation which are parameters for the Gaussian function. An analytical subthreshold swing model is presented from the Poisson’s equation, and it is shown that this model is in a good agreement with the numerical model. As a result, the SS changes linearly according to the geometric mean of the top and bottom oxide film thicknesses, and if the projected range is less than half of the silicon thickness, the SS decreases as the top gate oxide film is smaller. Conversely, if the projected range is bigger than a half of the silicon thickness, the SS decreases as the bottom gate oxide film is smaller. In addition, the SS decreases as Vfbb-Vfbf increases when the projected range is near the top gate, and the SS decreases as Vfbb-Vfbf decreases when the projected range is near the bottom gate. It is necessary that one should pay attention to the selection of the top/bottom oxide thickness and the gate metal in order to reduce the SS when designing an AJLDG MOSFET.

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.

We propose a SPICE model of drain-induced barrier lowering (DIBL) for a junctionless cylindrical surrounding gate (JLCSG) MOSFETs. To this end, the potential distribution in the channel is obtained via the Poisson equation, and the threshold voltage model is presented for the JLCSG MOSFET. In a JLCSG nano-structured MOSFET, a channel radius affects the carrier transfer as well as the channel length and oxide thickness; therefore, DIBL should be expressed as a function of channel length, channel radius, and oxide thickness. Consequently, it can be seen that DIBLs are proportional to the power of -3 for the channel length, 2 for the channel radius, 1 for the thickness of the oxide film, and the constant of proportionality is 18.5 when the SPICE parameter, the static feedback coefficient η, is between 0.2 and 1.0. In particular, as the channel radius and the oxide film thickness increase, the value of η remains nearly constant.

In this study, we compared the threshold-voltage extraction methods of accumulation-type JLDG (junctionless double-gate) MOSFETs (metal-oxide semiconductor field-effect transistors). Threshold voltage is the most basic element of transistor design; therefore, accurate threshold-voltage extraction is the most important factor in integrated-circuit design. For this purpose, analytical potential distributions were obtained and diffusion-drift current equations for these potential distributions were used. There are the ø_min method, based on the physical concept; the linear extrapolation method; and the second and third derivative method from the I_d-V_g relation. We observed that the threshold-voltages extracted using the maximum value of TD (third derivatives) and the ø_min method were the most reasonable in JLDG MOSFETs. In the case of 20 nm channel length or more, similar results were obtained for other methods, except for the linear extrapolation method. However, when the channel length is below 20 nm, only the ø_min method and the TD method reflected the short-channel effect.