Comparison of 3-Dimensional Quantum Effects in Nano
Devices Using the ATLAS3D BQP Model



With the MOSFET gate lengths scaling down to sub-20nms many kinds of devices have been proposed and researched such as double-gate, tri-gate, four-gate and gate-all-around (wire) MOSFETs.

In this work, the carrier distribution and capacitance of these 4-types of nano MOSFET were compared using the Bohm Quantum Potential Model [1] in ATLAS3D.


Nanodevice : Geometry and Structure

Figure 1, shows the nanodevice structures. (a) is a double-gate MOSFET, (b) is a tri-gate FET, (c) is a four-gate FET, and (d) is a Wire FET. All these structures have a common gate oxide thickness of Tox=1nm, silicon thickness of Tsi=5.6nm (on nanowire the diameter is 5.6nm), gate length of W=5.6nm, and total device length of L=8nm. Also, the doping level used is NA=1e16 cm-3 and ND=1e20 cm-3.

(a) Double-Gate FET(2)

(b) Tri-Gate FET(3)


(c)Four-Gate FET(4)


(d) All-around(Wire)-FET(all)

Figure 1 : Scheme of the Nano-Devices. Tox=1nm Tsi=5.6nm, L=5.6nm W=8nm(a) DG-FET, (b) Tri-Gate FET, (c) Four-Gate FET, (d) Wire FET.



The Bohm Quantum Potential (BQP) model is an expansion of the Wigner equation and calculates the effects of quantum confinement on the electron and hole concentration and C-V curves [1].

As we have 4 different structures, we compared carrier concentration on the center cutplane of the gate as shown in Figure 2.

Figure 2. Cutplane Position Carrier Distribution Comparison.

Figures 3 and 4 show the effects of carrier confinement on the center of the gate channel. The tri-gate FET with no gate electrode on bottom shows asymetrical confinement.


Figure 3. Electron Concentration with BQP Solution at Vgate=0.0V.


Figure 4. Hole Concentration with BQP Solution Vgate=0.0V.


Figure 5 shows that the electron concentration distribution at a gate voltage of 1.0V. From this concentration distribution it can be seen that the wire FET has an isotropic electron carrier concentration.


Figure 5. Electron Concentration with BQP Solution at Vgate=1.0V and Vdrain=0.4V.


The peak electron and hole concentrations of the 4 MOSFET types are shown in Table 1.


Electron Concentration
Hole Concentration
Tri-Gate FET
Four-Gate FET
Wire-Gate FET
Table 1. Peak carrier concentrations.

Figure 6 shows how the threshold voltage depends on the structure of the 4 devices. The dual gate FET has the lowest threshold voltage but the lowest above threshold conductance. But the four gate and wire FET show higher threshold voltages than the dual gate FET. The four FET has higher drain current then the wire FET because of the area and confinement effect of the FETs.


Figure 6. Comparision of IdVg and C-V Curves.



This article presents the basic characteristics of 4 types of nano devices using the BQP model in 3-Dimensional structures. The characteristics are very dependent on the device geometry so the carrier confinement distribution and C-V curves are consequently different. The BQP model is very effective and flexible at simulating quantum confinement effects for 3-Dimensional geometries.


  1. Simulation Standard Vol. 14, No. 11, August 2004

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