Comparison of 3Dimensional Quantum Effects in Nano
Devices Using the ATLAS3D BQP Model
Introduction
With the MOSFET gate lengths scaling down to sub20nms many kinds of devices have been proposed and researched such as doublegate, trigate, fourgate and gateallaround (wire) MOSFETs.
In this work, the carrier distribution and capacitance of these 4types 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 doublegate MOSFET, (b) is a trigate FET, (c) is a fourgate 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 N_{A}=1e16 cm^{3} and N_{D}=1e20 cm^{3}.


Figure 1 : Scheme of the NanoDevices. Tox=1nm Tsi=5.6nm, L=5.6nm W=8nm(a)
DGFET, (b) TriGate FET, (c) FourGate FET, (d) Wire FET. 
Simulation
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 CV 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 trigate 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.


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 CV Curves.

Conclusion
This article presents the basic characteristics of 4 types of nano devices using the BQP model in 3Dimensional structures. The characteristics are very dependent on the device geometry so the carrier confinement distribution and CV curves are consequently different. The BQP model is very effective and flexible at simulating quantum confinement effects for 3Dimensional geometries.
Reference
 Simulation Standard Vol. 14, No. 11, August 2004