## 4 Results and Discussions  
The PS quantum corrections offer a precise charge distribution within the simulated NWTs' channel [5]. And Figure 3 gives the Phi ovals represented on a two-dimensional cross-section at the center of the gate. It is noteworthy that patterns of isotropic charge distribution derived from the PS simulations are comparable (in terms of their characteristics) to Phi, and despite the voltage-dependent nature of the charge distributions, the Phi ovals' signatures can be identified at every gate voltage. Figure 3: The Poisson-Schrödinger (PS) simulations’ charge distribution results. Here, the Phi ovals (marked in white) emphasize the comparability between the golden ratio and the charge distribution within the 5 nm \(\times\) 8.10 nm NWT cross-section. The slice cut is at the middle of NWT channel at gate bias (0, 0.1, 0.2, 0.5, 0.6, 0.7) Volt at high drain voltage V\({}_{\text{D}}\) = 0.7 V. The gate length Lg = 12 nm. Figure 2: Flowchart for the overall simulation method. MC: Monte-Carlo. For the purpose of evaluating the effect that the NWT cross-section dimension has on device performance in a reasonable manner, Figure 4 gives the gate voltage against the quantum mobile charge within the channel (for the initial 9 NWTs given in Table 1). Here, the alignment of the Q\({}_{\text{M}}\)-V\({}_{\text{G}}\) curves takes place by altering the gate work function, and the reader should recognize that the mobile charge is predicted in the middle of the channel. Perhaps the centrally interesting result to arise from our consideration of the Q\({}_{\text{M}}\)-V\({}_{\text{G}}\) attributes in Figure 4 relates to the fact that the greatest level of quantum charge is associated with NWTs which have the Phi and 1/Phi dimensional ratios. When comparatively examined against every other elliptical device, the NWT whose cross-section is precisely circular is associated with the lowest level of quantum charge. In Tables 2 and 3, a certain gate voltage (V\({}_{\text{G}}\)) is used for the \(<\)110\(>\) and \(<\)100\(>\) crystallographic orientations, thus facilitating a comparative examination of the simulated gate capacitance (C\({}_{\text{G}}\)) and mobile quantum charge in the channel per-unit-length (Q\({}_{\text{M}}\)). Q\({}_{\text{M}}\) is in a direct and proportional relationship to the NWT gate capacitance, in view of the following equation:  
\[\text{Q}_{\text{M}}=\text{C}_{\text{G}}(\text{V}_{\text{G}}-\text{V}_{\text{T }}), \tag{1}\]  
where V\({}_{\text{T}}\) and V\({}_{\text{G}}\) denote the threshold voltage and gate voltage, respectively. In view of this, it is reasonable to conclude that the fall in NWT gate capacitance brings about an attendant fall in the channel's mobile charge, thus reducing the overall level of transistor performance. In view of the information given in Tables 2 and 3, it is evidently the case that for the two crystallographic orientations, capacitance is greatest when the wires reflect Phi. As for the wires with the \(<\)100\(>\) crystallographic orientation, the charges in the Phi and 1/Phi instances are exactly the same, which can be accounted in reference to the m\({}_{\text{Y}}\) and m\({}_{\text{Z}}\) effective masses (of electrons). Hence, it could conceivably be hypothesized that the two recent successful industrial attempts to build NWTs with cross-sectional AR \(\approx\) 1 (circular NWT [8; 9] and AR \(\approx\) 3.5 (sheet NWT) [10] have overlooked the fact that AR contributes to NWT performance (in this study, the term \"sheet NWT\" refers to any NWT where 0.5 \(\geq\) AR \(\geq\) 2). Figure 5 compares the effect of 9 cross-section aspect ratios for Si NWTs on the I\({}_{\text{D}}\)-V\({}_{\text{G}}\) curves. Consistent with the data presented so far, the NWTs with cross-sections equal to 1/Phi and Phi own the highest I\({}_{\text{on}}\) at low drain voltage as well as at high drain voltage. Figure 4: 9 NWT cross-section aspect ratios and the gate voltage dependence of the NWTs’ quantum mobile charge.