## 4 Analysis and Discussion  
The three main parameters listed in Tables 1-4 are associated with certain physical meanings. It is interesting to see the linearly dependent association as shown in Figure 5 such that the kink and (V\({}_{\text{GS}}\)-Vth) are strongly correlated and linearly dependent to each other as well. This demonstrates and enhances the idea of the kink effects addressing the phonon disturbances on, scattering from, and coupling with the carriers degrading the electrical performances. Figure 5: _Cont._  
Furthermore, \(\rm k_{N}\), with geometrical fixed sizes, was proportional to mobility (\(\rm u\)), which is demonstrated as a constant value at fixed \(\rm V_{GS}\). However, at different applied \(\rm V_{GS}\) bias, mobility was definitely varied and proportional to (\(\rm V_{GS}\)-Vth)\({}^{-1/3}\), as shown in Figure 6a,b. That is due to the stronger (\(\rm V_{GS}\)-Vth) field attracting more carriers closer to the interface between the gate oxide and the strongly inversed silicon layer where carriers move, confronting more obstacles. As for the power of (\(-1/3\)), there shall be a mechanism that provides the association between the speed of carrier and the source-drain field, which is perpendicularly influenced from the gate side. Figure 5: (\(\rm V_{GS}\)-Vth) versus \(\rm V_{GS}\), and versus \(\rm V_{GS}\). (**a**) FinFET W120L90, (**b**) MOSFET L180, (**c**) MOS FET L090. Figure 6: _Cont._  
Moreover, the threshold voltages (Vth) varied at various V\({}_{\text{GS}}\) not only for FinFET but also for MOSFET, where V\({}_{\text{tho}}\) may be written as follows:  
\[ \begin{array}{l}V_{\text{tho}}\ =\ \left(-0.56-\left|\Phi_{p}\right|\right)_{ FB}-\frac{Q_{\text{ox}}^{\prime}}{C_{\text{ox}}^{\prime}}+2\big{|}\Phi_{p} \big{|}+\frac{Q_{\text{dep}}^{\prime}}{C_{\text{ox}}^{\prime}}\\ with\\ \big{|}\Phi_{p}\big{|}\ =\ \frac{kT}{e}\ln(\frac{p}{n_{i}}),\\ \text{and}\\ Q_{dep}\ =\ peD\ =\ \sqrt{2\varepsilon_{Si}pe\big{|}2\Phi_{p}\big{|}}\end{array}  \tag{4}\]  
where \"FB\" means flat-band voltage, Q\({}_{\text{ox}}\) is the charge located in the oxide layer, C\({}_{\text{ox}}\)' is the unit capacitance, and Q\({}_{\text{dep}}\) is the space charge in the depletion region. Also, p is defined to be the concentration in p-type semiconductor, and D means the thickness of the depletion region. V\({}_{\text{GS}}\) = 2 \(\mid\) \(\Phi\) \(\mid\) is the basic applied voltage that causes the strongly inversed layer for V\({}_{\text{tho}}\). V\({}_{\text{tho}}\) is called the zero-order threshold voltage and is thought to be the minimum Gate bias which enables the Fermi energy to be lower than the intrinsic Fermi energy and simultaneously sustain the space charge in the induced depletion region. Somehow, Equation (4) is rewritten as the following fitting formula:  
\[ \begin{array}{l}V_{th}\ =\ -0.56-\frac{Q_{\text{ox}}^{\prime}}{C_{\text{ox}} ^{\prime}}+\big{|}\Phi_{p}\big{|}+\frac{\sqrt{2\varepsilon_{Si}pe\big{|}2 \Phi_{p}\big{|}}}{C_{\text{ox}}}\\ V_{th}\ \stackrel{{\Phi\rightarrow\Phi_{p}+\alpha_{eff}V_{GS}}}{{ \rightarrow}}V_{tho}+\alpha_{eff}f(V_{\text{GS}})+\beta_{eff}\sqrt{f(V_{GS})} \\ with\\ \big{|}\beta_{eff}\big{|}\ =\ \frac{\sqrt{4\varepsilon_{Si}pe}}{C_{OX}},\\ \text{and}\\ f(V_{GS})\stackrel{{ empirically}}{{\rightarrow}}=\ \left\{\begin{array}{l}1-V_{GS} ^{\prime}(FinFET)\\ V_{GS},(MOSFET)\end{array}\right.\end{array}  \tag{5}\]_where_  
\(C_{\textit{GX\_FinfFET}}\ =\ (\frac{\varepsilon_{\textit{OX}}}{24\times 10^{-10}})\ =\ (\frac{3\,9\times 8.85\times 10^{-12}}{24\times 1 0^{-10}})\)_,  
\(C_{\textit{GX\_MOSFET}}\ =\ (\frac{\varepsilon_{\textit{OX}}}{60\times 10^{-10}})\ =\ (\frac{5.2\times 8.85\times 10^{-12}}{60 \times 10^{-10}})\)_,  
_and_  
\(\varepsilon_{Si}\ =\ 11.9\varepsilon_{o}\ =\ 11.9\times 8.85\times 10^{-12}F/m\)  
In Equation (5), \(\alpha_{\text{eff}}\) (effective screening parameter) and \(\beta_{\text{eff}}\) are the slopes of _f(V\({}_{\textit{GS}}\))_ and _[f(V\({}_{\textit{GS}}\))]12_, respectively.