## 2 Preparation and Measurements
### Fitting \(\rm{I_{DS}}\)-\(\rm{V_{DS}}\) and \(\rm{I_{DS}}\)-\(\rm{V_{GS}}\)  
FinFET transistors which are similar to MOSFET have two-regime modified electrical characteristics as expressed in the following:  
\[I_{DS}(\rm{T}\it{i}\rm{o}\rm{e}\rm{)}=k_{N}[(V_{GS}-V_{th})V_{DS}-{V_{DS}}^{2} /2](1+\lambda V_{DS}) \tag{1}\]  
\[I_{DS}(\it{S}\it{S}\it{S}\it{S}\it{S}\it{S}\it{S}\it{S}\it{S}\  
to test the goodness-of-fit for each transistor with different channel lengths and channel widths. One way is to fix Kn. Kn fixed at a certain value may help to find different corresponding values of Vth and \(\lambda\) at different values of V\({}_{\rm{G}}\) (0.25 V, 0.5 V, 0.75 V, and 1.0 V) by the minimum requirement in Equation (3). All the minimum values at V\({}_{\rm{G}}\) = 0.25 V, 0.5 V, 0.75 V, and 1.0 V are summed over and give a final total minimum deviation at the specific fixed Kn. Different final total minimum deviations are compared as shown in Figure 1a for the transistor denoted by W120L100. The least minimum deviation determines the final Kn of the respective transistor. All the Kn values are collected and listed in Table 1[14; 15; 16; 17; 18; 19; 20; 21; 22]. \begin{table}
\begin{tabular}{c c c c} \hline
**Gate Sizes** & **Kn(A/V2)** & \(\boldsymbol{\lambda}\)**(1/V)** & **Vth(V)** \\ \hline W120L100 & \(1.56\times 10^{-4}\) & 0.305 & \(-0.250\) \\ W120L160 & \(1.36\times 10^{-4}\) & 0.170 & \(-0.150\) \\ W120L240 & \(1.13\times 10^{-4}\) & 0.130 & \(-0.025\) \\ \hline \end{tabular}
\end{table} 
Table 1: Three ways to collect fixed parameters of various transistors. Figure 1: \(Cont\). The second way is to fix Vth. Vth fixed at a certain value may help to find different corresponding Kn and \(\lambda\) values at different values of V\({}_{\rm G}\) = 0.25 V, 0.5 V, 0.75 V, and 1.0 V by the minimum requirement in Equation (3). All the minimum values at V\({}_{\rm G}\) = 0.25 V, 0.5 V, 0.75 V, and 1.0 V are summed over and give a final total minimum deviation at the specific fixed Vth. Different final total minimum deviations are compared as shown in Figure 1b for the transistor denoted by W120L100. The least minimum deviation determines the final \(\lambda\) Vth of the respective transistor. All the \(\lambda\) values are collected and listed in Table 1.  
The third way is to fix \(\lambda\). The \(\lambda\) fixed at a certain value may help to find different corresponding Kn and Vth values at different values of V\({}_{\rm G}\) = 0.25 V, 0.5 V, 0.75 V, and 1.0 V by the minimum requirement in Equation (3). All the minimum values at V\({}_{\rm G}\) = 0.25 V, 0.5 V, 0.75 V, and 1.0 V are summed over and give a final total minimum deviation at the specific fixed \(\lambda\). Different final total minimum deviations are compared as shown in Figure 1c for the transistor denoted by W120L100. The least minimum deviation determines the final \(\lambda\) of the respective transistor. All the \(\lambda\) values are collected and listed in Table 1.  
As shown in Figure 1a-c, the transistor W120L100 has the final fixed Kn = 1.56 \(\times\) 10\({}^{-4}\) A/V2, the final fixed \(\lambda\) = 0.305 (1/V), and the final fixed Vth = \(-\)0.25 V. In addition, the corresponding total minimum deviations are 6.25 \(\times\) 10\({}^{-10}\) A\({}^{2}\), 1.27 \(\times\) 10\({}^{-11}\) A\({}^{2}\), and 2.38 \(\times\) 10\({}^{-10}\) A\({}^{2}\), respectively. The value \(\lambda\) = 0.305 and the final minimum deviation 1.27 \(\times\) 10\({}^{-11}\) A\({}^{2}\) has the final minimum deviation as compared with the other two ways of parameter-fixing. As shown in Figure 2a-c, the transistor W120L160 has the final Kn = 1.36 \(\times\) 10\({}^{-4}\) A/V2, \(\lambda\) = 0.170 (1/V), and Vth = \(-\)0.150 V. In addition, the corresponding minimum deviations are 8.82 \(\times\) 10\({}^{-10}\) A\({}^{2}\), 2.14 \(\times\) 10\({}^{-10}\) A\({}^{2}\), and 1.83 \(\times\) 10\({}^{-10}\) A\({}^{2}\), respectively.