*3.1. Extraction of Threshold Voltage (VT*0*), Specific Current (IS) and Slope Factor (n)*

The values of the threshold voltage (*VT*0), the specific current (*IS*) and slope factor (*n*) were extracted from the *gm*/*ID* curve [16] illustrated in Figure 5b, which was measured with the circuit configuration in Figure 5a.

**Figure 5.** (**a**) Circuit to extract parameters from (**b**) the *gm*/*ID* and *ID* curves.

Based on the method described in [16], the values of the threshold voltage and the specific current were determined through the *gm*/*ID* characteristic written in (20), which was valid for all regions of operation.

$$\frac{\mathcal{S}\_m}{I\_D} = \frac{1}{I\_D} \frac{\partial I\_D}{\partial V\_G} = \frac{2}{n\phi\_l(\sqrt{1+i\_f} + \sqrt{1+i\_r})}\tag{20}$$

$$\frac{V\_{DS}}{\phi\_t} = \sqrt{1 + i\_f} - \sqrt{1 + i\_r} + \ln\left(\frac{\sqrt{1 + i\_f} - 1}{\sqrt{1 + i\_r} - 1}\right) \tag{21}$$

Expression (21) is obtained by applying the UICM to the drain and source terminals. For *if* <sup>=</sup> 3 and *VDS*<sup>=</sup> *<sup>φ</sup><sup>t</sup>* <sup>2</sup> , expression (21) results in *ir* = 2.12; under these conditions, *VT*<sup>0</sup> corresponds to the gate voltage at which *gm*/*ID* = 0.531(*gm*/*ID*)*max*, while *IS* corresponds to *ID*/0.88, where *ID* is the drain current at *VGB* = *VT*0. The method described for the extraction of the values of *VT*<sup>0</sup> and *IS* assumes that the variation of the slope factor with the gate voltage is negligible. The slope factor (*n*) can be extracted from (22), which is the asymptotic value of the *gm*/*ID* curve in a weak inversion. The points used to determine *VT*0, *IS* and *n* are shown in Figure 5b.

$$\left(\frac{\mathcal{G}\_m}{I\_D}\right)\_{\max} \approx \frac{1}{n\phi\_t} \tag{22}$$

The DIBL factor (*σ*) does not appear in (20) because the short-channel effects, namely DIBL, velocity saturation and channel length modulation are not relevant in the linear region. Consequently, the extraction of *VT*0, *IS* and *n* in the linear region is also valid for short-channel devices.
