# Lateral Capacitance-Voltage Method of NanoMOSFET for Detecting the Hot Carrier Injection
## 4 Simulations Results and Discussions
Figure 4 shows a map of the distribution of minority charge carriers in the substrate for two cases: (a) the case considering the non-embedding of a local charge into the gate oxide and (b) the case considering the embedding of a local charge. This distribution is appropriate to the applied voltage V\({}_{\rm ds}\) = 0.5 V, which corresponds to the range of the maximum variation of the lateral capacitances in the C-V  
Figure 3: C–V dependences of drain–substrate junction without embedded charge (**1**) and at embedding the local oxide charge near the drain (**2**). Figure 2: C–V dependences of drain–substrate junction at different gate lengths of MOSFET. dependence. The distribution patterns (in Figure 4) reveal that, in the case where a local oxide charge was embedded, the effective width of the depletion layer (the width of the transition region with an electron concentration exceeding \(5\times 10^{15}\) cm\({}^{-3}\)) was narrower than in the case where no local oxide charge was embedded. Consequently, in case a local oxide charge was embedded, the capacitance was higher at the aforementioned specific value of the applied voltage (V\({}_{\text{ds}}\) = 0.5 V). This is clearly depicted in the C-V dependence of the lateral transitions in Figure 3. At high applied voltages, the distribution of the charge carriers in the substrate did not practically differ in the cases mentioned above, as it is shown in Figure 3 (see the range of variation of the applied voltages in which the C-V dependency coincides in Figure 3). The amplitude of changes in capacitances \(\Delta\text{C}_{\text{dsmax}}\) and \(\Delta\text{C}_{\text{ssmax}}\) depends on the linear size (d) of the embedded local oxide charge (Figure 5). As can be seen from Figure 5, \(\Delta\text{C}_{\text{dsmax}}\) increased linearly with increasing d. In contrast, after crossing the center/middle of the oxide along the channel, the capacitance \(\Delta\text{C}_{\text{dsmax}}\) reached saturation (see top point in the red curve in Figure 5) and afterwards decreased with a further increase in d. This reveals the weakening of the influence of the local oxide charge on the redistribution of charge carriers in the vicinity of the drain when increasing the distance up to source. As it appears in Figure 5, the capacitance \(\Delta\text{C}_{\text{ssmax}}\) also rose linearly with increasing d. This evolution reached saturation after passing through the middle of the oxide and kept increasing (at a significantly high rate) with a further increase in d. This reveals the increased effect of the local oxide charge on the redistribution of charge carriers in the vicinity of the source as the distance from the source decreases. After reaching the end of the gate oxide, the local charge covered all the gate oxide, and consequently the capacitances of both side junctions were under the same conditions. Overall, Figure 5 shows the dependence of the amplitude of changes in capacitances (\(\Delta\text{C}_{\text{dsmax}}\) and \(\Delta\text{C}_{\text{ssmax}}\)) on the linear size (d) of the embedded local oxide charge. As clearly depicted in Figure 5, the capacitances \(\Delta\text{C}_{\text{dsmax}}\) and \(\Delta\text{C}_{\text{ssmax}}\) at d = 100 nm were equal. Such behavior of the lateral capacitances eases the estimation of the linear size of the embedded oxide charge. The aforementioned dependence of the capacitances on the linear size had a peak (see the top point in Figure 5) that corresponds to the expansion of the charged area towards the middle of the oxide layer along the channel. This peak is a very important  
Figure 4: Minor carrier concentration distribution in substrate (base) in case of absence (**a**) and presence (**b**) of embedding local oxide charge. V\({}_{\text{ds}}\) = 0.5 V and the indicated concentration is in cm\({}^{-3}\). critical point that can appropriately be used for the calibration of the dependence and to accurately estimate the size of the charged area.