## 3 Results and Discussion
### Device Structure Dependence of RTN
#### 3.6.2. Asymmetry Source and Drain Width MOSFETs  
Figure 28 shows the layout structure of rectangular and trapezoidal shape MOSFETs used in this experiment [62; 63]. In the trapezoidal MOSFETs, when current flows from the left to right direction, the source has a wide gate width, and when current flows from the right to left direction, the source has a shallow gate width. The Gumbel plots of \(\mathrm{V_{RMS}}\) for trapezoidal ((a)\(\mathrm{W_{D}}\) < \(\mathrm{W_{S}}\) and (b) \(\mathrm{W_{S}}\) < \(\mathrm{W_{D}}\)) and (c) rectangular MOSFETs are shown in Figure 29[62]. The gate width of rectangular MOSFETs was set as the average of the gate width of trapezoidal MOSFETs. \(\mathrm{I_{DS}}\) was varied from 0.1 to 11 \(\mathrm{\mu A}\) for constant \(\mathrm{V_{BS}}\) of \(-\)1.9 V and \(\mathrm{V_{DS}}\) of 1.4 V. In (c) rectangular MOSFETs, similar phenomena, as shown in Figure 19, are obtained. In contrast, in the trapezoidal MOSFETs, \(\mathrm{V_{RMS}}\) increases with an increase in \(\mathrm{I_{DS}}\) (\(\mathrm{V_{GS}}\)), and those of \(\mathrm{W_{D}}\) < \(\mathrm{W_{S}}\) are larger than those of \(\mathrm{W_{S}}\) < \(\mathrm{W_{D}}\). \(\mathrm{V_{DS}}\) is larger than \(\mathrm{V_{GS}}\) in this experiment. MOSFETs were operated in the saturation region, and the channel formed near the source. Increasing \(\mathrm{I_{DS}}\) increases electron density in the channel, and the electron density at the source of MOSFETs with \(\mathrm{W_{D}}\) < \(\mathrm{W_{S}}\) is less than that with \(\mathrm{W_{S}}\) < \(\mathrm{W_{D}}\). These characteristics indicate that the influence of a charged trap reduces at a high carrier density condition [39; 60; 62]. This means that the electron density and the location in the channel are important factors affecting RTN characteristics. RTN characteristics were evaluated for various \(\mathrm{V_{DS}}\) using rectangular and trapezoidal MOSFETs. Figure 30 shows the Gumbel plots of \(\mathrm{V_{RMS}}\) for trapezoidal ((a) \(\mathrm{W_{D}}\) < \(\mathrm{W_{S}}\) and (b) \(\mathrm{W_{S}}\) < \(\mathrm{W_{D}}\)) and (c) rectangular MOSFETs. \(\mathrm{V_{DS}}\) was varied from 0.1 V to 1.4 V for constant \(\mathrm{I_{DS}}\) of 10 \(\mathrm{\mu A}\) and \(\mathrm{V_{BS}}\) of \(-\)1.9 V [63]. The \(\mathrm{V_{DS}}\) dependance of \(\mathrm{V_{RMS}}\) for the (c) rectangular and (b) trapezoidal with \(\mathrm{W_{S}}\) < \(\mathrm{W_{D}}\) MOSFETs is the same, and \(\mathrm{V_{RMS}}\) increases as \(\mathrm{V_{DS}}\) increases, monotonically. The dependance of (b) trapezoidal with \(\mathrm{W_{S}}\) < \(\mathrm{W_{D}}\) on \(\mathrm{V_{DS}}\) is larger than that of rectangular MOSFETs. In contrast, \(\mathrm{V_{RMS}}\) increases with an increase in \(\mathrm{V_{DS}}\) at less than 0.3 V; however, \(\mathrm{V_{RMS}}\) decreases with an increase in \(\mathrm{V_{DS}}\) at \(>\)0.3V for trapezoidal  
Figure 28. Layout diagrams of the measured transistors with various gate shapes. Figure 29. Gumbel plots of \(\mathrm{V_{RMS}}\) for trapezoidal and rectangular MOSFETs. \(\mathrm{I_{DS}}\) was varied from 0.1 to 11 \(\mathrm{\mu A}\) for constant \(\mathrm{V_{BS}}\) of \(-\)1.9 V and \(\mathrm{V_{DS}}\) of 1.4 V.  
MOSFETs with \(W_{\text{S}}>W_{\text{D}}\). When \(V_{\text{DS}}\) is smaller than the pinch-off voltage (\(V_{\text{CS}}\)-\(V_{\text{TH}}=0.3\) V in this experiment), the channel is uniformly formed under the gate oxide, and the channel vanishes at the drain edge at the pinch-off voltage. The vanished region expands with increasing \(V_{\text{DS}}\). On the other hand, \(I_{\text{DS}}\) was set at a constant of 10 \(\mu\)A, and this means that \(V_{\text{CS}}\) decreases as \(V_{\text{DS}}\) increases at less than a pinch-off voltage of 0.3V. In rectangular MOSFETs, \(V_{\text{RMS}}\) increases with a decrease in \(V_{\text{CS}}\), which is the same effect as shown in Figure 7. In trapezoidal MOSFETs with \(W_{\text{S}}<W_{\text{D}}\), \(V_{\text{DS}}\) dependance was enhanced by reducing the channel width.