# Electrical Coupling of Monolithic 3D Inverters (M3 INVs): MOSFET and Junctionless FET
## 4 Inverter Characteristics  
Mixed-mode circuit simulation of ATLAS was used to verify the inverter characteristics by both M3 INV-MOS and M3 INV-JL including the electrical coupling.  
Figures 5 and 6 show the voltage transfer characteristics (VTC) of M3 INV-MOS and M3 INV-JL, respectively. Figures 5a and 6a show the simulation results of \(L_{G}\) = 20 nm and Figures 5b and 6b show those of \(L_{G}\) = 50 nm. M3 INV-MOS shifts VTC from right to left as \(T_{ILD}\) increases, but M3 INV-JL shifts VTC from left to right as \(T_{ILD}\) increases.  
Figure 7 shows \(\Delta V_{m}\) versus \(T_{ILD}\) of both M3 INV-MOS and M3 INV-JL. As \(T_{ILD}\) decreases, \(\Delta V_{m}\) increases. When \(T_{ILD}\) is over 30 nm, \(\Delta V_{m}\) are below 10 mV, and thus the coupling in the structures can be ignored. In the case of M3 INV-MOS, the larger \(L_{G}\), the larger \(\Delta V_{m}\), but in the case of M3 INV-JL, the smaller \(L_{G}\), the larger \(\Delta V_{m}\).  
Figure 5: Voltage transfer characteristics of M3 INV-MOS cell with (a) \(L_{G}\) = 20 nm and (b) \(L_{G}\) = 50 nm. \(V_{all}\) (=1 V) is DC-biased.  
Figure 6: Voltage transfer characteristics of M3 INV-JL cell with (a) \(L_{G}\) = 20 nm and (b) \(L_{G}\) = 50 nm. \(V_{all}\) (=1 V) is DC-biased.  
Figure 8 show the static noise margin (SNM) windows of M3 INV-MOS and M3 INV-JL with \(L_{\text{G}}\) = 20 nm, respectively. The SNMs were measured as noise margin high (NM\({}_{\text{H}}\)) and noise margin low (NM\({}_{\text{L}}\)) extracted from VTCs of M3 INV-MOS and M3 INV-JL. Figure 9 shows the noise margins of M3 INV-MOS and M3 INV-JL at different \(L_{\text{G}}\)s and \(T_{\text{ILD}}\)s. In the case of M3 INV-MOS, SNM increases as \(T_{\text{ILD}}\) decreases. On the other hand, in the case of M3 INV-JL, SNM decreases when \(T_{\text{ILD}}\) decreases. When \(T_{\text{ILD}}\) is over 30 nm, the maximum variations of SNM of both M3 INV-MOS and M3 INV-JL are below 20 mV, and thus the coupling in both structures can be also ignored.  
Figure 10 show the transient responses of M3 INV-MOS and M3 INV-JL with \(L_{\text{G}}\) = 20 nm at different \(T_{\text{ILD}}\)s, respectively. Table 2 shows the propagation delays extracted from the transient response in Figure 10. As \(T_{\text{ILD}}\) decreases, propagation delays of M3 INV-MOS and M3 INV-JL are lower than \(T_{\text{ILD}}\)s. The same trend is observed for M3 INV-MOS and M3 INV-JL.  
Figure 8: Static noise margin (SNM) characteristics of **(a)** M3 INV-MOS cell and **(b)** M3 INV-JL cell. Here \(L_{\text{G}}\) = 20 nm and \(V_{\text{{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{ \it{ \it{      }}}}}}}}}}}}}}}=1\) V. Black, red, green, and blue lines denote the coupled voltage transfer characteristics (VTCs) of M3 INV-MOS and M3 INV-JL with \(T_{\text{ILD}}\) = 5, 10, 50, and 100 nm, respectively.  
Figure 9: SNMs of M3 INV-MOS and M3 INV-JL cells at different \(T_{\text{ILD}}\)s. Filled and empty symbols denote SNMs of M3 INV-MOS and M3 INV-JL with \(T_{\text{ILD}}\) = 5, 10, 50, and 100 nm, respectively. Squares, circles, and triangles denote SNMs of M3 INV-MOS and M3 INV-JL with \(L_{\text{G}}\) = 20, 30, and 50 nm, respectively.  
M3 INV-JL increase and decrease, respectively. As \(L_{G}\) increases, propagation delays of both M3 INV-MOS and M3 INV-JL increase. When \(T_{ILD}\) is over 30 nm, the maximum variations of propagation delay of both M3 INV-MOS and M3 INV-JL are below 0.2 ps, and thus the coupling in the structures can be also ignored.