3.3.3 NMOS Transistors

A long-channel ( L_G = 2.0 $\mu$m) and a short-channel ( L_G = 0.2 $\mu$m) NMOS transistor were considered. The substrate doping level was N_A = 10¹⁵ cm^-3 and the maximum of the drain and source Gaussian contact doping peaks was N_D = 10²⁰ cm^-3 for both transistors. The device thickness was W = 1 $\mu$m and the oxide thickness d_ox = 5 nm.

For the long-channel device non-local effects were expected to play a minor role. The doping profiles of both transistors are shown in Fig. 3.12a and Fig. 3.12b, respectively. Although these transistors are very simple compared to state of the art, they allow for studying the principal effects.

For long-channel devices, the drain current in the pinch-off region can be calculated from simple analytical models as [25]

$${\frac{\mu \cdot \varepsilon_{\mathit{ox}}}{2 \cdot d_{\mathit{ox}}}} {\frac{W}{L_{G}}}$$ (3.69)

with V_th being the threshold voltage. For short-channel devices (3.69) becomes invalid as velocity saturation occurs in the channel. However, the ratio W/L_G still determines the drain current. Thus, in the figures I_D ^. L_G/W is shown instead of I_D.

The numerical simulations were performed using the mobility models (3.41) for DD and (3.50) for HD. For the HD transport model, simulations with $\eta$ = 0 (uncorrected surface distance model) and $\eta$ = 1 (corrected surface distance model) were carried out. The broadening of the carrier distributions for the long-channel device is shown in Fig. 3.13 and Fig. 3.14 for immediately before the pinch-off point and inside the pinch-off point, respectively. A comparison of the output characteristics for both transport models is shown in Fig. 3.15 and Fig. 3.16. As expected, the device with $\ensuremath{L_{G} =0.2~{\mu}m}$ shows typical short-channel behavior and I_D ^. L_G/W is reduced by 50%. Due to velocity overshoot in the channel, the HD currents are considerably higher than for the DD transport model.

Figure 3.12: Doping profiles of a) the long-channel and b) the short-channel NMOS transistor.

Figure 3.13: Electron concentration before the pinch-off point for the long-channel NMOS for both transport models ( x = 2.12 $\mu$m).

Figure 3.14: Electron concentration in the pinch-off point for the long-channel NMOS for both transport models ( x = 2.12 $\mu$m).

Figure 3.15: Comparison of the output characteristics of the long-channel NMOS for both transport models.

Figure 3.16: Comparison of the output characteristics of the short-channel NMOS for both transport models.

Figure 3.17: Comparison of the output characteristics of the long-channel PMOS for both transport models.

Figure 3.18: Comparison of the output characteristics of the short-channel PMOS for both transport models.