5.2.1 Gate-Source Spacer Length

The output and transfer characteristics for a device with zero barrier height for electrons is shown in Fig. 5.7. The increase of the gate-source spacer length results in a decrease of the on-current while the off-current is not affected. The on-current is mostly due to carrier injection through the source sided SCHOTTKY barrier whereas the off-current in CNT-FETs is mostly due to parasitic carrier injection at the drain sided SCHOTTKY barrier, (see Section 5.2.2). Therefore, the off-current is not affected by the scaling of the gate-source spacer length.

Both tunneling and thermionic emission contribute to the current. The thermionic emission current is controlled by the barrier height and is independent of the barrier width. On the other hand, the tunneling current decreases exponentially with the barrier width. Fig. 5.8 shows that by increasing the gate-source spacer length the width of the SCHOTTKY barrier at the source-sided metal-CNT interface is increased. As a result, the current is reduced.

Figure 5.7: The effect of the gate-source spacer length ( $L_\textrm {GS}$) on a) the output characteristics with $V_\textrm {G}$=0.5 V and b) the transfer characteristics with $V_\textrm {D}$=0.8 V. The results are for a device with zero barrier height for electrons ( $\ensuremath {\mathrm{q}}\Phi_\textrm{Be}$=0).

Figure 5.8: The effect of the gate-source spacer length ( $L_\textrm {GS}$) on the current. The normalized current spectrum based on a ballistic transport model for a devices with zero barrier height for electrons is shown for a) $L_\textrm {GS}$=1 nm, b) $L_\textrm {GS}$= 5 nm, and c) $L_\textrm {GS}$=10 nm. The bias point is $V_\textrm {G}$= 0.6 V and $V_\textrm {D}$= 0.8 V.

Figure 5.9 shows the relative variation of the on-current versus the gate-source spacer length for devices with negative, zero, and positive barrier height for electrons, assuming ballistic transport. The results indicate that scaling of the gate-source space length affects the on-current of devices with positive barrier height more effectively.

Figure 5.10 shows the current density spectrum for devices with negative, zero, and positive barrier height for electrons, assuming ballistic transport. Electrons with energies lower than the barrier height have to tunnel through the source-sided metal-CNT interface barrier to reach the channel, whereas electrons with higher energies are injected by thermionic emission. The relative contributions of thermionic and tunneling strongly depend on the barrier height and the bias point. As shown in Fig. 5.10, at high gate bias even for devices with zero or negative barrier height the tunneling current contributes considerably to the total current. However, in a device with negative barrier height the tunneling current has a smaller contribution to the total current as compared to devices with non-negative barrier height. Therefore, the current is less sensitive to the variation of the gate-source spacer length (Fig. 5.9).

In conclusion, the on-current of all device types decreases as the gate-source spacer length increases. The reduction of the on-current strongly depends on the relative contribution of the tunneling current. To improve the static response it is more appropriate to reduce the gate-source spacer length. However, the reduction of this spacer results in an increase of the gate-source parasitic capacitances which can severely affect the dynamic response of the device. For optimal performance the length of this spacer has to be carefully selected, see Section 5.3.

Figure 5.9: The relative variation of the on-current versus the gate-source spacer length ( $L_\textrm {GS}$) for devices with different barrier heights for electrons. In a device with negative barrier height the tunneling current has a smaller contribution to the total current as compared to other device types. Therefore, the current is less sensitive to the variation of the gate-source spacer length.

Figure 5.10: The effect of the barrier height at the metal-CNT interface on the current. The normalized current spectrum based on a ballistic model transport is shown for a device with a) negative (q $\Phi _\textrm {Be}$=-0.3 eV), b) zero (q $\Phi _\textrm {Be}$=0), and c) positive barrier height for electrons (q $\Phi _\textrm {Be}$=+0.3 eV). The operating point is $V_\textrm {G}$=0.6 V and $V_\textrm {D}$=0.8 V.

M. Pourfath: Numerical Study of Quantum Transport in Carbon Nanotube-Based Transistors