Electromigration Forces on Ions in Carbon Nanotubes

We calculate the electromigration forces on ions such as adsorbed alkali metal atoms in a carbon nanotube transistor. The forces are especially large in the turn-on regime of the transistor and much smaller in the off and on states. Electromigration in the channel is driven almost exclusively by the wind force. The sign of the “effective valence” $Z^{*}$ is independent of the actual charge sign but can be reversed with gate voltage, providing a dramatic illustration of the quantum character of the wind force. Our self-consistent nonequilibrium Green’s function calculations treat a ballistic device within a tight-binding approximation.

Figure 1

Variation of current and force with gate voltage $V_g$ at low bias voltage $V_{\mathrm{b}}=50\mathrm{mV}$. (a) The current without an ion (solid black line) and with an ion of $Q=+1e$ (dashed red line) or $Q=-1e$ (dashed-dotted green line) located inside the NT at a radial distance of 0.16 nm from the NT wall. The inset displays a cross section of the cylindrical device geometry, where the source (S) and drain (D) metal electrodes and the surrounding oxide ($\epsilon$) are denoted. (b) The current-induced force on the positive ion (solid red line) and the change of the current due to the ion (dashed red line). (c) The force and the current change for the negative ion (solid and dashed green lines).

Figure 2

Variation of (a) current and (b)–(c) force with bias voltage at $V_g=-0.9\mathrm{V}$. (a) The current without the ion (solid black curve) and with an ion of $Q=+1e$ (dashed red curve) or an ion of $Q=-1e$ (dashed-dotted green curve) inside the NT at a radial distance of 0.16 nm from the NT wall. In (b) and (c), the force on the positive or negative ion is shown by solid red or green lines, respectively. The dashed red and green lines mark the current change due to the ion. Open circles depict the wind force; see text for details.

Figure 3

Dependence of (a) current and (b) force on the radial position of the ion. The voltages are $V_b=+0.3\mathrm{V}$ and $V_g=-0.9\mathrm{V}$, and the ion charge is $Q=+1e$ (solid red curve) or $Q=-1e$ (dashed green curve). Vertical lines mark NT wall ($R_{\mathrm{NT}}$) and oxide boundary ($R_{\mathrm{ox}}$).