Transmission of low-energy negative ions through insulating nanocapillaries

A simulation is performed to study the transmission of low-energy $\mathrm{C}{\mathrm{l}}^{-}$ ions through $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ nanocapillaries. For the trajectory simulations, there are several processes involved: the image forces induced by the projectile; the electrostatic force from the deposited charges; the scattering from the inner surface and charge exchange. The simulation reproduces the main features of the experiments; i.e., the double peak structure in the transmitted angular distribution and the transmitted fractions of $\mathrm{C}{\mathrm{l}}^{-}$, $\mathrm{C}{\mathrm{l}}^{+}$, and $\mathrm{C}{\mathrm{l}}^0$ were found in the charge state distribution. The transmitted $\mathrm{C}{\mathrm{l}}^{-}$ ions are centered around the beam direction while the transmitted fractions of $\mathrm{C}{\mathrm{l}}^0$ and $\mathrm{C}{\mathrm{l}}^{+}$ are centered around the tilt angles. The role of the deposited charge is also studied by simulations. With the deposited charge, it is found that $\mathrm{C}{\mathrm{l}}^{-}$ is dominant in the transmission and the majority of the ions, centered around the tilt angle, are mainly from the single deflection by the negative charge patches on the inner surfaces of the capillaries, and only a few directly transmitted $\mathrm{C}{\mathrm{l}}^{-}$ ions are centered around the incident direction. There are also a few transmitted fractions of $\mathrm{C}{\mathrm{l}}^0$ and $\mathrm{C}{\mathrm{l}}^{+}$ from close surface scatterings. In the case that there are no negative charge patches, the simulation agrees with the experiment in detail: The majority of the directly transmitted $\mathrm{C}{\mathrm{l}}^{-}$ ions are centered around the incident direction while only a few scattered $\mathrm{C}{\mathrm{l}}^{-}$ ions are centered around the tilt angle from the single close collisions with the inner surfaces of the capillaries. There is a portion, comparable to the transmitted fraction of $\mathrm{C}{\mathrm{l}}^{-}$, of the transmitted fractions of $\mathrm{C}{\mathrm{l}}^0$ and $\mathrm{C}{\mathrm{l}}^{+}$, centered around the tilt angle, from the single scatterings with the inner surfaces of the capillaries. This confirms that at the present experimental conditions there are most probably no negative charge patches formed to guide the negative ions through insulating $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ nanocapillaries.

Figure 1

A schematic view of the tilt angle ψ and observation angle ϕ.

Figure 2

The angular distribution: (a) experiment, and (b) simulation, and charge state distributions of transmitted projectiles: (c) experiment, and (d) simulation, for 16-keV $\mathrm{C}{\mathrm{l}}^{-}$ at tilt angle of $1.6^{\circ }$.

Figure 3

The peak position of the angular distribution of transmitted neutrals ($\mathrm{C}{\mathrm{l}}^0$) as a function of the tilt angle. The solid line is the linear function that shows the peak position of transmitted neutral shifts according to the tilt angle (see the text).

Figure 4

The intensity of transmitted $\mathrm{C}{\mathrm{l}}^{-}$ (a), $\mathrm{C}{\mathrm{l}}^0$ (b), and $\mathrm{C}{\mathrm{l}}^{+}$ (c) vs the tilt angle for 16-keV $\mathrm{C}{\mathrm{l}}^{-}$ ions. The dashed line in (a) indicates the angle within which the geometrical transmission occurs (see the text) and the solid line in (b) is the scattering probability (see the text).

Figure 5

The intensity ratio of transmitted $\mathrm{C}{\mathrm{l}}^{+}$ to $\mathrm{C}{\mathrm{l}}^0$ vs the tilt angle for 16-keV $\mathrm{C}{\mathrm{l}}^{-}$.

Figure 6

The laboratory coordinate system $({\widehat{i}}_l,{\widehat{j}}_l,{\widehat{k}}_l)$, membrane coordinate system $({\widehat{i}}_m,{\widehat{j}}_m,{\widehat{k}}_m)$, and capillary coordinate system $({\widehat{i}}_c,{\widehat{j}}_c,{\widehat{k}}_c)$.

Figure 7

The schematic view of the image charges induced by the incident ion.

Figure 8

(Top) Coordinates and (bottom) the deposited charge distribution for the tilt angle of $1.6^{\circ }$ from the geometrical hit probability (see the text).

Figure 9

The simulated two-dimensional transmitted angular distributions (a) and their corresponding projections (b) as well as the charge state distributions (c) for various deposited negative charges as indicated on the top of the graphs for 16-keV $\mathrm{C}{\mathrm{l}}^{-}$ at the tilt angle of $1.6^{\circ }$.

Figure 10

The simulated ratio of transmitted $\mathrm{C}{\mathrm{l}}^{+}$ to $\mathrm{C}{\mathrm{l}}^0$ for various deposited negative charges for 16-keV $\mathrm{C}{\mathrm{l}}^{-}$ incident to the capillaries at the tile angle of $1.6^{\circ }$.