Scaling laws for guiding of highly charged ions through nanocapillaries in an insulating polymer

Guided transmission of highly charged ions through nanocapillaries in insulating PET polymers was investigated. Samples with highly parallel capillaries were used to study the ion guiding with a variety of ionic species, such as ${\text{Ne}}^{7+}$, ${\text{Ne}}^{9+}$, ${\text{Ar}}^{9+}$, ${\text{Ar}}^{13+}$, and ${\text{Xe}}^{25+}$. The incident energy was varied within the range of $3-40$ keV. The fraction of transmitted ions was measured as a function of the capillary tilt angle. The results are used to evaluate the guiding angle, which is a measure of the guiding power specifying the ability of a material to guide ions. Moreover, the angular profile of the transmitted ions was studied as a function of their energy and charge state. The profile width and the guiding angle were found to follow the same scaling law indicating that they are both determined by the main charge patch in the entrance region of the capillary.

Figure 1

Capillary guiding of ions in an insulating capillary. In the entrance region the main charge patch is created that deflects the ions to the capillary exit. The quantity $U$ is a characteristic potential across the capillary diameter and $\psi$ is the tilt angle. The exit region is affected by a symmetric potential of depth $U_t$ in which the ions can gain perpendicular velocity $v_{\perp }$. The deflection angle $\alpha$ is obtained from $\text{tan}\alpha =v_{\perp }/v_{\parallel }$, where $v_{\parallel }$ is the longitudinal velocity of the ion. Both potentials $U$ and $U_t$ are likely be produced by the dominant charge in the entrance patch.

Figure 2

Ultrahigh vacuum chamber built essentially by a $\mu$ metal. The ion beam is focused in a lens system and directed on the target sample containing capillaries. The transmitted ions are measured with an electrostatic analyzer, which is rotatable around the chamber axis.

Figure 3

Density plot showing capillaries with a diameter of $\sim 200\text{nm}$ and a density of ${10}^8{\text{cm}}^{-2}$. The foil surface is evaporated with a gold layer of 20 nm thickness. The graph was obtained by means of scanning electron microscopy.

Figure 4

Transmission profiles of ${\text{Ne}}^{7+}$ ions measured for tilt angles $\psi$ in the range of $0°-15°$. The incident energies are 3, 5, 7, and 10 keV as indicated in the graphs. The experimental data are fitted by Gaussian functions given as solid lines.

Figure 5

Transmission profiles of 7 keV ${\text{Ne}}^{7+}$, 13 keV ${\text{Ar}}^{13+}$, and 25 keV ${\text{Xe}}^{25+}$ measured for tilt angles $\psi =0°,5°,\text{and}8°$. Note the similarities of corresponding profiles obtained with a constant energy-to-charge ratio of the projectile. The experimental data are fitted by Gaussian functions given as solid lines.

Figure 6

Properties of the ${\text{Ne}}^{7+}$ transmission profiles given in Fig. 4. The upper row shows the FWHM ${\sigma }_t$ of the profiles and the lower row shows the fraction $f\left(\psi \right)$ of transmitted ions as a function of the tilt angle. The dashed lines (upper row) shall guide the eye and the solid lines (lower row) represent Gaussian fit functions. The guiding angle ${\psi }_c$, given at each graph in the lower row, characterizes the $1/e$ drop of the corresponding Gaussian function.

Figure 7

Fraction $f\left(\psi \right)$ of transmitted ions derived from the transmission profiles partially given in Fig. 5. The upper and lower rows show the fraction $f\left(\psi \right)$ of transmitted ${\text{Ar}}^{13+}$ and ${\text{Xe}}^{25+}$ ions, respectively, as a function of the tilt angle. The solid lines represent Gaussian fit functions. The guiding angle ${\psi }_c$, given at each graph, characterizes the $1/e$ drop of the corresponding Gaussian function.

Figure 8

Scaling laws for the width ${\sigma }_t$ (FWHM) of the transmission profile and the guiding angle ${\psi }_c$. In (a) and (b) the quantities ${\text{sin}}^{-2}{\sigma }_t$ and ${\text{sin}}^{-2}{\psi }_c$, respectively, are plotted as a function of the energy-to-charge ratio $E_p/q$. In (c) the ratio ${\psi }_c/{\sigma }_t$ is plotted showing its constancy within the experimental uncertainties. The solid lines represent fit functions discussed in the text.