Absolute photoionization cross sections for ${\mathrm{Xe}}^{4+}$, ${\mathrm{Xe}}^{5+}$, and ${\mathrm{Xe}}^{6+}$ near $13.5\mathrm{nm}$: Experiment and theory

Absolute photoionization cross-section measurements for a mixture of ground and metastable states of ${\mathrm{Xe}}^{4+}$, ${\mathrm{Xe}}^{5+}$, and ${\mathrm{Xe}}^{6+}$ are reported in the photon energy range of $4d\to nf$ transitions, which occur within or adjacent to the $13.5\mathrm{nm}$ window for extreme ultraviolet lithography light source development. The reported values allow the quantification of opacity effects in xenon plasmas due to these $4d\to nf$ autoionizing states. The oscillator strengths for the $4d\to 4f$ and $4d\to 5f$ transitions in ${\mathrm{Xe}}^{q+}$ $(q=1–6)$ ions are calculated using nonrelativistic Hartree-Fock and random phase approximations. These are compared with published experimental values for ${\mathrm{Xe}}^{+}$ to ${\mathrm{Xe}}^{3+}$ and with the values obtained from the present experimental cross-section measurements for ${\mathrm{Xe}}^{4+}$ to ${\mathrm{Xe}}^{6+}$. The calculations assisted in the determination of the metastable content in the ion beams for ${\mathrm{Xe}}^{5+}$ and ${\mathrm{Xe}}^{6+}$. The experiments were performed by merging a synchrotron photon beam generated by an undulator beamline of the Advanced Light Source with an ion beam produced by an electron cyclotron resonance ion source.

Figure 1

(Color online) Absolute photoionization cross section for ${\mathrm{Xe}}^{6+}$ ions. The open circles indicate our measured absolute photoionization cross section to which the experimental photoion-yield (small dots) spectrum measured at an energy resolution of $60\mathrm{meV}$ is normalized. The dotted (blue) curve corresponds to the $5s$ photoionization cross section of ${\mathrm{Xe}}^{6+}$ from the five-channel RPA calculation ($L$ form) including $5s\to np,\epsilon p$, $4d\to nf,\epsilon f$, $4d\to np,\epsilon p$, $4p\to nd,\epsilon d$, and $4p\to ns,\epsilon s$. The solid (red) curve contains the RPA oscillator strength of these transitions and RPA autoionizing widths where the contributions of the ground and metastable species have been weighted by $\frac{2}{3}$ and $\frac{1}{3}$, respectively (see Table ).

Figure 2

(Color online) ${\mathrm{Xe}}^{5+}$ photoionization cross sections in the vicinity of the $4d\to 4f$ transition obtained in experiment (solid curve with black dots) and calculated for the $5^2{P}_{1∕2}$ and $5^2{P}_{3∕2}$ states (dash and dash-dot blue curves, respectively), and for a mixture of 67% ground and 33% metastable ions (solid red curve). See text for details. For the purpose of comparison the theoretical curves have been shifted by $-3.32\mathrm{eV}$ from their original position with respect to the experimental data.

Figure 3

(Color online) ${\mathrm{Xe}}^{5+}$ photoionization cross sections in the vicinity of the $4d\to 5f$ transition calculated for the $5^2{P}_{1∕2}$ (blue dashed line) and $5^2{P}_{3∕2}$ (blue dash-dot line) states, and for a mixture of 67% ground and 33% metastable ions (red solid line). See text for details.

Figure 4

Our absolute cross-section measurements for photoionization of ${\mathrm{Xe}}^{4+}$ are indicated by open circles with error bars, to which an energy scan performed at a resolution of $60\mathrm{meV}$ was normalized. The inset shows the $13.5\mathrm{nm}\pm 2\%$ region of interest for EUV lithography on an expanded energy scale.

Figure 5

Comparison plot of the measurements for $4d\to nf$ transitions in ${\mathrm{Xe}}^{4+}$ at three different energy resolutions ($60$, $30$, and $15\mathrm{meV}$).

Figure 6

Absolute photoionization cross-section measurements in the energy ranges of the $4d\to 4f$ transitions in ${\mathrm{Xe}}^{4+}$, ${\mathrm{Xe}}^{5+}$, and ${\mathrm{Xe}}^{6+}$. The vertical dashed lines indicate the energies at which strong absorption lines have been observed in LPP plasmas [4].

Figure 7

Comparison of measured $4d\to 4f$ oscillator strengths from references [15, 19] and the present work, with RPA values.