Radium single-ion optical clock

We explore the potential of the electric quadrupole transitions 7s\,^2S_{1/2} - 6d\,^2D_{3/2}, 6d\,^2D_{5/2} in radium isotopes as single-ion optical frequency standards. The frequency shifts of the clock transitions due to external fields and the corresponding uncertainties are calculated. Several competitive $^A$Ra$^+$ candidates with $A=$ 223 - 229 are identified. In particular, we show that the transition 7s\,^2S_{1/2}\,(F=2,m_F=0) - 6d\,^2D_{3/2}\,(F=0,m_F=0) at 828 nm in $^{223}$Ra$^+$, with no linear Zeeman and electric quadrupole shifts, stands out as a relatively simple case, which could be exploited as a compact, robust, and low-cost atomic clock operating at a fractional frequency uncertainty of $10^{-17}$. With more experimental effort, the $^{223,225,226}$Ra$^+$ clocks could be pushed to a projected performance reaching the $10^{-18}$ level.Comment: 20 pages, 1 figur

Microdroplet-tin plasma sources of EUV radiation driven by solid-state-lasers (Topical Review)

Plasma produced from molten-tin microdroplets generates extreme ultraviolet light for state-of-the-art nanolithography. Currently, CO2 lasers are used to drive the plasma. In the future, solid-state mid-infrared lasers may instead be used to efficiently pump the plasma. Such laser systems have promise to be more compact, better scalable, and have higher wall-plug efficiency. In this Topical Review, we present recent findings made at the Advanced Research Center for Nanolithography (ARCNL) on using 1 and 2 μm wavelength solid-state lasers for tin target preparation and for driving hot and dense plasma. The ARCNL research ranges from advanced laser development, studies of fluid dynamic response of droplets to impact, radiation-hydrodynamics calculations of, e.g. ion 'debris', (EUV) spectroscopic studies of tin laser-produced-plasma as well as high-conversion efficiency operation of 2 μm wavelength driven plasma

Short-wavelength out-of-band EUV emission from Sn laser-produced plasma

We present the results of spectroscopic measurements in the extreme ultraviolet (EUV) regime (7-17 nm) of molten tin microdroplets illuminated by a high-intensity 3-J, 60-ns Nd:YAG laser pulse. The strong 13.5 nm emission from this laser-produced plasma is of relevance for next-generation nanolithography machines. Here, we focus on the shorter wavelength features between 7 and 12 nm which have so far remained poorly investigated despite their diagnostic relevance. Using flexible atomic code calculations and local thermodynamic equilibrium arguments, we show that the line features in this region of the spectrum can be explained by transitions from high-lying configurations within the Sn$^{8+}$-Sn$^{15+}$ ions. The dominant transitions for all ions but Sn$^{8+}$ are found to be electric-dipole transitions towards the $n$=4 ground state from the core-excited configuration in which a 4$p$ electron is promoted to the 5$s$ sub-shell. Our results resolve some long-standing spectroscopic issues and provide reliable charge state identification for Sn laser-produced plasma, which could be employed as a useful tool for diagnostic purposes.Comment: 11 pages, 4 figure

Laser-to-droplet alignment sensitivity relevant for laser-produced plasma sources of extreme ultraviolet light

We present and experimentally validate a model describing the sensitivity of the tilt angle, expansion and propulsion velocity of a tin micro-droplet irradiated by a 1 {\mu}m Nd:YAG laser pulse to its relative alignment. This sensitivity is particularly relevant in industrial plasma sources of extreme ultraviolet light for nanolithographic applications. Our model has but a single parameter: the dimensionless ratio of the laser spot size to the effective size of the droplet, which is related to the position of the plasma critical density surface. Our model enables the development of straightforward scaling arguments in turn enabling precise control the alignment sensitivity.Comment: 7 pages, 5 figure

Single-collision scattering of keV-energy Kr ions off a polycrystalline Cu surface

In the keV-energy regime, the scattering of krypton ions off a copper sample has been studied. In addition to the broad energy spectrum arising from multiple-collision scattering, the energy distributions of the backscattered ions exhibit prominent peaks at energies where single-collision (SC) scattering peaks are expected. Such SC peaks were shown to be absent in Sn – Mo/Ru scattering, systems of similar mass ratio and thus similar kinetics. The present Kr on Cu results allow for a comparison to a simulation package as SRIM. An important difference found between the present experiment and the predictions of SRIM is that the SC contribution is observed to decrease with scattering angle, whereas SRIM predicts this contribution to be constant. The intensity of the experimental SC peaks, though much weaker than in the SRIM simulations, may be used as markers to improve SRIM in its description of low-energy heavy particle scattering off surfaces

Decay rate measurement of the first vibrationally excited state of MgH+^+ in a cryogenic Paul trap

We present a method to measure the decay rate of the first excited vibrational state of simple polar molecular ions being part of a Coulomb crystal in a cryogenic linear Paul trap. Specifically, we have monitored the decay of the $|\nu$=$1,J$=$1 \rangle_X$ towards the $|\nu$=$0,J$=$0 \rangle_X$ level in MgH$^+$ by saturated laser excitation of the $|\nu$=$0,J$=$2 \rangle_X$-$|\nu$=$1,J$=$1 \rangle_X$ transition followed by state selective resonance enhanced two-photon dissociation out of the $|\nu$=$0,J$=$2 \rangle_X$ level. The technique enables the determination of decay rates, and thus absorption strengths, with an accuracy at the few percent level.Comment: 5 pages, 4 figure

High-energy ions from Nd:YAG laser ablation of tin microdroplets:Comparison between experiment and a single-fluid hydrodynamic model

We present the results of a joint experimental and theoretical study of plasma expansion arising from Nd:YAG laser ablation (laser wavelength λ = 1.064 μm) of tin microdroplets in the context of extreme ultraviolet lithography. Measurements of the ion energy distribution reveal a near-plateau in the distribution for kinetic energies in the range 0.03-1 keV and a peak near 2 keV followed by a sharp fall-off in the distribution for energies above 2 keV. Charge-state resolved measurements attribute this peak to the existence of peaks centered near 2 keV in the Sn3+-Sn8+ ion energy distributions. To better understand the physical processes governing the shape of the ion energy distribution, we have modelled the laser-droplet interaction and subsequent plasma expansion using two-dimensional radiation hydrodynamic simulations. We find excellent agreement between the simulated ion energy distribution and the measurements both in terms of the shape of the distribution and the absolute number of detected ions. We attribute a peak in the distribution near 2 keV to a quasi-spherical expanding shell formed at early times in the expansion

Energy- and charge-state-resolved spectrometry of tin laser-produced plasma using a retarding field energy analyzer

We present a method to obtain the individual charge-state-dependent kinetic-energy distributions of tin ions emanating from a laser-produced plasma from their joint overlapping energy distributions measured by means of a retarding field energy analyzer (RFA). The method of extracting charge state specific parameters from the ion signals is described mathematically, and reinforced with experimental results. The absolute charge-state-resolved ion energy distributions is obtained from ns-pulse Nd:YAG-laser-produced microdroplet tin plasmas in a setting relevant for state-of-the-art extreme ultraviolet nanolithography

Optical spectroscopy of complex open 4dd-shell ions Sn7+^{7+}-Sn10+^{10+}

We analyze the complex level structure of ions with many-valence-electron open [Kr] 4$d^\textrm{m}$ sub-shells ($\textrm{m}$=7-4) with ab initio calculations based on configuration-interaction many-body perturbation theory (CI+MBPT). Charge-state-resolved optical and extreme ultraviolet (EUV) spectra of Sn$^{7+}$-Sn$^{10+}$ ions were obtained using an electron beam ion trap. Semi-empirical spectral fits carried out with the orthogonal parameters technique and Cowan code calculations lead to 90 identifications of magnetic-dipole transitions and the determination of 79 energy ground-configuration levels, questioning some earlier EUV-line assignments. Our results, the most complete data set available to date for these ground configurations, confirm the ab initio predictive power of CI+MBPT calculations for the these complex electronic systems.Comment: 18 pages, 5 figure