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

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

Cross-calibration of a combined electrostatic and time-of-flight analyzer for energy- and charge-state-resolved spectrometry of tin laser-produced plasma

We present the results of the calibration of a channeltron-based electrostatic analyzer operating in time-of-flight mode (ESA-ToF) using tin ions resulting from laser-produced plasma, over a wide range of charge states and energies. Specifically, the channeltron electron multiplier detection efficiency and the spectrometer resolution are calibrated, and count rate effects are characterized. With the obtained overall response function, the ESA-ToF is shown to accurately reproduce charge-integrated measurements separately and simultaneously obtained from a Faraday cup (FC), up to a constant factor the finding of which enables absolute cross-calibration of the ESA-ToF using the FC as an absolute benchmark. Absolute charge-state-resolved ion energy distributions are obtained from ns-pulse Nd:YAG-laser-produced microdroplet tin plasmas in a setting relevant for state-of-the-art extreme ultraviolet nanolithography

EUV spectroscopy of highly charged Sn13+-Sn15+ ions in an electron-beam ion trap

Extreme-ultraviolet (EUV) spectra of Sn13+-Sn15+ ions have been measured in an electron-beam ion trap (EBIT). A matrix inversion method is employed to unravel convoluted spectra from a mixture of charge states typically present in an EBIT. The method is benchmarked against the spectral features of resonance transitions in Sn13+ and Sn14+ ions. Three new EUV lines in Sn14+ confirm its previously established level structure. This ion is relevant for EUV nanolithography plasma but no detailed experimental data currently exist. We used the Cowan code for first line identifications and assignments in Sn15+. The collisional-radiative modeling capabilities of the Flexible Atomic Code were used to include line intensities in the identification process. Using the 20 lines identified, we have established 17 level energies of the 4p44d configuration as well as the fine-structure splitting of the 4p5 ground-state configuration. Moreover, we provide state-of-the-art ab initio level structure calculations of Sn15+ using the configuration-interaction many-body perturbation code ambit. We find that the here-dominant emission features from the Sn15+ ion lie in the narrow 2% bandwidth around 13.5 nm that is relevant for plasma light sources for state-of-the-art nanolithography

Radiation transport and scaling of optical depth in Nd:YAG laser-produced microdroplet-tin plasma

Experimental scaling relations of the optical depth are presented for the emission spectra of a tin-droplet-based, 1-μm-laser-produced plasma source of extreme-ultraviolet (EUV) light. The observed changes in the complex spectral emission of the plasma over a wide range of droplet diameters (16-65 μm) and laser pulse durations (5-25 ns) are accurately captured in a scaling relation featuring the optical depth of the plasma as a single, pertinent parameter. The scans were performed at a constant laser intensity of 1.4 × 1011 W/cm2, which maximizes the emission in a 2% bandwidth around 13.5 nm relative to the total spectral energy, the bandwidth relevant for industrial EUV lithography. Using a one-dimensional radiation transport model, the relative optical depth of the plasma is found to linearly increase with the droplet size with a slope that increases with the laser pulse duration. For small droplets and short laser pulses, the fraction of light emitted in the 2% bandwidth around 13.5 nm relative to the total spectral energy is shown to reach high values of more than 14%, which may enable conversion efficiencies of Nd:YAG laser light into - industrially - useful EUV radiation rivaling those of current state-of-the-art CO2-laser-driven sources

Deriving relativistic momentum and energy

We present a new derivation of the expressions for momentum and energy of a relativistic particle. In contrast to the procedures commonly adopted in textbooks, the one suggested here requires only the knowledge of the composition law for velocities along one spatial dimension, and does not make use of the concept of relativistic mass, or of the formalism of four-vectors. The basic ideas are very general and can be applied also to kinematics different from the Newtonian and Einstein ones, in order to construct the corresponding dynamics.Comment: 15 pages, 2 figure

Prominent radiative contributions from multiply-excited states in laser-produced tin plasma for nanolithography

Extreme ultraviolet (EUV) lithography is currently entering high-volume manufacturing to enable the continued miniaturization of semiconductor devices. The required EUV light, at 13.5 nm wavelength, is produced in a hot and dense laser-driven tin plasma. The atomic origins of this light are demonstrably poorly understood. Here we calculate detailed tin opacity spectra using the Los Alamos atomic physics suite ATOMIC and validate these calculations with experimental comparisons. Our key finding is that EUV light largely originates from transitions between multiply-excited states, and not from the singly-excited states decaying to the ground state as is the current paradigm. Moreover, we find that transitions between these multiply-excited states also contribute in the same narrow window around 13.5 nm as those originating from singly-excited states, and this striking property holds over a wide range of charge states. We thus reveal the doubly magic behavior of tin and the origins of the EUV light