Nicola Murphy

4f collapse, level density inflation and the emergence of 'compound-like' atomic states in rare earth ions

4f collapse in rare earth ions produces an enormous level density due to the occurrence of near-degeneracies of 4f/5p and 4f/5s binding energies. As a result, there is a complete breakdown of the single-particle approximation and the level and line spectra satisfy many of the distributions associated with random matrix theory. Similar behaviour has been previously reported in spectra associated with wavefunction contraction effects or atoms containing open 4f subshells; here the effects of combining both phenomena are explored. In particular it is shown that the adjacent level separations satisfy a Wigner distribution, while transitions between them obey the Porter-Thomas distribution. Detailed Hartree-Fock calculations show that there is a strong correlation between line strength and transition energy. This correlation is pursued and parametrized for the particular case of 4f→5d, 5p→5d and 5s→5p transitions in Sm IX within the unresolved transition array model.

Simplified modeling of 13.5 nm unresolved transition array emission of a Sn plasma and comparison with experiment

One key aspect in the drive to optimize the radiative output of a laser-produced plasma for extreme ultraviolet lithography is the radiation transport through the plasma. In tin-based plasmas, the radiation in the 2% bandwidth at 13.5 nm is predominantly due to 4d-4f and 4p-4d transitions from a range of tin ions (Sn7+ to Sn12+). The complexity of the configurations involved in these transitions is such that a line-by-line analysis is, computationally, extremely intensive. This work seeks to model the emission profiles of each ion by treating the transition arrays statistically, thus greatly simplifying radiation transport modeling. The results of the model are compared with experimental spectra from tin-based laser-produced plasmas.

13.5nm extreme ultraviolet emission from tin based laser produced plasma sources

An examination of the influence of target composition and viewing angle on the extreme ultraviolet spectra of laser produced plasmas formed from tin and tin doped planar targets is reported. Spectra have been recorded in the 9–17nm region from plasmas created by a 700mJ, 15ns full width at half maximum intensity, 1064nm Nd:YAG laser pulse using an absolutely calibrated 0.25m grazing incidence vacuum spectrograph. The influence of absorption by tin ions (SnI–SnX) in the plasma is clearly seen in the shape of the peak feature at 13.5nm, while the density of tin ions in the target is also seen to influence the level of radiation in the 9–17nm region.

Conversion efficiency of a laser-produced Sn plasma at 13.5 nm, simulated with a one-dimensional hydrodynamic model and treated as a multi-component blackbody

Efficiency optimization of a stable and debris free plasma source at 13.5 nm, is at the forefront of current extreme ultraviolet lithographic (EUVL) research efforts. To date, 1–2.5% soft x-ray conversion efficiencies (CEs) within a 2% bandwidth (BW) around 13.5 nm and into 2π steradians have been attained experimentally for laser-produced plasmas containing Sn at power densities of 0.5–5 × 1011 W cm−2. In order to complement these experimental endeavours, we have undertaken to study the CE, for the given wavelength regime, in the optically thick limit. We have achieved this by coupling time-dependent and steady-state collisional-radiative (CR) equations to the output of the one-dimensional hydrodynamic code MED103 (MEDUSA), where a solid sphere of radius 50 µm was uniformly irradiated by a high intensity laser pulse with a Gaussian temporal profile. The ion populations obtained from these CR results were then used in an integrated spatio-temporal figure of merit (FOM) together with in-band weighted dipole oscillator strengths and transition energies. The maximum FOM, when divided by the laser energy, was found to occur in the range of peak power densities of 2–3 × 1011 W cm−2 for the steady-state and time-dependent models, respectively. The hydrodynamic variables of these peak power densities were then used in a radiative transfer calculation in which the many-celled spherical plasma was treated as a multi-component blackbody. It is found that CEs of 3.5–6% within the 2% BW per 2π steradians may be achieved. These results are of particular relevance to EUVL technologies where a minimum CE of 3% is required by industry.

Angle-resolved absolute out-of-band radiation studies of a tin-based laser-produced plasma source

Out-of-band radiation emitted from an extreme ultraviolet laser-produced plasma, formed on a solid tin target, was measured over several angles between 25° and 85° with respect to the target normal for six energy bands between 200 and 1000nm. The optical and target system was rotated with respect to the detector and the intensity of the radiation was measured using an absolutely calibrated filter/photodiode combination. The emission was dominated by radiation in the 214nm band. A cosine function fitted to the angular distribution of the total radiation yielded an exponent of 0.23±0.02.

Variable composition laser-produced Sn plasmas—a study of their time-independent ion distributions

The time-independent ion distributions of variable composition laser-produced Sn plasmas are studied for a wide range of electron temperatures and atomic number densities, the purpose of which is to elucidate the effect that varying the number density of Sn within a mixed species plasma has upon the steady state populations of Sn and its ions. Particular emphasis will be placed on binary mixtures of Sn with Li, C, O or Sm and more specifically the charge states Sn8+ to Sn13+ within these mixed plasmas, where it will be assumed that the plasma is optically thin. It is found that using these composites has relatively little effect upon the Sn ion population distributions for plasma atomic number densities of less than approximately 1019.5 cm−3. However, for greater values of number densities the Sn ion populations can be shifted by as much as 10–15 eV for Li mixtures. These results are of particular relevance to current research being carried out on extreme ultraviolet lithographic technologies for the optimization of XUV sources in the 13.5 nm wavelength region, which include composite target investigations.

A spatio-temporal study of variable composition laser-produced Sn plasmas

Laser-produced Sn plasmas are at present a major contender in the challenge to find a suitable replacement for the currently used excimer-laser technology, which has wavelengths of 248 and 193 nm, and that is utilized in projection lithography. These wavelengths are to be superseded by soft x-ray sources in the 13.5 nm wavelength regime for utilization in extreme ultraviolet lithographic (EUVL) technologies. To date, considerable international efforts have been channelled into the experimental realization and optimization of various tin based EUV sources. Therefore, in order to compliment these experimental accomplishments we have undertaken a spatio-temporal study of the free electron number density, atomic number density, average charge state and expansion kinetic energy of Sn and SnO2 plasmas. This has been achieved by coupling the collisional radiative equations to the one-dimensional Lagrangian fluid dynamic model MED103 (MEDUSA), thus obtaining the spatial and temporal histories of the aforementioned variables within a laser-produced plasma of spherical geometry, generated using a Gaussian laser pulse at 1064 nm. The evolution of ion stages Sn 4+ to Sn 13+ within a fluid cell is also presented. In addition, the dependence of the Sn fractional ion populations upon the atomic number density within variable composition plasmas of binary mixtures formed from Sn and oxygen and Sn combined with samarium is investigated. The overwhelming influence of both the atomic and free electron number densities within these plasmas is highlighted. (Some figures in this article are in colour only in the electronic version)

13.5 nm emission from composite targets containing tin

The aim of this study is to investigate ways to maximise the efficiency of tin based laser produced plasmas as sources of EUV radiation in the 2% band centered on 13.5 nm. It has been found that targets containing below 15% tin atoms by number emit more brightly in the spectral region around 13.5 nm than pure tin targets. Furthermore, if the remaining material in the target is composed on primarily low-Z atoms, then both plasma continuum radiation and Bremsstrahlung radiation are greatly reduced. In addition, if the target is illuminated with a prepulse, the conversion efficiency shows a distinct increase. The third parameter under examination is the laser power density, which controls the ion distribution in the plasma. The influence of low-Z atoms on the tin ion distribution in the plasma has been investigated and found to be of little consequence. Measurements were made in the region from 9-17 nm on an absolutely calibrated 0.25-m flat field grazing incidence spectrograph, and on two 2-m grazing incidence spectrographs. Spectra and conversion efficiency data from a range of target materials and illumination regimes are presented.

Recent Progress in the Development of Sources for EUV Lithography

Currently the emission of both Xe and Sn are being investigated as sources for EUV lithography. In Xe the bulk of the emission in the region of interest, 13.5 nm, originates from one ion stage, Xe XI, while in Sn, the emission at this wavelength arises from resonance transitions in a range of stages and thus is potentially more intense. However essentially no data for these ions exists making modeling of the plasma processes involved and estimation of the conversion efficiencies attainable and their dependence on experimental parameters extremely difficult. Here we provide an overview of some recent results obtained by our group and compare them with data from other researchers.

Optimizing an EUV source for 13.5 nm

The emission spectra of laser produced plasmas of pure tin targets are dominated by recombination continuum emission throughout the entire EUV spectral region with intense structure due to line emission dominating the spectra in the 13 - 14 nm region. This feature arises from resonant 4p64dn - 4p54dn+1 + 4p64dn-14f emission lines that are generally concentrated in a narrow band, 5 - 10 eV wide, which overlaps considerably in adjacent ion stages to form an intense unresolved transition array (UTA). Such plasmas are optically thick; the strongest lines are attenuated and frequently appear in absorption. However, if tin comprises a few percent of a predominantly low-Z matrix, the recombination is suppressed and the plasmas can become optically thin to resonance radiation. Under these conditions, resonance line emission can dominate the spectra. The application of a collisional radiative (CR) model, combined with ab initio atomic structure calculations, allows one to estimate the laser plasma parameters that will optimize the UTA as efficient narrow bandwidth emitters of EUV radiation. The dependence on laser power density of both in-band emission and debris generation from pure tin targets is presented. The influence of a pre-pulse on the plasma output is also investigated.