Modeling of EUV Emission and Conversion Efficiency from
Laser-Produced Tin Plasmas for Nanolithography
S S Harilal1,2, J J MacFarlane1,2, I E Golovkin2, P R Woodruff2 and P Wang2
1
2
Hyperion Scientific, Inc., 455 Science Dr. Suite 100, Madison, WI 53711
Prism Computational Sciences, Inc., 455 Science Drive, Suite 140, Madison, WI 53711
Extreme ultraviolet lithography (EUVL) is a leading candidate for use in next-generation high volume manufacturing of
semiconductor chips that require feature sizes less than 32 nm. The essential requirement for enabling this technology
is to have a reliable, clean and powerful EUV source which efficiently emits light at a wavelength of 13.5 nm. Laserproduced plasma EUV sources are strong candidates for use in EUVL light source systems. The development and
optimization of high-efficiency EUV sources requires not only well-diagnosed experiments, but also a good
understanding of the physical processes affecting the emitting plasma, which can be achieved with the help of accurate
numerical simulation tools. Here, we investigate the radiative properties of tin and tin-doped foam plasmas heated by
1.06 µm laser beams with 10 ns pulse widths. Results from simulations are compared with experimental conversion
efficiencies and emission spectra.
Keywords: Atomic physics, radiation-hydrodynamics, EUV lithography, atomic spectroscopy, laser-produced plasmas,
spectral analysis, radiation transport.
1. Introduction
EUV lithography will require bright, efficient radiation sources at wavelengths near 13.5 nm.1,2 The selection
of wavelength is based on the availability of Mo/Si multi-layer mirrors (MLM) that reflect ~ 60 - 70% of the in-band
radiation centered at 13.5 nm (with a 2% bandwidth). The essential requirement for enabling this technology is to have
a reliable, clean and powerful light source at 13.5 nm. In principle, either laser-produced plasmas (LPP) or discharge
produced plasmas (DPP) could be used as sources for EUV lithography, and both technologies are racing towards
power levels above 100 W of clean in-band power at intermediate focus (IF). Laser-generated plasmas containing
lithium, xenon or tin are potentially good emission sources at 13.5 nm. Recent studies have shown that tin appears to
have greater promise for EUVL, as it provides a higher conversion efficiency (CE) than lithium or xenon.3 The
optimization of EUV emission from plasma sources, and in particular the conversion efficiency, is a critical component
in reducing the cost of ownership (CoO) of EUVL light source systems.
There are many ongoing experimental efforts to optimize the 13.5 nm conversion efficiency. An important
aspect in understanding the key physics processes in LPP and DPP experiments is the ability to simulate the dynamic
evolution of the plasma and the detailed wavelength-dependent radiation output. Well-benchmarked simulation tools
are important not only for obtaining a good understanding of plasma conditions achieved in EUVL experiments, but are
also crucial for guiding the development path of high-efficiency EUV radiation sources.
To study the radiative properties of EUV plasma sources and optimize their 13.5 nm radiation output, Prism
has developed and is applying a broad suite of plasma radiation simulation tools. These simulation tools include highfidelity modeling of the key physical processes occurring in laser-produced plasmas. In this paper, we discuss results
from our investigations of laser-produced tin and tin-doped foam targets irradiated by λL = 1.06 µm laser light. We
discuss the dependence of CE and spectral emission on laser intensity and compare the simulated emission spectra
obtained from mass-limited tin targets with experimental results.
Emerging Lithographic Technologies XII, edited by Frank M. Schellenberg
Proc. of SPIE Vol. 6921, 692133, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.772716
Proc. of SPIE Vol. 6921 692133-1
2. Plasma Codes
To simulate the interaction of laser radiation with a target, we use a 1-D Lagrangian radiationmagnetohydrodynamics code4, HELIOS-CR. In this code, the equation of motion is solved for a single fluid in which
the ions and electrons are assumed to be co-moving. Contributions to the equation of motion include pressure due to
electrons, ions, radiation and the magnetic field. Both electrons and ions are assumed to have a Maxwellian distribution
of energies based on their temperatures. Plasma thermal conductivity is treated using a Spitzer conductivity model, or
one of a variety of models based on table look-up or user-specified values. HELIOS-CR simulations can be performed
for targets composed of several different materials. The equation of state for each material utilizes either SESAME5 or
PROPACEOS3,4 tabular data. Multi-frequency opacity data for single- or multi-element targets are generated using the
PROPACEOS code. PROPACEOS includes bound-bound, bound-free and free-free contributions to the opacity, and
utilizes atomic data from the ATBASE database (described below). The equation of state data include contributions
from ion and electron kinetic energies, electron degeneracy, configuration effects from Coulomb interactions, ionization
and excitation. In general, HELIOS-CR utilizes tabular equation of state and opacity data generated under the
assumption of local thermodynamic equilibrium (LTE). In cases where non-LTE effects are important, HELIOS-CR
has the capability to perform non-equilibrium atomic kinetics calculations inline, in which case the full set of multilevel atomic rate equations is solved at each time step in the simulation. Radiation is transported using either a multifrequency flux-limited diffusion model or a multi-angle ray trace model. In the cylindrical and spherical geometry
simulations discussed below, the flux-limited diffusion model is used. The absorption of laser energy by the plasma is
calculated using an inverse Bremsstrahlung model with the restriction that no laser energy can pass beyond the critical
surface. The incident laser light is modeled as a multi-ray, conical beam.
3. Atomic Data
The models used in computing atomic data have been discussed elsewhere4. Briefly, the emission feature
around 13.5 nm is comprised of a very large number of closely spaced emission lines from moderately-ionized Sn,
producing unresolved transition arrays (UTAs). The emission seen in the 13 - 15 nm spectral region occurs primarily
from 4f - 4d and 4d - 4p transitions in ions from ~ Sn6+ to ~ Sn19+. We use the ATBASE suite of codes to generate a full
set of atomic energy level and atomic transition data for our simulations. In our Sn atomic models used for the
calculations described here, a total of ~ 500,000 energy levels distributed over all ionization states for tin are included,
for which a total of ~ 1 x 107 oscillator strengths and transition energies are computed. Both relativistic effects and
configuration interaction effects are included when determining line positions and the intensities of the transitions
within the UTA.
4. Results and Discussion
The radiative properties of LPP sources depend both on the target properties and laser beam properties. The
plasma heating strongly depends on laser intensity – not only its peak, but also its time history6. The laser wavelength
also affects plasma heating as shorter wavelength laser light tends to penetrate deeper into the plasma. The target
composition, its geometry and initial state also play a significant role in the evolution of plasma conditions and radiative
output in LPP experiments7-10. Thus, there are a wide variety of adjustments to the target and laser system
configurations that can be made to alter the heating of the plasma and its spectral emission.6-8 The development of highCE sources is most readily achieved by utilizing a combination of modeling tools and well-diagnosed experiments.
Here, we discuss modeling of a series of LPP experiments carried out at the University of California, San
Diego2,10. The targets used in these experiments include solid-density tin thick targets and low-density tin-doped foam
Proc. of SPIE Vol. 6921 692133-2
targets. The energy source used was fundamental radiation from a Nd:YAG laser (λL = 1.06 µm) with a pulse width of
10 ns FWHM (Full Width Half Maximum). The spot size used in the experiments was 60 µm. The CE of the in-band
radiation was estimated using an absolutely calibrated energy monitor which contained a soft x-ray detecting
photodiode and two Mo-Si multilayer mirrors2.
Figure 1 shows typical results from a HELIOS simulation for a planar Sn target irradiated by a 1.06 µm, 10 ns
laser pulse with an incident laser intensity of 0.3 TW/cm2. Here, the temperature, electron density, laser energy
deposition, and average charge state spatial profiles are shown at simulation times of 5, 10, 15 and 20 ns (where t = 15
ns corresponds to the peak of the Gaussian laser pulse). The laser beam is incident from the right. The results show
that for this laser pulse, the temperature of the plasma reaches more than 30 eV and the mean charge state of Sn is > 10
at the peak of the laser pulse. The evolution of the electron density and the laser deposition rate are also shown in
Figure 1.
Figure 2 compares CEs (at 13.5 nm with 2% bandwidth) of laser-produced pure Sn plasmas calculated using
HELIOS for planar, cylindrical, and spherical geometries. Because HELIOS is a 1-D radiation-hydrodynamics code, it
does not capture the multi-dimensional aspects of the expanding plasma plume. When the laser spot size is large
compared to the plasma expansion, it is more suitable to use planar geometry in modeling the radiation emitted by laserheated foils. However, when the laser spot is very small compared to the size of the plasma expansion, a curvilinear
geometry such as 1-D spherical geometry is more suitable. Comparing the results from all 3 geometries gives an
indication of the potential errors in the CE predictions due to neglecting multi-dimensional effects.
Also shown in Figure 2 are the experimentally estimated CE values of Sn plasmas as a function of laser
2
intensity . Since the target used in the experiment was a 1 mm-thick Sn slab with a 60 µm spot size, the plasma
expansion should be more spherical in nature7. Figure 2 shows that the CE peaks at a laser intensity of ~ 4 x 1011
W/cm2 for both the cylindrical and spherical simulations, which is in reasonably good agreement with the
experimentally measured values of CE2. In both the cylindrical and spherical cases, the peak CEs predicted are
somewhat higher that the ~ 2.0% values determined from experiments.
Previous studies showed that a narrower emission feature near 13.5 nm can be obtained without compromising
the conversion efficiency2 by using lower density targets. It has been reported that a target using 0.5% Sn by mass is
enough to provide a CE similar to that of solid Sn.2,10 The targets used in that study were in the form of Sn-doped foam
beads which were fabricated by dispersing SnO2 (which contains 78.8% of Sn by mass) into a resourcinol formaldehyde
solution (with a density of 100 mg/cm3), and then dried. The atomic percentages of these targets were: Sn (1.8%), O
(17.2%), C (27%), and H (54%). This corresponds to a Sn density fraction of 0.5%. A typical time-integrated emission
spectrum obtained from a Sn-doped foam target is shown in Figure 3. Figure 3 also shows the corresponding simulated
spectrum obtained using HELIOS. The HELIOS simulations were performed using frequency-dependent opacity and
equation of state data for an elemental mixture consistent with that used in the experiment. The simulated spectra in
Figure 3(a) shows the structure within the Sn UTA bands, along with narrow emission lines from Li-like oxygen – O5+
at λ = 12.99 nm (2p–4d) and 15.00 nm (2s–3p). Figure 3(b) compares results from the same calculation with the
recorded spectrum, but in this case the calculated spectrum is convolved with the instrumental spectral resolution of the
transmission spectrograph used in the experiment (λ/∆λ ~ 200). Here, it is seen that the simulated convolved spectrum
is in excellent agreement with the recorded spectrum.
Proc. of SPIE Vol. 6921 692133-3
14
5 ns
10 ns
15 ns
20 ns
30
5 ns
10ns
15 ns
20 ns
12
Mean charge
Electron temperature (eV)
40
20
10
10
8
6
4
2
0
0.000
0.005
0.010
0
0.015
0.000
0.005
Laser deposition rate (J/g/s)
-3
Electron density (cm )
10
5 ns
10 ns
15 ns
20 ns
21
20
10
19
10
18
0.000
0.005
0.010
0.015
Position (cm)
Position (cm)
10
0.010
0.015
8.0x10
15
6.0x10
15
4.0x10
15
2.0x10
15
0.0
5ns
10ns
15ns
20ns
0.000
0.005
0.010
0.015
Position (cm)
Position (cm)
Figure 1. Calculated temperature (upper left), density (lower left), mean charge (upper right) and laser deposition rate
(lower right) profiles at simulation times 5, 10, 15, 20 ns for a planar Sn target irradiated by a λL = 1.06µm, 10 ns
(FWHM) Gaussian laser pulse. The peak of the laser pulse is at 15 ns and the laser beam is propagating from right to
left.
Figure 2:
Comparison of calculated CEs with
experimentally estimated CEs for Sn targets heated by
a λ=1.06 µm, 10 ns FWHM laser pulse. Results are
shown from 1-D radiation-hydrodynamics simulations
using planar (solid curve), cylindrical (dashed curve)
and spherical (dot-dashed curve) geometry.
CE (%)
3
experimental
HELIOS planar
HELIOS Spherical
HELIOS Cylindrical
2
1
0
0.1
1
2
Laser power density (TW/cm )
Proc. of SPIE Vol. 6921 692133-4
1.0
Recorded
Simulated
with λ/∆λ = 200
Intensity (arb. u.)
0.8
Figure 3: Measured emission spectrum (red
curve) obtained from a 0.5% Sn-doped foam
target (Sn1.8O17.2C27H54) LPP experiment is
shown along with simulated spectra. (a)
Simulated spectrum without instrumental
broadening.
(b) Simulated spectrum
convolved with λ/∆λ = 200. Narrow oxygen
lines are seen near 13.0 and 15.0 nm.
Recorded
simulated
(a)
(b)
5+
O
0.6
0.4
5+
5+
O
O
5+
O
0.2
0.0
13
14
15
16
13
14
15
16
Wavelength (nm)
5. Summary
We have investigated the hydrodynamic evolution and radiative emission from Sn and Sn-doped
foam targets heated by λL = 1.06 µm laser light with 10 ns pulse widths. Calculated 13.5 nm conversion
efficiencies and emission spectra were compared with experimentally measured values. The sensitivity of
the results from the 1-D radiation-hydrodynamics simulations to the assumed geometry (planar, cylindrical,
spherical) was also studied, as the laser spot size used in the experiments is expected to influence the
geometric expansion of the plasma. The calculated results with cylindrical geometry were seen to be in
best agreement with measurements from experiments which used a 60-µm spot size, both in terms of the
peak CE seen and the value of the incident laser intensity at which the peak CE was observed. The
simulated spectral emission from low-density tin-doped targets was found to be in excellent agreement with
experimental data.
6. References
1
B. Marx, "EUV lithography - Laser-produced-plasma sources shine brighter", Laser Focus World 39, 34
(2003).
2
S.S. Harilal, M.S. Tillack, B. O'Shay, Y. Tao and A. Nikroo, "Extreme ultraviolet spectral purity and
magnetic ion debris mitigation with low density tin targets", Optics Letters 31, 1549-1551 (2006).
3
J.J. MacFarlane, P. Wang, I.E. Golovkin and P.R. Woodruff, "Optimization of EUV/SXR plasma radiation
source characteristics", Proc. SPIE 6151, 61513Y (2006).
4
J.J. MacFarlane, I.E. Golovkin and P.R. Woodruff, "HELIOS-CR - A 1-D radiation-magnetohydrodynamics code with inline atomic kinetics modeling", Journal of Quantitative Spectroscopy
& Radiative Transfer 99, 381-397 (2006).
5
S.P. Lyon and J.D. Johnson "SESAME: The Los Alamos National Laboratory Equation of State
Database", Technical report, Los Alamos National Laboratory (2002)
6
J.J. MacFarlane, I.E. Golovkin, P.R. Woodruff, D.R. Welch, B.V. Oliver, T.A. Mehlhorn and R.B.
Campbell, "Simulation of the ionization dynamics of aluminum irradiated by intense short-pulse
lasers", Inertial Fusion Sciences and Applications 2003, 457-460 (2004).
Proc. of SPIE Vol. 6921 692133-5
7
S.S. Harilal, "Influence of spot size on propagation dynamics of laser-produced tin plasma", Journal of
Applied Physics 102, 123306 (2007).
8
S.S. Harilal, B. O'Shay, Y. Tao and M.S. Tillack, "Ambient gas effects on the dynamics of laser-produced
tin plume expansion", Journal of Applied Physics 99, 083303 (2006).
9
P. Woodruff, J.J. MacFarlane, I. Golovkin and P. Wang, "Simulation of EUV spectral emission from laserproduced tin-doped water plasmas", Proc. of SPIE 6517, 65173N (2007).
10
S.S. Harilal, B. O'Shay, M.S. Tillack and Y. Tao, "Spectral control of emission from tin doped targets for
extreme ultraviolet lithography", Journal Physics D 39, 484-487 (2006).
Proc. of SPIE Vol. 6921 692133-6