Practical extreme ultraviolet (EUV) sources yield the desired 13.5 nm radiation but also generate debris, significantly limiting the lifespan of the collector mirror in lithography. In this study, we explore the role of buffer gas in transporting debris particles within an EUV source vessel using direct numerical simulations. Our study involves a 2 × 1 × 1m3 rectangular cavity with an injecting jet flow subjected to sideward outlet. Debris particles are introduced into the cavity with specified initial velocities, simulating a spherical radiating pattern with particle diameters ranging from 0.1 to 1 μm. Varying the inflow velocity (from 1 to 50 m/s) of the buffer gas reveals a morphological transition in the flow field. At low inflow velocities, the flow remains steady, whereas higher inflow velocities induce the formation of clustered corner rolls. Upon reaching sufficiently high inflow velocities, the jet flow can penetrate the entire cavity, impacting the end wall. Interestingly, the resulting recirculation flow leads to the spontaneous formation of spiraling outflow. The distinct flow structures at various inflow velocities lead to distinct patterns of particle transport. For low-speed gas, it is efficient in expelling all particles smaller than 0.4 μm, while for high-speed gas, those fine particles accumulate near the end wall and are challenging to be extracted. Our findings highlight the significance of controlling flow conditions for effective debris particle transport and clearance in diverse applications especially in EUV source vessels.

1.
T. W.
Johnston
and
J. M.
Dawson
, “
Correct values for high frequency power absorption by inverse bremsstrahlung in plasmas
,”
Phys. Fluids
16
,
722
722
(
1973
).
2.
G. M.
Blumenstock
,
C.
Meinert
,
N. R.
Farrar
, and
A.
Yen
, “
Evolution of light source technology to support immersion and EUV lithography
,”
Proc. SPIE
5645
,
188
195
(
2005
).
3.
A.
Pirati
,
J.
van Schoot
,
K.
Troost
,
R.
van Ballegoij
,
P.
Krabbendam
,
J.
Stoeldraijer
,
E.
Loopstra
,
J.
Benschop
,
J.
Finders
,
H.
Meiling
et al, “
The future of EUV lithography: Enabling Moore's Law in the next decade
,”
Proc. SPIE
10143
,
57
72
(
2017
).
4.
G. D.
Hutcheson
, “
Moore's law, lithography, and how optics drive the semiconductor industry
,”
Proc. SPIE
10583
,
1058303
(
2018
).
5.
V.
Bakshi
,
EUV Lithography
(
SPIE Press
,
2018
).
6.
N.
Fu
,
Y.
Liu
,
X.
Ma
, and
Z.
Chen
, “
EUV lithography: State-of-the-art review
,”
J. Microelectron. Manuf.
2
,
1
6
(
2019
).
7.
G.
Mainfray
and
G.
Manus
, “
Multiphoton ionization of atoms
,”
Rep. Prog. Phys.
54
,
1333
(
1991
).
8.
A.
Endo
,
T.
Abe
,
H.
Hoshino
,
Y.
Ueno
,
M.
Nakano
,
T.
Asayama
,
H.
Komori
,
G.
Soumagne
,
H.
Mizoguchi
,
A.
Sumitani
, and
K.
Toyoda
, “
CO2 laser-produced Sn plasma as the solution for high-volume manufacturing EUV lithography
,”
Proc. SPIE
6703
,
670309
(
2007
).
9.
T.
Aota
,
Y.
Nakai
,
S.
Fujioka
,
E.
Fujiwara
,
M.
Shimomura
,
H.
Nishimura
,
N.
Nishihara
,
N.
Miyanaga
,
Y.
Izawa
, and
K.
Mima
, “
Characterization of extreme ultraviolet emission from tin-droplets irradiated with Nd:YAG laser plasmas
,”
J. Phys.: Conf. Ser.
112
,
042064
(
2008
).
10.
K. M.
Nowak
,
T.
Ohta
,
T.
Suganuma
,
J.
Fujimoto
,
H.
Mizoguchi
,
A.
Sumitani
, and
A.
Endo
, “
CO2 laser drives extreme ultraviolet nano-lithography—Second life of mature laser technology
,”
Opto-Electron. Rev.
21
,
345
354
(
2013
).
11.
M.
van de Kerkhof
,
F.
Liu
,
M.
Meeuwissen
,
X.
Zhang
,
R.
de Kruif
,
N.
Davydova
,
G.
Schiffelers
,
F.
Wählisch
,
E.
van Setten
,
W.
Varenkamp
,
K.
Ricken
,
L.
de Winter
,
J.
McNamara
, and
M.
Bayraktar
, “
Spectral purity performance of high-power EUV systems
,”
Proc. SPIE
11323
,
1132321
(
2020
).
12.
D. C.
Brandt
,
I. V.
Fomenkov
,
A. I.
Ershov
,
W. N.
Partlo
,
D. W.
Myers
,
N. R.
Böwering
,
N. R.
Farrar
,
G. O.
Vaschenko
,
O. V.
Khodykin
,
A. N.
Bykanov
,
J. R.
Hoffman
,
C. P.
Chrobak
,
S. N.
Srivastava
,
I.
Ahmad
,
C.
Rajyaguru
,
D. J.
Golich
,
D. A.
Vidusek
,
S. D.
Dea
, and
R. R.
Hou
, “
LPP source system development for HVM
,”
Proc. SPIE
7271
,
727103
(
2009
).
13.
M.
Poirier
,
T.
Blenski
,
F.
de Gaufridy de Dortan
, and
F.
Gilleron
, “
Modeling of EUV emission from xenon and tin plasma sources for nanolithography
,”
J. Quant. Spectrosc. Radiat. Transfer
99
,
482
492
(
2006
).
14.
T.
Ando
,
S.
Fujioka
,
H.
Nishimura
,
N.
Ueda
,
Y.
Yasuda
,
K.
Nagai
,
T.
Norimatsu
,
M.
Murakami
,
K.
Nishihara
,
N.
Miyanaga
,
Y.
Izawa
,
K.
Mima
, and
A.
Sunahara
, “
Optimum laser pulse duration for efficient extreme ultraviolet light generation from laser-produced tin plasmas
,”
Appl. Phys. Lett.
89
,
151501
(
2006
).
15.
S. S.
Harilal
,
M. S.
Tillack
,
Y.
Tao
,
B.
O'Shay
,
R.
Paguio
, and
A.
Nikroo
, “
Extreme-ultraviolet spectral purity and magnetic ion debris mitigation by use of low-density tin targets
,”
Opt. Lett.
31
,
1549
1551
(
2006
).
16.
V. Y.
Banine
,
K. N.
Koshelev
, and
G. H. P. M.
Swinkels
, “
Physical processes in EUV sources for microlithography
,”
J. Phys. D
44
,
253001
(
2011
).
17.
M.
Yan
,
Y.
Zhang
,
J.
Zhu
,
H.
Zang
,
Z.
Ding
,
X.
Zhao
, and
R.
Li
, “
Printing of liquid metal by laser-induced thermal bubble at the liquid-liquid interface
,”
Phys. Fluids
35
,
123346
(
2023
).
18.
L.
Jun
,
L.
Shengnan
,
Q.
Lehua
, and
L.
Ni
, “
Generation of the small tin-droplet streams with a manipulable droplet spacing via the forced velocity perturbation
,”
Phys. Fluids
35
,
013612
(
2023
).
19.
S. J.
Haney
,
K. W.
Berger
,
G. D.
Kubiak
,
P. D.
Rockett
, and
J.
Hunter
, “
Prototype high-speed tape target transport for a laser plasma soft-x-ray projection lithography source
,”
Appl. Opt.
32
,
6934
6937
(
1993
).
20.
M.
Richardson
,
C.-S.
Koay
,
K.
Takenoshita
,
C.
Keyser
, and
M.
Al-Rabban
, “
High conversion efficiency mass-limited Sn-based laser plasma source for extreme ultraviolet lithography
,”
J. Vac. Sci. Technol.
22
,
785
790
(
2004
).
21.
K.
Takenoshita
,
C.-S.
Koay
,
S.
Teerawattansook
,
M.
Richardson
, and
V.
Bakshi
, “
Debris characterization and mitigation from microscopic laser-plasma tin-doped droplet EUV sources
,”
Proc. SPIE
5751
,
563
571
(
2005
).
22.
J.
Pankert
,
R.
Apetz
,
K.
Bergmann
,
G.
Derra
,
M.
Janssen
,
J.
Jonkers
,
J.
Klein
,
T.
Kruecken
,
A.
List
,
M.
Loeken
,
C.
Metzmacher
,
W.
Neff
,
S.
Probst
,
R.
Prummer
,
O.
Rosier
,
S.
Seiwert
,
G.
Siemons
,
D.
Vaudrevange
,
D.
Wagemann
,
A.
Weber
,
P.
Zink
, and
O.
Zitzen
, “
Integrating Philips' extreme UV source in the alpha-tools
,”
Proc. SPIE
5751
,
260
271
(
2005
).
23.
C.-S.
Koay
,
S.
George
,
K.
Takenoshita
,
R.
Bernath
,
E.
Fujiwara
,
M.
Richardson
, and
V.
Bakshi
, “
High conversion efficiency microscopic tin-doped droplet target laser-plasma source for EUVL
,”
Proc. SPIE
5751
,
279
292
(
2005
).
24.
L.
She
,
Y.
Fang
,
L.
Hu
,
R.
Su
, and
X.
Fu
, “
Mitigating jitter in droplet stream by uniform charging
,”
Phys. Fluids
34
,
111704
(
2022
).
25.
S. S.
Harilal
, “
Influence of spot size on propagation dynamics of laser-produced tin plasma
,”
J. Appl. Phys.
102
,
123306
(
2007
).
26.
G.
Niimi
,
Y.
Ueno
,
K.
Nishigori
,
T.
Aota
,
H.
Yashiro
, and
T.
Tomie
, “
Experimental evaluation of stopping power of high-energy ions from laser-produced plasma by a magnetic field
,”
Proc. SPIE
5037
,
370
377
(
2003
).
27.
L. A.
Shmaenok
,
C. C.
de Bruijn
,
H. F.
Fledderus
,
R.
Stuik
,
A. A.
Schmidt
,
D. M.
Simanovski
,
A. V.
Sorokin
,
T. A.
Andreeva
, and
F.
Bijkerk
, “
Demonstration of a foil trap technique to eliminate laser plasma atomic debris and small particulates
,”
Proc. SPIE
3331
,
90
94
(
1998
).
28.
S.
Bollanti
,
F.
Bonfigli
,
E.
Burattini
,
P.
Di Lazzaro
,
F.
Flora
,
A.
Grilli
,
T.
Letardi
,
N.
Lisi
,
A.
Marinai
,
L.
Mezi
,
D.
Murra
, and
C.
Zheng
, “
High-efficiency clean EUV plasma source at 10-30 nm, driven by a long-pulse-width excimer laser
,”
Appl. Phys. B
76
,
277
284
(
2003
).
29.
D. J. W.
Klunder
,
M. M. J. W.
van Herpen
,
V. Y.
Banine
, and
K.
Gielissen
, “
Debris mitigation and cleaning strategies for Sn-based sources for EUV lithography
,”
Proc. SPIE
5751
,
943
951
(
2005
).
30.
W.
Soer
,
D.
Klunder
,
M.
van Herpen
,
L.
Bakker
, and
V.
Banine
, “
Debris mitigation for EUV sources using directional gas flows
,”
Proc. SPIE
6151
,
61514B
(
2006
).
31.
S.
Harilal
,
B.
O'Shay
,
Y.
Tao
, and
M.
Tillack
, “
Ion debris mitigation from tin plasma using ambient gas, magnetic field and combined effects
,”
Appl. Phys. B
86
,
547
547
(
2007
).
32.
D.
Bleiner
and
T.
Lippert
, “
Stopping power of a buffer gas for laser plasma debris mitigation
,”
J. Appl. Phys.
106
,
123301
(
2009
).
33.
D. B.
Abramenko
,
M. V.
Spiridonov
,
P. V.
Krainov
,
V. M.
Krivtsun
,
D. I.
Astakhov
,
V. V.
Medvedev
,
M.
van Kampen
,
D.
Smeets
, and
K. N.
Koshelev
, “
Measurements of hydrogen gas stopping efficiency for tin ions from laser-produced plasma
,”
Appl. Phys. Lett.
112
,
164102
(
2018
).
34.
J.
Cao
,
P.
Wang
, and
Y.
Liu
, “
Influence of dual purging jets on interferometric measurement of optical path difference
,”
Phys. Fluids
36
,
015108
(
2024
).
35.
M.
Gad-el Hak
, “
The fluid mechanics of microdevices the Freeman scholar lecture
,”
J. Fluids Eng.
121
,
5
33
(
1999
).
36.
A.
Agrawal
,
H. M.
Kushwaha
, and
R. S.
Jadhav
,
Microscale Flow and Heat Transfer
(
Springer
,
2020
).
37.
S.
Alafnan
, “
The self-diffusivity of natural gas in the organic nanopores of source rocks
,”
Phys. Fluids
34
,
042004
(
2022
).
38.
K.
Kobayashi
,
K.
Aoki
,
H.
Tabe
,
H.
Fujii
,
T.
Nara
,
H.
Takashima
,
N.
Oshima
, and
M.
Watanabe
, “
Couette flow at high Knudsen number between wall and liquid boundaries
,”
Phys. Fluids
35
,
082021
(
2023
).
39.
Y.
Ding
,
B.
Li
,
J.
Li
,
S.
Duan
,
H.
Song
, and
X.
Zeng
, “
A study of gas transport mechanisms in shale's confined nanopores: Examining irregularity, adsorption effects, and stresses
,”
Phys. Fluids
35
,
126108
(
2023
).
40.
H.
Struchtrup
and
P.
Taheri
, “
Macroscopic transport models for rarefied gas flows: A brief review
,”
IMA J. Appl. Mathematics
76
,
672
697
(
2011
).
41.
T.
Veltzke
,
M.
Baune
, and
J.
Thöming
, “
The contribution of diffusion to gas microflow: An experimental study
,”
Phys. Fluids
24
,
082004
(
2012
).
42.
H.
Song
,
M.
Yu
,
W.
Zhu
,
P.
Wu
,
Y.
Lou
,
Y.
Wang
, and
J.
Killough
, “
Numerical investigation of gas flow rate in shale gas reservoirs with nanoporous media
,”
Int. J. Heat Mass Transfer
80
,
626
635
(
2015
).
43.
J.
Mouro
,
M.
Ferreira
,
A. V.
Silva
, and
D. C.
Leitao
, “
Derivation of analytical expressions for the stress/strain distributions, bending plane and curvature radius in multilayer thin-film composites
,”
J. Micromech. Microeng.
31
,
113003
(
2021
).
44.
R.
Verzicco
and
P.
Orlandi
, “
A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates
,”
J. Comput. Phys.
123
,
402
414
(
1996
).
45.
R.
Ostilla-Monico
,
Y.-T.
Yang
,
E.
van der Poel
,
D.
Lohse
, and
R.
Verzicco
, “
A multiple-resolution strategy for Direct Numerical Simulation of scalar turbulence
,”
J. Comput. Phys.
301
,
308
321
(
2015
).
46.
E. P.
van der Poel
,
R.
Ostilla-Mónico
,
J.
Donners
, and
R.
Verzicco
, “
A pencil distributed finite difference code for strongly turbulent wall-bounded flows
,”
Comput. Fluids
116
,
10
16
(
2015
).
47.
C. B.
Zhao
,
Y. Z.
Zhang
,
B. F.
Wang
,
J.-Z.
Wu
,
K. L.
Chong
, and
Q.
Zhou
, “
Modulation of turbulent Rayleigh-Bénard convection under spatially harmonic heating
,”
Phys. Rev. E
105
,
055107
(
2022
).
48.
K. L.
Chong
,
G.
Ding
, and
K.-Q.
Xia
, “
Multiple-resolution scheme in finite-volume code for active or passive scalar turbulence
,”
J. Comput. Phys.
375
,
1045
1058
(
2018
).
49.
X.-L.
Guo
,
J.-Z.
Wu
,
B.-F.
Wang
,
Q.
Zhou
, and
K. L.
Chong
, “
Flow structure transition in thermal vibrational convection
,”
J. Fluid Mech.
974
,
A29
(
2023
).
50.
M. R.
Maxey
and
J. J.
Riley
, “
Equation of motion for a small rigid sphere in a nonuniform flow
,”
Phys. Fluids
26
,
883
889
(
1983
).
51.
R.
Gatignol
, “
The Faxén formulae for a rigid particle in an unsteady non-uniform Stokes flow
,”
J. Mec. Theor. Appl.
9
,
143
160
(
1983
).
52.
S.-T.
Tsai
, “
Sedimentation motion of sand particles in moving water (I): The resistance on a small sphere moving in non-uniform flow
,”
Theor. Appl. Mech. Lett.
12
,
100392
(
2022
).
53.
P. F.
DeCarlo
,
J. G.
Slowik
,
D. R.
Worsnop
,
P.
Davidovits
, and
J. L.
Jimenez
, “
Particle morphology and density characterization by combined mobility and aerodynamic diameter measurements. Part 1: Theory
,”
Aerosol Sci. Technol.
38
,
1185
1205
(
2004
).
54.
W. C.
Hinds
and
Y.
Zhu
,
Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles
(
John Wiley & Sons
,
2022
).
55.
M.
Allen
and
O.
Raabe
, “
Re-evaluation of millikan's oil drop data for the motion of small particles in air
,”
J. Aerosol Sci.
13
,
537
547
(
1982
).
56.
M. D.
Allen
and
O. G.
Raabe
, “
Slip correction measurements of spherical solid aerosol particles in an improved Millikan apparatus
,”
Aerosol Sci. Technol.
4
,
269
286
(
1985
).
57.
J. E.
Brockmann
and
D. J.
Rader
, “
APS response to nonspherical particles and experimental determination of dynamic shape factor
,”
Aerosol Sci. Technol.
13
,
162
172
(
1990
).
58.
K. L.
Chong
,
C. S.
Ng
,
N.
Hori
,
R.
Yang
,
R.
Verzicco
, and
D.
Lohse
, “
Extended lifetime of respiratory droplets in a turbulent vapor puff and its implications on airborne disease transmission
,”
Phys. Rev. Lett.
126
,
034502
(
2021
).
59.
C. S.
Ng
,
K. L.
Chong
,
R.
Yang
,
M.
Li
,
R.
Verzicco
, and
D.
Lohse
, “
Growth of respiratory droplets in cold and humid air
,”
Phys. Rev. Fluids
6
,
054303
(
2021
).
60.
W.
Yang
,
Z.-H.
Wan
,
Q.
Zhou
, and
Y.
Dong
, “
On the energy transport and heat transfer efficiency in radiatively heated particle-laden Rayleigh-Bénard convection
,”
J. Fluid Mech.
953
,
A35
(
2022
).
61.
W.
Yang
,
Y.-Z.
Zhang
,
B.-F.
Wang
,
Y.
Dong
, and
Q.
Zhou
, “
Dynamic coupling between carrier and dispersed phases in Rayleigh-Bénard convection laden with inertial isothermal particles
,”
J. Fluid Mech.
930
,
A24
(
2022
).
62.
W.
Yang
,
B.-F.
Wang
,
Q.
Tang
,
S.
Zhou
, and
Y.
Dong
, “
Transport modes of inertial particles and their effects on flow structures and heat transfer in Rayleigh-Bénard convection
,”
Phys. Fluids
34
,
043309
(
2022
).
63.
C.-B.
Zhao
,
J.-Z.
Wu
,
B.-F.
Wang
,
T.
Chang
,
Q.
Zhou
, and
K. L.
Chong
, “
Human body heat shapes the pattern of indoor disease transmission
,” preprint arXiv:2303.13235 (
2023
).
64.
A. Y.
Vinokhodov
,
K. N.
Koshelev
,
V.
Krivtsun
,
M. S.
Krivokorytov
,
Y. V.
Sidelnikov
,
S.
Medvedev
,
V. O.
Kompanets
,
A. A.
Melnikov
, and
S. V.
Chekalin
, “
Formation of a fine-dispersed liquid-metal target under the action of femto-and picosecond laser pulses for a laser-plasma radiation source in the extreme ultraviolet range
,”
Quantum Electron.
46
,
23
(
2016
).
65.
O.
Shishkina
,
S.
Wagner
, and
S.
Horn
, “
Influence of the angle between the wind and the isothermal surfaces on the boundary layer structures in turbulent thermal convection
,”
Phys. Rev. E
89
,
033014
(
2014
).
66.
C.-B.
Zhao
,
B.-F.
Wang
,
J.-Z.
Wu
,
K. L.
Chong
, and
Q.
Zhou
, “
Suppression of flow reversals via manipulating corner rolls in plane Rayleigh-Bénard convection
,”
J. Fluid Mech.
946
,
A44
(
2022
).
67.
H. N.
Yoshikawa
,
C.
Mathis
,
S.
Satoh
, and
Y.
Tasaka
, “
Inwardly rotating spirals in a nonoscillatory medium
,”
Phys. Rev. Lett.
122
,
014502
(
2019
).
68.
E.
Bodenschatz
,
J. R.
de Bruyn
,
G.
Ahlers
, and
D. S.
Cannell
, “
Transitions between patterns in thermal convection
,”
Phys. Rev. Lett.
67
,
3078
3081
(
1991
).
69.
Q.
Zhou
,
C.
Sun
, and
K.-Q.
Xia
, “
Morphological evolution of thermal plumes in turbulent Rayleigh-Bénard convection
,”
Phys. Rev. Lett.
98
,
074501
(
2007
).
70.
Y.
Zhang
and
Q.
Zhou
, “
Low-Prandtl-number effects on global and local statistics in two-dimensional Rayleigh-Bénard convection
,”
Phys. Fluids
36
,
015107
(
2024
).
71.
B. B.
Plapp
,
D. A.
Egolf
,
E.
Bodenschatz
, and
W.
Pesch
, “
Dynamics and selection of giant spirals in Rayleigh-Bénard convection
,”
Phys. Rev. Lett.
81
,
5334
5337
(
1998
).
72.
J. C.
Kalita
and
P.
Kumar
, “
Vortex dynamics of accelerated flow past a mounted wedge
,”
Phys. Fluids
35
,
123607
(
2023
).
You do not currently have access to this content.