Optical emission spectroscopy (OES) is a highly valuable tool for plasma characterization due to its nonintrusive and versatile nature. The intensities of the emission lines contain information about the parameters of the underlying plasma–electron density n e and temperature or, more generally, the electron energy distribution function (EEDF). This study aims to obtain the EEDF and n e from the OES data of argon plasma with machine learning (ML) techniques. Two different models, i.e., the Kernel Regression for Functional Data (KRFD) and an artificial neural network (ANN), are used to predict the normalized EEDF and Random Forest (RF) regression is used to predict n e. The ML models are trained with computed plasma data obtained from Particle-in-Cell/Monte Carlo Collision simulations coupled with a collisional–radiative model. All three ML models developed in this study are found to predict with high accuracy what they are trained to predict when the simulated test OES data are used as the input data. When the experimentally measured OES data are used as the input data, the ANN-based model predicts the normalized EEDF with reasonable accuracy under the discharge conditions where the simulation data are known to agree well with the corresponding experimental data. However, the capabilities of the KRFD and RF models to predict the EEDF and n e from experimental OES data are found to be rather limited, reflecting the need for further improvement of the robustness of these models.

1.
G. S.
Oehrlein
and
S.
Hamaguchi
,
Plasma Sources Sci. Technol.
27
,
023001
(
2018
).
2.
K.-D.
Weltmann
et al.,
Plasma Process. Polym.
16
,
1800118
(
2019
).
3.
I.
Adamovich
et al.
J. Phys. D: Appl. Phys.
55
,
373001
(
2022
).
4.
R.
Engeln
,
B.
Klarenaar
, and
O.
Guaitella
,
Plasma Sources Sci. Technol.
29
,
063001
(
2020
).
5.
J.
Benedikt
,
H.
Kersten
, and
A.
Piel
,
Plasma Sources Sci. Technol.
30
,
033001
(
2021
).
6.
B. M.
Goldberg
,
T.
Hoder
, and
R.
Brandenburg
,
Plasma Sources Sci. Technol.
31
,
073001
(
2022
).
7.
Ts. V.
Tsankov
and
U.
Czarnetzki
,
Plasma Sources Sci. Technol.
26
,
055003
(
2017
).
8.
G.
Gifford
, “Applications of optical emission spectroscopy in plasma manufacturing systems,” in Advanced Techniques for Integrated Circuit Processing (International Society for Optics and Photonics, Santa Clara, CA, 1991), Vol. 1392, pp. 454–465.
9.
10.
V. M.
Donnelly
,
J. Phys. D: Appl. Phys.
37
,
R217
(
2004
).
11.
E.
Restrepo
and
A.
Devia
,
J. Vac. Sci. Technol. A
22
,
377
(
2004
).
12.
N.
Ohno
,
M. A.
Razzak
,
H.
Ukai
,
S.
Takamura
, and
Y.
Uesugi
,
Plasma Fusion Res.
1
,
028
(
2006
).
13.
D.
Hope
,
T.
Cox
, and
V.
Deshmukh
,
Vacuum
37
,
275
(
1987
).
14.
T.
Mehdi
,
P.
Legrand
,
J.
Dauchot
,
M.
Wautelet
, and
M.
Hecq
,
Spectrochim. Acta B: At. Spectrosc.
48
,
1023
(
1993
).
15.
X.-M.
Zhu
and
Y.-K.
Pu
,
J. Phys. D: Appl. Phys.
43
,
015204
(
2009
).
16.
F. J.
Arellano
,
M.
Gyulai
,
Z.
Donkó
,
P.
Hartmann
,
Ts. V.
Tsankov
,
U.
Czarnetzki
, and
S.
Hamaguchi
,
Plasma Sources Sci. Technol.
32
,
125007
(
2023
).
17.
D.
Lopaev
,
A.
Volynets
,
S.
Zyryanov
,
A.
Zotovich
, and
A.
Rakhimov
,
J. Phys. D: Appl. Phys.
50
,
075202
(
2017
).
18.
S.
Iordanova
and
I.
Koleva
,
Spectrochim. Acta B: At. Spectrosc.
62
,
344
(
2007
).
19.
A.
Palmero
,
E.
Van Hattum
,
H.
Rudolph
, and
F.
Habraken
,
J. Appl. Phys.
101
,
053306
(
2007
).
20.
Z.
Navrátil
,
P.
Dvořák
,
O.
Brzobohatỳ
, and
D.
Trunec
,
J. Phys. D: Appl. Phys.
43
,
505203
(
2010
).
21.
S.
Siepa
,
S.
Danko
,
Ts. V.
Tsankov
,
T.
Mussenbrock
, and
U.
Czarnetzki
,
J. Phys. D: Appl. Phys.
47
,
445201
(
2014
).
22.
K.
Evdokimov
,
M.
Konischev
,
V.
Pichugin
, and
Z.
Sun
,
Resour.-Effic. Technol.
3
,
187
(
2017
).
23.
E.
Desjardins
,
M.
Laurent
,
A.
Durocher-Jean
,
G.
Laroche
,
N.
Gherardi
,
N.
Naudé
, and
L.
Stafford
,
Plasma Sources Sci. Technol.
27
,
015015
(
2018
).
24.
K.-B.
Chai
and
D.-H.
Kwon
,
Spectrochim. Acta B: At. Spectrosc.
183
,
106269
(
2021
).
25.
H.
Horita
,
D.
Kuwahara
,
H.
Akatsuka
, and
S.
Shinohara
,
AIP Adv.
11
,
075226
(
2021
).
26.
D.
Nishijima
,
S.
Kajita
, and
G.
Tynan
,
Rev. Sci. Instrum.
92
,
023505
(
2021
).
27.
J.-H.
Park
,
J.-H.
Cho
,
J.-S.
Yoon
, and
J.-H.
Song
,
Coatings
11
,
1221
(
2021
).
28.
K.
Shojaei
and
L.
Mangolini
,
J. Phys. D: Appl. Phys.
54
,
265202
(
2021
).
29.
T.
van der Gaag
,
H.
Onishi
, and
H.
Akatsuka
,
Phys. Plasmas
28
,
033511
(
2021
).
30.
Y.
Ralchenko
,
Mem. Soc. Astron. Ital. Supplement
8
,
96
(
2005
).
31.
U.
Fantz
,
Plasma Sources Sci. Technol.
15
,
S137
(
2006
).
32.
Z.
Donkó
,
Plasma Sources Sci. Technol.
20
,
024001
(
2011
).
33.
Z.
Donkó
,
A.
Derzsi
,
M.
Vass
,
B.
Horváth
,
S.
Wilczek
,
B.
Hartmann
, and
P.
Hartmann
,
Plasma Sources Sci. Technol.
30
,
095017
(
2021
).
34.
T.
Akiba
,
S.
Sano
,
T.
Yanase
,
T.
Ohta
, and
M.
Koyama
, “Optuna: A next-generation hyperparameter optimization framework,” in Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Anchorage, AK, August 2019 (Association for Computing Machinery, New York, 2019), pp. 2623–2631.
35.
M.
Iwayama
,
S.
Wu
,
C.
Liu
, and
R.
Yoshida
,
J. Chem. Inf. Model.
62
,
4837
(
2022
).
36.
T.
Kessler
,
G.
Dorian
, and
J. H.
Mack
, “Application of a rectified linear unit (ReLU) based artificial neural network to cetane number predictions,” in Internal Combustion Engine Division Fall Technical Conference, Vol. 58318 (American Society of Mechanical Engineers, Seattle, WA, 2017), p. V001T02A006.
37.
J. E.
Choi
and
S. J.
Hong
,
Meas.: Sens.
16
,
100046
(
2021
).
38.
A. D.
Bonzanini
,
K.
Shao
,
D. B.
Graves
,
S.
Hamaguchi
, and
A.
Mesbah
,
Plasma Sources Sci. Technol.
32
,
024003
(
2023
).
39.
T. K.
Ho
, “Random decision forests,” in Proceedings of 3rd International Conference on Document Analysis and Recognition, Vol. 1 (IEEE, Montreal, 1995), pp. 278–282.
41.
T.
Hastie
,
R.
Tibshirani
,
J. H.
Friedman
, and
J. H.
Friedman
,
The Elements of Statistical Learning: Data Mining, Inference, and Prediction
(
Springer
,
New York
,
2009
), Vol. 2.
42.
F.
Pedregosa
et al.,
J. Mach. Learn. Res.
12
,
2825
(
2011
).
43.
Z.
Donkó
,
Ts. V.
Tsankov
,
P.
Hartmann
,
F. J.
Arellano
,
U.
Czarnetzki
, and
S.
Hamaguchi
, “Self-consistent calculation of the optical emission spectrum of an argon capacitively coupled plasma based on the coupling of particle simulation with a collisional-radiative model,”
J. Phys. D Appl. Phys.
57, 375209 (2024).
You do not currently have access to this content.