Sputtering of a single-element material surface by monatomic ion impact is one of the simplest and most fundamental phenomena of plasma–surface interaction. Despite its seemingly simple and well-defined nature, its collision cascade dynamics is so complex that no widely applicable formula of the sputtering yield has ever been derived analytically from the first principles. When the first-principles approach to a complex problem fails to unveil its nature, a data-driven approach, or machine learning, may be used to transform the problem into a tractable model. In this study, regression models of sputtering yields of such systems were constructed based on publicly available data derived from a large number of past experiments. The analysis has also identified the descriptors (i.e., physical variables characterizing the surface and incident ion species) on which the sputtering phenomena depend most strongly and presented quantitative evaluation on how sensitively the regression models depend on each descriptor or group of descriptors. Information obtained in this study can facilitate an understanding of the fundamental workings of the sputtering phenomena in the absence of rigorous analytical theory.

1.
Modern Semiconductor Device Physics
, edited by
S. M.
Sze
(
John Wiley and Sons
,
New York
,
1998
).
2.
Handbook of Semiconductor Manufacturing Technology
, edited by
R.
Doering
and
Y.
Nishi
(
CRC Press
,
2007
).
3.
K.
Nojiri
,
Dry Etching Technology for Semiconductors
(
Springer
,
2015
).
4.
B. N.
Chapman
,
Glow Discharge Processes: Sputtering and Plasma Etching
(
Wiley-Interscience
,
1980
).
5.
Plasma Processing of Semiconductors
, edited by
P.
Williams
(
Springer
,
The Netherlands
,
1997
).
6.
M. A.
Lieberman
and
A. J.
Lichtenberg
,
Principles of Plasma Discharges and Materials Processings
(
Wiley–Interscience
,
2005
).
7.
W. N. G.
Hitchon
,
Plasma Processes for Semiconductor Fabrication
(
Cambridge University Press
,
2005
).
8.
T.
Makabe
and
Z. L.
Petrovic
,
Plasma Electronics
(
Routledge
,
2016
).
9.
I.
Adamovich
,
S. D.
Baalrud
,
A.
Bogaerts
,
P. J.
Bruggeman
,
M.
Cappelli
,
V.
Colombo
,
U.
Czarnetzki
,
U.
Ebert
,
J. G.
Eden
,
P.
Favia
,
D. B.
Graves
,
S.
Hamaguchi
,
G.
Hieftje
,
M.
Hori
,
I. D.
Kaganovich
,
U.
Kortshagen
,
M. J.
Kushner
,
N. J.
Mason
,
S.
Mazouffre
,
S. M.
Thagard
,
H.
Metelmann
,
A.
Mizuno
,
E.
Moreau
,
A. B.
Murphy
,
B. A.
Niemira
,
G. S.
Oehrlein
,
Z. L.
Petrovic
,
L.
Pitchford
,
Y. K.
Pu
,
S.
Rauf
,
O.
Sakai
,
S.
Samukawa
,
S.
Starikovskaia
,
J.
Tennyson
,
K.
Terashima
,
M. M.
Turner
,
M. C. M.
van de Sanden
, and
A.
Vardelle
,
J. Phys. D: Appl. Phys.
50
,
323001
(
2017
).
10.
G. S.
Oehrlein
and
S.
Hamaguchi
,
Plasma Sources Sci. Technol.
27
,
023001
(
2018
).
11.
K.-D.
Weltmann
,
J. F.
Kolb
,
M.
Holub
,
D.
Uhrlandt
,
M.
Šimek
,
K.
Ostrikov
,
S.
Hamaguchi
,
U.
Cvelbar
,
M.
Černák
,
B.
Locke
,
A.
Fridman
,
P.
Favia
, and
K.
Becker
,
Plasma Processes Polym.
16
,
1800118
(
2019
).
12.
J. W.
Coburn
and
H. F.
Winters
,
J. Appl. Phys.
50
,
3189
(
1979
).
13.
P.
Sigmund
,
Thin Solid Films
520
,
6031
(
2012
).
14.
Sputtering by Particle Bombardment
, edited by
R.
Behrisch
and
W.
Eckstein
(
Springer-Verlag
,
Berlin, Heidelberg
,
2007
).
15.
Y.
Yamamura
and
H.
Tawara
,
At. Data Nucl. Data Tables
62
,
149
(
1996
).
16.
K.
Karahashi
and
S.
Hamaguchi
,
J. Phys. D: Appl. Phys.
47
,
224008
(
2014
).
17.
R. E.
Lee
,
J. Vac. Sci. Technol.
16
,
164
(
1979
).
18.
Y.
Yamamura
,
Y.
Itikawa
, and
N.
Itoh
, “
Angular dependence of sputtering yields of monatomic solids
,”
Report No. IPPJ-AM-26
,
1983
, p.
1
.
19.
S.
Hamaguchi
,
IBM J. Res. Develop.
43
,
199
(
1999
).
20.
M.
Dalvie
,
R. T.
Farouki
, and
S.
Hamaguchi
,
IEEE Trans. Electron Devices
39
,
1090
(
1992
).
21.
A. A.
Mayo
,
S.
Hamaguchi
,
J. H.
Joo
, and
S. M.
Rossnagel
,
J. Vac. Sci. Technol., B
15
,
1788
(
1997
).
22.
S.
Hamaguchi
,
M.
Dalvie
,
R.
Farouki
, and
S.
Sethuraman
,
J. Appl. Phys.
74
,
5172
(
1993
).
23.
S.
Hamaguchi
and
M.
Dalvie
,
J. Electrochem. Soc.
141
,
1964
(
1994
).
24.
P.
Sigmund
,
Particle Penetration and Radiation Effects: General Aspects and Stopping of Swift Point Charges
(
Springer
,
2006
).
25.
A.
Shukri
, Ph.D. thesis (
Ecole Polytechnique
,
2015
).
26.
P. C.
Weakliem
,
C. J.
Wu
, and
E. A.
Carter
,
Phys. Rev. Lett.
69
,
200
(
1992
).
27.
H.
Feil
,
J.
Dieleman
, and
B. J.
Garrison
,
J. Appl. Phys.
74
,
1303
(
1993
).
28.
M. E.
Barone
and
D. B.
Graves
,
J. Appl. Phys.
77
,
1263
(
1995
).
29.
H.
Ohta
and
S.
Hamaguchi
,
J. Chem. Phys.
115
,
6679
(
2001
).
30.
H.
Ohta
and
S.
Hamaguchi
,
J. Vac. Sci. Technol.
18
,
2373
(
2001
).
31.
H.
Yamada
and
S.
Hamaguchi
,
J. Appl. Phys.
96
,
6147
(
2004
).
32.
M.
Taguchi
and
S.
Hamaguchi
,
Thin Solid Films
515
,
4879
(
2007
).
33.
T.
Kawase
and
S.
Hamaguchi
,
Thin Solid Films
515
,
4883
(
2007
).
34.
D. B.
Graves
and
P.
Brault
,
J. Phys. D: Appl. Phys.
42
,
194011
(
2009
).
35.
Y.
Murakami
,
S.
Horiguchi
, and
S.
Hamaguchi
,
Phys. Rev. E
81
,
041602
(
2010
).
36.
S.
Yoshimura
,
A.
Toh
,
S.
Sugimoto
,
M.
Kiuchi
, and
S.
Hamaguchi
,
Jpn. J. Appl. Phys., Part 1
45
,
8204
(
2006
).
37.
T.
Ito
,
K.
Karahashi
,
M.
Fukasawa
,
T.
Tatsumi
, and
S.
Hamaguchi
,
J. Vac. Sci. Technol., A
29
,
050601
(
2011
).
38.
T.
Ito
,
K.
Karahashi
,
M.
Fukasawa
,
T.
Tatsumi
, and
S.
Hamaguchi
,
Jpn. J. Appl. Phys., Part 1
50
,
08KD02
(
2011
).
39.
Y.
Kitazoe
and
N.
Hiraoka
,
Surf. Sci.
111
,
381
(
1981
).
40.
Y.
Yamamura
,
Nucl. Instrum. Methods Phys. Res.
194
,
515
(
1982
).
41.
Y.
Yamamura
and
J.
Bohdansky
,
Vacuum
35
,
561
(
1985
).
42.
R.
Janev
,
Y.
Ralchenko
,
T.
Kenmotsu
, and
K.
Hosaka
,
J. Nucl. Mater.
290–293
,
104
(
2001
).
43.
K. I.
Grais
,
A.
Shaltout
,
S.
Ali
,
R.
Boutros
,
K.
El-behery
, and
Z.
El-Sayed
,
Phys. B: Condens. Matter
405
,
1775
(
2010
).
44.
H. C.
Dam
,
V. C.
Nguyen
,
T. L.
Pham
,
A. T.
Nguyen
,
K.
Terakura
,
T.
Miyake
, and
H.
Kino
,
J. Phys. Soc. Jpn.
87
,
113801
(
2018
).
45.
P. C.
Zalm
,
J. Appl. Phys.
54
,
2660
(
1983
).
46.
H.
Kino
,
K.
Ikuse
,
D. H.
Chi
, and
S.
Hamaguchi
(
2020
). “
Prediction of plasma etching yields by machine learning to reveal the complexity of underlying physics
,” Zenodo. .
47.
H.
Liu
and
L.
Yu
,
IEEE Trans. Knowl. Data Eng.
17
,
491
(
2005
).
48.
V.
Bolón-Canedo
,
N.
Sánchez-Maroño
, and
A.
Alonso-Betanzos
,
Knowl. Inf. Syst.
34
,
483
(
2013
).
49.
H.
Kino
,
K.
Ikuse
,
D. H.
Chi
, and
S.
Hamaguchi
(
2020
). “
Characterization of descriptors in machine learning for data-based sputtering yield prediction
,” Zenodo. .
50.
H.
Kino
,
K.
Ikuse
,
D. H.
Chi
, and
S.
Hamaguchi
(
2020
). “
Prediction of plasma etching yields by machine learning to reveal the complexity of underlying physics
,” Zenodo. .
51.
P.
Virtanen
,
R.
Gommers
,
T. E.
Oliphant
,
M.
Haberland
,
T.
Reddy
,
D.
Cournapeau
,
E.
Burovski
,
P.
Peterson
,
W.
Weckesser
,
J.
Bright
,
S. J.
van der Walt
,
M.
Brett
,
J.
Wilson
,
K. J.
Millman
,
N.
Mayorov
,
A. R. J.
Nelson
,
E.
Jones
,
R.
Kern
,
E.
Larson
,
C.
Carey
,
İ.
Polat
,
Y.
Feng
,
E. W.
Moore
,
J.
Vand erPlas
,
D.
Laxalde
,
J.
Perktold
,
R.
Cimrman
,
I.
Henriksen
,
E. A.
Quintero
,
C. R.
Harris
,
A. M.
Archibald
,
A. H.
Ribeiro
,
F.
Pedregosa
,
P.
van Mulbregt
,
SciPy 1.0 Contributors
, “
SciPy 1.0: Fundamental algorithms for scientific computing in python
,”
Nat. Methods
17
,
261
272
(
2020
).
52.
F.
Pedregosa
,
G.
Varoquaux
,
A.
Gramfort
,
V.
Michel
,
B.
Thirion
,
O.
Grisel
,
M.
Blondel
,
P.
Prettenhofer
,
R.
Weiss
,
V.
Dubourg
,
J.
Vanderplas
,
A.
Passos
,
D.
Cournapeau
,
M.
Brucher
,
M.
Perrot
, and
E.
Duchesnay
,
J. Mach. Learn. Res.
12
,
2825
(
2011
).
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