Abstract

Silicon is one of the commonly used semiconductors for various industrial applications. Traditional silicon synthesis methods are often expensive and cannot meet the continuously growing demands for high-purity Si; electrodeposition is a promising and simple alternative. However, the electrodeposited products often possess nonuniform thicknesses due to various sources of uncertainty inherited from the fabrication process; to improve the quality of the coating products, it is crucial to better understand the influences of the sources of uncertainty. In this paper, uncertainty quantification (UQ) analysis is performed on the silicon electrodeposition process to evaluate the impacts of various experimental operation parameters on the thickness variation of the coated silicon layer and to find the optimal experimental conditions. To mitigate the high experimental and computational cost issues, a Gaussian process (GP) based surrogate model is constructed to conduct the UQ study with finite element (FE) simulation results as training data. It is found that the GP surrogate model can efficiently and accurately estimate the performance of the electrodeposition given certain experimental operation parameters. The results show that the electrodeposition process is sensitive to the geometric settings of the experiments, i.e., distance and area ratio between the counter and working electrodes; whereas other conditions, such as the potential of the counter electrode, temperature, and ion concentration in the electrolyte bath are less important. Furthermore, the optimal operating condition to deposit silicon is proposed to minimize the thickness variation of the coated silicon layer and to enhance the reliability of the electrodeposition experiment.

References

1.
Green
,
M. A.
,
2004
, “
Recent Developments in Photovoltaics
,”
Sol. Energy
,
76
(
1–3
), pp.
3
8
.10.1016/S0038-092X(03)00065-3
2.
El Abedin
,
S. Z.
,
Borissenko
,
N.
, and
Endres
,
F.
,
2004
, “
Electrodeposition of Nanoscale Silicon in a Room Temperature Ionic Liquid
,”
Electrochem. Commun.
,
6
(
5
), pp.
510
514
.10.1016/j.elecom.2004.03.013
3.
Cui
,
Y.
, and
Lieber
,
C. M.
,
2001
, “
Functional Nanoscale Electronic Devices Assembled Using Silicon Nanowire Building Blocks
,”
Science
,
291
(
5505
), pp.
851
853
.10.1126/science.291.5505.851
4.
Zhao
,
X. W.
,
Schoenfeld
,
O.
,
Kusano
,
J.
,
Aoyagi
,
Y.
, and
Sugano
,
T.
,
1994
, “
Violet and Blue-Light Emissions From Nanocrystalline Silicon Thin-Films
,”
Jpn. J. Appl. Phys. Part 2-Lett.
,
33
(
Part 2, No. 5A
), pp.
L649
L651
.10.1143/JJAP.33.L649
5.
Tong
,
S.
,
Liu
,
X. N.
, and
Bao
,
X. M.
,
1995
, “
Study of Photoluminescence in Nanocrystalline Silicon Amorphous-Silicon Multilayers
,”
Appl. Phys. Lett.
,
66
(
4
), pp.
469
471
.10.1063/1.114059
6.
Vijayalakshmi
,
S.
,
George
,
M. A.
,
Sturmann
,
J.
, and
Grebel
,
H.
,
1998
, “
Pulsed-Laser Deposition of Si Nanoclusters
,”
Appl. Surf. Sci.
,
127-129
, pp.
378
382
.10.1016/S0169-4332(97)00659-4
7.
Xie
,
X. Y.
,
Wan
,
Q.
,
Liu
,
W. L.
,
Men
,
C. L.
,
Lin
,
Q.
, and
Lin
,
C. L.
,
2003
, “
Nanoscale Silicon Prepared on Different Substrates Using Electron-Beam Evaporation and Their Field-Emission Property
,”
Appl. Surf. Sci.
,
217
(
1–4
), pp.
39
42
.10.1016/S0169-4332(03)00561-0
8.
Chen
,
X. L.
,
Gerasopoulos
,
K.
,
Guo
,
J. C.
,
Brown
,
A.
,
Wang
,
C. S.
,
Ghodssi
,
R.
, and
Culver
,
J. N.
,
2011
, “
A Patterned 3D Silicon Anode Fabricated by Electrodeposition on a Virus-Structured Current Collector
,”
Adv. Funct. Mater.
,
21
(
2
), pp.
380
387
.10.1002/adfm.201001475
9.
Lupan
,
O.
,
Pauporte
,
T.
, and
Viana
,
B.
,
2010
, “
Low-Temperature Growth of ZnO Nanowire Arrays on p-Silicon (111) for Visible-Light-Emitting Diode Fabrication
,”
J. Phys. Chem. C
,
114
(
35
), pp.
14781
14785
.10.1021/jp104684m
10.
Pauporté
,
T.
,
Qi
,
S.
, and
Viana
,
B.
,
2018
, “
Low Temperature Electrodeposition of Silicon Layers
,”
Oxide-Based Materials and Devices IX
,
International Society for Optics and Photonics
, 10533, p. 105332S.10.1117/12.2294944
11.
Colletti
,
L. P.
,
Flowers
,
B. H.
, and
Stickney
,
J. L.
,
1998
, “
Formation of Thin Films of CdTe, CdSe, and CdS by Electrochemical Atomic Layer Epitaxy
,”
J. Electrochem. Soc.
,
145
(
5
), pp.
1442
1449
.10.1149/1.1838502
12.
Pauporte
,
T.
,
Yoshida
,
T.
,
Goux
,
A.
, and
Lincot
,
D.
,
2002
, “
One-Step Electrodeposition of ZnO/Eosin Y Hybrid Films From a Hydrogen Peroxide Oxygen Precursor
,”
J. Electroanal. Chem.
,
534
(
1
), pp.
55
64
.10.1016/S0022-0728(02)01105-1
13.
Pandey
,
R. K.
,
Sahu
,
S.
, and
Chandra
,
S.
,
1996
,
Handbook of Semiconductor Electrodeposition
, CRC Press, Boca Raton, FL.
10.1201/9781315213989
14.
Munisamy
,
T.
, and
Bard
,
A. J.
,
2010
, “
Electrodeposition of Si From Organic Solvents and Studies Related to Initial Stages of Si Growth
,”
Electrochim. Acta
,
55
(
11
), pp.
3797
3803
.10.1016/j.electacta.2010.01.097
15.
Katayama
,
Y.
,
Yokomizo
,
M.
,
Miura
,
T.
, and
Kishi
,
T.
,
2001
, “
Preparation of a Novel Fluorosilicate Salt for Electrodeposition of Silicon at Low Temperature
,”
Electrochemistry
,
69
(
11
), pp.
834
836
.10.5796/electrochemistry.69.834
16.
Wahab
,
H. A.
,
Noordin
,
M. Y.
,
Izman
,
S.
, and
Kurniawan
,
D.
,
2013
, “
Quantitative Analysis of Electroplated Nickel Coating on Hard Metal
,”
Sci. World J.
,
2013
, pp.
1
6
.10.1155/2013/631936
17.
Broughton
,
J.
, and
Brett
,
M.
,
2005
, “
Variations in MnO2 Electrodeposition for Electrochemical Capacitors
,”
Electrochim. Acta
,
50
(
24
), pp.
4814
4819
.10.1016/j.electacta.2005.03.006
18.
Illy
,
B. N.
,
Cruickshank
,
A. C.
,
Schumann
,
S.
,
Da Campo
,
R.
,
Jones
,
T. S.
,
Heutz
,
S.
,
McLachlan
,
M. A.
,
McComb
,
D. W.
,
Riley
,
D. J.
, and
Ryan
,
M. P.
,
2011
, “
Electrodeposition of ZnO Layers for Photovoltaic Applications: Controlling Film Thickness and Orientation
,”
J. Mater. Chem.
,
21
(
34
), pp.
12949
12957
.10.1039/c1jm11225b
19.
Matlosz
,
M.
,
Vallotton
,
P. H.
,
West
,
A.
, and
Landolt
,
D.
,
1992
, “
Nonuniform Current Distribution and Thickness During Electrodeposition Onto Resistive Substrates
,”
J. Electrochem. Soc.
,
139
(
3
), pp.
752
761
.10.1149/1.2069297
20.
Solovjev
,
D.
,
Solovjeva
,
I.
, and
Litovka
,
Y. V.
,
2020
, “
Synthesis of the Suboptimal Control Algorithm for Electroplating Processes Under Conditions of Uncertainty in the Range of Processed Products
,”
IOP Conf. Series Mater. Sci. Eng.
,
709
(
2
),
p. 022063
. 10.1088/1757-899X/709/2/022063
21.
Bai
,
G. X.
, and
Wang
,
P. F.
,
2016
, “
An Internal State Variable Mapping Approach for Li-Plating Diagnosis
,”
J. Power Sources
,
323
, pp.
115
124
.10.1016/j.jpowsour.2016.05.040
22.
Zheng
,
Z.
,
Chen
,
B.
,
Gurumukhi
,
Y.
,
Cook
,
J.
,
Ates
,
M. N.
,
Miljkovic
,
N.
,
Braun
,
P. V.
, and
Wang
,
P.
,
2019
, “
Surrogate Model Assisted Design of Silicon Anode Considering Lithiation Induced Stresses
,”
IEEE International Reliability Physics Symposium (IRPS)
, Monterey, CA, Mar. 31–Apr. 4, pp.
1
6
.10.1109/IRPS.2019.8720601
23.
Zheng
,
Z. Y.
,
Chen
,
B.
,
Fritz
,
N.
,
Gurumukhi
,
Y.
,
Cook
,
J.
,
Ates
,
M. N.
,
Miljkovic
,
N.
,
Braun
,
P. V.
, and
Wang
,
P. F.
,
2019
, “
Lithiation Induced Stress Concentration for 3D Metal Scaffold Structured Silicon Anodes
,”
J. Electrochem. Soc.
,
166
(
10
), pp.
A2083
A2090
.10.1149/2.1031910jes
24.
Zheng
,
Z.
,
Chen
,
B.
,
Fritz
,
N.
,
Gurumukhi
,
Y.
,
Cook
,
J.
,
Ates
,
M. N.
,
Miljkovic
,
N.
,
Braun
,
P. V.
, and
Wang
,
P.
,
2020
, “
The Impact of Non-Uniform Metal Scaffolds on the Performance of 3D Structured Silicon Anodes
,”
J. Energy Storage
,
30
, p.
101502
.10.1016/j.est.2020.101502
25.
Zheng
,
Z.
,
Chen
,
B.
,
Xu
,
Y.
,
Fritz
,
N.
,
Gurumukhi
,
Y.
,
Cook
,
J.
,
Ates
,
M. N.
,
Miljkovic
,
N.
,
Braun
,
P. V.
, and
Wang
,
P.
,
2021
, “
A Gaussian Process Based Crack Pattern Modeling Approach for Battery Anode Materials Design
,”
J. Electrochem. Energy Convers. Storage
,
18
(
1
), p.
011011
.10.1115/1.4046938
26.
Chen
,
K. S.
, and
Evans
,
G. H.
,
2004
, “
Two-Dimensional Modeling of Nickel Electrodeposition in LIGA Microfabrication
,”
Microsyst. Technol.-Micro- Nanosyst.-Inf. Storage Process. Syst.
,
10
(
6–7
), pp.
444
450
.10.1007/s00542-004-0373-8
27.
Lupo
,
C.
, and
Schlettwein
,
D.
,
2019
, “
Modeling of Dendrite Formation as a Consequence of Diffusion-Limited Electrodeposition
,”
J. Electrochem. Soc.
,
166
(
1
), pp.
D3182
D3189
.10.1149/2.0231901jes
28.
Wheeler
,
D.
,
Josell
,
D.
, and
Moffat
,
T. P.
,
2003
, “
Modeling Superconformal Electrodeposition Using the Level Set Method
,”
J. Electrochem. Soc.
,
150
(
5
), pp.
C302
C310
.10.1149/1.1562598
29.
Ng
,
S. S. Y.
,
Xing
,
Y.
, and
Tsui
,
K. L.
,
2014
, “
A Naive Bayes Model for Robust Remaining Useful Life Prediction of Lithium-Ion Battery
,”
Appl. Energy
,
118
, pp.
114
123
.10.1016/j.apenergy.2013.12.020
30.
Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P., 1989, “Design and Analysis of Computer Experiments,”
Statist. Sci.
, 4(4), pp. 409–423.
10.1214/ss/1177012413
31.
Wang
,
L. P.
,
Beeson
,
D.
,
Akkaram
,
S.
, and
Wiggs
,
G.
,
2005
, “
Gaussian Process Meta-Models for Efficient Probabilistic Design in Complex Engineering Design Spaces
,”
Proceedings of the ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Long Beach, CA, Sept. 24–28, pp. 785–798.10.1115/DETC2005-85406
32.
Jensen
,
W. A.
,
2017
, “
Response Surface Methodology: Process and Product Optimization Using Designed Experiments 4th Edition
,”
J. Qual. Technol.
,
49
(
2
), pp.
186
187
.10.1080/00224065.2017.11917988
33.
Haykin
,
S.
, and
Network
,
N.
,
2004
, Neural Networks: A Comprehensive Foundation, Prentice Hall, Upper Saddle River, NJ.
34.
Lophaven
,
S. N.
,
Nielsen
,
H. B.
,
Sondergaard
,
J.
, and
Dace
,
A.
,
2002
,
A Matlab Kriging Toolbox
,
Technical University of Denmark
,
Kongens Lyngbyand
, Report No. IMMTR-2002.
35.
Forrester
,
A.
,
Sobester
,
A.
, and
Keane
,
A.
,
2008
,
Engineering Design Via Surrogate Modelling: A Practical Guide
,
Wiley
, Hoboken, NJ.10.1002/9780470770801
36.
Fan
,
X.
,
Wang
,
P.
, and
Hao
,
F.
,
2019
, “
Reliability-Based Design Optimization of Crane Bridges Using Kriging-Based Surrogate Models
,”
Struct. Multidiscip. Optim.
,
59
(
3
), pp.
993
1005
.10.1007/s00158-018-2183-0
37.
Zheng
,
Z.
,
Xu
,
Y.
,
Chen
,
B.
, and
Wang
,
P.
,
2019
, “
Gaussian Process Based Crack Initiation Modeling for Design of Battery Anode Materials
,”
ASME
Paper No. DETC2019-97547.10.1115/DETC2019-97547
38.
Bird
,
R. B.
,
2002
, “
Transport Phenomena
,”
ASME Appl. Mech. Rev
,
55
(
1
), pp.
R1
R4
.10.1115/1.1424298
39.
Newman
,
J.
, and
Thomas-Alyea
,
K. E.
,
2012
,
Electrochemical Systems
,
Wiley
, Hoboken, NJ.
40.
Kamata
,
M.
, and
Paku
,
M.
,
2007
, “
Exploring Faraday's Law of Electrolysis Using Zinc–Air Batteries With Current Regulative Diodes
,”
J. Chem. Educ.
,
84
(
4
), p.
674
.10.1021/ed084p674
41.
Moats
,
M. S.
,
Hiskey
,
J. B.
, and
Collins
,
D. W.
,
2000
, “
The Effect of Copper, Acid, and Temperature on the Diffusion Coefficient of Cupric Ions in Simulated Electrorefining Electrolytes
,”
Hydrometallurgy
,
56
(
3
), pp.
255
268
.10.1016/S0304-386X(00)00070-0
42.
Rubinstein
,
R. Y.
, and
Kroese
,
D. P.
,
2016
,
Simulation and the Monte Carlo Method
, Vol.
10
,
Wiley
, Hoboken, NJ.10.1002/9781118631980
43.
Melkumyan
,
A.
, and
Ramos
,
F.
,
2009
, “
A Sparse Covariance Function for Exact Gaussian Process Inference in Large Datasets
,” Pasadena, CA, July 14–17,
IJCAI
, Menlo Park, CA, pp.
1936
1942
.10.5555/1661445.1661755
44.
Wang
,
Z. Q.
, and
Wang
,
P. F.
,
2014
, “
A Maximum Confidence Enhancement Based Sequential Sampling Scheme for Simulation-Based Design
,”
ASME J. Mech. Des.
,
136
(
2
), p.
021006
.10.1115/1.4026033
45.
Wang
,
P. F.
,
Wang
,
Z. Q.
, and
Almaktoom
,
A. T.
,
2014
, “
Dynamic Reliability-Based Robust Design Optimization With Time-Variant Probabilistic Constraints
,”
Eng. Optim.
,
46
(
6
), pp.
784
809
.10.1080/0305215X.2013.795561
46.
Wang
,
Z. Q.
, and
Wang
,
P. F.
,
2015
, “
A Double-Loop Adaptive Sampling Approach for Sensitivity-Free Dynamic Reliability Analysis
,”
Reliab. Eng. Syst. Saf.
,
142
, pp.
346
356
.10.1016/j.ress.2015.05.007
47.
Quemper
,
J.-M.
,
Dufour-Gergam
,
E.
,
Frantz-Rodriguez
,
N.
,
Gilles
,
J.-P.
,
Grandchamp
,
J.-P.
, and
Bosseboeuf
,
A.
,
2000
, “
Effects of Direct and Pulse Current on Copper Electrodeposition Through Photoresist Molds
,”
J. Micromech. Microeng.
,
10
(
2
), pp.
116
119
.10.1088/0960-1317/10/2/303
48.
Mottershead
,
J.
,
Mares
,
C.
,
Friswell
,
M.
, and
James
,
S.
,
2000
, “
Selection and Updating of Parameters for an Aluminium Space-Frame Model
,”
Mech. Syst. Signal Process.
,
14
(
6
), pp.
923
944
.10.1006/mssp.2000.1303
49.
Nobari
,
A.
,
Ouyang
,
H. J.
, and
Bannister
,
P.
,
2015
, “
Uncertainty Quantification of Squeal Instability Via Surrogate Modelling
,”
Mech. Syst. Signal Process.
,
60–61
, pp.
887
908
.10.1016/j.ymssp.2015.01.022
50.
Schenk
,
C. A.
,
2005
,
And G.I. Schuëller, Uncertainty Assessment of Large Finite Element Systems
, Vol.
24
,
Springer Science & Business Media
, Secaucus, NJ.
51.
Lundstedt
,
T.
,
Seifert
,
E.
,
Abramo
,
L.
,
Thelin
,
B.
,
Nyström
,
Å.
,
Pettersen
,
J.
, and
Bergman
,
R.
,
1998
, “
Experimental Design and Optimization
,”
Chemomet. Intell. Lab. Syst.
,
42
(
1–2
), pp.
3
40
.10.1016/S0169-7439(98)00065-3
You do not currently have access to this content.