The electrodissolution of p-type silicon in a fluoride-containing electrolyte is a prominent electrochemical oscillator with a still unknown oscillation mechanism. In this article, we present a study of its dynamical states occurring in a wide range of the applied voltage–external resistance parameter plane. We provide evidence that the system possesses inherent birhythmicity, and thus at least two distinct feedback loops promoting oscillatory behavior. The two parameter regions in which the different limit cycles exist are separated by a band in which the dynamics exhibit bistability between two branches with different multimode oscillations. Following the states along one path through this bistable region, one observes that each branch undergoes a different transition to chaos, namely, a period doubling cascade and a quasiperiodic route with a torus-breakdown, respectively, making Si electrodissolution one of the few experimental systems exhibiting bichaoticity.

1.
M.
Alamgir
and
I. R.
Epstein
, “
Birhythmicity and compound oscillation in coupled chemical oscillators: Chlorite-bromate-iodide system
,”
J. Am. Chem. Soc.
105
,
2500
2502
(
1983
).
2.
M.
Alamgir
and
I. R.
Epstein
, “
Experimental study of complex dynamical behavior in coupled chemical oscillators
,”
J. Phys. Chem.
88
,
2848
2851
(
1984
).
3.
B. R.
Johnson
,
J. F.
Griffiths
, and
S. K.
Scott
, “
Characterisation of oscillations in the H2+ O2 reaction in a continuous-flow reactor
,”
J. Chem. Soc. Faraday Trans.
87
,
523
533
(
1991
).
4.
A.
Goldbeter
,
Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour
(
Cambridge University Press
,
1997
).
5.
O.
Decroly
and
A.
Goldbeter
, “
Birhythmicity, chaos, and other patterns of temporal self-organization in a multiply regulated biochemical system
,”
Proc. Natl. Acad. Sci. U.S.A.
79
,
6917
6921
(
1982
).
6.
D.
Battogtokh
and
J. J.
Tyson
, “
Turbulence near cyclic fold bifurcations in birhythmic media
,”
Phys. Rev. E
70
,
7
(
2004
); preprint arXiv:0402040[arXiv:q-bio.SC].
7.
M.
Stich
,
M.
Ipsen
, and
A. S.
Mikhailov
, “
Self-organized stable pacemakers near the onset of birhythmicity
,”
Phys. Rev. Lett.
86
,
4406
4409
(
2001
); preprint arXiv:0011033 [nlin].
8.
M.
Stich
,
M.
Ipsen
, and
A. S.
Mikhailov
, “
Self-organized pacemakers in birhythmic media
,”
Physica D
171
,
19
40
(
2002
).
9.
D.
Biswas
,
T.
Banerjee
, and
J.
Kurths
, “
Control of birhythmicity through conjugate self-feedback: Theory and experiment
,”
Phys. Rev. E
94
,
1
7
(
2016
). arXiv:1610.04722
10.
D.
Biswas
,
T.
Banerjee
, and
J.
Kurths
, “
Control of birhythmicity: A self-feedback approach
,”
Chaos
27
,
064608
(
2017
).
11.
S.
Yanchuk
and
P.
Perlikowski
, “
Delay and periodicity
,”
Phys. Rev. E
79
,
1
9
(
2009
). arXiv:0902.3748
12.
T.
Erneux
and
J.
Grasman
, “
Limit-cycle oscillators subject to a delayed feedback
,”
Phys. Rev. E
78
,
1
8
(
2008
).
13.
P.
Ghosh
,
S.
Sen
,
S. S.
Riaz
, and
D. S.
Ray
, “
Controlling birhythmicity in a self-sustained oscillator by time-delayed feedback
,”
Phys. Rev. E
83
,
036205
(
2011
).
14.
T.
Nagy
,
E.
Verner
,
V.
Gáspár
,
H.
Kori
, and
I. Z.
Kiss
, “
Delayed feedback induced multirhythmicity in the oscillatory electrodissolution of copper
,”
Chaos
25
,
064608
(
2015
).
15.
I.
Miethe
,
V.
García-Morales
, and
K.
Krischer
, “
Irregular subharmonic cluster patterns in an autonomous photoelectrochemical oscillator
,”
Phys. Rev. Lett.
102
,
94
101
(
2009
).
16.
I.
Miethe
and
K.
Krischer
, “
Ellipsomicroscopic studies of the anodic oxidation of p-type silicon in fluoride containing electrolytes during current oscillations
,”
J. Electroanal. Chem.
666
,
1
10
(
2012
).
17.
K.
Schönleber
and
K.
Krischer
, “
High-amplitude versus low-amplitude current oscillations during the anodic oxidation of p-type silicon in fluoride containing electrolytes
,”
Chem. Phys. Chem.
13
,
2989
2996
(
2012
).
18.
S.
Cattarin
,
I.
Frateur
,
M.
Musiani
, and
B.
Tribollet
, “
Electrodissolution of p-Si in acidic fluoride media modeling of the steady state
,”
J. Electrochem. Soc.
147
,
3277
(
2000
).
19.
K.
Schönleber
,
M.
Patzauer
, and
K.
Krischer
, “
A comparison of modeling frameworks for the oscillatory silicon electrodissolution
,”
Electrochim. Acta
210
,
346
351
(
2016
).
20.
M.
Eddowes
, “
Anodic dissolution of p- and n-type silicon: Kinetic study of the chemical mechanism
,”
J. Electroanal. Chem. Interfacial Electrochem.
280
,
297
311
(
1990
).
21.
D. J.
Blackwood
,
A. M.
Borazio
,
R.
Greef
,
L. M.
Peter
, and
J.
Stumper
, “
Electrochemical and optical studies of silicon dissolution in ammonium fluoride solutions
,”
Electrochim. Acta
37
,
889
896
(
1992
).
22.
M. M.
Salman
,
M.
Patzauer
,
D.
Koster
,
F.
LaMantia
, and
K.
Krischer
, “
Electro-oxidation of silicon in fluoride-containing electrolyte: A physical model for the regime of negative differential resistance
,”
Eur. Phys. J. Special Topics
227
,
2641
2658
(
2019
).
23.
X. G.
Zhang
,
Electrochemistry of Silicon and Its Oxide
(
Kluwer Academic/Plenum Publishers
,
New York
,
2001
), p.
510
.
24.
M.
Patzauer
,
R.
Hueck
,
A.
Tosolini
,
K.
Schönleber
, and
K.
Krischer
, “
Autonomous oscillations and pattern formation with zero external resistance during silicon electrodissolution
,”
Electrochim. Acta
246
,
315
321
(
2017
).
25.
M. T.
Koper
, “
The theory of electrochemical instabilities
,”
Electrochim. Acta
37
,
1771
1778
(
1992
).
26.
F.
Blaffart
,
Q.
Van Overmeere
,
F.
Van Wonterghem
, and
J.
Proost
, “
In situ monitoring of electrochemical oscillations during the transition between dense and porous anodic silica formation
,”
J. Electrochem. Soc.
161
,
874
879
(
2014
).
27.
V.
Afraimovich
and
L. P.
Shilnikov
, “
Invariant two-dimensional tori, their breakdown and stochasticity
,”
Am. Math. Soc. Transl.
149
,
210
212
(
1991
).
28.
V. S.
Anishchenko
,
M. A.
Safonova
, and
L. O.
Chua
, “
Confirmation of the Afraimovich-Shilnikov Torus-breakdown theorem via a torus circuit
,”
IEEE Trans. Circuits Syst. I Fundam. Theory Appl.
40
,
792
800
(
1993
).
29.
D. R.
Turner
, “
Electropolishing silicon in hydrofluoric acid solutions
,”
J. Electrochem. Soc.
105
,
402
408
(
1958
).
30.
H.
Föll
,
M.
Leisner
,
A.
Cojocaru
, and
J.
Carstensen
, “
Self-organization phenomena at semiconductor electrodes
,”
Electrochim. Acta
55
,
327
339
(
2009
).
31.
F.
Ozanam
,
J. N.
Chazalviel
,
A.
Radi
, and
M.
Etman
, “
Resonant and nonresonant behavior of the anodic dissolution of silicon in fluoride media: An impedance study
,”
J. Electrochem. Soc.
139
(
9
),
2491
2501
(
1992
).
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