We describe an experiment to fabricate atomic-scale contacts using electrochemically grown silver wires. The formation of a single-wire junction is directly observed and captured by an optical microscope, while electrical conductance of the wire, simultaneously recorded, is shown to be quantized. Further, a diffusion-limited aggregate (DLA) simulation is performed to compare the observed fractal formed by the silver dendrites. Our experiment directly exposes undergraduate students to exciting contemporary physics ranging from atomic-scale switches to fractal formation, all on a single experimental platform.

1.
C.
Rackson
,
A.
Watt
, and
W. J.
Kim
, “
Effect of surface contact potential in atomic-size contacts
,”
Phys. Lett. A
379
,
2239
2244
(
2015
).
2.
J. L.
Costa-Krämer
,
N.
García
,
P.
Garca-Mochales
, and
P. A.
Serena
, “
Nanowire formation in macroscopic metallic contacts: quantum mechanical conductance tapping a table top
,”
Surf. Sci. Lett.
342
,
L1144
L1149
(
1995
).
3.
J. L.
Costa-Krämer
,
N.
García
, and
H.
Olin
, “
Conductance quantization histograms of gold nanowires at 4 K
,”
Phys. Rev. B
55
,
12910
12913
(
1997
).
4.
D. L.
Bakker
,
Y.
Noat
,
A. I.
Yanson
, and
J. M.
van Ruitenbeek
, “
Effect of disorder on the conductance of a Cu atomic point contact
,”
Phys. Rev. B
65
,
235416
(
2002
).
5.
E. L.
Foley
,
D.
Candela
,
K. M.
Martini
, and
M. T.
Tuominen
, “
An undergraduate laboratory experiment on quantized conductance in nanocontacts
,”
Am. J. Phys.
67
,
389
393
(
1999
).
6.
E. H.
Huisman
,
F. L.
Bakker
,
J. P.
van der Pal
,
R. M.
de Jonge
, and
C. H.
van der Wal
, “
Public exhibit for demonstrating the quantum of electrical conductance
,”
Am. J. Phys.
79
,
856
860
(
2011
).
7.
R.
Tolley
,
A.
Silvidi
,
C.
Little
, and
K. F.
Eid
, “
Conductance quantization: A laboratory experiment in a senior-level nanoscale science and technology course
,”
Am. J. Phys.
81
,
14
19
(
2013
).
8.
C. Z.
Li
and
N. J.
Tao
, “
Quantum transport in metallic nanowires fabricated by electrochemical deposition/dissolution
,”
Appl. Phys. Lett.
72
,
894
896
(
1998
).
9.
M.
Akai-Kasaya
,
K.
Nishihara
,
A.
Saito
,
Y.
Kuwahara
, and
M.
Aono
, “
Quantum point-contact switches using silver particles
,”
Appl. Phys. Lett.
88
,
023107
(
2006
).
10.
N.
Tao
Electrochemical fabrication of metallic quantum wires
,”
J. Chem. Edu.
82
,
720
726
(
2005
).
11.
M. R.
Calvo
,
A. I.
Mares
,
V.
Climent
,
J. M.
van Ruitenbeek
, and
C.
Untiedt
, “
Formation of atomic-sized contacts controlled by electrochemical methods
,”
Phys. Stat. Sol.
204
,
1677
1685
(
2007
).
12.
A. F.
Morpurgo
,
C. M.
Marcus
, and
D. B.
Robinson
, “
Controlled fabrication of metallic electrodes with atomic separation
,”
Appl. Phys. Lett.
74
,
2084
2086
(
1999
).
13.

In principle, the intercept a should be zero as the junction resistance approaches infinity and hence X approaches zero. But, in our by calibration, the largest value of resistance used was Rmax = 12.9 kΩ, and this rather small Rmax may have caused a deviation from the zero-intercept, as evidenced by the finite value of the offset parameter (170 μV). Alternatively, we suspect that the non-zero intercept reflects a small amount of electronic pickup at 100 kHz in the open circuit (i.e., no resistor connected across the electrode).

14.
T. A.
Witten
, Jr.
and
L. M.
Sander
, “
Diffusion-limited aggregation, a kinetic critical phenomenon
,”
Phys. Rev. Lett.
47
,
1400
1403
(
1981
).
15.
T. C.
Halsey
, “
Diffusion-limited aggregation: A model for pattern formation
,”
Phys. Today
53
(
11
),
36
41
(
2000
).
16.
M.
Matsushita
,
M.
Sano
,
Y.
Hayakawa
,
H.
Honjo
, and
Y.
Sawada
, “
Fractal structures of zinc metal leaves grown by electrodeposition
,”
Phys. Rev. Lett.
53
,
286
289
(
1984
).
17.
D.
Barkey
,
F.
Oberholtzer
, and
Q.
Wu
, “
Kinematic anisotropy and dendritic growth in electrochemical deposition
,”
Phys. Rev. Lett.
75
,
2980
(
1995
).
18.
H.
Hahn
,
R.
Krupke
,
F.
Schramm
,
T.
Scherer
,
B.
Dinga
, and
X.
Song
, “
Silver nanowires growth via branch fragmentation of electrochemically grown silver dendrites
,”
Chem. Commun.
0
,
1130
1132
(
2009
).
19.
H.
Gould
and
J.
Tobochnik
,
An Introduction to Computer Simulation Methods
, 2nd ed. (
Addison-Wesley Publishing Company
,
CA
,
1996
), p.
477
.
20.
S.
Nakabayashi
,
H.
Sakaguchi
,
R.
Baba
, and
E.
Fukushima
, “
Quantum contact by colliding 2D fractal
,”
Nano Lett.
1
,
507
510
(
2001
).
21.
A.
Wlasenko
,
F.
Soltani
,
D.
Zakopcan
,
D.
Sinton
, and
G. M.
Steeves
, “
Diffusion-limited and advection-driven electrodeposition in a microfluidic channel
,”
Phys. Rev. E
81
,
021601
(
2010
).
22.

As another driving mechanism, advection can be also introduced. See the article by A. Wlasenko et al. (Ref. 21).

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