To increase measurement throughput of atomic force microscopy (AFM), multiple cantilevers can be placed in close proximity to form an array for parallel throughput. In this paper, we have measured the relationship between amplitude and tip-sample separation distance for an array of AFM cantilevers on a shared base actuated at a constant frequency and amplitude. The data show that discontinuous jumps in output amplitude occur within the response of individual beams. This is a phenomenon that does not occur for a standard, single beam system. To gain a better understanding of the coupled array response, a macroscale experiment and mathematical model are used to determine how parameter space alters the measured amplitude. The results demonstrate that a cusp catastrophe bifurcation occurs due to changes in individual beam resonant frequency, as well as significant zero-frequency coupling at the point of jump-to-contact. Both of these phenomena are shown to account for the amplitude jumps observed in the AFM array.

References

1.
Casuso
,
I.
,
Rico
,
F.
, and
Scheuring
,
S.
,
2011
, “
Biological AFM: Where We Come From–Where We Are–Where We May Go
,”
J. Mol. Recognit.
,
24
(
3
), pp.
406
413
.
2.
Polesel-Maris
,
J.
,
Aeschimann
,
L.
,
Meister
,
A.
,
Ischer
,
R.
,
Bernard
,
E.
,
Akiyama
,
T.
,
Giazzon
,
M.
,
Niedermann
,
P.
,
Staufer
,
U.
,
Pugin
,
R.
,
Rooij
,
N.
,
Vettiger
,
P.
, and
Heinzelmann
,
H.
,
2007
, “
Piezoresistive Cantilever Array for Life Sciences Applications
,”
J. Phys.: Conf. Ser.
,
61
, pp.
955
959
.
3.
Seong
,
M.
,
Somnath
,
S.
,
Kim
,
H. J.
, and
King
,
W. P.
,
2014
, “
Parallel Nanoimaging Using an Array of 30 Heated Microcantilevers
,”
RSC Adv.
,
4
(
47
), pp.
24747
24754
.
4.
Loizeau
,
F.
, and
Favre
,
M.
,
2013
, “
2D Cantilever Array With Spherical Tips for Parallel Force Spectroscopy on Cancerous Cells
,”
17th International Conference on Solid-State Sensors, Actuators and Microsystems
(
TRANSDUCERS & EUROSENSORS
), Barcelona, Spain, June 16–20, pp.
1186
1189
.
5.
Schneider
,
A.
,
Ibbotson
,
R.
,
Dunn
,
R.
, and
Huq
,
S.
,
2011
, “
Arrays of SU-8 Microcantilevers With Integrated Piezoresistive Sensors for Parallel AFM Applications
,”
Microelectron. Eng.
,
88
(
8
), pp.
2390
2393
.
6.
Sarov
,
Y.
,
Ivanov
,
T.
,
Frank
,
A.
, and
Rangelow
,
I. W.
,
2011
, “
Thermally Driven Multi-Layer Actuator for 2D Cantilever Arrays
,”
Appl. Phys. A
,
102
(
1
), pp.
61
68
.
7.
Zhao
,
X.
, and
Dankowicz
,
H.
,
2006
, “
Characterization of Intermittent Contact in Tapping-Mode Atomic Force Microscopy
,”
ASME J. Comput. Nonlinear Dyn.
,
1
(
2
),
p
. 109.
8.
Raman
,
A.
,
Melcher
,
J.
, and
Tung
,
R.
,
2008
, “
Cantilever Dynamics in Atomic Force Microscopy
,”
Nano Today
,
3
(
1–2
), pp.
20
27
.
9.
Dick
,
A.
,
Balachandran
,
B.
, and
Yabuno
,
H.
,
2009
, “
Utilizing Nonlinear Phenomena to Locate Grazing in the Constrained Motion of a Cantilever Beam
,”
Nonlinear Dyn.
,
57
(
3
), pp.
335
349
.
10.
Jackson
,
S.
,
Gutschmidt
,
S.
,
Roeser
,
D.
, and
Sattel
,
T.
,
2016
, “
Development of a Mathematical Model and Analytical Solution of a Coupled Two-Beam Array With Nonlinear Tip Forces for Application to AFM
,”
Nonlinear Dyn.
,
87
(2), pp.
775
787
.
11.
Dankowicz
,
H.
, and
Schilder
,
F.
,
2013
,
Recipes for Continuation
,
SIAM
, Philadelphia, PA.
You do not currently have access to this content.