The atomic force microscope (AFM) system has evolved into a useful tool for direct measurements of intermolecular forces with atomic-resolution characterization that can be employed in a broad spectrum of applications. The non-contact AFM offers unique advantages over other contemporary scanning probe techniques such as contact AFM and scanning tunneling microscopy, especially when utilized for reliable measurements of soft samples (e.g., biological species). Current AFM imaging techniques are often based on a lumped-parameters model and ordinary differential equation (ODE) representation of the micro-cantilevers coupled with an adhoc method for atomic interaction force estimation (especially in non-contact mode). Since the magnitude of the interaction force lies within the range of nano-Newtons to pica-Newtons, precise estimation of the atomic force is crucial for accurate topographical imaging. In contrast to the previously utilized lumped modeling methods, this paper aims at improving current AFM measurement technique through developing a general distributed-parameters base modeling approach that reveals greater insight into the fundamental characteristics of the microcantilever-sample interaction. For this, the governing equations of motion are derived in the global coordinates via the Hamilton’s Extended Principle. An interaction force identification scheme is then designed based on the original infinite dimensional distributed-parameters system which, in turn, reveals the unmeasurable distance between AFM tip and sample surface. Numerical simulations are provided to support these claims.

1.
Goeken
,
M.
, and
Kempf
,
M.
,
1999
, “
Microstructural Properties of Superalloys Investigated by Nanoindentations in an Atomic Force Microscope
,”
Acta Mater.
,
47
(
3
), pp.
1043
1052
.
2.
Kempf
,
M.
,
Go¨ken
,
M.
, and
Vehoff
,
H.
,
1998
, “
Nanohardness Measurements for Studying Local Mechanical Properties of Metals
,”
Appl. Phys. A: Mater. Sci. Process.
,
66
, pp.
S843–S846
S843–S846
.
3.
Nagashima
,
N.
,
Matsuoka
,
S.
, and
Miyahara
,
K.
,
1996
, “
Nanoscopic Hardness Measurement by Atomic Force Microscope
,”
JSME International Journal, Series A: Mechanics and Material Engineering
,
39
(
3
), pp.
456
462
.
4.
Yamamoto
,
A.
,
Watanabe
,
A.
,
Tsubakino
,
H.
, and
Fukumoto
,
S.
,
2000
, “
AFM Observations of Microstructures of Deposited Magnesium on Magnesium Alloys
,”
Materials Science Forum
,
350
, pp.
241
246
.
5.
Gahlin
,
R.
, and
Jacobson
,
S.
,
1998
, “
Novel Method to Map and Quantify Wear on a Micro-Scale
,”
Wear
,
222
(
2
), pp.
93
102
.
6.
Miyahara
,
K.
,
Nagashima
,
N.
,
Ohmura
,
T.
, and
Matsuoka
,
S.
,
1999
, “
Evaluation of Mechanical Properties in Nanometer Scale Using AFM-Based Nanoindentation Tester
,”
Nanostruct. Mater.
,
12
(
5
), pp.
1049
1052
.
7.
Sundararajan
,
S.
, and
Bhushan
,
B.
,
2001
, “
Development of a Continuous Microscratch Technique in an Atomic Force Microscope and Its Application to Study Scratch Resistance of Ultrathin Hard Amorphous Carbon Coatings
,”
J. Mater. Res.
,
16
(
2
), pp.
437
445
.
8.
Chen
,
W.
,
Ahmed
,
H.
, and
Nakazoto
,
K.
,
1995
, “
Coulomb Blockade at 77 K in Nanoscale Metallic Islands in a Lateral Nanostructure
,”
Appl. Phys. Lett.
,
66
(
24
), p.
3383
3383
.
9.
Klein
,
D. L.
,
McEuen
,
P. L.
,
Katari
,
J. E. B.
,
Roth
,
R.
, and
Alivisatos
,
A. P.
,
1996
, “
Approach to Electrical Studies of Single Nanocrystals
,”
Appl. Phys. Lett.
,
68
(
18
), p.
2574
2574
.
10.
Bezryadin
,
A.
,
Dekker
,
C.
, and
Schmid
,
G.
,
1997
, “
Electrostatic Trapping of Single Conducting Nanoparticles Between Nanoelectrodes
,”
Appl. Phys. Lett.
,
71
(
9
), pp.
1273
1275
.
11.
Basso, M., Giarre, L., Dahleh, M., and Mezic, I., 1998, “Numerical Analysis of Complex Dynamics in Atomic Force Microscopes,” Proceedings of the IEEE Conference on Control Applications, Trieste, Italy, pp. 1026–1030.
12.
Fung
,
R.
, and
Huang
,
S.
,
2001
, “
Dynamic Modeling and Vibration Analysis of Atomic Force Microscope
,”
ASME J. Vibr. Acoust.
,
123
, pp.
502
509
.
13.
Ashhab
,
M.
,
Salapaka
,
M.
,
Dahleh
,
M.
, and
Mezic
,
I.
,
1999
, “
Dynamical Analysis and Control of Microcantilevers
,”
Automatica
,
35
, pp.
1663
1670
.
14.
Hsu, S., and Fu, L. 1999, “Robust Output High-Gain Feedback Controllers for the Atomic Force Microscope Under High Data Sampling Rate,” Proceedings of the IEEE International Conference on Control Applications, Kohala Coast-Island, HI, pp. 1626–1631.
15.
Banks
,
H.
, and
Inman
,
D.
,
1991
, “
On Damping Mechanisms in Beams
,”
ASME J. Appl. Mech.
,
58
, pp.
716
723
.
16.
Dadfarnia, M., Jalili, N., Xian, B., and Dawson, D. M., 2003, “An Investigation of Damping Mechanisms in Translational Euler-Bernoulli Beams Using a Lyapunov-Based Stability Approach,” Proceedings of the 2003 ASME International Mechanical Engineering Congress and Exposition, Symposium on Active Vibration and Noise Control, Washington DC, November 2003.
17.
Fang, Y., Dawson, D., Feemster, M., and Jalili, N., 2002, “Nonlinear Control Techniques for the Atomic Force Microscope System,” Proceedings of 2002 International Mechanical Engineering Congress and Exposition (IMECE’02), New Orleans, Louisiana.
18.
Fang, Y., Feemster, M., Dawson, D., and Jalili, N., 2002, “Active Interaction Force Identification for Atomic Force Microscope Applications,” Proceedings of 41st IEEE Conference on Decision Control (CDC’02), Las Vegas, Nevada.
19.
Slotine, J., and Li, W., 1991, Applied Nonlinear Control, Prentice Hall, Englewood Cliffs, New Jersey, 1991.
20.
Dixon, W. E., Dawson, D. M., Zergeroglu, E., and Behal, A., 2001, Nonlinear Control of Wheeled Mobile Robots, Springer-Verlag, London Ltd.
21.
Kristic, M., Kanellakopoulos, I., and Kokotovic, P., 1995, Nonlinear and Adaptive Control Design, John Wiley and Sons, Inc., New York.
22.
Diken
,
H.
,
2000
, “
Vibration Control of a Rotating Euler-Bernoulli Beam
,”
J. Sound Vib.
,
232
(
3
), pp.
541
551
.
23.
Luo
,
Z.-H.
, and
Guo
,
B.-Z.
,
1997
, “
Shear Force Feedback Control of a Single-Link Flexible Robot With a Revolute Joint
,”
IEEE Trans. Autom. Control
,
42
(
1
), pp.
53
65
.
24.
Kasai, S., and Matsuno, F., 2000, “Force Control of One-link Flexible Arms Mounted on a Linear Motor With PD and Shear Force (PDSF) Feedback,” IECON Proceedings (Industrial Electronics Conference), 26th Annual Conference of the IEEE Electronics Society IECON 2000, Nagoya, pp. 195–200.
25.
Luo
,
Z.-H.
, and
Feng
,
D.-X.
,
1999
, “
Nonlinear Torque Control of a Single-Link Flexible Robot
,”
J. Rob. Syst.
,
16
(
1
), pp.
25
35
.
26.
Rabe
,
U.
,
Turner
,
J.
, and
Arnold
,
W.
,
1998
, “
Analysis of the High Frequency Response of Atomic Force Microscope Cantilevers
,”
Appl. Phys. A: Mater. Sci. Process.
,
A66
(
7
), pp.
277
282
.
27.
Fleming
,
A.
, and
Moheimani
,
S.
,
2003
, “
Adaptive Piezoelectric Shunt Damping
,”
Smart Mater. Struct.
,
12
(
1
), pp.
18
28
.
28.
Fleming
,
A.
,
Behrens
,
S.
, and
Moheimani
,
S.
,
2002
, “
Optimization and Implementation of Multimode Piezoelectric Shunt Damping Systems
,”
IEEE/ASME Trans. Mechatron.
,
7
(
1
), pp.
87
94
.
29.
Luo
,
Z.-H.
,
Kitamura
,
N.
, and
Guo
,
B.-Z.
,
1995
, “
Shear Force Feedback Control of Flexible Robot Arms
,”
IEEE Trans. Rob. Autom.
,
11
(
5
), pp.
760
765
.
30.
Meirovitch, L., 1997, Principles and Techniques of Vibrations, Prentice Hall, Upper Saddle River, New Jersey.
You do not currently have access to this content.