High-frequency response of atomic-force microscope cantilevers

Joseph A Turner, Sigrun Hirsekorn, Ute Rabe, Walter Arnold

Research output: Contribution to journalArticle

146 Citations (Scopus)

Abstract

Recent advances in atomic-force microscopy have moved beyond the original quasistatic implementation into a fully dynamic regime in which the atomic-force microscope cantilever is in contact with an insonified sample. The resulting dynamical system is complex and highly nonlinear. Simplification of this problem is often realized by modeling the cantilever as a one degree of freedom system. This type of first-mode approximation (FMA), or point-mass model, has been successful in advancing material property measurement techniques. The limits and validity of such an approximation have not, however, been fully addressed. In this article, the complete flexural beam equation is examined and compared directly with the FMA using both linear and nonlinear examples. These comparisons are made using analytical and finite difference numerical techniques. The two systems are shown to have differences in drive-point impedance and are influenced differently by the interaction damping. It is shown that the higher modes must be included for excitations above the first resonance if both the low and high frequency dynamics are to be modeled accurately.

Original languageEnglish (US)
Pages (from-to)966-979
Number of pages14
JournalJournal of Applied Physics
Volume82
Issue number3
DOIs
StatePublished - Aug 1 1997

Fingerprint

frequency response
microscopes
approximation
simplification
dynamical systems
degrees of freedom
damping
atomic force microscopy
impedance
low frequencies
excitation
interactions

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

High-frequency response of atomic-force microscope cantilevers. / Turner, Joseph A; Hirsekorn, Sigrun; Rabe, Ute; Arnold, Walter.

In: Journal of Applied Physics, Vol. 82, No. 3, 01.08.1997, p. 966-979.

Research output: Contribution to journalArticle

Turner, Joseph A ; Hirsekorn, Sigrun ; Rabe, Ute ; Arnold, Walter. / High-frequency response of atomic-force microscope cantilevers. In: Journal of Applied Physics. 1997 ; Vol. 82, No. 3. pp. 966-979.
@article{515f7e1fcd47443ab05417f6efad16f3,
title = "High-frequency response of atomic-force microscope cantilevers",
abstract = "Recent advances in atomic-force microscopy have moved beyond the original quasistatic implementation into a fully dynamic regime in which the atomic-force microscope cantilever is in contact with an insonified sample. The resulting dynamical system is complex and highly nonlinear. Simplification of this problem is often realized by modeling the cantilever as a one degree of freedom system. This type of first-mode approximation (FMA), or point-mass model, has been successful in advancing material property measurement techniques. The limits and validity of such an approximation have not, however, been fully addressed. In this article, the complete flexural beam equation is examined and compared directly with the FMA using both linear and nonlinear examples. These comparisons are made using analytical and finite difference numerical techniques. The two systems are shown to have differences in drive-point impedance and are influenced differently by the interaction damping. It is shown that the higher modes must be included for excitations above the first resonance if both the low and high frequency dynamics are to be modeled accurately.",
author = "Turner, {Joseph A} and Sigrun Hirsekorn and Ute Rabe and Walter Arnold",
year = "1997",
month = "8",
day = "1",
doi = "10.1063/1.365935",
language = "English (US)",
volume = "82",
pages = "966--979",
journal = "Journal of Applied Physics",
issn = "0021-8979",
publisher = "American Institute of Physics Publising LLC",
number = "3",

}

TY - JOUR

T1 - High-frequency response of atomic-force microscope cantilevers

AU - Turner, Joseph A

AU - Hirsekorn, Sigrun

AU - Rabe, Ute

AU - Arnold, Walter

PY - 1997/8/1

Y1 - 1997/8/1

N2 - Recent advances in atomic-force microscopy have moved beyond the original quasistatic implementation into a fully dynamic regime in which the atomic-force microscope cantilever is in contact with an insonified sample. The resulting dynamical system is complex and highly nonlinear. Simplification of this problem is often realized by modeling the cantilever as a one degree of freedom system. This type of first-mode approximation (FMA), or point-mass model, has been successful in advancing material property measurement techniques. The limits and validity of such an approximation have not, however, been fully addressed. In this article, the complete flexural beam equation is examined and compared directly with the FMA using both linear and nonlinear examples. These comparisons are made using analytical and finite difference numerical techniques. The two systems are shown to have differences in drive-point impedance and are influenced differently by the interaction damping. It is shown that the higher modes must be included for excitations above the first resonance if both the low and high frequency dynamics are to be modeled accurately.

AB - Recent advances in atomic-force microscopy have moved beyond the original quasistatic implementation into a fully dynamic regime in which the atomic-force microscope cantilever is in contact with an insonified sample. The resulting dynamical system is complex and highly nonlinear. Simplification of this problem is often realized by modeling the cantilever as a one degree of freedom system. This type of first-mode approximation (FMA), or point-mass model, has been successful in advancing material property measurement techniques. The limits and validity of such an approximation have not, however, been fully addressed. In this article, the complete flexural beam equation is examined and compared directly with the FMA using both linear and nonlinear examples. These comparisons are made using analytical and finite difference numerical techniques. The two systems are shown to have differences in drive-point impedance and are influenced differently by the interaction damping. It is shown that the higher modes must be included for excitations above the first resonance if both the low and high frequency dynamics are to be modeled accurately.

UR - http://www.scopus.com/inward/record.url?scp=5244345703&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=5244345703&partnerID=8YFLogxK

U2 - 10.1063/1.365935

DO - 10.1063/1.365935

M3 - Article

VL - 82

SP - 966

EP - 979

JO - Journal of Applied Physics

JF - Journal of Applied Physics

SN - 0021-8979

IS - 3

ER -