SPMW A fresh look to amplitude-modulation AFM: Force minimization, interaction measurement, and the quest for high resolution

By Udo D. Schwarz

Yale University

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Frequency modulation atomic force microscopy (FM-AFM) has been able to deliver high-resolution atomic-scale images in ultrahigh vacuum for over one decade. In addition, there have been recent reports where atomic resolution has been achieved in air and liquids using FM-AFM [1]. Achieving molecular resolution using amplitude modulation atomic force microscopy (AM-AFM) has been much more challenging [2,3]. It is widely believed that the tip-sample interaction action forces have to be reduced compared to standard AM-AFM operation for increased resolution. The so-called Q-Control method, allowing the active modification of the effective cantilever damping by increasing or decreasing the apparent Q-value of the cantilever, promises to reduce tip-sample interactions.

To explore the potential of AM-AFM for high-resolution applications in air and liquids, we analyzed the imaging process of Q-controlled AM-AFM. Analytical as well as numerical approaches are applied to solve the equation of motion describing the cantilever dynamics with and without Q-Control in the presence of a model tip-sample interaction force. Based on this analysis, the characteristics of Q-controlled AM-AFM are compared to conventional AM-AFM carried out in amplitude modulation mode without active Q-Control (“tapping mode”) as well as to FM-AFM. Explicit consideration of tip-sample forces permits insight into the imaging properties of Q-controlled AM-AFM. It is found that an increased Q-factor prevents the oscillating cantilever to jump into a repulsive imaging regime during tip-sample approach, which often occurs during conventional tapping mode imaging in air. In addition, our analysis reveals which parts of the tip-sample force curve are contributing to contrast formation for the different imaging conditions. Based on these findings, we conclude that under ambient conditions, the restriction of the maximal tip-sample force to specific parts of the attractive regime, which is triggered by the activation of the Q-Control feedback, is the main reason for the enhanced imaging quality reported in several experimental studies in air if compared to conventional tapping mode imaging without Q-Control [4]. Despite this improvement, atomic resolution might still not be achieved since the regime of short-ranged attractive forces might not be reached, i.e., forces might actually be too low. In contrast, it is the almost complete absence of an attractive interaction that causes the resolution deficits in liquids. Nonetheless, even in liquids repulsive forces can by greatly lowered by the application of Q-Control [5]. Finally, we present a method that allows recovering the tip-sample interaction potential from the simultaneous measurement of amplitude-distance and phase-distance curves, allowing local force spectroscopy similar to the one only possible so far for FM-AFM in vacuum [6].


Udo D. Schwarz graduated in 1989 from the University of Basel, Switzerland, receiving his Ph.D. in physics from the same institution in 1993. Subsequently, he continued his work as a staff scientist at the Institute of Applied Physics of the University of Hamburg, Germany, where completed his “habilitation” (German accreditation degree for lecturers) in 1999. In 2001, Prof. Schwarz moved to the Materials Science Department of the Lawrence Berkeley National Laboratory in Berkeley, California. Since mid-2002, he works as an associate professor at Yale’s Mechanical Engineering Department. His research interests are in nanomechanics, nanotribology, and the local measurement of atomic-scale interactions including high-resolution atomic-scale imaging. More specifically, he uses scanning probe microscopy techniques (predominantly scanning force microscopy) to study problems in contact mechanics on the nanometer scale, friction, adhesion, lubrication, and the physics of dielectrics, semiconductors, and metals.


In conjunction with H. Hölscher (Yale University)


  1. T. Fukuma et al., Appl. Phys. Lett. 86, 034103; 86, 193108; 87, 034101 (2005).
  2. Y. Seo et al., Appl. Phys. Lett. 83, 1860 (2003).
  3. D. Klinov and S. Maganov, Appl. Phys. Lett. 84, 2697 (2004).
  4. H. Hölscher, D. Ebeling, and U. D. Schwarz, J. Appl. Phys. 99, 084311 (2006).
  5. H. Hölscher and U. D. Schwarz, App. Phys. Lett. 89, 073117 (2006)
  6. H. Hölscher, Appl. Phys. Lett. (in press).

Cite this work

Researchers should cite this work as follows:

  • Udo D. Schwarz (2007), "SPMW A fresh look to amplitude-modulation AFM: Force minimization, interaction measurement, and the quest for high resolution," http://nanohub.org/resources/2208.

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