True atomic resolution in vacuum with a force microscope is now obtained routinely by using the frequency shift of an oscillating cantilever as the imaging signal. Here, a calculation is presented that relates the frequency shift to the forces between tip and sample for both large and small oscillation amplitudes. Also, the frequency versus distance data for van der Waals dominated tip-sample interactions is related to the geometry of the tip apex. Published frequency versus distance data are used to show that the apex of tips providing atomic resolution is faceted and not rounded. Further, an extended jump-to-contact criterion for large amplitudes is established.

• Received 8 July 1997

DOI:https://doi.org/10.1103/PhysRevB.56.16010

This article appears in the following collection:

Scanning Probe Microscopy: From Sublime to Ubiquitous

This collection marks the 35th anniversary of scanning tunneling microscopy (STM) and the 30th anniversary of atomic force microscopy (AFM). These papers, all published in the Physical Review journals, highlight the positive impact that STM and AFM have had, and continue to have, on physical science research. The papers included in the collection have been made free to read.