Surface recovery in scanning probe microscopy

Scanning probe microscopy (SXM), which includes techniques such as scanning tunneling microscopy (STM) and scanning force microscopy (SFM), is becoming increasingly popular for analyzing surface structure at the sub-micron level. As the probe used for scanning is non- ideal, the image output by SXM is dependent on the shape and size of the probe. The use and success of SXM strongly depend on methods for ensuring the accuracy of the images produced by SXM. In this paper, we derive models of the effects of the probe shape geometry on the image produced by SXM. Methods are formulated for recovering the true surface from the imaged surface and for indicating where the surface reconstruction is exact and where it is uncertain. We formulate these methods both for images scanned in a `contact' mode and those scanned in a `non-contact' mode. It is shown that scanning in a non-contact mode by a non- ideal probe is equivalent to scanning in a non-contact mode by an ideal probe followed by scanning in a contact mode by the non-ideal probe. The methods developed in this paper can be used to recover a surface scanned by a scanning probe microscope, given the shape of the probe used for scanning, and for visualizing the scanning and recovery of surfaces by different probe shapes.