LATERAL DISPLACEMENT MAPS OBTAINED FROM
SCANNING PROBE MICROSCOPE IMAGES
A DISSERTATION
Presented to the Faculty of the Graduate School of the
UNIVERSITY OF MISSOURI-ROLLA
and
UNIVERSITY OF MISSOURI-ST. LOUIS
In Partial Fulfillment of the Requirements for the Degree
DOCTOR OF PHILOSOPHY
in
PHYSICS
1997
Phil B. Fraundorf, Advisor
Bernard J. Feldman
Edward B. Hale
Oran A. Pringle
Joseph W. Newkirk
(All rights reserved 1997, Chang Shen)
We have investigated a method to study the nanomechanical properties of surfaces by correlation-based lateral displacement mapping. The method is applicable to all scanning tip microscopes without additional special hardware. The approach is also relevant to other displacement mapping tasks, such as stereo image analysis, and can be extended to n-dimensions as well. By studying lateral differences of two images of essentially the same object, we obtained quantitative information on either the physical changes of the object or the sample-probe interaction during image acquisition. In particular, vector lateral displacements were used to study the changes between image pairs and can also be used to convert a two-dimensional stereo to a three-dimensional topographic map.
We applied this method to the study of surface friction using air-based scanning tunneling images. By studying the lateral displacement of a pair of scanning tip microscopy images of a hologram sample, we showed that the lateral displacement map has a doubled spatial frequency in comparison to the topographic hologram grating structure. A constant normal force model was used to interpret this result. This explanation works well if the friction force was assumed proportional to the normal force. A theoretical model was also offered to explain the differences between lateral-force and scanning-force microscope images.
In order to infer the lateral force from measured lateral displacements, we assumed a continuum model of tip bending under lateral force. Two approaches, one analytical and one numerical, were used. The results suggested that tips of some shapes might be very sensitive to lateral forces, enabling study of scan-dependent transverse forces in high vacuum STM.