Comparison between a scanned (left) and a geometrical corrected
(right) STM image
Gray-scale plot of the topography of a copper(111) 1x1 surface covering an
area of 35 A x 35 A, reconstructed from a differential STM image [1]. (a)
shows geometrical distortions denoted by three crossing black lines and
(b) is the corrected image.
Correction of geometrical distortions in scanning tunneling and atomic
force microscopes caused by piezo hysteresis and nonlinear feedback
Geometrical distortions of scanning tunneling or atomic force microscope
pictures can be caused by delayed response of the piezo-ceramics and
errors of the nonlinear feedback system. The images are adversely affected
mostly at the boundaries where the tip motion is reversed and also at
surface steps. Assuming logarithmic corrections for the time dependence
of the piezo response and for the feedback nonlinearity, it is shown how
these errors can be eliminated. The procedure is applied to test
samples: well-ordered clean single-crystal copper and gold surfaces, for
which the correction parameters are determined as a function of temperature,
scan velocity, and the place where the tips move into the scanned
area. Gathering this information from various test samples, a data base
can be built up that can be used to correct other samples recorded under
the same conditions.
Gray-scale image of STM topography from a gold(110) surface
exhibiting 1x2 reconstruction recorded at low temperatures [2].
(a) and (b) are difference values between the successive scans recorded from
the right to the left and the left to the right. The area is 345 A x 307 A,
(a) shows large differences at the step borders as a result of geometrical
distortions and (b) small differences after corrections. (c) is the average of
the corrected images of both scan directions.
Two successive scans from last figure taken at a y-value of 5 A away from the
top (horizontal black line in last figure). To avoid a merging of the curves,
the trace of the scan from left to right is shifted upward and that from right
to left downward by 0.5 A. The thicker curve between them shows the averaged
corrected scans. The stars denote the locations of rather strong oscillations.
To obtain horizontal envelopes of the surface corrugation (except in the
regions where the steps occur) a smooth function of the entire scanned area
is subtracted.
[1] E.P. Stoll and J.K. Gimzewski, J. Vac. Sci. Technol. B, 9, 643
(1991).
[2] R. Gaisch, J.K. Gimzewski, B. Reihl, R.R. Schlittler, W. Schneider,
E.P. Stoll, and M. Tschudy, unpublished results (1992).
For more information see:
Correction of geometrical distortions in scanning tunneling and atomic
force microscopes caused by piezo hysteresis and nonlinear feedback
Erich Stoll, Rev. Sci. Instrum.,
65, 2868 (1994).
