0 Copyright 1993 American Chemical Society
SEPTEMBER 1993
VOLUME 9, NUMBER 9
Letters Distance Measurements by Atomic Force Microscopy on the Angstrom Scale: The Effect of the Specimen Height Daniel Snbtivy and G. Julius Vancso' Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario M5S lA1, Canada Received May 10,1993 Interatomic distances obtained on muscovite mica in atomic force microscopy (AFM) experiments are discussed as a function of specimenthickness. It is shown that a systematicerror in AFM can be eliminated by using a correction factor which depends on the length of the tube of the piezo scanner used. Various forms of scanning probe microscopy (SPM)' which were developed since the advent of the scanning tunneling microscope2have been extensivelyused to study the arrangement of moleculesat surfaces of solids. Surface reconstruction, monomolecular layers, and crystal structures in two dimensions can now be studied from a true molecular perspective,' to mention just a few examples. Naturally, quantitative analyses of interatomic or intermolecular distances a t the sample surface require proper calibration of the microscopes. This can be done in atomic force microscopy (AFM)3 if the nanograph of a sample with known atomic/molecular structure is available. A sample commonly used for this purpose is muscovite mica which yields consistent and easy-to-obtain AFM images. The crystal structure of muscovite mica (an Al silicate with K+ counterions) has a 5.2-A repeat unit within the hexagonal layers of the mica sheet.4 In this paper AFM nanographs of muscovite mica will be studied at different sample thicknesses to show that sample thickness has a significant influence on intermolecular/interatomic distances obtained by AFM in the angstrom scale. (1) Scanning TunnelingMicroscopy Vol.Zand II; Ghtherodt, H.-J., Wiesendanger, R., Eds.; Springer: Berlin, 1992. (2) Binnig, G.; Rohrer, H. Reo. Mod. Phys. 1986,59,615. (3)Binnig, G * Quate, C. F.; Gerber, C. Phys. Reu. Lett. 1986,56,930. (4) Laudolt-Bhtein, Zahlenwerte undhtnktionen;Eucken,A., Ed.; Springer: Berlin, 1965; Vol. 1, Part 4, p 109.
Table I. Repeat Dirtanoe of Mioa Imager Obtained by AFM EB E Function of Sample Thicknerr sample thickness repeat diatance etandard deviation (")
(A)
(+A)
0.96 1.81 2.65 3.49
5.38 4.93 4.61 4.30
0.23 0.12
0.09 0.08
Commercial AFM instrumentation was pioneered by Digital Instruments with their NanoScope line. These instruments includevarious scan heads for surfacestudies in different size ranges. The feature common to all scan heads is a piezoelectric tube which moves the sample with respect to the stationary AFM tip-cantilever probe. The length of the piezo tube varies dependingon the maximum scan size targeted. For molecular/atomic studies, the socalled A scanner is used. This scanner has a piezo tube of ca. 15mm length. During the scam of flat surfaces, the tube is moved in the x-y plane with a tube axis in the z direction, The sample is usually fued with an adhesive to a magnetic disk of typically 1.0 mm thickness (thisvalue varies somewhat). This disk is held in place by a magnet at the top of the tube. While scanning is performed, preselected locations at the sample surface will be moved on a spherical surface, which, in the case of the A scanner, has an area maximum ca. 1 pm X 1 pm. The center of this sphere lies on the symmetry (or z ) axis of the tube, beneath
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Langmuir, Vol. 9;No. 9, 1993
Letters
Figure 1. (a, left) AFM image of muscovite mica: sample thickness, 0.96 mm; scan size, 50 A X 50 A. (b,right) AFM image of muscovite mica: sample thickness, 3.49 mm; scan size, 50 A X 50 A. 1.3 1
I
1.2 0
1.1 C .I
: 1.0
uE
0.9
0.8
i 0
,
, 1
.
, 2
.
Sample thickness
d hml
, 3
.
I 4
Figure 2. Correctionfactor vs. specimenthickness for mica AFM images.
the scanned area. For this geometry (with the given radius and circumference) it is clear that, for all practical purposes, the curvature of the scanned x-y spot can be neglected. On the other hand, as this study shows, specimen thickness influences interatomic/intermolecular distances obtained on AFM nanographs. Obviously this effect is more significant if short piezo tubes are used, since the length of the radius of the sphere on which the specimen points are moved increases with an increase in tube length. The influence of specimen thickness was studied on muscovite mica (supplied by J. B. EM Services Inc., Quebec, Canada) using a NanoScope I1 (Digital Instruments) system, an A type scan head and NanoTip cantilevers with a nominal force constant of 0.38 N m-l. Imaging was performed by utilizing the “height” imaging mode at a scan rate of 26 Hz. The high pass filter was set to 4 and the low pass filter to 1. The same mica specimen was studied and the distance of the scanned surface from the top end at the piezo tube was varied by using different numbers of magnetic sample holder disks. The thickness of the disks was measured by a Nikon profile projector (Model 6C) which allows projection and thickness measurements without mechanical contact. Typical mica nanographs, reproduced in parts a and b of Figure 1,respectively, show the well-known features of
AFM mica images. The specimen was mounted on one sample holder disk (specimen and disk thickness 0.96 mm) for the scan shown in Figure l a while four disks were used (resulting in a total thickness of specimen and disks of 3.49 mm) for the nanograph captured in Figure lb. The nominal scan size for both images was the same and was obtained by using the supplier’s calibration data (Digital Instruments). It is clear that the distancesbetween the spotlikefeatures on Figure l a are larger than the features shown in Figure lb. How can data then be obtained without a systematic error? To determine a “true” distance value, a correctipn factor C(d)must be used to rescale each individual image and take into account the different sample thicknesses d. The value of C(d)is defined as the quotient of the observed distance obtained at given specimen thicknesses and the expected 5.2-Arepeat distance. The length of the observed repeat unit was determined in this study by using the autocorrelation function of at least ten images for each sample height. Packing data were averaged for the three possible directions of the hexagonal lattice of mica. The results with the standard deviation are shown in Table I. By use of the repeat distance values obtained, the correction factor as a function of d was determined and plotted in Figure 2. A linear extrapolation of data for a zero packing distance yielded a radius of r = 9.56 mm for the sphere on which the scanned area is located at d = 0. In conclusion,a proper rescaling of the nanographs using the procedure described above to correct the calibration eliminates an important systematic error in AFM experiments.
Acknowledgment. This work was financially supported by the Ontario Centre for Materials Research and by the Natural Sciences and Engineering Research Council of Canada. The authors wish to thank Ms. Anne Klemperer for her help with the preparation of the manuscript.
