Langmuir 1994,10, 5-7
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Atomic Force Microscopy Probe Tip Visualization and Improvement of Images Using a Simple Deconvolution Procedure Peter Markiewicz and M. Cynthia Goh* Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario M5S 1A1, Canada Received August 2 6 , 1 9 9 9 A simple numerical procedure for separating the probe tip from images obtained by atomic force microscopy (AFM) is presented. The importance of this is 2-fold first, it provides a way of visualizing the probe tip in a nondestructive manner, which is useful in eliminating artifacta; second, it enables the deconvolutionof the probe tip from the image,resulting in a more accuratepicture of the sample. Examples of deconvolution using both an idealized tip and a real tip are given. Such a quick and effectiveprocedure enables incorporating the visualization of AFM tips as a daily routine.
Since its inception less than a decade ago, the atomic force microscope' has suffered the inevitable comparison with traditional electron microscopy. Unlike the electron microscope, very little sample preparation is required for the AFM, hence obviating the need for harsh treatments such as fixation, denaturing, and staining which could distort the actual structures that one is attempting to observe. The added ability to examine structures in their native fluids was a major attraction of the AFM, particularly for nonconductive material such as biological molecules. Furthermore, the AFM is capable of resolution down to molecular level for both conductive and nonconductive samples.2 However, studies involving highly three-dimensional structures can be complicated by the fact that although the vertical resolution is always excellent, the AFM produces misshapen lateral features on steeply sloped samples. Distortions in AFM images are, in part, due to an inherent fault of the imaging process; whereas an electron beam can be extremely focused, the AFM probe must have finite dimensions to be usable. In this report we would like to point out how the dimensions of the force-sensingtip used for AFM imaging can produce major distortions and how a simple numerical procedure can remove this effect producing a more accurate representation of the sample. AFM images are a reconstruction from digital data that comprise of the response of a probe tip to a sample's topography as the tip is raster scanned across the surface. Ideally, a single atom on the tip is responsible for the probing? Realistically,however,the probe tip, while small, is not a single atoma4 For the analyses of periodicity, packing, step height, and area of adsorbed species on most films, the finite size of the tip does not present a problem as these measurements are unaffected by the nonideal interactions between tip and sample. In cases where the sample is highly three dimensional, a number of distortions in the AFM data, both qualitatively and quantitatively, are obtained. An obvious case is where a cylindrical object lying on a flat surface can appear much wider than it is
* To whom correspondence should be addressed.
* Abstractpublishedin Advance ACS Abstracts, January 15,1994.
(1) Binnig, G.; Quate, C. F.; Gerber, Ch. Phys. Reu. Lett. 1986,56,930.
( 2 ) Frommer, J. Angew. Chem., Int. Ed. Engl. 1992,31, 1298. (3) Ohnesorge, F.; Binnig, G. Science 1993,260, 1461. (4) Presently, the most commonly employed tips are made of silicon nitride, square pyramidal in shape, with a nominal radiua at the apex of about 30 nm.19
0743-7463/94/2410-0005$04.50/0
high, as has been reported in the case of DNA.6 Although the height of the DNA strand is accurately measured, the AFM images show the width to be 3 to 4 times this value. In imaging deep crevices or steep features, the tip and its supporting structure are unable to penetrate due to their relatively large size, giving rise to poor determination of the depth of holes or the width of protuberances. Figure 1A illustrates the AFM imaging process for a sphere on a flat substrates6 The image obtained assumes that the tip apex is the sole contact point with the sample. This condition holds true as the tip moves along the flat substrate, but once the sample is encountered, the point of contact is no longer at the apex of the probe. This off-center contact prematurely raises the probe tip. The instrument, however, interprets this change in height as a real sample feature below the tip and ita reconstruction resulta in the shaded area in Figure 1A. For the sample shown, as the tip moves further along the sample, the distortion lessens until contact is once again established at the apices of both the tip and sample. After thismnnimnl vertical displacement the distortion resumes at the other side of the sample. The resulting image, which is a convolution of the geometry of the sample and the probe, features a correct sample height but an overestimated sample width. The distortions due to the finite width of the probe tip are most severe when the samples examined are approximately the size of the probe. In order to circumvent these problems, numerous attempta a t making tips with higher aspect ratios or smaller radii have been made.'-g These processes are limited by the fact that as the tip approaches atomic dimensions it becomes toofragile to withstand the forces encountered in the AFM. While ~
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(5) Murray, M. N.; Hamma, H. G.; Bezanilla, M.;Sano,T.; Ogletree,
D. F.; Kolbe, W.; Smith, C. L.; Cantor, C. R.; Spengler, S.; H " a , P. K.; Salmeron, M. R o c . Natl. Acad. Sci. U.S.A. 1993,90,3811. Hansma, H. G.; Vasenka, J.; Siegerist, C.; Kelderman, G.; Morrett, H.; Siheimer, R. L.; Elings, V.; Bustamante, C.;Hansma, P. K. Science 1992,256,1180. Thundat, T.; Warmack, R. J.; Allison, D. P.; Bottomley, L. A,; Lourenco, A. J.; Ferrell, T. L. J. Vac. Sci. Technol. A 1991, IO, 630. Allen, M. J.; Hud, N. V.; Balloch, M.; Tench, R. J.; Siekhaus, W.J.; Balhom, R. Ultramicroscopy 1992,424, 1095. (6) It is assumed that the tip doea not twist during scanning. Thii negleds any lateral forces or binding which could change the tilt of the tip. (7) Kado, H.; Yokoyama, K.; Tohda, T. Rev. Sci. Instrum. 1992,63, 3330. (8) Keller, D. J.; Chih-Chung, C. Surf. Sci. 1992,268, 333. Yamaki, M.; Miwa, T.; Yoshimura, H.; Nagayama, K. J. Vac.Sci. Teehn0l.B 1992, 10, 2447. (9) Wolter, 0.; Bayer, Th.; Greschner, J. J. Vac. Sci. Technol.B 1991, 9, 1353.
1994 American Chemical Society
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6 Langmuir, Vol. 10, No.1, 1994 A
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Figure 1. An illustration of the AFM imaging process for a spherical sample on a flat surface with a parabolic tip. (A) The data collected is for the tip apex as it moves across the sample, resulting in the shaded profile which is a combination of the two geometries. (B)To deconvolute the tip from the sample, the data obtained is etched away (as shown by the darker area) by placing a facsimile of the tip at each of the original data points (open circles). (C) Conversely, using the sample geometry at each original data point yields an image of the tip.
these new tips will lessen the problem of distorted images, they will not allow the full elimination of it. In the face of this technical limitation, one is forced to turn to a mathematical treatment of the data. Such a deconvolution treatment has been proposed using Legendre transforms assuming spherical,1° hyperbolic, and parabolicll tip geometries. The effectiveness of the procedure depends on how well this assumption corresponds to the actual tip. In this report we present an alternative deconvolution scheme based on knowing that the AFM data represents the apex position, as described in Figure 1. The approach is to position a facsimile of the tip at the acquiredpoints and recreate the surfaceby taking into account the physical space occupied by the tip. Thus, instead of merely indicating the position of the tip apex, the data now reflect the volume of the tip. The remaining AFM data correspond to a more realistic picture of the sample. (Note that information related to the areas which the tip could not access can still not be recovered.) In practice, the AFM image is recreated from the matrix containing the digitized topography. When a specific tip geometry is approximated, a second matrix containing a representation of the tip, scaled to correspond to the size of the AFM data, is computed. Each point from the original AFM file is used as the vertical displacement of the reconstructed tip apex, from which the location of the remainder of the tip can be calculated. A third data file initially contains the original AFM data, which is to be modified by the deconvolution process. With the tip position fiied, the surroundingdata points are interrogated to determine if they conflict with the tip geometry, as shown in Figure 1B. If the height of a point from the AFM data is less than that of the virtual tip, the data are left unaltered. Otherwise,the data are whittled down to the value of the tip geometry. Whereas the example illustrated in Figure 1B is in the plane of the page, the deconvolution program uses a three-dimensional tip. To a first approximation, an ideal mathematical model can be used for the tip, the simplest being a sphere. The tip dimensions can be estimateddirectly from the AFM images of samples on a flat substrate. By assuming spherical geometriesfor both the tip and the sample, the dimensions are calculated as d = w2/4h where d is the tip diameter and w is the apparent width measured for the sample of height h. The application of such deconvolution to an AFM image obtained by using a Nanoscope I1 (Digital Instruments, Santa Barbara, CA) is illustrated. A raw image of paired helical filaments (PHF),12 which were extracted from (10) Chicon, R.; Ortuno, M.; Abellan, J. Surf. Sci. 1987,181,107. (11) Keller, D. Surf. Sci. 1991,253,353. (12) Wisniewski, H. K.; Men, P. A.; Iqbal, K.J. Neuropathol. Exp. Neurol. 1984,43,643.
Figure 2. (A) Unprocessed images of PHF are correct in height but have distorted width. (B) Deconvolution using a 50-nm sphere diameter reveals a twisted ribbon structure,with a height and width of 12 nm.
Alzheimer's diseased brain and air-dried on mica, is given in Figure 2A. These appear as distorted ropelike structures with periodicity (a measurement unaffected by tip geometry) of 80 nm, in agreement with literature values.13 Maximal height and width are 12 and 50 nm, respectively. By use of the estimated 50-nm spherical tip diameter, the deconvoluted image (Figure 2B) reveals that a twisted ribbon structure was previously obscured by the tip.14 For larger samples, modeling the tip as a sphere is not sufficient as it fails to account for any irregularities that might be present. Hence, it is important to have information about the actual tip geometry. Furthermore, this information is also useful as defective tips can give rise to major qualitative changes in the images. The tip defects can be due to faulty manufacturing or could also be due to impurities picked up from the surface during the scan. It is generally found that someprobe tips give better images than others and that a defective tip can produce readily observable irregularities. In such cases, the usual procedure is to keep changing the cantilevers until a good tip is found. This procedure is quite problematic when one is exploring rare events and unknown samples, as one may have very little idea of what constitutes a "good" image. Rather than relying on the interpretation of the image quality, it is thus very important to have a way of visualizing the probe tip. Examination of the probe tip is usually performed using electron microscopy; unfortunately, this requires coating which changes the tip. Even within the same wafer of tips, a wide variation of quality has been found, which makes the assessment of tip quality by examination of a representative sample highly questionable. Hence, one needs a nondestructive way of examining the same probe tip that is used for imaging. Several methods of inferring tip information using the AFM have been attempted.15-17 We would like to show how deconvolution can be employedfor the visualization of the probe tip using the fact that the raw image obtained comprises both the tip and the sample. Thus, imaging a sample of known size and geometry provides a means of obtaining tip data (Figure 1C). Polybead-amino microspheres (Polysciences, Warrington, PA)18 were dried onto freshly cleaved mica and imaged using a variety of tips. The nominal diameter (260 nm) was used in the numerical routine. An image of a typical probe tip extracted in this manner is shown in (13) Crowther, R A. Roc. Natl. Acad. Sci. U S A . 1991,88,2288. (14) Pollanen, M. S.; Markiewin, P.; Bergeron, C.; Goh, M. C.
Submitted for publication. (15) Thundat, T.;Zheng,X.-Y.; Sharp,S. L.; Allison, D. P.; Warmack, R., J.; Joy, D. C.; Ferrell, T. L. Scanning Microsc. 1992,6,903. (16)Grutter,P.; Zimmerman-Edling,W.; Brodbeck, D. Appl. Phys.
Lett. 1992,60, 2741. L.; Heyvaert, (17) Hellemans,L.; Waeyaert,K.; Hennau,F.;St~~lunan, I.; Van Haesendonck, C. J . Vac. Sci. Technol. B 1991,9,1309. (18) Li, Y.; Lindsay, S. Rev. Sci. Instrum. 1991,62,2630.
Langmuir, VoZ. 10, No. 1, 1994 7
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Figure3. Tip informationobtained from using calibrationspheres for (A) a standard tip and (B) and a tip with a prominent outgrowth (double tip). The first column is of the tip contours (33 nm line spacing). The middle column is a representationof the data as seen from an oblique angle to compare with the scanning electron micrographs (SEM) shown in the third. All tip data have been rotated by 180' and inverted to reflect the positioning in ihe AFM. A
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Figure 4. (A) Raw images of the calibration spheres show exaggerated distortions when imaged with the defective tip in Figure 3B. The smaller hill to the lower right is a ghost image resulting from the double tip. (B) Using the tip information in the deconvolution procedure, a truer structure of the spherical samples is obtained.
Figure 3A. The open angle is square pyramidal in shape, as expected. If we attempt to fit a sphere to the apex of the pyramid, we obtain a radius of about 30 nm, in agreementwith literature values.lg The values were found to vary, most likely due to the polydispersity of the calibration spheres as indicated in their measured height which ranged from 250 to 275 nm. For the abnormal tip shown in Figure 3B, the radii and irregularities are verified by SEM estimates. A slight tilt to the visualized tips are apparent in all figures. This reflects the fact that the cantilevers were slightly bent from their free standing position which, for the Nanoscope 11, is approximately 16'. With the shape of the probe tip obtained as an AFM data file, it is possible to use this information instead of an idealized shape in order to separate it out of the AFM (19) Albrecht,T. R.; Akamine,S.; Carver,T. E.; Quate, C. F. J. Vac. Sci. Technol. A 1990,8,3386.
image and get a more realistic picture of the sample under study. Figure 4A illustrates results of imaging the calibration spheres with the double tip shown in Figure 3B. It would have been easy to misinterpret this image were it not known beforehand that the samplesare spheres. Using the tip data, this original image can be processed to eliminate the tip effect, thus producing the final image of the calibration spheres in Figure 4B. It can be seen that the deconvoluted images show a spherical structure. We have presented a simple algorithm for separating out the tip and sample in the images obtained by AFM. Using ideal tip geometries makes possible the reinterpretation of previously obtained images of structures such as DNA. The more powerful offshoot of the deconvolution process is the ability of directly visualizing the AF'M tip. The information regarding the actual tip geometry can then be used in deconvoluting the tip from the AF'M images. This procedurehas been shown useful in providing more reliable quantitative measurements of sample width, as well as clarifyingsome features of the sample. Although the examples given here used spheres of known sizes, the deconvolutionschemecan employother surface structures to visualize the AFM probe tip in a nondestructive manner; in particular, microlithographic techniques for creating standard patterns can be used for tip calibration. Since the tip visualization is simple, quick, and nondestructive, it is suggested that this routine should be a standard procedure for AFM users both before and after imaging. This would ensure that the tip has not been deformed and/or contaminated in the imaging process and can subsequently be used to deconvolute its effects from the sample. Acknowledgment. We acknowledge support from NSERC Canada and the Centre of Excellence for Molecular and Interfacial Dynamics.
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