Langmuir 1994, 10, 1340-1344
1340
Height Amplifications of Scanning Tunneling Microscopy Images in Air John T. Woodward and Joseph A. Zasadzinski' Department of Physics and Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, Santa Barbara, California 93106 Received December 20, 1993. I n Final Form: February 28, 1994" Scanning tunneling microscopy (STM) measurements in air often show variations in feature heights accompaniedby surfacedeformation inconsistent with an idealized,noninteractingscanningtip and surface separated by a vacuum gap. Such deformation is usually ascribed to enhanced contact forces due to a highly curved liquid meniscus linking the STM (or atomic force microscope) tip to the sample, although little quantitative information is available about surface deformation, especially for STM images. We used standard STM techniquesto image chemically homogeneousplatinum replicas of Langmuir-Blodgett multilayers with known step heights in humid air and in a dry Nz atmosphere. Identical surface features were amplified when imaged in humid air but reverted to their original height on imaging in dry Nz.This shows that capillary forces can be the dominant interaction between tip and sample, even in STM, and that these forces are capable of deforming soft materials.
Introduction Scanning tunneling microscope (STM)l images often exhibit unrealistic height measurements of surface features or feature heights that change from place to place or from time to time on a sample.2 A number of theoretical models have proposed that interactions between the STM tip and sample due to specific quantum and atomic scale interact i o n ~or , ~that bulk compression by the scanning tip or by solid surface contamination at regions of low surface cond~ctivity4~~ can lead to amplifications of surface features. However, much of this work has been limited to specific tip-sample interactions or specific surfaces, usually under ultrahigh vacuum or other specialized conditions. While it has been generally recognized in atomic force microscopy that strong capillary forces arise when the AFM tip (which is also covered with a layer of contamination) contacts the thin liquid film of water or other contamination that is common to most surfaces when imaging in humid air,68 less attention has been given to these same capillary forces altering STM images. In fact, in related papers on STM imaging by ionic conduction through condensed water films, Yuan et aL9Joconcluded that the local forces and pressures developed within a
* To whom correspondenceshould be addressed at the Department of Chemical and Nuclear Engineering. Abstract published in Advance ACS Abstracts, April 1, 1994. (1)Binnig, G.; Rohrer, H.; Gerber, Ch.; Weible, E. Phys. Reu. Lett. 1982, 49, 57. (2) Hansma, P. K.; Tersoff, J. J. Appl. Phys. 1987,61, R1. Hallmark, V. M.; Chiang, S.; Rabolt, J. F.; Swalen, J. D. Phys. Reu. Lett. 1987,59, 2879. Binnig, G.; Fuchs, H.; Gerber, Ch.; Rohrer, H.; Stoll, E.; Tosatti, E. Europhys. Lett. 1986, I, 31. Coleman, R. V. Phys. Reu. Lett. 1985,55, 394. (3) Chen, C. J. Phys. Rev. Lett. 1992,69,1656. Tersoff, J.; Lang, N. D. Phys. Reu. Lett. 1990,65,1132. Yuan, J.-Y.;Shao, Z. Ultramicroscopy 1990,34,223. Ciraci, S.; Baratoff, A.; Batra, I. P. Phys. Rev. B 1990,47, 7618. (4) Soler, J. M.; Baro, A. M.; Garcia, N.; Rohrer, H. Phys. Rev. Lett. 1986,57, 444. (5) Mamin, H. J.; Ganz, E.; Abraham, D. W.; Thomson, R. E.; Clarke, J. Phys. Reu. B 1986,34, 9015. (6) Erlandsson, R.; McClelland, G. M.; Mate, C. M.; Chiang, S. J.Vac. Sci. Technol. A 1988,6, 266. (7) Weisenhorn, A. L.; Hansma, P. K.; Albrecht, T. R.; Quate, C. F. Appl. Phys. Lett. 1989,54,2651. Blackman, G. S.; Mate, C. M.;Philpott, M. R. Phys. Rev. Lett. 1990, 65, 2270. (8) Baselt, D. R.; Baldeschwieler, J. D. J. Vac. Sci. Technol. B 1992, 10, 2316. Jarvis, S. P.; Oral, A.; Weihs, T. P.; Pethica, J. B. Reu. Sci. Inatrum. 1993,64, 3515. (9) Yuan, J.-Y.; Shao, Z.; Gao, C. Phys. Reu. Lett. 1991, 67, 863. (10)Yuan, J.-Y.; Shao, Z.; Gao, C. Phys. Rev. Lett. 1992, 68, 2564.
condensed layer of fluid cannot give rise to sample deformation during imaging. However,we and others have suggested previously that these capillary forces have the same potential to cause the image to differ from the actual surface topography as in AFM images.6J1J2 In this work we show quantitatively that capillary condensation from humid air couples the STM tip to the sample and can lead to significant amplification of surface features. The amplification is reversed by imaging in a dry atmosphere. For the majority of STM images (especially those of soft, flexible or hydrophilic surfaces) that are obtained under ambient conditions, the forces due to capillary condensation are appreciable and can lead to both transient and permanent surface deformation.12 In most descriptions of scanning tunneling microscopy, there is no physical coupling between the STM tip and sample, even though there are at least three significant interactions to consider: (1)electrostatic interaction due to the potential difference between the tip and sample; (2) van der Waals attraction; (3) capillary attraction due to the Laplace pressure generated by the formation of a highly curved fluid meniscus connecting the tip and sample.11J3 These forces can cause the STM tip, while traversing a surface feature with an actual height, 2, to distort the surface being measured, resulting in an amplified height, Z*. Followingthe multiple spring models of other a ~ t h o r s , we ~ J consider ~ the tip and sample to be attached by a spring of spring constant, kl. A second spring of spring constant, kz, connects the sample to the STM base. Regardless of the functional form of k l and kz,this combination of springs will amplify a surface feature of actual height Z by
z* = Z(k1 + k2)/k2
(1)
where Z* is the height measured by the STM. In most applications where the sample is a uniformly rigid solid firmly mounted to the base, ka is very large compared to kl and no amplification is evident (k2 would be related to the bulk compressibility or elastic modulus of the sample (11) Woodward, J. T.; Zasadzinski, J. A.; Hansma, P. K. J. Vac. Sci. Technol. 1991, B9, 1231. (12) Woodward, J. T.; Zasadzinski, J. A.; Schwartz, D. K. Phys. Rev. Lett. 1992, 68, 2563. (13) Coombs, C. H.; Pethica, J. B. IBM J. Res. Deu. 1986, 30,455.
0143-1463/9~/2410-1340$04.50/00 1994 American Chemical Society
Langmuir, Vol. 10, No. 5, 1994 1341
Letters
REPLICA
T
Figure 1. Schematic showing a fluid meniscus connecting the STM tip to the replica. The figure is not to scale. being imaged5). However, if the sample is soft, nonuniform, or wealky connected to the base, as is often the case for organic or biological films, or even layered solids, k2 can be much less than kl, leading to large amplifications. To determine a rough estimate of these two important spring constants, we first assume that the force and spring constants between the tip and sample can be approximated by the linear combination of electrostatic, van der Waals, and capillary forces.llJ2 For a spherical tip of radius R and a tip-sample distance D, the van der Waals force is
FvdW = AR/6D2
(2)
where A is the Hamaker ~ 0 n s t a n t . l ~The Hamaker constant for two platinum wires in air or an electrolyte is 20 X 10-20 5-15 The electrostatic force between a sphere held at a potential, VO,and a grounded plane is given by
in the limit of R >> D. The capillary force due to the meniscus between the sample and tip is
FL = 4aRy
COS B / ( l +
D/d)
(4)
where y is the surface tension of the condensate and B is the liquid-solid contact angle. d is the distance the tip extends into the meniscus and is given by (yVIRT) cos B/ln(P/P,) where Vis the condensate molar volume, R the gas constant, T the temperature, and PIP, the relative humidity.14 For water, y = 0.073 J/m2 and d = -(1.08 nm)/ln(P/P,).14 By use ofthese approximations, the spring constant kl = -dF/dD is k, = atV;R/D2
+ AR/3D3+ 4aRy COS B/d(l + D/d)2 (5)
and is governed by the Laplace pressure for relative humidities over 1076 as shown in Table 1. From the exact meniscus profiles and interaction forces in ref 16, we (14)Israelachivili,J. N.Intermolecular and SurfaceForces;Academic Press: London, 1991;p 177,330-332. (15)Derjaguin,B. V.; Rabinovich, Y. I.; Churaev, N. V. Nature 1978, 272,313. (16)Zasadzinski, J. A.; Sweeney, J. B.; Davis, H. T.; Scriven, L. E. J. Colloid Interface Sci. 1987,119,108. Orr, F.M.; Scriven, L. E.; Rivas, A. P. J. Fluid Mech. 1975,67,723.
calculate that the pressure within the meniscus can exceed 100 atm, which is sufficient to damage soft materials,17J8 although it would only lead to small deformations of crystalline solids such as g r a ~ h i t e .The ~ wide range of local pressures experienced by samples during scanning may explain the irreproducibility typically found in imaging biological materials. For k2, the spring constant between the sample and the STM base, we consider for illustrative purposes metal surface replicas that we and others have used to obtain STM images of nonconductive surfaces of organic or biological materials.1s23 However, the general principles used should be valid to estimate k2 for many of the weakly supported samples common to STM imaging. Replicas are thin metal films mounted on porous metal mesh; where the replica is in direct contact with the mesh, k2 is large. However, for the part of the replica that is loosely suspended over a pore of area, a
k2 = E!P/0.14(1- v2)a
(6)
where E is Young’s modulus of the replica, v is Poisson’s ratio, and Tis the thickness of the replica.24 Metal surface replicas prepared for transmission electron microscopy are about 25 nm thick with E z 2 X 1Olo N/m2and v z 0.3 and are mounted on a mesh with 30-pm spacings. Hence, k2 = 0.003 N/m in the center of the mesh. Together with our earlier estimate of kl, eq 1suggests a possible 1000fold amplification, which is clearly outside the limits of our approximations but also indicative of potential artifacts due to tip-sample interactions. Most importantly to reliable imaging, we cannot determine whether the particular area being imaged is well supported or not during a particular STM scan. As a result, we expect, and have found, that feature heights often vary with location on the surface. This effect will not be appreciable for chemically and physically homogeneous “bulk” samples (>1 mm thick), although even if the sample is “bulk”, any weak point in the mounting or adhesion of the surface to the substrate or the substrate to the STM base can lead to amplification of surface features. This also suggests that certain areas of a sample might be highly amplified, leading to permanent local distortion of the surface, where other areas might not be distorted as much if at all. As controlling the properties of the sample surface are difficult, and we do not know the details of the interaction a priori, it is important to identify the impact of capillary forces on test images and then minimize these forces for reliable imaging of unknown surfaces.
Results To properly test these ideas, we have made two types of specimens, one bulk and one thin film, with identical chemical composition and surface features and with wellknown feature heights. We chose metal shadowed Langmuir-Blodgett multilayer islands of cadmium arachidate (17) Evans, E.; Needham, D. J.Phys. Chem. 1987,91,4219. (18) Helm, C. A.; Israelachvili,J. N.; McGuiggan, P. M. Biochemistry
1992,31, 1794. (19)Amrein, M.;Stasiak, A.;Gross, H.;Stoll, E.;Travaglini,G.Science 1988,240,514. (20)Hanema, P. K.;Elings, V. B.; Marti, 0.;Braker, E. Science 1988, 242,209. (21)Zasadzinski,J. A.; Schneir, J.; Gurley, J.; Elings, V.; Hansma, P. K.Science 1988,239,1014. (22)Zasadzinski,J. A.; Bailey, S.J. Electron Microsc. Tech. 1989,13, 309. (23)Obcemea, C. H.; Vidic, B. Ultramicroscopy 1992, 42, 1019. (24)Roark, R. J.Formulas for Stress and Strain; McGraw-Hill: New York, 1965; p 225.
1342 Langmuir, Vol. 10, No. 5, 1994
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Table 1. Calculated Values for the Spring Constants and Forces of the Three Interactions We Have Considered Both in a Dry Environment (P/P.= 0.0) and for a Water Meniscus at Various Relative Humidities.
PIP,= 0.0 F (nN)
interaction
kl (Nlm)
electrostatic van der Waals Laplace total
0.01 3.3 0.0 3.31
0.01 1.7
0.0 1.71
PIP,= 0.10 F (nN)
kl (Nlm) 1.1 3.3 10.0 14.4
1.1 1.7 14.6 17.4
PIP,= 0.50 F (nN)
kl (Nlm) 1.1 3.3 11.0 15.4
1.1 1.7 28.0 30.8
PIP,= 0.75 F (nN)
kl (N/m) 1.1 3.3 7.6 12.0
1.1 1.7 36.2 39.0
a Note that kl is nearly constant over a wide range of relative humidities, and the dominant interaction is the Laplace pressure due t o the meniscus.
deposited on 1 mm thick mica substrates. The original specimen surface consists of bilayer islands of cadmium arachidate of 1-2 pm in extent that vary in height by a bilayer from adjacent areas.25 The thickness of the bilayer is known from X-ray diffraction and AFM images to be 5.5 11111.26~~’ To make the surfaces conductive and chemically uniform, 1.5-2 nm of platinum was applied by electron beam evaporation at a 45’ angle while the sample was rotated.28 This sample could then be imaged directly with the STM as the “bulk”sample. For the thin film samples, we deposited an additional 30 nm of carbon as a backing film to a second set of platinum-coated LB island surfaces on mica, followed by a 200 nm thick layer of silver.” These multilayer metal films were then stripped from the mica substrate using hydrofluoric acid, washed repeatedly in Millipore filtered water, and mounted, platinum side up, on silver wire mesh filters (SPI Supplies, West Chester, PA) with a nominal 0.2-pm pore size.11 STM (Nanoscope 11,Digital Instruments, Santa Barbara, CA) images were obtained with cut platinum/iridium tips at 100 mV bias voltage, a 1.0-nA tunneling current, and a scan rate of 5.8 Hz. Step heights were measured by taking bearing plots of roughly equal areas on both sides of a step and taking the difference between the peak values to be the step height. To control the environment and eliminate condensation between the tip and sample, we enclosed the STM in a bell jar with a base plate that allowed us to evacuate the chamber with a rotary pump to
