Surface energy maps of nanostructures: Atomic force microscopy and numericalsimulation studyÁdám Mechler, Janos Kokavecz, Peter Heszler, and Ratnesh Lal

Citation: Applied Physics Letters 82, 3740 (2003); doi: 10.1063/1.1577392 View online: http://dx.doi.org/10.1063/1.1577392 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/82/21?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Depth sensing and dissipation in tapping mode atomic force microscopy Rev. Sci. Instrum. 75, 2529 (2004); 10.1063/1.1771495 Noncontact atomic force microscopy study of copper-phthalocyanines: Submolecular-scale contrasts intopography and energy dissipation J. Appl. Phys. 95, 4742 (2004); 10.1063/1.1690485 Atomic force microscopy study of surface roughening of sputter-deposited TiN thin films J. Appl. Phys. 92, 3559 (2002); 10.1063/1.1504497 Effect of hydrogen etching on 6H SiC surface morphology studied by reflection high-energy positron diffractionand atomic force microscopy Appl. Phys. Lett. 76, 1119 (2000); 10.1063/1.125957 Role of the surface morphology in cement gel growth dynamics: A combined nuclear magnetic resonance andatomic force microscopy study J. Appl. Phys. 82, 449 (1997); 10.1063/1.365836

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APPLIED PHYSICS LETTERS VOLUME 82, NUMBER 21 26 MAY 2003

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Surface energy maps of nanostructures: Atomic force microscopyand numerical simulation study

Adam Mechlera),b)

Neuroscience Research Institute, University of California, Santa Barbara, California 93016

Janos KokaveczDepartment of Optics and Quantum Electronics, University of Szeged, H-6701 Szeged, Hungary

Peter Heszlerb)

Department of Solid State Physics, University of Uppsala, SE-75121 Sweden

Ratnesh Lala)

Neuroscience Research Institute, University of California, Santa Barbara, California 93016

~Received 31 October 2002; accepted 25 March 2003!

Topography and surface energy distribution of etched graphite were examined by atomic forcemicroscopy~AFM!. AFM images show atomic monolayer deep circular holes~etch pits!. At certainimaging conditions, these etch pits appear surrounded by rims. Numerical simulation of AFMimages reveals that the rims are formed due to an increased surface energy zone at the edges. Thevertical dimension of the rim correlates with the magnitude of the local surface energy. Such acorrelation between the imaging features and the surface energy profiles can be used to demarcatelocal chemical constituents in a composite nanomaterial. ©2003 American Institute of Physics.@DOI: 10.1063/1.1577392#

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Surface-related processes and technologies, such aserogeneous catalysis, nanopatterning, surface adsorpadhesion-based devices, and nanoelectronics dependcally on the physicochemical properties of atomically dfined surface structures in nanomaterials. The surface enof nanostructures plays a key role in their physicocheminteractions with external perturbations. The energeticsatomic steps is widely studied for various kinds of materibased on geometrical considerations1 and numericalcalculations.2 Theoretical models of surface topography stein crystals with only covalent bonds are available.3 However,such models for crystals with both covalent and vanWaals ~vdW! interactions are not well studied. Moreovethere is a paucity of tools for mapping different energesites at atomic scale.

Graphite is of special interest due to its uniqstructure—between the covalently bound crystal she~0001! only second-order vdW interactions exist, leadinganisotropy in physical properties. Steps and terraces perdicular to the basal plane are commonly used to study sanisotropy. However, due to the vdW nature of the layelayer interaction, these structures are instable. Such instity often relaxes into ripples and upfoldings4 which can leadto fullerene and nanotube formation. For the one atommonolayer deep circular holes~etch pits! formed on thegraphite basal plane, the upfolding is sterically prohibitwhich maintains the high-energy state. However, there aredata on the quantification of the energy of the edge sites

Atomic scale surface structures have been studied exsively using atomic force microscopy~AFM!. In a previouswork, using AFM, we observed nontopographically definrims around the edges of the etch pit~hereafter denoted a

a!Electronic mail: mechler@lifesci.ucsb.edu; lal@lifesci.ucsb.edub!Research Group on Laser Physics of the Hungarian Academy of Scie

University of Szeged, M-6701, Hungary.

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edges! on the topography images.5 The aim of our presenwork is ~a! to separate the real topography~defined as theplane of the undisturbed surface atoms! and the nontopo-graphically defined features and~b! to perform numericalsimulations to relate these features to surface energy incrat the edges compared to the basal plane.

Freshly cleaved highly oriented pyrolytic graphite6

~HOPG! samples were annealed in a quartz tube furnac650 °C in ambient air for 30 min to obtain one monolaydeep etch pits.7 These etch pits are mainly circular and at reoccurrences hexagonal.8 AFM measurements were peformed on the annealed HOPG surfaces inamplitude-controlled dynamic working modes: NC~noncontact!, IC~intermittent contact! and PI ~phase imaging! modes as de-scribed previously.5,9–12 Two different AFM systems wereused to visualize the monoatomic graphite steps. TopoMtrix® Explorer™ TMX2000~with a tube scanner of verticarange 0.8mm; Si3N4 probes!13 was used in IC and NCmodes to determine the parameter settings where thewere visible. Digital Instruments MultiMode™ AFM with anE scanner14 was used in both IC and PI modes using TESP14

probes to study the dependence of the rim height onsystem parameters. A typical scan range of 2.432.4mm2 andscanning speeds of 2–8mm21 were applied. Measurementwere performed with free amplitudes of a range of 5–100and setpoint~feedback! amplitudes of 60%–90%.

For the numerical simulations, the AFM probe is asumed to be a damped harmonic oscillator driven by abrating piezotranslator. The drive frequency is chosslightly above the resonance in order to simulate the tworking conditions. The oscillating probe is moved into tforce field of the surface. The force law equation is

ma5(i

Fi5Foscillator1F lip–surface, ~1!

wherea andm are the acceleration and effective mass ofes,

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3741Appl. Phys. Lett., Vol. 82, No. 21, 26 May 2003 Mechler et al.

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tip, respectively,Foscillator represents the forces acting indriven harmonic oscillator, andF tip–surface is the interactionforce. In contact with the surface, the Dugdatheory16-based Maugis continuum mechanics,17 was applied.This formalism adequately describes the force hystercaused by the elastic neck formation, that is, the materelated energy dissipation of the interaction. Tnonmaterial-dependent energy dissipation is included in~measured! quality factor of the cantilever probe. In the Nregion of the interaction, vdW forces dominate.15

The contact and NC parts are matched where the‘‘jumps to contact’’ ~or breaks away from the surface! andthus the vdW force is established. The main parameters~de-tailed in Ref. 18! determining the force–separation functioare the tip–sample reduced curvature, the reduced elmodulus, and the Dupre` adhesion energyÃ. The latter oneincludes the surface energies (g1-tip, g2-sample! of the in-teracting materials

Ã52Ag1g2. ~2!

The surface energy depends on the crystallographic orietion of the surface. For graphite, two values are known:the ~0001! basal plane, it is 0.11 J/m2, while for zig-zagstructure of carbon atoms, it is about 5 J/m2.19 In the modelof the monolayer steps, the material and geometric pareters can be calculated or estimated, except the Dupre` energy~and consequently, the surface energy! which is the only un-known variable. The width of the higher surface energy ais considered as the interatomic distance at the edges. Imtantly, the fitting of the simulations to the experimental rsults opens a possibility for determining the surface ener

The method we apply is to examine relative changesthe amplitude and phase signal. When comparing the calations to the experiments, unknown or unaccurate pareters of the interaction and the system often undermineeffort to calculate the absolute amplitude and phase datawas shown, e.g., in Refs. 11, 20, and 21. For relatchanges, however, when the probe scans a pattern of rence and unknown materials, the effect of the unknownrameters is the same. Hence the changing of certain matparameters can be quantitatively determined.

Dynamic mode AFM images show rims with a verticdimension of 0–3 Å~see, e.g., Fig. 1: left-panel! on thetopography images. The important parameters influencthe measured rim height are the free~i.e., far from the sur-face! oscillating amplitude and the setpoint~the amplitude infeedback relative to the free amplitude!. The rims are visiblewhen working in NC mode~6.7 nm free amplitude; setpoinamplitude.84%!. The rims disappear~Fig. 1: middle! whendecreasing the setpoint amplitude~moving the probe closeto the surface! or increasing the free amplitude~several tensof nms!, that is, when transition to IC mode occurThe top–bottom asymmetry in Fig. 1 reflects the effeof the feedback mechanism~sections shown perpendiculato the scan direction! and the—sometimes observable8—hexagonality of the etch pit. Small rims~,1 Å! arevisible in IC mode only when applying high~;100 nm! freeamplitudes and;60% setpoint amplitude.

Phase images were recorded simultaneously with thepography data. No phase difference could be observedrticle is copyrighted as indicated in the article. Reuse of AIP content is s

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tween the basal plane and the edges while imaging in themode~low free amplitude!, that is, when rims are visible onthe topography images. When imaging in the IC mode~withlow free amplitude!, the rims disappear in the topographimages~Fig. 1: middle!, however, a considerable phase dference can be seen between the basal plane and the edg~Fig. 1: right-panel!. A phase shift of 1.33°~60.47, sd!,along a zone of;6 nm width, was observed. Significantlythe phase ‘‘rim’’ at the edges becomes indistinguishable frthe background noise when the free amplitude is set higthe IC mode. Based on these results, we concluded thaNC mode images show an increased attractive force atedges while the low amplitude IC mode shows the truepography. However, in the latter case, the effect of thecreased force is visible in the phase images.

For further investigation of the observed rims, numericsimulation of the AFM imaging of the edges was performusing the above described model. The calculations werecused on the following three areas, the dependence of theappearance on the~1! applied free amplitude,~2! setpointamplitude, and~3! surface energy. The phase shift was acalculated for each cases.

For the first series of calculations, the setpoint amplituand the surface energy at the edge were set at 80% andJ/m2, respectively. In the rim height versus free amplitudiagram @Fig. 2~A!#, three different areas can be distinguished. When applying low amplitudes, the tip moves invdW attractive force field, the rim is high@Fig. 2~A!, h#. Inaccordance with the experiments, increasing the free amtude decreases the rim height.;9 nm free amplitude@Fig.2~A!, .# the rim height is minimum and falls into sub-Årange, that is, below the vertical resolution limit~;0.25 Åfor the Explorer,;0.33 Å for the NanoScope! of the scan-ners used. Increasing the free amplitude, the rim heightcreases again@Fig. 2~A!, s#, then slowly ‘‘saturates’’. Thephase shift first rises from a zero value up to 20° then drwith the increasing free amplitude@Fig. 2~A!, s#.

In order to define the parameter range for the appearaof the rims, the setpoint was varied at a constant~6 nm! freeamplitude. The surface energy was set to be 4 J/m2. Figure2~B! displays the function of the simulated rim height on tsetpoint amplitude. At low setpoint amplitudes, that is, whthe probe is close to the surface, the rim is high@correspond-ing to the region of the simulated plot indicated in Fig. 2~B!,

FIG. 1. Dynamic mode topography~left-panel, middle! and phase~right-panel! AFM images of one monolayer deep etch pits on graphite surfaThe line profiles shown are taken perpendicular to the scan direction. Lpanel image: Imaged by NC mode. At the edge site nontopography onated rim can be seen. Middle image: Imaged by low amplitude~‘‘soft’’ !tapping mode. No rim can be seen. Right-panel image: Phase imagcorded simultaneously with the middle image. Phase shift at the edgereveals increased attractive forces.

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3742 Appl. Phys. Lett., Vol. 82, No. 21, 26 May 2003 Mechler et al.

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by a h#. However, in this case, the signal shows a ringinlike behavior, having a standard deviation of;50% of therim height. Increasing the setpoint amplitude~elevating theprobe!, the rim height first decreases@Fig. 2~B!, .# thenincreases again@Fig. 2~B!, s# and the ringing disappearsThe phase shift steadily decreases and disappears at;80%setpoint showing the tendencies determined by the simtions. We then performed further numerical simulationsdetermine the rim height dependence on the surface enOur experimental data and simulations~Figs. 1 and 2! showthat a reasonable rim height can be only measured wapplying low free amplitudes with a high setpoint amplitudAccordingly, we chose 6 nm free amplitude with 80% a90% setpoint. The rim height dependence on the surfaceergy shows a steep increase up to;5 J/m2 surface energy@Fig. 3, ., h# then saturates~Fig. 3!. As can be seen, thcurves have a similar shape for both 80% and 90% setpo

The aforementioned results show that by applying ctain scanning conditions, rims appear at the etch pit edgethe topography AFM images. Since topography is definedthe plane of the undisturbed atoms of a surface, these rimnot represent real topography. Based on the measuremperformed at different AFM scanning modes and the numcal calculations, the appearance of these rims show thaincreased adhesive force~due to increased surface energ!appears at the edge site. There was a very good qualitaagreement between the experiments and the calculatHowever, the measured phase shifts were smaller by a faof 3–5 than what was predicted and in addition the measurim heights~up to 3 Å! were higher by a factor of;2 thanthe predicted values. We owe this deviation to the compbending geometry of the cantilever probe beyond our meling capability.22,23 While less likely, the effect of tip shapcannot be excluded implicitly. Significantly, however, theis no other technique available to measure surface enwith higher accuracy at nanometer scale.

Importantly, the relative changes of the surface eneup to 0–5 J/m2 range can be well monitored with the applie

FIG. 2. ~A! Calculated function of the rim height on the free amplitudSetpoint amplitude is 80%, surface energy 4 J/m2, free amplitude is tuned inthe range of 5–30 nm.~B! Calculated function of the rim height on thsetpoint amplitude. Free amplitude 6 nm, surface energy 4 J/m2, and set-point amplitude is tuned from 49% to 95%.

FIG. 3. Calculated function of the rim height on the surface energy ofstep edge. Free amplitude is 6 nm, setpoint amplitudes are~a! 80% and~b!90%, respectively.rticle is copyrighted as indicated in the article. Reuse of AIP content is s

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probes and AFM systems on the nanometer scale. Examian unknown sample, the model can predict the set of pareters needed to visualize this relative surface energy mapalso point out that the surface energy map can be calibrby a well-known surface structure. Since surface energyferences reveal either~i! different binding structure of thesame material, or~ii ! presence of chemically different material, such correlation between the imaging features andsurface energy profiles could be used to demarcate lchemical constituents. The model potentially includesonly the way of the demarcation but also the identificationthe different constituents. Accordingly, in the future, AFmeasurements can be used to quantify of physicochemproperties of nanostructures.

Our results explain the phase shifts observed experimtally at the edges as surface energy-related features. Sucinterpretation of phase images lends support to the PI mas an analytical method.

In conclusion, we report the visualization of surface eergy differences on nanometer/atomic scale by IC-AFM iaging. A distinction between the real topography and thehesion signal is presented. Numerical simulation reveaclear correlation between the subtracted adhesion signallocal surface energy changes. Our results open the possibthat the AFMs are able to measure relative surface enechanges quantitatively.

This work was supported by NATO-NSF~R.L. andA.M.!, Philip Morris & NIH ~RL! and the Hungarian Scientific Research Fund~OTKA! Grant Nos. T34381, T34825and TS040759~A.M. and J.K.!. The authors acknowledgHai Lin and Cristian Ionescu-Zanetti for their valuable comments.

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