Theory predicts that the currents in scanning tunneling microscopy (STM) and
the attractive forces measured in atomic force microscopy (AFM) are directly
related. Atomic images obtained in an attractive AFM mode should therefore be
redundant because they should be \emph{similar} to STM. Here, we show that
while the distance dependence of current and force is similar for graphite,
constant-height AFM- and STM images differ substantially depending on distance
and bias voltage. We perform spectroscopy of the tunneling current, the
frequency shift and the damping signal at high-symmetry lattice sites of the
graphite (0001) surface. The dissipation signal is about twice as sensitive to
distance as the frequency shift, explained by the Prandtl-Tomlinson model of
atomic friction.Comment: 4 pages, 4 figures, accepted at Physical Review Letter

C. F. Quate

F. J. Giessibl

G. A. Tomlinson

H. Hölscher

H. J. Hug

J. Mannhart

L. Prandtl

S. Hembacher

English

arXiv

Hembacher, Stefan

Giessibl, Franz Josef

Mannhart, Jochen

Quate, Calvin F.

OPUS Augsburg

Local Spectroscopy and Atomic Imaging of Tunneling Current, Forces, and Dissipation on Graphite

Crossref

Theory predicts that the currents in scanning tunneling microscopy (STM) and the attractive forces measured in atomic force microscopy (AFM) are directly related. Atomic images obtained in an attractive AFM mode should therefore be redundant because they should be similar to STM. Here, we show that while the distance dependence of current and force is similar for graphite, constant-height AFM and STM images differ substantially depending on the distance and bias voltage. We perform spectroscopy of the tunneling current, the frequency shift, and the damping signal at high-symmetry lattice sites of the graphite (0001) surface. The dissipation signal is about twice as sensitive to distance as the frequency shift, explained by the Prandtl-Tomlinson model of atomic friction

Giessibl, Franz J.

University of Regensburg Publication Server

PRL 94, 056101 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending11 FEBRUARY 2005Local Spectroscopy and Atomic Imaging of Tunneling Current, Forces, and Dissipationon GraphiteS. Hembacher, F. J. Giessibl,* and J. MannhartInstitute of Physics, Electronic Correlations and Magnetism, Experimentalphysik VI, Universita¨t Augsburg,Universita¨tsstrasse 1, D-86135 Augsburg, GermanyC. F. QuateGinzton Lab, Stanford University, Stanford, California 94305-4085, USA(Received 27 September 2004; published 9 February 2005)0031-9007=Theory predicts that the currents in scanning tunneling microscopy (STM) and the attractive forcesmeasured in atomic force microscopy (AFM) are directly related. Atomic images obtained in an attractiveAFM mode should therefore be redundant because they should be similar to STM. Here, we show thatwhile the distance dependence of current and force is similar for graphite, constant-height AFM and STMimages differ substantially depending on the distance and bias voltage. We perform spectroscopy of thetunneling current, the frequency shift, and the damping signal at high-symmetry lattice sites of thegraphite (0001) surface. The dissipation signal is about twice as sensitive to distance as the frequencyshift, explained by the Prandtl-Tomlinson model of atomic friction.DOI: 10.1103/PhysRevLett.94.056101 PACS numbers: 68.37.Ef, 62.25.+g, 68.37.Ps, 81.05.UwFIG. 1 (color). Crystal structure of graphite. The unit cell(green) consists of two layers with inequivalent basis atoms (white) and  (red). The  atoms have direct neighbors in theadjacent atomic layers as indicated by the dotted lines; the atoms are above a hollow site (h). (a) Perspective view,showing three layers formed by hexagonal rings. (b) Top viewwith surface unit vectors u and v. The line   v u con-nects the , , and h lattice points, spaced by 142 pm.The capability of scanning tunneling microscopy (STM)[1] and atomic force microscopy (AFM) [2] to resolvesingle atoms in real space makes them powerful tools forsurface science and nanoscience. When operating AFM inthe repulsive mode, protrusions in the images simply relateto the atoms because of Pauli’s exclusion law. In contrast,the interpretation of STM images is more complicated. TheTersoff-Hamann approximation [3], valid for tips in ans state, interprets STM images as a map of the chargedensity of the sample at the Fermi energy. Depending onthe state of the tip, atoms can be recorded as either pro-trusions or holes, and tip changes can reverse the atomiccontrast [4,5]. Theoretical predictions regarding the rela-tion of forces and tunneling currents I state that tunnelingcurrents and attractive forces are directly related; thus,AFM would not provide any new physical insights overSTM. Chen [5] has found that the square of the attrac-tive energy between tip and sample should be proportionalto I with experimental evidence in [6]. Hofer and Fisher [7]suggested that the interaction energy and I should bedirectly proportional, which is experimentally found in[8,9]. In this Letter, we investigate the experimental re-lationships between tunneling currents and conservativeas well as dissipative forces for graphite probed with aW tip by performing local spectroscopy on specific latticesites. While force spectroscopy on specific lattice sites [10]and combined force and tunneling spectroscopy on unspe-cific sample positions [8,9] have been performed before,the measurements reported here encompass site-specificspectra of currents and forces, supplemented by simulta-neous constant-height measurements of currents and forcesthat allow a precise assessment of the validity of thetheories regarding currents and forces in scanning probeexperiments.05=94(5)=056101(4)$23.00 05610In graphite (see Fig. 1), the electrons at EF are concen-trated at the  sites, and only these atoms are ‘‘seen’’ bySTM at low-bias voltages.The state-of-the-art method for atomic resolution forcemicroscopy is frequency modulation AFM (FM-AFM)[11], where the frequency shift f of an oscillating canti-lever with stiffness k, eigenfrequency f0, and oscillationamplitude A is used as the imaging signal [12,13]. Thebonding energy between two adjacent graphite layers atdistance 	 can be approximated by a Morse potentialVM  Ebond2ez	  e2z	 (1)with Ebond  23 meV and   8 nm1 per atom pair[14]. The ‘‘normalized frequency shift’’ x; y; z kA3=2fx; y; z=f0 connects the physical observable f1-1  2005 The American Physical SocietyPRL 94, 056101 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending11 FEBRUARY 2005and the underlying forces Fts with range , where  0:4Fts0:5 [see Eqs. (35)–(41) in [13] ]. For covalent bonds,the typical bonding strength is on the order of 1 nN with1 A, resulting in 4 fN mp , where a negative signindicates attractive interaction. For graphite, the interlayerbonds are much weaker and the potential of Eq. (1) resultsin min  0:1 fNmp. The interaction of a tip atom with agraphite surface may be stronger than the interlayer bondsbut should still result in min < 1 fNmp, posing a chal-lenge for AFM imaging. True atomic resolution on graph-ite by AFM has so far been obtained only at lowtemperatures, first by Allers et al. [15] using large-amplitude FM-AFM with f  63 Hz, f0  160 kHz,k  35 N=m, and A  8:8 nm; thus   11:4 fN mp . Inspectroscopic measurements by the same group, a mini-mum of   60 fN mp has been observed [Fig. 1(b) in[16] ]. Because this value is more than 2 orders of magni-tude greater than the estimate above, it is expected thatlong-range forces have caused a large contribution in thatexperiment. Here, we use FM-AFM with sub-nm ampli-tudes which greatly reduces the influence of long-rangeforces [13] and enables simultaneous STM operation [17].We use a low-temperature STM-AFM operating at 4.9 Kin ultrahigh vacuum [18]. The microscope uses a qPlussensor [19] for simultaneous STM-AFM operation (k 1800 N=m, f0  11 851:75 Hz, quality factor Q 20 000). All data (spectroscopy and images) are recordedat A  0:25 nm. The tip is prepared by dc etching (3 V) ofa polycrystalline tungsten wire. The frequency shift ismeasured with a commercial phase-locked-loop detector(EasyPLL by Nanosurf AG, Liestal, Switzerland). The in-strument is thermally well connected to a liquid He bathcryostat at 4.2 K, leading to a drift rate of 20 pm=h.Nonconservative tip-sample interactions lead to damping,and the energy Ets that has to be provided for eachoscillation cycle to keep A constant is recorded simulta-neously with I and f.FIG. 2 (color). Simultaneous records of (a) tunneling current,(b) frequency shift, and (c) damping. Image size 3 nm 1 nm,tip bias 100 mV, and scanning speed 40 nm=s.05610To check if the three data channels I, f, and Ets areproduced by the same tip atom, we have scanned an areathat contains a step edge (Fig. 2). The step edge appears atthe same position in all three data channels; thus the signalsare produced by the same tip atom.The physics of the interaction is best explored by per-forming I, , and Ets spectroscopy at the high-symmetrylattice sites. Figure 3 shows Iz, z, and Etsz taken atthe -, -, and h-lattice sites. All three signals initiallyincrease roughly exponentially, as shown in the log-scaleinsets. The correspondence between experimental imagesand the lattice sites is established by the analysis below.The current increases exponentially in the distanceregime from z  0 to z  100 pm, followed by a step-like increase for smaller distances. We assume that thetip is essentially in contact with the upper graphite layerfor distances smaller than 100 pm. Given that the elec-trical conductivity of graphite is small at low tempera-tures and small in the z direction, we conclude that thesteplike increase in current for distances smaller than100 pm is caused by an increasing number of graphitelayers becoming available for charge transport. The currentspectra in Fig. 3(a) are maximal for most distances onFIG. 3 (color). Experimental spectra of I, , and Ets as afunction of distance for a tip bias of 160 mV. The gray curves aretaken at position ‘‘1’’ in Fig. 4(a), the black curves at position‘‘2,’’ and the red curves at position ‘‘3.’’ The insets are views ofIz, z, and Etsz for 0:1 nm< z< 0 on logarithmicscales.1-2FIG. 4 (color). Constant-height measurements of I, , andEts in attractive and repulsive distance regimes for a tip biasof 160 mV (a)–(c) and 60 mV (d)–(f). The hexagons show theproposed positions of  (white) and  (red) atoms. The bright-ness is proportional to jIj, , and Ets. The inset in (c) (leftpanel) shows a higher harmonic image [23], indicating that thetip state is not perfectly symmetric with respect to the z axis.PRL 94, 056101 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending11 FEBRUARY 2005site 3. Because site 3 is a current maximum, we identify itas a  position.The normalized frequency shift  decreases down to adistance of  170 pm, followed by a slight increasedown to  550 pm and a sharper increase for evensmaller distances. For z <800 pm,  remains constantbecause the cantilever remains in contact with the sampleduring the entire oscillation cycle. In the z range from 0 to100 pm where the short-range chemical bonding forcesstart to emerge, the magnitude of  increases exponent-ially (see the inset). It is believed that the short-rangeforces between AFM tips and graphite originate fromvan der Waals forces [16] with their typical 1=z7-distancedependence. The experimental data shows that when theinteratomic distance approaches the atomic diameters, anexponential force dependence prevails.The damping signal initially also increases exponen-tially for z < 0, reaches a plateau for z <170 pm, decaysto zero from z <600 pm, and remains zero for z <800 pm because the cantilever remains in contact forthe whole oscillation cycle. This points to a dampingmechanism as described by Prandtl [20] and Tomlinson[21], where the energy loss is caused by a plucking actionof the atoms on each other. The energy loss per cycle issimply related to the maximal attractive force Ftsmin andthe stiffness of the sample ksample with EtsF2tsmin=2ksample [22].The insets are logarithmic plots of Iz, z, andEtsz for 0:1 nm< z< 0, showing an almost expo-nential distance dependence in that range. For the tunnel-ing current, we find a decay constant I  13 nm1 at the site and I  15 nm1 at sites 1 and 2, leading to anapparent barrier height of  2 eV. The decay constant of and thus the interaction potential [Eq. (39) in [13] ] is  12 nm1 at the  site and   16 nm1 at sites 1 and 2.The decay constants for I and  are equal within themeasurement accuracy; thus the theory by Hofer andFisher [7] appears to hold for the interaction of W withgraphite. The damping signal decays with Ets 20 nm1 at the  site and Ets  30 nm1 at sites 1and 2 as expected from an energy loss proportional to thesquare of the attractive force.The normalized frequency spectra shown in Fig. 3(b) arerather similar, except for the gray curve recorded at site 1.In the distance regime from 600 to 800 pm, the graycurve is shifted by  40 pm. If the C sample atoms andthe W tip atom are assumed to be hard spheres with adiameter of 142 and 273 pm, respectively, the W tip atomcould protrude 56 pm deeper on top of the hollow sites thanat  or  sites. We therefore conclude that position 1 (graycurves) corresponds to a hollow site [h in Fig. 1(b)].Interestingly, Fig. 3(c) shows that the dissipation is signifi-cantly larger on the hollow site than on top of  or  sites.The three data channels were acquired simultaneously andthe range from z  1:7 nm to 0.6 nm and back to1:7 nm was ramped within 60 s. The sequence of the05610three sites was scanned 3 times, so a total of six spectra wascollected for each , , and h site. While the drift rate ofour instrument is very low, piezocreep caused z offsets ofconsecutive scans. These offsets were calibrated by com-parison with constant-height scans which provide precisecross references for I, , and Ets at the , , and h sitesfor a given z value.The local spectra at high-symmetry sites were sup-plemented by constant-height scans at various z posi-tions shown in Fig. 4. Figures 4(a)– 4(c) show I, ,and Ets at a tip bias of 160 mV in the fully attractivemode at z100 pm (a), in a weakly repulsive regimeat z350 pm (b), and a fully repulsive mode at1-3PRL 94, 056101 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending11 FEBRUARY 2005z750 pm (c). If the attractive interaction between tipand sample was mediated only by the electronic states thatcontribute to the tunneling current, the I and  images inFig. 4(a) should be exactly inverse. Evidently, this is notthe case. We therefore conclude that electronic states thatdo not contribute to the tunneling current may contribute toattractive interaction. In the repulsive regime shown inFig. 4(c), the repulsion is strongest above the  sites, al-most as strong on the  sites, and weakest on hollow sites,in agreement with Fig. 3(a) and the Pauli exclusion law.The current has a local maximum on top of the  sites, andEts has a pronounced maximum at the hollow sites.Because of the long time scales involved in damping mea-surements, atomically resolved energy loss measurementsare prone to lateral shifts [24] for fast scanning. The scan-ning speeds used in the data of Fig. 4 were 0:3 nm=s;therefore, time delays in the acquisition channels are neg-ligible, and the I, , and Ets images match precisely inforward and backward scans. In our previous simultaneousSTM-AFM measurement on graphite [17], we found alateral shift of 68 pm of the current maxima with respectto the corresponding  maxima. While the tip is not per-fectly symmetric with respect to the z axis (see the Fig. 4caption), it is evidently more symmetric than in [17].Arai and Tomitori [25] have recently shown that forceinteractions are also a function of bias. Figures 4(d)– 4(f)show constant-height images at a different tip bias of60 mV. In the attractive regime shown in Fig. 4(d), theI and  images are approximately inverse; i.e., the localminimum in  coincides with the local maxima in I. In therepulsive regime shown in Fig. 4(f), again the repulsion isstrongest above the  sites, almost as strong on the  sites,and weakest on hollow sites.While the distance dependencies of current, force, anddissipation as revealed by constant-height images and localspectroscopic measurements are qualitatively similar, thecontrast observed in the constant-height images is largerthan expected from the local spectra. The reason for thesesubtle discrepancies is revealed by the constant-height datashown in Fig. 4. Frequency shift and current images aredifferent in all distance regimes, and slight shifts betweenthe high-symmetry points in I and  images are present.In summary, the spectroscopy experiments show that thez dependence of force and current is roughly the same aspredicted in Hofer-Fisher theory [7] for graphite. However,the constant-height experiments prove that attractive forcesand currents are not directly related and STM and AFMdo provide different information. The dissipation measure-ments reveal that the theories on atomic friction introducedby Prandtl [20] and Tomlinson [21] are the key mechanismfor damping on the atomic scale when imaging softsamples. The spatial resolution that is possible by scanningprobe microscopy scales with the decay lengths of physicalobservables [26]. At the onset of damping, the decay lengthof dissipation is only half the value of the force. This offersan alternate explanation of the impressive resolution ob-tained in damping images [27].05610This work is supported by the Bundesministerium fu¨rBildung und Forschung (Project No. EKM13N6918).We thank M. Herz for discussions and K. Wiedenmannand H. Bielefeldt for help in the construction of themicroscope.1-4*Electronic address: franz.giessibl@physik.uni-augsburg.de[1] G. Binnig, H. Rohrer, C. Gerber, and E. Weibel, Phys. Rev.Lett. 49, 57 (1982).[2] G. Binnig, C. F. Quate, and C. Gerber, Phys. Rev. Lett. 56,930 (1986).[3] J. Tersoff and D. R. Hamann, Phys. Rev. Lett. 50, 1998(1985).[4] J. V. Barth, H. Brune, G. Ertl, and R. J. Behm, Phys. Rev. B42, 9307 (1990).[5] C. J. Chen, J. Phys. Condens. Matter 3, 1227 (1991).[6] C. Loppacher, M. Guggisberg, S. Scha¨r, R. Bennewitz,O. Pfeiffer, M. Bammerlin, V. Barwich, A. Baratoff,E. Meyer, and H.-J. Gu¨ntherodt, Phys. Rev. B 62, 16 944(2000).[7] W. A. Hofer and A. J. Fisher, Phys. Rev. Lett. 91, 036803(2003).[8] A. Schirmeisen, G. Cross, A. Stalder, P. Gru¨tter, andU. Du¨rig, New J. Phys. 2, 29 (2000).[9] G. Rubio-Bollinger, P. Joyez, and N. Agrait, Phys. Rev.Lett. 93, 116803 (2004).[10] M. Lantz, H. J. Hug, R. Hoffmann, P. van Schendel,P. Kappenberger, S. Martin, A. Baratoff, and H.-J.Gu¨ntherodt, Science 291, 2580 (2001).[11] T. R. Albrecht, P. Grutter, H. K. Horne, and D. Rugar,J. Appl. Phys. 69, 668 (1991).[12] R. Garcia and R. Perez, Surf. Sci. Rep. 47, 197 (2002).[13] F. J. Giessibl, Rev. Mod. Phys. 75, 949 (2003).[14] M. C. Schabel and J. L. Martens, Phys. Rev. B 46, 7185(1992).[15] W. Allers, A. Schwarz, U. D. Schwarz, and R. Wiesen-danger, Appl. Surf. Sci. 140, 247 (1999).[16] H. Ho¨lscher, A. Schwarz, W. Allers, U. D. Schwarz, andR. Wiesendanger, Phys. Rev. B 61, 12 678 (2000).[17] S. Hembacher, F. J. Giessibl, J. Mannhart, and C. F. Quate,Proc. Natl. Acad. Sci. U.S.A. 100, 12539 (2003).[18] S. F. Hembacher, Ph.D. thesis, Universita¨t Augsburg,Augsburg, Germany, 2003.[19] F. J. Giessibl, Appl. Phys. Lett. 73, 3956 (1998).[20] L. Prandtl, Z. Angew. Math. Mech. 8, 85 (1928).[21] G. A. Tomlinson, Philos. Mag. 7, 905 (1929).[22] F. J. Giessibl, H. Bielefeldt, S. Hembacher, and J. Mann-hart, Ann. Phys. (Leipzig) 10, 887 (2001).[23] S. Hembacher, F. J. Giessibl, and J. Mannhart, Science305, 380 (2004).[24] M. Gauthier, R. Perez, T. Arai, M. Tomitori, andM. Tsukada, Phys. Rev. Lett. 89, 146104 (2002).[25] T. Arai and M. Tomitori, Phys. Rev. Lett. 93, 256101(2004).[26] E. Stoll, Surf. Sci. Lett. 143, L411 (1984).[27] H. J. Hug and A. Baratoff, in Noncontact Atomic ForceMicroscopy, edited by S. Morita, R. Wiesendanger, andE. Meyer (Springer, Berlin, Heidelberg, New York, 2002),Chap. 20, pp. 395– 432.

OPUS - Augsburg University Publication Server

Online-Publikationserver Augsburg

http://epub.uni-regensburg.de/25276/1/giessibl.pdf

Local spectroscopy and atomic imaging of tunneling current, forces and
  dissipation on graphite

Local spectroscopy and atomic imaging of tunneling current, forces and dissipation on graphite

Abstract

Similar works

Full text

Available Versions

OPUS Augsburg

Crossref

University of Regensburg Publication Server

OPUS - Augsburg University Publication Server

Online-Publikationserver Augsburg