DOI: 10.1126/science.289.5478.422 , 422 (2000); 289Science

et al.Franz J. Giessibl,Surface Observed by Atomic Force MicroscopySubatomic Features on the Silicon (111)-(7×7)

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problem is that we have neglected the spin onthe intervening oxygen. The third is that Eq.1 describes the ground state for a single FMbond, implying that neutron scattering shouldbe elastic, not inelastic as seen experimentally.

The first difficulty has a simple resolution.At finite hole densities, the polarization cloudsoverlap and the isolated impurity model is in-adequate. A crude model, which considers theoverlaps, simply truncates the polarizationclouds at neighboring impurity sites. BecauseFM impurity bonds are randomly distributed,the inversion symmetry characterizing isolatedimpurities is broken, thus allowing intensity atq 5 p. Because we know the impurity density,x, from neutron activation analysis, the onlyparameters in such a description are the extentof the polarization cloud, k21, which we adjust-ed to optimize the fit to our data. As shown bythe red lines in Fig. 4, the model provides agood account of the data with k21 5 8.1 6 0.2,7.3 6 0.2, and 7.2 6 0.5 for x 5 0.04, 0.095,and 0.14 respectively. These values are close tothe exponential decay length of 6.03 calculatedfor the AFM spin polarization at the end of anS 5 1 chain (25).

The modeling described so far does notinclude the spins of the holes responsible forthe effective FM couplings between Ni21

ions. The holes reside in oxygen orbitals ofY22xCaxBaNiO5 (5) but are almost certainlynot confined to single, isolated oxygens. Weconsequently generalized Eq. 1 to take intoaccount the hole spins, with—for the sake ofdefiniteness—the same net amplitude as ei-ther of the Ni21 spins next to the FM bondand distributed (with exponential decay) over, lattice sites centered on the FM bond. Aslong as , exceeds the modest value of 2,comparable to the localization length de-duced from transport data (5), the pro-nounced asymmetry about p that occurswhen , 5 0 is relieved sufficiently to producefits indistinguishable from those in Fig. 4.

How do we account for the inelasticity ofthe incommensurate signal? One approach isto view the chain as consisting not of theoriginal S 5 1 degrees of freedom but of thecomposite spin degrees of freedom inducedaround holes. The latter interact throughoverlapping AFM polarization clouds andhole wave functions, to produce effectivecouplings of random sign because the impu-rity spacing can be even or odd multiples ofthe Ni-Ni separation. With weak interchaincoupling, the ground state is likely to be aspin glass, as deduced from other experi-ments (10) on Y22xCaxBaNiO5. The “incom-mensurate” nature of the excitations contin-ues to follow from the structure factor of thespin part of the hole wave functions.

In summary, we have measured the magnet-ic fluctuations in single crystals of a dopedone-dimensional spin liquid. At energies abovethe spin gap, the triplet excitations of the parent

compound, Y2BaNiO5, persist with doping.However, below the gap, we find new excita-tions with a broad spectrum and characteristicwave vectors that are displaced from the zoneboundary by an amount of order the inversecorrelation length for the parent. The incom-mensurate fluctuations, encountered here in adoped one-dimensional transition metal oxide,resemble those seen in metallic cuprates. How-ever, one-dimensionality makes them easier tomodel for Y2BaNiO5, and our analysis revealsthat “incommensurate” peaks arise naturallyeven without hole order because of the charac-teristic spin density modulation that developsaround a defect in the singlet ground state of aquantum spin liquid. This phenomenon ac-counts for the weak dependence of the incom-mensurability on doping in the one-dimensionalnickelate. Indeed, Y22xCaxBaNiO5 gives us aquantitative impression of the magnetic po-larization cloud associated with the holes in adoped transition metal oxide. Our results im-ply that the spin part of the hole wave func-tion is actually the edge state nucleated by thehole in a quantum spin fluid.

References and Notes1. S.-W. Cheong et al., Phys. Rev. Lett. 67, 1791 (1991).2. S. M. Hayden et al., Phys. Rev. Lett. 68, 1061 (1992).3. H. A. Mook et al., Nature 395, 580 (1998).4. J. M. Tranquada, B. J. Sternlieb, J. D. Axe, Y. Nakamura,

S. Uchida, Nature 375, 561 (1995).5. J. F. DiTusa et al., Phys. Rev. Lett. 73, 1857 (1994).6. J. Darriet and L. P. Regnault, Solid State Commun. 86,

409 (1993).

7. J. F. DiTusa et al., Physica B 194-196, 181 (1994).8. G. Xu et al., Phys. Rev. B 54, R6827 (1996).9. T. Sakaguchi, K. Kakurai, T. Yokoo, J. Akimitsu, Phys.

Soc. Jpn. 65, 3025 (1996).10. K. Kojima et al., Phys. Rev. Lett. 74, 3471 (1995).11. E. Dagotto, J. Riera, A. Sandvik, A. Moreo, Phys. Rev.

Lett. 76, 1731 (1996).12. Z.-Y. Lu, Z.-B. Su, L. Yu, Phys. Rev. Lett. 74, 4297

(1995).13. K. Penc and H. Shiba, Phys. Rev. B 52, R715 (1995).14. S. Fujimoto and N. Kawakami, Phys. Rev. B 52, 6189

(1995).15. E. S. Sorensen and I. Affleck, Phys. Rev. B 51, 16115

(1995).16. R. A. Hyman, K. Yang, R. N. Bhatt, S. M. Girvin, Phys.

Rev. Lett. 76, 839 (1996).17. I. Affleck, T. Kennedy, E. H. Lieb, H. Tasaki, Phys. Rev.

Lett. 59, 799 (1987).18. T. Kennedy, J. Phys. Condens. Matter 2, 5737 (1990).19. F. D. M. Haldane, Phys. Lett. 93A, 464 (1983).20. C. H. Chen, S.-W. Cheong, A. S. Cooper, Phys. Rev.

Lett. 71, 2461 (1993).21. J. M. Tranquada, D. J. Buttrey, V. Sachan, J. E. Lorenzo,

Phys. Rev. Lett. 73, 1003 (1994).22. S.-H. Lee and S.-W. Cheong, Phys. Rev. Lett. 79, 2514

(1997).23. V. J. Emery and G. Reiter, Phys. Rev. B 38, 4547

(1988).24. A. Aharony et al., Phys. Rev. Lett. 60, 1330 (1988).25. S. R. White and D. A. Huse, Phys. Rev. B 48, 3844

(1993).26. We thank T. M. Rice, A. J. Millis, and Q. Huang for useful

discussions and A. Krishnan for transmission electronmicroscopy measurements. Work at Johns Hopkins Uni-versity was supported by the NSF under DMR-9453362.Work at Louisiana State University was supported bythe NSF under DMR-9702690 and the State of Louisi-ana Board of Regents under LEQSF(RF/1996-99)-RD-A-05. This work used neutron research facilities supportedby the National Institute of Standards and Technology(NIST) and the NSF through DMR-9423101.

2 March 2000; accepted 25 May 2000

Subatomic Features on theSilicon (111)-(737) SurfaceObserved by Atomic Force

MicroscopyFranz J. Giessibl,* S. Hembacher, H. Bielefeldt, J. Mannhart

The atomic force microscope images surfaces by sensing the forces between asharp tip and a sample. If the tip-sample interaction is dominated by short-rangeforces due to the formation of covalent bonds, the image of an individual atomshould reflect the angular symmetry of the interaction. Here, we report on adistinct substructure in the images of individual adatoms on silicon (111)-(737), two crescents with a spherical envelope. The crescents are interpretedas images of two atomic orbitals of the front atom of the tip. Key for theobservation of these subatomic features is a force-detection scheme withsuperior noise performance and enhanced sensitivity to short-range forces.

In atomic force microscopy (AFM) (1), sur-faces are imaged with atomic resolution bybringing a probe into close proximity and

sensing the interaction force while scanningthe surface. It has been shown that a dynamicmode of imaging is required for resolvingreactive surfaces like Si(111) in an ultrahighvacuum where chemical bonding between atip and a sample can occur (2, 3). Frequency-modulation AFM (FM-AFM) (4 ) enables fastimaging in a vacuum and is now the com-monly used imaging technique. In FM-AFM,

Experimentalphysik VI, Center for Electronic Correla-tions and Magnetism (EKM), Institute of Physics, Uni-versity of Augsburg, 86135 Augsburg, Germany.

*To whom correspondence should be addressed. E-mail: franz.giessibl@physik.uni-augsburg.de

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a cantilever beam with eigenfrequency f0 andspring constant k holding a sharp tip at its freeend oscillates with a constant amplitude A.When this cantilever is brought close to asample, the tip-sample forces cause a fre-quency shift Df, which is used as the imagingsignal. The relevant imaging parameter inFM-AFM is the “normalized frequency shift”g 5 Df kA3/2/f0, when A is large in compari-son to the range of the tip-sample forces (5).

A recent study has shown that the optimalsignal-to-noise ratio is obtained for ampli-tudes roughly equal to the range of interatom-ic forces, much smaller than the currentlyused values of A ; 10 nm (6 ). Stable oper-ation at small amplitudes is, however, onlypossible if the cantilever is sufficiently stiff(5). An additional advantage of small ampli-tudes is the reduced sensitivity to long-rangeforces and the enhanced sensitivity to short-range forces (7 ). Unprecedented spatial res-olution has been observed with a force sensordesigned in accordance with these findings(8). This sensor was used in the present study.

Because of its complexity, the Si(111)-(737) surface (Fig. 1) has been an intriguingobject of study to many surface scientists. AfterBinnig et al. succeeded in imaging the top atomlayer of Si(111)-(737) in their landmark exper-iments by scanning tunneling microscopy(STM) (9), Takayanagi et al. developed thedimer-adatom-stacking fault (DAS) model(10), which is now commonly accepted. Ac-cording to this model (Fig. 1, A and B), sixadatoms are located in each half of the unit cell.The adatoms are bound by covalent bondsformed by 3sp3 hybrid orbitals. One of the four3sp3 hybrid orbitals is pointing perpendicular tothe surface and forms a dangling bond. Brom-mer et al. (11) have computed the coordinatesof all the atoms in the 737 unit cell by molec-ular dynamics calculations and have found that

the four inequivalent adatom sites have a dif-ferent height (Fig. 1B).

In 1995, the Si(111)-(737) surface wasfirst imaged with FM-AFM (2, 3). TheseFM-AFM images looked similar to the STMimages acquired at positive sample bias(empty states). It has been determined that theformation of a chemical bond between thefront atom of the tip and the adatoms isresponsible for the experimentally observedatomic contrast (12).

In the present work, the Si(111)-(737) sur-face was investigated using FM-AFM with op-timized resolution. The microscope is a home-built scanning tunneling microscope/atomicforce microscope based on a commercial scan-ning tunneling microscope (ThermoMicro-scopes, Sunnyvale, California). The electronicsoperating the force sensor is also homebuilt,relying on a commercial frequency demodulator(Nanosurf AG, Liestal, Switzerland). The vacu-um chamber, pumped with an ion and titaniumsublimation pump, has a base pressure of 5 310211 mbar. An 11 mm by 14 mm piece of aboron-doped (p-type) Si(111) wafer was used asa sample, and the 737 reconstruction was ob-tained by heating the sample to 1300°C for 30 swith an electron beam heater while keeping thepressure during heating below 5 3 1029 mbar.The force sensor, described in detail in (8), ismade of a quartz tuning fork with an etchedtungsten tip attached to it. The spring constant ofthe sensor was k 5 1800 N/m, the eigenfre-quency was f0 5 16,860 Hz, and all data wererecorded with an amplitude A 5 0.8 nm.

The experiment was started by operatingthe microscope in the STM mode, with thefeedback being controlled by the tunnelingcurrent. A tunneling voltage of 11.6 V wasapplied to the oscillating tip. The tunnelingcurrent was collected at the sample, and theset point was adjusted to 60 pA. The surface

was scanned to find a clean spot that dis-played large areas of reconstructed silicon.Also, controlled collisions between the tipand sample were performed to shape the tipso that good STM images were obtained. Thecorresponding frequency shift was approxi-mately –150 Hz. These STM images showedonly a single maximum per adatom. Next, thetip was withdrawn, and the feedback wasswitched to frequency-shift control. As theset point of the frequency shift was slowlydecreased while the tip was scanning, thecorrugation of the image was increased untilan optimal value was reached.

Figure 2 shows a panel of consecutivelyrecorded topographic images (obtained atconstant frequency shift) of the silicon sur-face. The sequence from Fig. 2A to 2B showsthat the window for the frequency shift whereoptimal resolution is obtained is rather small.Three features of Fig. 2, B to D, are quiteremarkable: the adatoms display a distinctsubstructure, with the image of each adatomcomposed of two crescents; the corner holesare very deep in comparison to previousAFM images (;180 pm); and the verticalresolution is excellent, such that the heightdifferences of the four distinct types of ada-toms can be measured (Fig. 1, C and D). Theranking in the experimental height of theadatoms is equal for FM-AFM and low-en-ergy electron diffraction (LEED) data: 1 isthe highest, and 2, 4, and 3 follow, with 3being the lowest. However, the height differ-ences measured by FM-AFM are about threetimes as large as the values measured byLEED and four to seven times as large as thevalues of the theoretical data (11). The dis-crepancy in magnitude between the LEEDand the FM-AFM data is probably due toelastic deformations of the tip and sample.The mean height of the adatoms in the left

B

A

2

1

0 10 20 30 40 50

Distance (Å)

Hei

gh

t (Å

)

D

C

1 2

1 23 4

3 4

10 Å

Fig. 1. (A) Top view and(B) side view of theDAS model of Si(111)-(737) (11). Adatomsand rest atoms are em-phasized by large andsmall black spheres, re-spectively. The left halfof the unit cell has astacking fault; the righthalf is unfaulted. The12 adatoms within oneunit cell belong to fourdifferent classes. Thethree adatoms withinone class are related bysymmetry operations(rotation by 2p/3). Thetheoretical equilibriumpositions of adatoms 1,2, and 4 are 8.5, 3.1,and 3.8 pm higherthan adatom 3, respectively, whereas the height differences as mea-sured by LEED are 12, 8, and 4 pm, respectively (11). (C) FM-AFMimage (raw data) of the Si(111)-(737) unit cell (section of Fig.

2B, left). (D) Profile of (C). Adatoms 1, 2, and 4 are 34, 19, and 15 pmhigher than adatom 3, respectively.

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and right lower image sections of Fig. 2D(acquired at Df 5 –140 Hz) is only 18 pmgreater than the mean height in the upperimage sections (acquired at Df 5 –160 Hz).The observation that the image contrastchanges substantially by such a small changein the minimal tip-sample distance leads tothe conclusion that the minimal tip-sampledistance is of the order of the next-neighbordistances in the bulk and is much smaller thanpreviously estimated (2).

At first glance, the double-peaked ada-toms look like a typical double-tip image.However, in a common double-tip image, thedistance between the two subimages has to beat least as large as the next-neighbor distancein the tip material, which is 316 pm fortungsten (13), whereas the experimental dis-tance between the observed maxima is only220 pm. If the tip had two “mini tips” inter-acting with the sample, where the two tips aredisplaced by 220 pm plus a surface latticevector, the atomic defects in the left uppersections of Fig. 2, B to D, should appearagain on a different location in the image,

displaced by roughly one lattice vector. Fur-thermore, an image obtained by a superposi-tion of two closely spaced single-tip imageswould yield an elliptical envelope of the ada-tom image, whereas the envelope of the ex-perimental images is spherical.

The nominal depth of the corner holes is445 pm (11), but in typical STM experiments, adepth of 200 pm is observed. The first AFMimage of Si(111)-(737) was recorded with A 534 nm, and the corner-hole depth was 73 pm(2), suggesting that AFM is sensitive to bothshort- and long-range interactions. The influ-ence of the long-range interactions causes thecontrast to decrease (7). Lantz et al. have im-aged Si(111)-(737) at low temperatures withA 5 5 nm (14) and found a corner-hole depthof ;120 pm, whereas Uchihashi et al. (15)have measured a depth of ;170 pm with A 516 nm. Here, we found a depth of 180 pm withA 5 0.8 nm, which confirms our theoreticalfindings that smaller amplitudes reduce the sen-sitivity to long-range forces and enhance theimage contrast (7).

For further analysis, the structure of a sin-

gle-adatom image was studied (Fig. 3 shows amagnification of Fig. 2B). Because the structur-al and electronic arrangements of silicon arewell known and a single dangling bond peradatom is predicted, the split adatom must becaused by the tip, according to the reciprocityprinciple (16). For an explanation of this ada-tom image, we first looked at the electronicstructure of tungsten. Tungsten condenses in abody-centered cubic structure where each atomhas eight next neighbors. According to Pauling(17), metals also display a partly covalent bind-ing character. Assuming that the tip-sampleinteraction is formed by covalent bonds be-tween tungsten and the 3sp3 hybrid orbitals ofthe silicon adatom, three or four maxima (de-pending on the orientation of the tungsten tipcluster) would be expected for each adatom(18). Thus, the experimental image cannot havebeen created with a tungsten tip. However,experimental evidence has been found in STMwhere “controlled collisions” between a tung-sten tip and silicon lead to picking up a siliconcluster from the sample (19, 20). Because theplanes with the lowest surface energy in silicon

100 Å

B

A1.0 Å

2.1 Å

0

0

1.7 Å

1.3 Å

2.0 Å 2.5 Å

0

0 0

0

C

E

D

F

Fig. 2. Series of topo-graphic images ofSi(111)-(737) ob-served by FM-AFM.The fast scanning di-rection was from leftto right for the leftside and from right toleft for the right side.All images are rawdata, except for thebackground plane sub-traction. All imageswere recorded with ascanning speed of fourlines per second in thehorizontal direction,and the image size is256 by 256 pixels;thus, the acquisitiontime for one frame is64 s. The tip bias wasmaintained at 11.6 Vwith respect to thesample. The directionof the slow scan wasreversed after an im-age was completed; in(A), (C), and (E), theslow scan directionwas from top to bot-tom, and in (B), (D),and (F), the directionwas from bottom totop. (A) Frequencyshift Df 5 –130 Hz,weak contrast. (B)Df 5 2160 Hz, optimal contrast. A defect is seen in the left upper sectionof the image, and there are dual maxima for each adatom. (C) Df 5 2160Hz, image similar to (B). (D) Before the start of this scan, the tip wasdisplaced to the right by a distance of 2 nm; consequently, the defectappears shifted to the left by a distance of 2 nm. After 102 scan lines werecompleted, the set point of the frequency shift was set to Df 5 –140 Hz.From then on, each adatom showed only one maximum, the contrastdecreased, and the overall noise increased. Because the lateral positions

of the atoms are not shifted, the same tip atom is active in the lowerand upper sections of the image. (E) Df 5 –140 Hz, image comparableto lower section of (D). (F) Df 5 –160 Hz. The noise in the upper 35scan lines was very low again. However, at scan line 35, the tip hasapparently collapsed. This is evident because of the increased noiseand a shift in the image pattern by ;1 nm to the lower right. Afterthis tip change, excellent imaging conditions could not be retainedwith this tip.

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are (111) planes, the corner atoms of a siliconcluster with minimal surface energy expose twodangling bonds. If a silicon cluster on top of atungsten tip exposes a sharp tip perpendicular tothe sample plane, the front atom has two dan-gling bonds interacting with the single danglingbond of the adatom.

Stillinger and Weber (SW) have found aneight-parameter semiempirical analytic mod-el potential (21) that describes the nearest andnext nearest neighbor interaction in silicon.The parameters are fitted so that the bulkproperties of silicon are modeled very wellfor both the solid and the liquid phase at highand low pressure, that is, up to large inter-atomic distances that exist in the case ofAFM where chemical bonds are stretched upto the disintegration of the bond. The normal-ized frequency shift g was calculated in Fig.4, B and C, from the SW potential accordingto equation 12 in (7 ). The use of the large-amplitude approximation for g is justified(even with A 5 0.8 nm, the ratio between Aand the range of the SW potential is ;10), asshown by figure 2 in (7 ).

Figure 4A shows a tip consisting of asilicon cluster pointed in a ,100. direc-tion interacting with an adatom on Si(111)-(737). Figure 4B is a calculation of thenormalized frequency shift g in an xy planethat is elevated at z 5 310 pm above theplane connecting the centers of the ada-toms. One maximum appears at the adatompositions. When z is reduced to 285 pm, adouble maximum appears (Fig. 4C). Figure2, B and C, is in good agreement with Fig.4C, and the transition from Fig. 4B to 4C isexperimentally found in Fig. 2D. Figure 4Dshows the calculated adatom image whenthe tip is tilted around the y axis by 3°. Thetheoretical distance of the double peaks is;230 pm, and the experimentally founddistance is ;220 pm. The reduction of thedouble maxima at z 5 285 pm to a singlemaximum at z 5 310 pm (in a ball-and-stick model of the covalent bond, the dis-

tance of the two maxima would increase forincreasing z) is not an idiosyncrasy of theSW potential. The chemical bond betweenthe tip and sample can also be described asan overlap of atomic orbitals. A simplecalculation of the charge density of two3sp3 orbitals with an orientation like the tiporbitals in Fig. 4A using hydrogen-like

wave functions yields a similar result. Aslight deviation between theory and exper-iment is noted, however. The simulatedpicture in Fig. 4C shows two crescentsfacing each other, whereas the experimen-tally observed crescents in Fig. 2 open tothe right for the scan directions from left toright and open to the left with scan direc-tions from right to left. Also, within eachpair of crescents corresponding to one ada-tom, the left crescents are higher than theright ones for the scans from left to right;the crescents appear to be about equallyhigh for the scan from right to left. Thisheight difference suggests that the two tiporbitals were not oriented perfectly sym-metrical with respect to the sample normalvector but were slightly tilted, as simulatedin Fig. 4D. The asymmetry in images scannedfrom left to right and from right to left suggestthe presence of either minor feedback errors orsmall elastic deformations of the tip and sam-ple. However, a detailed analysis of the feed-back parameters and more experiments in aconstant height mode have confirmed the mainobservation of subatomic structure by AFM(18).

References And Notes1. G. Binnig, C. F. Quate, Ch. Gerber, Phys. Rev. Lett. 56,

930 (1986).2. F. J. Giessibl, Science 267, 68 (1995).3. S. Kitamura and M. Iwatsuki, Jpn. J. Appl. Phys. 34,

L145 (1995).4. T. R. Albrecht, P. Grutter, D. Horne, D. Rugar, J. Appl.

Phys. 69, 668 (1991).5. F. J. Giessibl, Phys. Rev. B 56, 16010 (1997).6. iiii , H. Bielefeldt, S. Hembacher, J. Mannhart,

Appl. Surf. Sci. 140, 352 (1999).7. F. J. Giessibl and H. Bielefeldt, Phys. Rev. B 61, 9968

(2000).8. F. J. Giessibl, Appl. Phys. Lett. 76, 1470 (2000).9. G. Binnig, H. Rohrer, C. Gerber, E. Weibel, Phys. Rev.

Lett. 50, 120 (1983).10. K. Takayanagi, Y. Tanishiro, S. Takahashi, J. Vac. Sci.

Technol. A 3, 1502 (1985).11. K. D. Brommer, M. Needels, B. E. Larson, J. D. Joan-

noupoulos, Phys. Rev. Lett. 68, 1355 (1992).12. R. Perez, I. Stich, M. C. Payne, K. Terakura, Phys. Rev.

Lett. 78, 10835 (1997).13. N. Ashcroft and N. D. Mermin, Solid State Physics

(Saunders, Philadelphia, 1981).14. M. A. Lantz et al., Phys. Rev. Lett. 84, 2642 (2000).15. T. Uchihashi et al., Phys. Rev. B 56, 9834 (1997).16. C. J. Chen, Introduction to Scanning Tunneling Micros-

copy (Oxford Univ. Press, New York, 1993).17. L. Pauling, The Nature of the Chemical Bond (Cornell

Univ. Press, Ithaca, NY, ed. 2, 1957).18. In another experiment, using a metal tip, we observed

images of adatoms that displayed a fourfold symme-try; see supplemental material, available at www.sciencemag.org/feature/data/1050833.shl.

19. C. J. Chen, J. Vac. Sci. Technol. A 9, 44 (1991).20. J. E. Demuth, U. Kohler, R. J. Hamers, J. Microsc. 151,

299 (1988).21. F. H. Stillinger and T. A. Weber, Phys. Rev. B 31, 5262

(1985).22. We thank D. Schlom for discussions, K. Wiedenmann

for technical assistance, and Nanosurf AG for supply-ing components of the force sensor and a phase-locked–loop frequency demodulator. This work issupported by the Bundesministerium fur Bildung,Wissenschaft, Forschung und Technologie (projectnumber 13N6918/1).

28 March 2000; accepted 20 June 2000

Fig. 3. Enlargement of a single adatom image(from Fig. 2B, right).

z

A

C

B

0_

-8 fN√m

D

1 Å

1 Å

1 Å

Fig. 4. (A) Schematic drawing of the geometryused for the calculation, sketching the 3sp3

hybrid orbitals of the tip atom (green sphere)and sample adatoms (black spheres). Simulated2.8 Å by 2.8 Å constant height images (normal-ized frequency shift) of a single adatom for (B)z 5 310 pm, (C) z 5 285 pm, and (D) z 5 285pm with the tip tilted 3° around the y axis.

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