PHYSICAL REVIEW B 15 JANUARY 2000-IIVOLUME 61, NUMBER 4

Dynamic-mode scanning force microscopy study ofn-InAs„110…-„131… at low temperatures

A. Schwarz, W. Allers, U. D. Schwarz, and R. WiesendangerInstitute of Applied Physics and Microstructure Research Center, University of Hamburg, Jungiusstrasse 11,

D-20355 Hamburg, Germany~Received 15 July 1999!

We present results of an atomic-scale study onin situ cleaved InAs~110! in the dynamic mode of scanningforce microscopy~SFM! at low temperatures. On a defect-free surface, the dynamic mode SFM images alwaysexhibit strong maxima above the positions of the As atoms, where the total valence charge density has itsmaximum. Occasionally, with certain tips, the In atoms also become visible. However, their appearancestrongly depends on the specific tip-sample interaction: We observed protrusions as well as depressions at theposition of the In atoms. In this context, the role of the charge rearrangements induced by the specificelectronic structure of the tip on the contrast in atomic-scale images is discussed in detail. Additionally, weinvestigated the appearance and nature of two different types of atomically resolved point defects. The mostfrequently observed point defect manifests itself as a missing protrusion, indicating the existence of an Asvacancy. A second type of point defect is probably an In vacancy, which could be detected indirectly by itsinfluence on the two neighboring As atoms at the surface. At large tip-sample distances, these As atoms showa reduced corrugation compared to the surrounding lattice, while at smaller tip-sample distances the corruga-tion is increased. This distance-dependent contrast inversion is explained by a relaxation of the As atoms abovethe defect which is induced by an attractive tip-sample interaction.

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I. INTRODUCTION

InAs is a high-mobility, narrow-gap III-V semiconductoalready used in many applications, e.g., infrared detect1

and Hall sensors.2 Additionally, it is an essential part of several newly developed devices like mesoscoheterostructures,3 self-assembling quantum dots,4 and hybridferromagnetic-semiconductor structures.5 For the further de-velopment of such small devices and thin multilayer systewhere surface effects dominate over bulk properties, atailed knowledge of the surface structure and their characistics at the atomic scale is important. In particular, thevestigation of point defects in semiconductors isimportant matter, because they provide trap levels withinband gap, which determine many of their electric and optproperties.6

Up to now, real-space surface investigations on semicductors on the atomic level have been carried out primawith scanning tunneling microscopy~STM!. Although thistechnique is very powerful, it suffers from two drawbackFirst, it is restricted to conducting samples, which becomeserious problem for experiments at low temperature~i.e., ex-periments in high magnetic fields! on nondegenerate semconductor surfaces. Second, STM in the constant curmode follows contour lines of the local density of states nthe Fermi energy. Structural information is mixed with eletronic information, especially in the vicinity of defectwhere both the electronic structure close to the Fermi eneand the geometric structure of the atomic lattice chanTherefore, structural information cannot be extracted unabiguously from STM data.

Another method to investigate surfaces in real spacscanning force microscopy~SFM!.7 In 1995, Giessibl8

showed that ‘‘true’’ atomic resolution9 on Si~111!-(737) ispossible with the dynamic mode of scanning force micrcopy, which is also called noncontact atomic force micrcopy. In this mode, the cantilever is oscillated at its reson

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frequency f res with a fixed amplitudeA. Due to the tip-sample interaction, the oscillation frequency changes; thesulting frequency shiftD f is detected and used to drive thfeedback electronics~constant frequency shift mode! as wellas to record an image of the surface. In contrast to stcontact SFM, a ‘‘jump-to-contact’’ can be prevented10 andattractive short-range tip-sample interactions can be probwhich provide ‘‘true’’ atomic resolution, including the imaging of point defects. Note that long-range tip-sample intertions are also present, but do not contribute to contrastmation on the atomic scale. A significant advantage oSTM is the ability to achieve ‘‘true’’ atomic resolution eveon insulators.11–13 Therefore, this method can be usedsemiconductors in the whole range of doping concentratiand temperatures.

In this paper, we present an investigation of the~110!surface ofn-InAs using the dynamic mode of SFM. Aftershort description of the experimental setup, we will firpresent our results on the defect-free surface and giveinterpretation of the observed contrast, based on recentoretical work. From this starting point, we will discuss thmechanisms that are responsible for contrast formationand around two different types of atomically resolved podefects. The first point defect is located on the As sublatand can be interpreted straightforwardly as an As vacanThe second point defect, located on the In sublatticeshowing a distance-dependent contrast inversion, is proban In vacancy. To support our interpretations regardingpoint defects, we will compare our results with experimendata and theoretical calculations on~110! surfaces of similarIII-V semiconductors.14

II. EXPERIMENTAL SETUP

All measurements were carried out using our homebscanning force microscope for ultrahigh-vacuum and lo

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2838 PRB 61SCHWARZ, ALLERS, SCHWARZ, AND WIESENDANGER

temperature applications, which is described in deelsewhere.15 The microscope was primerily designedachieve atomic resolution in the static and dynamic molikewise. Using low temperatures minimizes thermal drand thereby ensures very stable imaging conditions.peak-to-peak noise level is 10 pm in a 2-kHz bandwidth~seethe line section of the raw data presented in Fig. 2!, whichcorresponds to an rms noise below 2 pm. Such a high rlution is a prerequisite for precision measurements of strtural properties at and around point defects, where hedifferences of only a few picometers are important. Furthmore, sensitive samples~InAs is prone to contamination! canbe measured for several days without surface degradatio

The sample, ann-doped InAs single crystal~sulfur:'331018 cm23), was cleaved parallel to the~110! surfacein the preparation chamber at pressures below 131027 Pa,and immediately transferred into the precooled microsclocated in the main chamber (p,131028 Pa!. The wholemicroscope was then lowered into a bath cryostat and countil equilibrium temperature was reached. During mostperiments both tip and sample were grounded. For msuremts with nonzero bias, the voltage was applied tosample. Then-doped ~antimony: 831017–531018 cm23)silicon tips16 used for the experiments were cleaned by argsputtering. The cantilevers had spring constants ofk'35–38 N/m and showed eigenfrequencies off 0'160–176 kHz. The instrument was operated in thenamic mode, based on the frequency modulation techniqu17

keeping the frequency shiftD f as well as the oscillationamplitudeA constant. The gray scale in all images througout this paper is chosen in a way that bright areas represtronger tip-sample interactions than dark areas~the tip-sample distance has to be increased in order to keepfrequency shift constant!.

III. CONTRAST FORMATION ON THE DEFECT-FREESURFACE

InAs crystallizes in the ZnS structure, showing zigzchains of alternating In~cations! and As ~anions! atomsalong the@110# direction @see Fig. 1~a!#. At the ~110! sur-face, the As atoms relax outwards and the In atoms inwaaccording to the bond rotation model, which is valid for moIII-V semiconductors.18 Therefore, the As sublattice is lifteby 80 pm above the In sublattice@see Fig. 1~b!#. The surfacerelaxation is accompanied by a charge transfer from thedangling bonds to the In dangling bonds.

In most dynamic mode SFM images, rows of bright prtrusions appear in atomic-scale images~see Fig. 2!. Zigzagchains of alternating In and As atoms, as one might expfrom the atomic structure displayed in Fig. 1~a!, are usuallynot visible. The same observation was made by Sugawet al. on InP~110!.19 The line section along the@110# direc-tion in Fig. 2 demonstrates that the corrugation amplitude22 pm is easily resolved. The corrugation amplitude in@001# direction is somewhat larger~26 pm!, but largest in the

@111# direction ~48 pm!.Sometimes, however, two features per surface unit

are imaged, as we already reported earlier.20 Figure 3 showstwo examples, which have been recorded with differ

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cantilevers.21 In both images, the second feature is visibbetween the bright protrusion: in~a!, it manifests itself as asecond, somewhat darker protrusion, while image b! exhibitsa strongly localized depression at that position. The solid lsections elucidate their different characteristics along@001# direction: In~a!, the second feature has the shape oshoulder'32 pm above the minima. In~b!, an'5-pm-deepdepression appears at the same position, which nereaches the level of the minima. The dashed line sectihave also been taken along the@001# direction, but across thebright protrusions. Their profiles are very similar to eaother, but the corrugation amplitudes are quite different:pm in ~a! and 18 pm in~b!. The nearest perpendicular distance between the rows of bright protrusions and the rowthe second features is about 110 pm in both images, ascated in the line sections. This value is in good agreemwith the perpendicular distance between the rows of AsIn atoms at the surface obtained from low-energy electrdiffraction experiments~100 pm!22 and recent theoreticacalculations~130 pm!.23

FIG. 1. ~a! Top view on the~110! cleavage plane of InAs~bondsare indicated by dashed lines!. The first-layer As and In atoms

alternate in zigzag chains along the@110# direction. The latticeconstants area5606 pm in the@001# direction andb5427 pm in

the@110# direction. The solid contour lines with the small numbeindicate a valence charge-density distribution approximately 0.3above the surface. They are normalized with respect to the mmum value, which lies above the As.~b! Side view of the relaxedsurface. The surface is As terminated, with the In atoms lyingpm below the As atoms. A charge transfer from the In danglbonds to the As dangling bonds takes place. Both dangling boare tilted by'30°, but in opposite directions~in the @001# and

@001# directions for the As and In dangling bonds, respectively!.

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How can these three different contrasts on InAs~110!-(131) be explained? An intuitive interpretation would leato the conclusion that in Fig. 2 only one atomic speciesimaged, while the two different maxima visible in Fig. 3~a!represent the zigzag configuration of the In and As atomthe ~110! surface. Since the surface is As terminated, omight identify the rows of bright protrusions in Figs. 2 an3~a! as As atoms, while the somewhat darker protrusionsidentified as the lower lying In atoms. The much higher crugation amplitude in Fig. 3~a! compared to Fig. 2 indicatea smaller tip-sample distance, i.e., a stronger tip-sampleteraction, which would support this interpretation. Moreoveven stronger support comes fromex situ x-ray-diffractionmeasurements on these samples, which show that if onecepts the bright protrusions to represent the positions ofAs atoms, the In atoms have indeed to be located exactthe positions of the somewhat darker maxima.

Care has to be taken with such a simple interpretatwhich is based on purely structural arguments. As long asquantity and the mechanisms, which govern the contrastmation, are unknown, it isa priori not clear how the featureobserved on atomic-scale images are related to the posiof the surface atoms.24 This becomes immediately clear bcomparing Figs. 3~a! and 3~b!: Obviously, the second somewhat darker protrusion in~a! and the depression in~b! havethe same relative position with respect to the bright maximThis means that the same spot on the surface can ex

FIG. 2. Atomically resolved InAs~110!-(131) as typically im-aged in dynamic scanning force microscopy~raw data!. White pro-trusions represent the positions of the As atoms. The section a

@110# shows a corrugation amplitude of'20 pm, and demon-strates that the peak-to-peak noise on thez piezo is about 10 pm('2-pm rms! in a 2-kHz bandwidth. Parameters:T514 K, k'36N/m, f res5160 kHz, A5612.7 nm,D f 5255.3 Hz, andUbias51250 mV.

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completely different contrasts in dynamic mode SFM images. Therefore, a better understanding of the contmechanism is needed for a reliable interpretationdynamic-mode SFM images.

To discuss this issue in more detail, we first determinetip-sample distance relevant for contrast formation in atomscale images. For the measurement of a quantity that valaterally on the atomic scale, the tip-sample distance habe on the order of the interatomic distances, i.e., some otenth of a nanometer. Taking a typically chosen oscillatamplitudeA of about610 nm, the required tip-sample sepration is only realized around the point of closest approaD. Guthner25 was able to obtain atomic resolution with aoscillation amplitude of610 nm on Si~111!-(737) in thedynamic mode of SFM and in the scanning tunneling mosimultaneously. Since a tunneling current only flows atip-sample distance of some tenths of a nanometer, thisstrong experimental indication that the point of closestproachD is indeed of this order.26

For such small tip-sample separationsD and for A@D,Ke et al.27 found that the frequency shiftD f is proportionalto the geometric mean of the tip-sample potentialVint(z) andthe forceF ts(z)52]Vint(z)/]z between tip and sample az5D, i.e.,D f }AuVint(D)F ts(D)u. With a different approachU. D. Schwarz found the approximate analytical expressD f }Vint(z5D)/Al, with l representing a characteristic dcay length ofVint(z) at z5D.28 As long as the tip-sample

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FIG. 3. Two examples of dynamic mode SFM images, whtwo features per surface unit cell are resolved on InAs~110!-(131). The bright protrusions are identified as the positions ofAs atoms. The second feature, an additional protrusion in~a! and adepression in~b!, is located between the bright protrusions, and cbe attributed to the presence of the lower-lying In atoms. Thesections in the@001# direction across the bright protrusions~dashedline! and across the second feature~solid line! elucidate the differ-ent characteristic of the contrasts from the As and In atomsdetailed explanation of the different characteristics is given intext. Parameters:~a! T514 K, k'36 N/m, f res5160 kHz, A5612.7 nm, andD f 5237.0 Hz; ~b! T578 K, k'38 N/m, f res

5176 kHz,A5611.0 nm, andD f 52447 Hz.

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2840 PRB 61SCHWARZ, ALLERS, SCHWARZ, AND WIESENDANGER

interaction force increases upon approach, both descriptof theD f dependence are approximately equivalent, beca]Vint(z)/]zuz5D

'Vint(D)/l(D) for typical tip-sample poten-tials. It is important to note that for short-range interactiol<0.1 nm, i.e., the short-ranged contribution to the totip-sample interaction will ideally only extend over the firatom at the tip apex.

In summary, contrast formation on the atomic scale indynamic mode of SFM is determined by the normal forbetween tip and sample and the tip-sample interaction potial at D'0.320.7 nm.29 Ciraci and co-workers30,31 foundthat the total force between tip and sampleFW ts can be ap-proximated by the sum of three different termsFW 1 , FW 2, andFW 3, namely,

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where rs denotes the valence charge density of the bsample,Dr the valence charge density modifacation duethe tip-sample interaction;RW t (RW s) andZW t (RW s) are the posi-tion vector and the core charge of a tip~sample! ion.

Note thatFW 1 is always attractive andFW 2 always repulsive,while the sign ofFW 3 depends on the specific distributionDr(rW). For large tip-sample distances,FW 1 is almost compen-sated for by the ion-ion repulsionFW 2, while FW 3 vanishes,becauseDr becomes negligible. In this regime, the tisample interaction is dominated by long-range van der Wforces. At small tip-sample distances, the strong ion-ionpulsion yields totally a repulsive force (uFW 2u.uFW 11FW 3u). Inthe intermediate regime,uFW 11FW 3u decays more slowly thanuFW 2u, leading to an electron-mediated attraction atD'0.3– 0.7 nm.30,31

Taking the three equations above, one can concludefor rs@uDru andl considerably smaller than the interatomdistancesaS at the surface, the positions of the maximathe tip-sample interaction, and thus the positions ofmaxima in dynamic mode SFM images, will be identicwith the maxima of the valence charge density. Such a sation is, e.g., realized for metallic Al~001! (aS50.286 nm@l).32 There, adhesive bond formation causes only smdeviations from the total valence charge density of thedisturbed sample. Consequently, the interaction force hamaximum above the Al surface atoms, exactly wheretotal valence charge density has its maximum.30

On InAs~110!, the interatomic distances between the sface As atoms are even larger than on Al~001!. In Fig. 1~a!,normalized contour lines of constant total valence chadensity are plotted for InAs~110!.34 Above the As atoms, thetotal valence charge density has its maximum, while it is fi

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times smaller at the position of the In atoms and has neia ~local! maximum nor a~local! minimum. Therefore, aslong asrs@uDru is fullfilled, the protrusions in Fig. 2 can bstraightforwardly interpreted as the positions of the Asoms, and the In atoms should remain invisible. This contion holds if either the tip-sample distanceD is compara-tively large ~what might result in a low resolution! or if tipand sample do not form strong bonds, and seems to beized more or less in most of the images@e.g., most of ourdata, including those presented here in the Figs. 2, 4, 5 anand all images published for InP~110! in Ref. 19#.

In contrast to the metallic Al~001! system mentionedabove, the Si tip as well as the InAs~110! surface exhibitdangling bonds. Perezet al.35 pointed out that these danglinbonds play an important role for contrast formation. For tcase of a Si tip scanning over a Si~111!-(535) sample, theyfound that the attractive normal force and the tip-sampleteraction energy is strongest above the adatoms, becauscharge of tip and sample rearranges significantly~largeuDru) and accumulates between the dangling bonds offoremost Si tip atom and the dangling bond of the surfaadatom, i.e., an ‘‘onset of covalent binding’’ occurs. Effecof this type led Ciraci and co-workers to the conclusion theven contrast reversal might occur for tip-sample systewhich form strong chemical bonds.31 Therefore, it is impor-tant to reconsider the situation for configurations of thetip, which are able to form strong bonds with the InAsample.

In the present case, the role of the dangling bonds habe taken into account. Their orientation is depicted in F1~b!: they are tilted by'30° in @001# and @001# directionsabove the As atoms and In atoms, respectively. Conquently, the features on atomic-scale images might notidentical with the true atomic positions anymore, but migbe slightly displaced in the@001# direction. However, such adisplacement would be very small: even if the interactiwould exclusively take place between the dangling bondsthe surface and the tip, the error would be below 10% oflength of the surface unit cell in the@001# direction~and zeroin all other directions!.23 Therefore, the identification oatomic-scale features with the position of the surface atowould still be a reasonably good approximation.

Let us now assume that the Si tip exhibits a reactive,completely empty, dangling bond. If this dangling bond aproaches the filled dangling bond of an As surface atom,resulting strong interaction will lead to a comparatively larvalue of uDru: Charge will be displaced from the As atomtoward the tip. As a consequence,FW 3 will be attractive, andthe maximum at the position of the As atom will be evmore enhanced.

At the position of the In atom, the interaction of the empdangling bond of the Si tip and the empty dangling bondthe In atom will also lead to a net accumulation of charbetween tip and sample, which, however, will probably nresult in an attractive force of the same order as on top ofAs atoms, since the charge which has to be displaced isavailable within the bonds itself and has to be providedthe surrounding valence band. Nevertheless, the chargeplacement will also cause an attractive forceFW 3, and theposition of the In atom might be visible as an additional, b

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PRB 61 2841DYNAMIC-MODE SCANNING FORCE MICROSCOPY . . .

smaller, protrusion. This scenario matches the experimedata presented in Fig. 3~a!. The very high corrugation amplitude of 75 pm indicates the predicted enhancement ofcorrugation amplitude above the positions of the As atoAt the positions of the In atoms additional protrusions avisible, seen as a shoulders in the line section of Fig. 3~a!.

On the other hand, a completely filled tip dangling boalso interacts strongly with the dangling bonds of the samIf the tip dangling bond approaches the filled dangling boof the As surface atom, charge has to be dislocated fromspace between the Si tip atom and the As sample atom, ling to a negativeDr in this area, and consequently torepulsive forceFW 3. Thus the maximum at the As atom postion will diminish. At the position of the In atom, howevethe filled tip dangling bond opposes the empty In danglbond, and charge transfer from the tip toward the sam

FIG. 4. Dynamic mode SFM image of InAs~110! with sevenmissing protrusions~white arrows! identified as As vacancies~seetext!. No lattice relaxation or an additional charge is visible arouthe vacancies. The line section shows a depression of about 1instead of a protrusion at the position of the As vacancy. Pareters: T514 K, k'36 N/m, f res5160 kHz, A5612.7 nm, andD f 5263.2 Hz.

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occurs. Since the charge can be moved comparatively eaa repulsive forceFW 3 of considerable strength is induced, anone would expect a well-expressed depression exactly aposition of the In dangling bond.

This second scenario corresponds nicely to the situatas is found in Fig. 3~b!. There, a depression localized prcisely at the position of the In atoms is clearly visible@cf. theline section of Fig. 3~b!#. Additionally, the total corrugationheight across the bright protrusions in the@001# direction isvery low @only 18 pm compared to 48 pm in Fig. 2, and ev75 pm in Fig. 3~a!#, which suggests that the predicted decment of the height of the maximum at the As atom positireally takes place. Therefore, to summarize the above fiings, we have seen that the contrast mechanism in dynaSFM is determined by electron-mediated attraction, whstrongly depends both on the total valence charge densitthe bare sample and on the ability of the tip to form bonbetween tip and sample.

Finally, it is worth comparing the contrast mechanismthe dynamic mode of SFM described above with the contmechanism valid for STM on InAs~110! ~or III-V semicon-ductors in general! at the atomic scale. Empty and fillestates are localized at the cation sites and anion sites, restively. Therefore, the contrast in STM strongly dependsthe sign of the applied bias voltage on III-Vsemiconductors.36 With a large positive sample bias the caion sublattice is imaged~tunneling from the STM tip intoempty states!, while the anion sublattice is imaged with largnegative sample bias~tunneling from filled states into theSTM tip!. This general behavior on~110! surfaces of III-Vsemiconductors was also confirmed for InAs.37 In ourpresent case of dynamic-mode SFM, we checked thatelectric field between the Si tip and the InAs sample, inducby the contact potential difference38 or an applied bias volt-age (61.8 V!, did not influence the general appearancethe atomically resolved surface. However, any added~attrac-

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FIG. 5. High-resolution image of an As-site defect oInAs~110!. During scanning from top to bottom, the As vacanwas moved; therefore, the As vacancy seems to be half-filled.figure illustrates that the As atoms around an As vacancy dorelax within the resolution of our instrument. As in Fig. 4, no cotrast induced by trapped charges is visible. Parameters:T514 K,k'36 N/m, f res5156 kHz,A5613.5 nm, andD f 52105.3 Hz.

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tive! electrostatic contribution to the total tip-sample interation had to be compensated for by an appropriate adjustmof D f to assure a sufficiently small tip-sample distanceachieve atomic resolution.

This comparison shows that the origin of the tip-saminteraction is inherently different for STM and dynamimode SFM. Therefore, additional and/or complementaryformation is available with both methods. This will be futher confirmed in the following sections, where the contrat and around two different types of point defects willdiscussed.

IV. POINT DEFECTS ON InAs „110…

A. As-site point defect

The most frequently observed type of point defectfreshly cleaved~110! surfaces was a missing protrusion.Fig. 4, seven of such missing protrusions, marked by arroare visible. They are close to a cleavage step on the rihand side of the image~not in the field of view!. Far awayfrom cleavage steps onn-InAs~110!, we only occasionallyfound missing protrusions, but never with such a high dsity. The line section across one point defect shows that

FIG. 6. Dynamic mode SFM image of a defect located on anlattice site of InAs~110!-(131). In ~a!, the two As atoms markedwith X (X sites! are displaced by 6 pm into the bulk~see the linesection for illustration!. In ~b!, the tip-sample distance is reduced badjusting a larger negative frequency shiftD f , and the position ofthe defect is slightly shifted due to a differentxy-offset voltage atthe scan piezos. Now theX-site As atoms appear to be 10 pm highthan the surrounding As atoms~see the line section!. This change isattributed to a stronger tip-sample interaction caused by the redtip-sample distance, which pulls the two weakly bound As atointo the vacuum region. The sketches below the line sections icate the tip-induced displacement of bothX-site As atoms. Parameters:T514 K, k'36 N/m, f res5160 kHz,A5612.7 nm,~a! D f5239.5 Hz, and~b! D f 5244.7 Hz.

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protrusion is replaced by a 15-pm-deep depression. Sprotrusions are associated with the positions of the As atoand these point defects are located on the As sublattice,can be straightforwardly interpreted as As vacancies. Tvacancies are probably formed during the cleavage produre, which would explain their enhanced density closethe step edge.

At higher magnification, conclusions about the surfastructure around the As vacancies can be drawn. The cirAs lattice site in Fig. 5 is half-empty~upper part! and half-filled ~lower part!. The scan direction was from top to botom. Apparently, this As lattice site had been a vacanwhich has probably been moved under the influence oftip. In this context, it is interesting to compare the strengththe tip-sample interactions in Figs. 4 and 5. A measurethe tip-sample interaction is the normalized frequency sg5D f / f 0kA3/2 introduced by Giessibl, which is independeof the parameter set (A, f 0 ,k) used during data acquisition.10

Taking the parameters given in Fig. 5,g can be estimated to238 f Nm1/2, nearly twice as high as theg calculated for theimage displayed in Fig. 4 (220 f Nm1/2). This might be thereason why the vacancy in Fig. 5 is moved by the tip, bthose in Fig. 4 are not. Other possible explanations areplausible: Thermal activation is unlikely at 14 K, and desotion of an As atom from the tip or a tip change would ngive such a smooth transition from an empty to a filledlattice site as in the image.

Comparing the upper half of the circle in Fig. 5~theempty As lattice site! with the lower half~filled As latticesite!, it can be concluded that the As atoms around anvacancy do not relax significantly. All distances betweprotrusions and the corrugation amplitudes of the protrusiremain the same within the resolution of our instrumeNote that we do not image the In sublattice here; thereforrelaxation of the surrounding In atoms cannot be excludThis finding is in agreement with results from G. Schwaet al., who calculated for GaP~110! that the relaxationaround a surface anion vacancy~P vacancy! is restricted tothe nearest-neighbor cations.39

Furthermore, it can be concluded from both Figs. 4 anthat the As vacancies are not charged. With STM, chaclouds were found around charged vacancies on varIII-V semiconductors.37,40,41The screened Coulomb potentiof a charged vacancy should lead to an additional elecstatic contribution to the total tip-sample interaction in a ccular area with a radius in the order of the screening len(lS'8 nm in our case! around the vacancy, which we neveobserved around As vacancies onn-InAs~110!. Moreover,Ebert et al.42 observed on InP~110! and GaP~110! thatcharged vacancies induce displacements up to two laconstants away from the defect, while neutral anion vaccies do not induce such a relaxation in the anion sublattictheir vicinity. They also exhibited no charge cloud arouthem. Neither a charge cloud, nor any distortions of thesublattice, are visible around the vacancies in our measments. An additional argument is that charged As vacanwould repel each other.43 However, the two vacancies encircled in Fig. 4 are very close together.

It is worth noting that in spite of the fact that imagesneutral anion vacancies acquired on similar III-V semicoductors with STM and dynamic mode SFM on InAs~110!

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PRB 61 2843DYNAMIC-MODE SCANNING FORCE MICROSCOPY . . .

look quite similar, the origin of the contrast is different.STM, the missing filled dangling bond of an anion vacanleads to a reduced tunneling current at negative samplewhich manifests itself in a depression. However, the contchanges with the sign and magnitude of the applied bvoltage.42 In dynamic-mode SFM, an As vacancy also resuin a depression, because the missing As atom leadsreduced charge density at that spot and leaves a geomehole behind. Thus, compared to STM measuremedynamic-mode SFM gives a more direct and intuitive vieof the surface geometry at and around anion vacancies.

B. In-site point defect

In Fig. 6, a different type of point defect is presenteBoth parts~a! and ~b! of the figure show the same poindefect on the sample recorded with a different frequeshift D f . The lower-frequency shift in Fig. 6~b! correspondsto a decreased tip-sample distance and consequentlystronger~attractive! tip-sample interaction than in Fig. 6~a!.

Accordingly, the corrugation amplitude in the@110# direc-tion of the unperturbed lattice increases from 10 pm in~a! to20 pm in ~b!. The increased tip-sample interaction causecontrast inversion at the defect, namely, at the neighboatoms marked withX. In ~a!, the maxima of theX-site pro-trusions appear'6 pm below the surrounding As sublatticwhile in ~b! they appear'10 pm above the surrounding Aatoms. Moreover, the depression atY is deeper@by 9 pm~a!and 6 pm~b!, respectively# compared to the equivalent undisturbed lattice sites.

It is not possible to specify the type of point defect eactly, but most commonly occurring point defects canruled out. Adsorbates appeared much more broadenednever so localized. Two neighboring impurities on As lattisites are very unlikely, and would induce a larger lattdistortion. Therefore, we assume that theX sites are actuallytwo As atoms influenced by a defect between them. Becaof the mirror symmetry with respect to the@001# direction,this point defect must be located on the In lattice below bX sites. The different symmetry with respect to the As sface atoms of interstitial atoms and subsurface defectscated on As sites would probably lead to a different appeance of the two As atoms at theX sites. Such a defect on thIn site could be an impurity atom, an antisite defect, or anvacancy. The latter is supported by the deep depressionY~see below!.

How can this contrast inversion occur? The simulationthe scanning process by Perezet al. revealed that surfaceatoms can be significantly displaced during scanning.35 Chouand Joannopoulos calculated that a SFM tip is able to fliporientation of Si dimers on Si~100!, and that this should beobservable at low temperatures.44 A defect below the Asatoms on theX sites, especially a missing In atom, wouweaken the stiffness of the surrounding lattice. Considerthis, an additional attractive tip-sample interaction migprovide enough energy to pull the two weakly bondedatoms above the In site defect toward the tip, e.g., intovacuum region. These local changes in the lattice paramereflect the different elastic properties around the point decompared to the undisturbed lattice.

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This scenario is consistent with calculations froG. Schwarzet al. for cation vacancies~Ga vacancies! onGaP~110!.39 They found that the two anions above the cativacancy would relax downwards, exactly like in Fig. 6~a! fora relatively weak attractive tip-sample interaction. Howevtheir calculated downward relaxation of 44 pm is mudeeper than the 6 pm measured in Fig. 6~a!. Three explana-tions could account for this. First, the downward relaxatifor a cation vacancy could be much smaller for InAs~110!than for GaP~110! ~they are similar, but not equal, materials!.Second, the defect might not be a vacancy, but an impuor an antisite defect, resulting in a much smaller downwrelaxation~no calculations for this case exist!. Third, the at-tractive tip-sample interaction necessary for a substantialinduced relaxation could already be present at largersample distances~this might happen in addition to the first osecond argument!.

From Sec. III, we know that the In lattice site is not located atY, but on the other side of the twoX-site As atoms.However, surprisingly the depression is deepest atY, while atthe real position of the In-site defect, the depression is onpm deeper in~a! and has the same level as the undisturblattice in ~b!. This could be explained with a simple geometrical reasoning, which favors the assumption that theserved point defect represents an In vacancy. In this casvisualized in Fig. 7, all three neighboring As atoms mocloser together. Such a relaxation has been found in theculation for the Ga~cation! vacancy on GaP~110! alreadymentioned above.39 The effect is a reduction of the interatomic distances between the As atoms of the first-second-layer As atoms around the In vacancy. Consequeon the other side of the two relaxed first-layer (X-site! Asatoms~at theY site! the charge density is reduced, i.e., mo

FIG. 7. Top view of the proposed relaxation around an In vcancy, as derived in analogy to GaP~110! from Ref. 39. All threeneighboring As atoms are displaced in such a manner that thetances between them are reduced. For a cation vacancGaP~110!, the total displacement of the first~second! layer anions is82 pm ~56 pm! ~see Ref. 39!. Due to the relaxation, the tip capenetrate deeper atY than at the location of the In vacancy.

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2844 PRB 61SCHWARZ, ALLERS, SCHWARZ, AND WIESENDANGER

‘‘space’’ becomes available, and the tip can penetrate deinto the surface. As in the case of the As vacancy, this deappears to be neutral at zero bias~same arguments as givein Sec. IV A for the charge state of the As vacancy!. Asample bias of1250 mV did not change the contrast, but,already stated in Sec. III,D f had to be readjusted to achievatomic resolution.

It is again instructive to compare our data with resuobtained by STM. As in the case of anion vacancies, expments on neutral cation vacancies on GaP~110! exhibited astrong dependence on sign and magnitude of the appliedvoltage.45 At negative bias voltages all four surrounding aions at the surface are influenced by the presence of a cavacancy. However, our data, and theoretical calculationsSchwarzet al.39 suggest that only two anions are signicantly relaxed downwards. Nevertheless, the dynamic-mSFM results presented in this section demonstrate thatwith this method quantitative structural information aroudefects cannot be extracted unambiguously, sinceinduced relaxations have to be considered even in the attive interaction regime. On the other hand, the observedinduced relaxation shows that elastic data on the atomic lcan be obtained from dynamic-mode SFM data.

V. SUMMARY

We presented results of an atomic-scale study ofInAs~110!-(131) surface by means of dynamic-mode SFperformed at low temperatures and in UHV. It was shothat dynamic scanning force microscopy images the surAs atoms as bright protrusions. However, under certain

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cumstances both species are visible. The observed concan be qualitatively explained with the total valence chadensity at the surface and the rearrangement of the chdistribution due to the tip-sample interaction.

Missing protrusions in the As sublattice are straightfowardly identified as As vacancies. It was found that As vcancies do not induce a measurable relaxation in therounding As sublattice. Furthermore, they appeared neuon n-doped material under our experimental conditions~zerobias!.

Another point defect, located on the In sublattice, coube detected by its influence on two neighboring surfaceatoms. These As atoms exhibited a distance-dependenttrast inversion, attributed to a tip-induced relaxation. Symetry arguments suggest that the defect is located on thsublattice. The contrast around the defect could be bestplained by an In vacancy. The observed relaxation givesdence that elastic properties can be measured on the atscale with dynamic-mode SFM.

ACKNOWLEDGMENTS

The authors would like to thank Phillip Ebert, MarkuMorgenstern, Hendrik Ho¨lscher, and Gu¨nther Schwarz forhelpful discussions, and Livio Fornasio for the determinatof the crystal orientation by x-ray-diffraction measuremenFinancial support from the VW foundation~Grant No. I/69649!, the BMBF ~Grant No. 13N6921/3!, and the Gra-duiertenkolleg ‘‘Physik nanostrukturierter Festko¨rper’’ isgratefully acknowledged.

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~1986!.8F. J. Giessibl, Science267, 68 ~1995!.9In the contact mode of SFM, only the translational symmetry

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10F. J. Giessibl, Phys. Rev. B56, 16 010~1997!.11M. Bammerlin, R. Luthi, E. Meyer, A. Baratoff, J. Lu¨, M. Gug-

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14This is justified since the surface structures of all these mateare very similar. That is, all materials relax qualitatively in tsame way; only the absolute values of the displacementsslightly different.

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15W. Allers, A. Schwarz, U. D. Schwarz, and R. WiesendangRev. Sci. Instrum.69, 221 ~1998!.

16Nanosensors, Aidlingen, Germany.17T. R. Albrecht, P. Gru¨tter, D. Horne, and D. Rugar, J. Appl. Phy

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Appl. Surf. Sci.140, 293 ~1999!.21Note that the adjusted frequency shiftD f is much larger for~b!

than for ~a!. However, this is not extraordinary for differencantilvers, and it is not possible to deduce that the tip-saminteraction relevant for atomic resolution is stronger in one iage or the other.

22C. B. Duke, C. Mailhot, A. Paton, D. J. Chadi, A. Khan, J. VaSci. Technol. B3, 1087~1985!.

23B. Engels, Ph. D. thesis, RWTH Aachen, KFA Ju¨lich, 1996.24In the static contact mode of SFM, this issue has been an o

question for a long time. Finally, it has been accepted tatomic-scale images are dominated by frictional forces, andprotrusions in the images are not necessarily identical watomic positions.

25P. Guthner, J. Vac. Sci. Technol. B24, 2428~1996!.26For simultaneous recording of a dynamic mode SFM image an

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PRB 61 2845DYNAMIC-MODE SCANNING FORCE MICROSCOPY . . .

STM image, the bandwidth of the current preamplifier has tomuch smaller than the frequency of the cantilever oscillation~30and 290 kHz, respectively, in Ref. 25!.

27S. H. Ke, T. Uda, and K. Terakura, Phys. Rev. B59, 13 267~1999!.

28U. D. Schwarz, Habilitation thesis, University of Hamburg, 19929In previous publications, it was often stated that the force der

tive is the quantity which influences the frequency of the calever ~e.g., Refs. 8, 19, and 35!. This is only valid for tip-sampleinteractions which do not vary significantly over the whole ocillation cycle, and therfore represents a reasonable approxtion only for long-range forces. For atomic-scale imaging, whshort-range forces are probed, such an assumption is not@see H. Ho¨lscher, U. D. Schwarz, and R. Wiesendanger, ApSurf. Sci.140, 344 ~1999!#.

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32At this point, it is important to note that the maximum of thvalence charge density is not in every case identical withlargest attractive interaction force, even ifrs @ uDru. If the inter-atomic distancesaS are very small, i.e. about comparable to tcharacteristic decay lengthl of the interaction, the influence oneighbor atoms on the tip has to be considered. This situatioe.g., realized within the surface structure of graphite~0001! ~seeRef. 33!. The in-plane nearest-neighbor distance betweengraphite atoms is very small (aS5142 pm!, and integration

leads to a largest attractive forceFW ts above the hollow sites othe honeycomb structure, where all six surrounding graphiteoms contribute to the tip-sample interaction. However, sucheffect can be excluded for InAs~110!, since the interatomic distances between the surface As atoms are much larger.

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33S. Ciraci, E. Tekman, and I. P. Batra, Phys. Rev. B41, 2763~1990!.

34The total valence charge density has been taken from Ref.The distribution is very similar for all~110! surface of III-Vsemiconductors with ZnS structure, and decays exponentiallarger tip-sample distances.

35R. Perez, M. C. Payne, I. Stich, and K. Terakura, Phys. Rev. L78, 678~1997!; R. Perez, I. Stich, M. C. Payne, and K. TerakurPhys. Rev. B58, 10 835~1998!.

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38The work functions ofn-InAs~110! and Si are both'4.90 eV,resulting in a contact potential difference close to zero. Nevtheless, due to the tip geometry, the work function of the Siwill be reduced. The problem of determining precisely the cotact potential difference betweenn-InAs~110! and a Si tip isneither trivial nor of major interest for the present purpose, awill be discussed in a forthcoming paper.

39G. Schwarz, A. Kley, J. Neugebauer, and M. Scheffler, PhRev. B58, 1392~1998!.

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43Note that the measurement in Figs. 4 and 5 were done with zbias, and that the actual charge state of a vacancy genedepends on the sign and absolute value of an applied biasage.

44K. Chou and J. D. Joannopoulos, Surf. Sci.328, 320 ~1995!.45P. Ebert and K. Urban, Phys. Rev. B58, 1401~1998!.